Orbit Ephemeris Failure Detection in a GNSS Regional
Paper Int’l J. of Aeronautical & Space Sci. 16(1), 89–101 (2015) DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.89 Orbit Ephemeris Failure Detection in a GNSS Regional Application Jongsun Ahn* and Young Jae Lee** Konkuk University, 120 Neundong-ro, Gwangin-gu, Seoul 143-701, South Korea Dae Hee Won*** University of Colorado at Boulder, 431 UCB, Boulder, CO 80309 USA Hyang-Sig Jun**** and Chanhong Yeom***** Korea Aerospace Research Institute, 169-84 Gwahang-no, Yuseong-gu, Daejeon 305-806, South Korea Sangkyung Sung****** and Jeong-Oog Lee******* Konkuk University, 120 Neundong-ro, Gwangin-gu, Seoul 143-701, South Korea Abstract To satisfy civil aviation requirements using the Global Navigation Satellite System (GNSS), it is important to guarantee system integrity. In this work, we propose a fault detection algorithm for GNSS ephemeris anomalies. The basic principle concerns baseline length estimation with GNSS measurements (pseudorange, broadcasted ephemerides). The estimated baseline length is subtracted from the true baseline length, computed using the exact surveyed ground antenna positions. If this subtracted value differs by more than a given threshold, this indicates that an ephemeris anomaly has been detected. This algorithm is suitable for detecting Type A ephemeris failure, and more advantageous for use with multiple stations with various long baseline vectors. The principles of the algorithm, sensitivity analysis, minimum detectable error (MDE), and protection level derivation are described and we verify the sensitivity analysis and algorithm availability based on real GPS data in Korea. Consequently, this algorithm is appropriate for GNSS regional implementation. Key words: GNSS, Integrity, Ephemeris Failure Detection, Baseline Length Estimation 1. Introduction sensors, has been conducted to address integrity issues [1] [2]. The main line of integrity issues includes threat definition, development of detection algorithms within time to alert, and the protection level (PL) for confidence in the user navigation solution. One of the threats facing GNSS involves orbit ephemerides, which are generated periodically at a ground control facility (a GPS Operation Control Segment) and are transmitted to the user by satellites [3]. The frequency of the ephemeris anomaly tends to decrease, however. Because the ramifications for user position error is critical, the system must include monitoring and detection processing [4][5]. The Global Navigation Satellite System (GNSS) is used to compute user navigation solutions with certain accuracy at any time and location of interest. With increasing GNSS applications, the civil aviation community has been trying to implement primary navigation systems using GNSS. To ensure aircraft safety in the civil aviation implementation of GNSS, the implemented system must meet integrity requirements. Research on various GNSS implemented systems and on the use of ground facilities, additional satellites, and navigation * Ph. D Candidate Professor ** *** Research Associate **** Principal Researcher ***** Principal Researcher ******Professor ******* Professor, Corresponding Author: [email protected] This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Received: November 5, 2014 Revised : February 26, 2015 Accepted: March 2, 2015 Copyright ⓒ The Korean Society for Aeronautical & Space Sciences (89~101)14-083.indd 89 89 http://ijass.org pISSN: 2093-274x eISSN: 2093-2480 2015-03-30 오후 3:48:25 introduce concept of the describe introduce the concept of the algorithm, describethetest statistics andalgorithm, a threshold, analyzetest statistics and a threshold, analy introduce the concept of the algorithm, describe test statistics and a threshold, analyze [14] between test derive statistics ephemeris failure, and derive the epheme sensitivity [14] between test statisticssensitivity and ephemeris failure, and theand ephemeris sensitivity [14] between test statistics and ephemeris failure, and derive the ephemeris introduce the MDE concept offor thealgorithm algorithm,availability. describe test level (EPL) and [15] In statistics section 3,and weafoth protection level (EPL) and MDE [15]protection for algorithm availability. In section 3, we focus on protection level (EPL) and MDE [15] for algorithm availability. In section 3, we focus on sensitivity [14] between testusing statistics failure, and deri evaluating above real and GPSephemeris data. So, we evaluated sen evaluating the algorithm described above using the realalgorithm GPS data.described So, we evaluated sensitivity evaluating the algorithm described above using real GPS data. So, we evaluated sensitivity protection performance level (EPL) and MDE [15] forephemeris algorithmprotection availability. In se Int’l J. of Aeronautical & Space Sci. 16(1), 89–101 (2015) and availability and level fo analysis and availability performanceanalysis using MDE and ephemeris protectionusing levelMDE for landing analysis and availability performance using MDE and ephemeris protection level for landing evaluating the of algorithm described above using real GPS data. So, we aircraft usingstations real GPS data multiple reference aircraft using real GPS data of multiple reference (RSs) in Korea. Finally, we stations (RSs) in Korea. Finally, w stations (RSs) in Korea. Finally, we describe the conclusions Ephemeris anomalies are conventionally divided into aircraft using real GPS data of multiple reference stations (RSs) in Korea. Finally, we analysis andand availability performance using MDE and ephemeris prot describe the future work in section 4. describe theoccurrence conclusions and future work in section 4. and future work inconclusions section 4. two groups (Types A and B) with respect to the describefailure the conclusions and future work in section 4. of satellite maneuvers. Type A is an ephemeris event aircraft using real GPS data of multiple reference stations (RSs) in Ko during the process of a satellite maneuver, whereas Type B describe the conclusions and future work in section 4. 2. Algorithm Baseline Length Estimation Algorithm can be issued in ephemeris generation transmission 2. Baseline Length Estimation Algorithm 2. or Baseline Length but Estimation 2. Baseline Length Estimation Algorithm no satellite maneuver is involved [6]. This introduces concept of the proposed algorithm (test statistics and This introduces the concept of thesection proposed algorithm (test statistics and threshold), This section introduces thetheconcept of the proposed Various methods have been proposed forsection the detection This section introduces the concept of the proposed algorithm (test statistics and threshold), 2. satellite Baseline Length Estimation Algorithm (testthestatistics and analyses the of both Type A and Type B ephemeris anomalies. Type of testalgorithm analyses sensitivity ofposition testthreshold), statistics according to satellite position error due to e analyses the sensitivity statistics according to error due to ephemeris sensitivity of test statistics according to satellite position B events can be detected by examining the consistency analyses the sensitivity of test statistics according to satellite position error due to ephemeris Thisthe section introduces the concept of the proposed algorithm (tes failure, and derives MDE, which the and derives the MDE,error whichdue is the performance parameter faultisdetection, the parameter of fault detection to ephemeris failure, andof derives theperformance MDE,and which between the broadcast ephemeris failure, and prior validated failure, and derives the MDE, which is the performance parameter of fault detection, andthe the is the performance parameter of fault detection, and ephemeris. The magnitude of detectable satellite position analyses the sensitivity of test statistics according to satellite position ephemeris protection level. ephemeris protection level. error due to a Type B anomaly depends on the validated time level. ephemeris protection level. ephemeris protection failure, and derives the MDE, which is the performance parameter of of a prior ephemeris. Representative2.1algorithms include 2.1 Principle of the Algorithm Principle of the Algorithm of the Algorithm the ephemeris-ephemeris test, YE-TE 2.1 test,Principle and almanac2.1 Principle of the Algorithm ephemeris protection level. the baseline length between reference st Thethedetection estimates The detection methodology estimates baselinemethodology length between reference station (RS) ephemeris test. They compute satellite position and monitor premeasured premeasured antenna antenna locations locations of of RSs RSs and and the the broadcast broadcast ephemeris ephemeris of of thethe satellite satellite [14]. [14]. The detection methodology estimates the baseline length between reference station (RS) The detection methodology estimates the baseline 2.1 Principle of the Algorithm consistency of results within a given threshold However, using range measurements of be RSvalidated. and the broadcast ephemeris to be vali antennas [7]. using range measurements antennas of RS and the broadcast ephemeris to The length between reference station (RS) antennas using range i range i T T measurements i i T of T RS and the broadcast ephemeris to be validated. The these algorithms have the limitation of requiring validated antennas ausing i T Tdetection methodology i T T betwee ABe AB i length e AeAeABe AB i measurements e BeBeerror-free i i to RS iantenna i The i be ephemeris isestimates of RS and the broadcast to betheRSbaseline is eassumed because antennalength location is baseline because location computed A iAephemeris iA iis i assumed BiBto ibei baseline A x Type x AB length eerror-free prior ephemeris, and hence cannot detect (1)(1) AB AB AB A eAeAeAB B B eBeBeAB T T T T baseline length is assumed to be error-free because RS antenna location is computed validated. The baseline length is assumed to be error-free e e e e e e e e A A AB AB B B AB AB failure. On the other hand, Type A failure is relatively more antennas using range measurements of RS and the broadcast ephem accurately precisely. Incomputed this section, wefordescribe accurately and precisely. In because this section, we and describe the is estimation method single RS antenna location accurately and the estimation method difficult to detect than Type B because there is no validated accurately and precisely. In this section, we describe the estimation method for single baseline length assumed to be error-free because RSone antenn In thislength section, we on describe the estimation method based two is RSs. According to the First Cosine Law, side prior ephemeris to compare with the ephemeris of a satellite baseline length based on twoprecisely. RSs. baseline According to the First Cosine Law, one side length of for single baseline length based on two RSs. According to the baseline length based on two RSs. According to the First Cosine Law, one side length of just after an orbit maneuver. One method of detecting Type and precisely. In this section, we describe the estima triangle can beaccurately computed the other two length triangle can be computed using theCosine other two sides’ length andusing their induced angle. In Fig. (1), and their induced angle. First Law, one side length of triangle can be sides’ computed A failure is to monitor the range measurement correction triangle can be computed using thethe other twotwo sides’ length andand theirtheir induced angle.angle. In Fig. using other sides’ length induced In(1), to the First Cosine baseline length basedimplementation. on two RSs. According (pseudorange correction, PRC) derived this law can be applied thisfrom law the can broadcast be applied in GNSS implementation. One sideinofGNSS the triangle represents One the side of the triangle rep (1), this law can be applied in GNSS implementation. Onethe ephemeris and the location of the ground this station law canantenna be applied inFig. GNSS implementation. One side of the triangle represents triangle can be computed using the other two sides’ length and their i side of the) triangle represents length the displacement ofthe theother displacement vector ( of ) determined and the other sides’ lengths can be determ xˆ AB of theerror displacement vector ( xˆlength and sides’the lengths can be with [7]. Other methods estimate satellitelength position with AB ˆ vector and the other sides’ lengths can be determined length of the displacement vector ( ) and the other sides’ lengths can be determined with x AB range measurements [8][9] or estimate the differential this law can be applied in GNSS implementation. One side of th range measurements received RSs. range measurements received by two RSs. The The Ai , Bi ) angle measurements ( Ai , Bi )with received by two RSs. The (induced is then computed by induced angle is then co range of ground stations with short range baseline vectors and i i ˆ ) received by two RSs. The induced angle is then computed bythe other sides’ lengths range measurements ( A , induced angle is then computed by the unit vector of length of the displacement vector ( x AB ) and B range measurements [10][13]. However, these algorithms ˆ i i ˆ the unit vector ( ) of the baseline and unit vectors ( eAi , eBi ) correspond x AB ( eA , eB ) corresponding thebaseline baselineand andunit unit vectors vectors thedirection unit vector ( x AB ) of the corresponding to to the the have some weaknesses. First, when the of satellite i i ˆ i i the unit vector ( x ) of premeasured the baseline and unit vectors ( eof corresponding tobythe eB )( two RSs. The induced an range measurements antenna locations and broadcast A , RSs B ) received A , the position error is orthogonal to the line-of-sight, ephemerisAB ephemeris of the satellite [14]. premeasured antenna locations of RSs and the broadcast ephemeris of the satellite [14]. failure on test statistics is small. Next, there is the limitation 4baseline and unit vectors ( ei , ei 4 the(A,unit vector ( of the xˆ AB ) i. Figure Figure 1. 1. Geometry Geometry condition condition of of two two RS RS antennas antennas (A, B) B) and and a satellite a satellite i. B A i T i T of baseline length (short baseline, 100-400 m), and using i T i T e A e AB 4 e B e AB x AB iA i T iB i T iA e A e AB iB e B e AB (1) (1) carrier phase measurement that must resolve integer e A e AB e B e AB ambiguity. 4 premeasured antenna locations of RSs and the broadcast ephemeris of the satellite [14]. To supplement these algorithms, we propose a detection The test statistic (TS) is defined by the following equation The test test statistic statistic (TS) (TS) is is defined defined byby thethe following following equation equation (2), (2), computed computed byby subtracting subtracting thethe algorithm using non-limited baselineThe length and code Tsubtracting i T (2), computedeiAby estimated baseline length i T i T e AB e B ethe AB i i i i x e e e e measurement for Type A failures. This methodology, based (1) A B i T i T A A AB B B AB AB e Apremeasured epremeasured e B one e AB AB the one ). ). ). estimated baseline baseline length length xˆ ABxˆ AB from from thethe premeasured one ( x( ABx AB on the law of cosines in trigonometry,estimated estimates the baseline lengths of multiple ground antennas. inˆ the i i detail We describe the methodology in more TS TS xAB xABxˆAB (2)(2) AB AB xAB following sections. In section 2, we introduce the concept of the algorithm, describe test statistics and a threshold, AsAs shown shown in in equation equation (1), (1), thethe test test statistic’s statistic’s variation variation depends depends onon thethe range range measurements measurements analyze sensitivity [14] between test statistics and ephemeris Figure 1. Geometry condition of two RS antennas (A, B) and a satellite i. and and thethe induced induced angle. angle. The range range measurements measurements areare assumed assumed to to bebe fault-free fault-free and and areare notnot failure, and derive the ephemeris protection level (EPL) and The MDE [15] for algorithm availability. In section 3, we focus treated treated further further in in this this work. work. WeWe focus focus onon thethe test test statistic’s statistic’s variation variation due due to to induced induced angle angle on evaluating the algorithm described above using real GPS The test statistic (TS) is defined by the following equation (2), computed by subtracting the data. So, we evaluated sensitivity analysis and availability error error resulting resulting from from broadcast broadcast ephemeris ephemeris failure. failure. performance using MDE and ephemeris protection level estimated baseline length xˆ AB from the premeasured one ( x AB ). Figure 1. Geometry condition of two RS antennas (A, B) and a satellite i. be for landing aircraft using real GPS data of multiple reference Fig. 1. Gerrors eometry condition of two RS antennas (A,conditions B)conditions and a satellite i.be However, However, range range measurement measurement errors in in the the ephemeris ephemeris under under normal normal must must i TS AB xAB xˆAB (2) accounted accounted forfor in in thethe test test statistic’s statistic’s accuracy. accuracy. The The range range measurement measurement errors errors areare defined defined asas As shown in equation (1), the test statistic’s variation depends on the range measurements i i i test statistic (TS) is defined by the following equation (2), computed by subtracting the (3)(3) to be fault-free and are not uu R uRui Ii Ii TiTi ccbu bu90 bi b u induced angle. The range measurements are assumed The uthe and DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.89 i i i estimated baseline length xˆ AB from the premeasured one ( x ). treated furtheri ini this work. We focus on the test statistic’s variation dueABto induced angle : True range range (m) (m) RuR: uTrue from ˆbroadcast ephemeris failure. error resulting i TS AB xAB xAB (2) However, range measurement errors in the ephemeris under normal conditions must be (89~101)14-083.indd 90 5 5 2015-03-30 오후 3:48:26 As shown in equation (1), the test statistic’s variation depends on the range measurements Figure 1. 1. Geometry condition of of two RSRS antennas (A,(A, B)B) and a satellite i. i. Figure Geometry condition two antennas and a satellite . Geometry condition of two RS antennas (A, B) and a satellite i. The testtest statistic (TS) is defined byby thethe following equation (2),(2), computed byby subtracting thethe The statistic (TS) is defined following equation computed subtracting est statistic (TS) is defined by the following equation (2), computed by subtracting the Ahn Orbit Jongsun Ephemeris Failure Detection in a GNSS Regional Application thethe premeasured one ( x(ABxAB ). ). estimated baseline length estimated baseline length xˆ ABxˆ AB from from premeasured one d baseline length xˆ AB from the premeasured one ( x AB ). methods posed a contradiction in this algorithm because i i (2) (2)(2) TS xABxAB xˆABxˆAB TS AB AB ˆ these methods use the broadcast ephemeris (to be Klobuchar model xAB xAB (2) Ionospheric delay Klobuchar model Message Iono. Parameter model validated bydelay test statistics). The test Klobuchar statistics and validated (with GPS Navigation Ionospheric delay Ionospheric AsAs shown equation (1), the test statistic’s variation As shown ininin equation (1),(1), thethe testtest statistic’s variation depends onon thethe range measurements (with Navigation Message Iono. Parame (with GPSGPS Navigation Message Iono. Parameter shown equation statistic’s variation depends range measurements Klobuchar model Klobuchar Klobuchar model model Troposheric delay Sasstamonien model ephemeris must be independent Klobuchar for reliablemodel ephemeris Ionospheric delay Ionospheric Ionospheric delay delay Ionospheric delay depends onvariation the range measurements and the induced angle. own in equation (1), the test statistic’s depends on the range measurements Troposheric delay Sasstamonien model Troposheric delay Sasstamonien model (with GPS Navigation Message Iono. Parameters) (with (with GPS GPS Navigation Navigation Message Message (with Iono. Iono. GPS Parameters) Parameters) Navigation Message Iono. Parameter Klobuchar model Satellite / Receiver clock Broadcast ephemeris fault detection. Innot addition, the required range is not /aWeighted least square Ionospheric delay and the induced angle. The range measurements are assumed beTroposheric fault-free and are and the induced angle. The range measurements are assumed be fault-free and are not The range measurements are assumed to be fault-free and to to (with GPS Navigation Iono. Parameters) Satellite /delay Receiver clock Broadcast ephemeris / Weighted square Satellite /Sasstamonien Receiver clock Broadcast ephemeris leastleast square Troposheric delay Sasstamonien model Troposheric Troposheric delay delay Sasstamonien model modelMessageSasstamonien model / Weighted i I : Ionosphere delay error (m) relative value, but an absolute measurement. The methods nduced angle. The range measurements are assumed to be fault-free and are not are not treated further in this work. We focus on theclock test Troposheric Sasstamonien model / /Weighted Satellite / /Receiver Broadcast ephemeris least square Satellite Satellite Receiver /delay Receiver clock Satellite Broadcast /Broadcast Receiver ephemeris clock ephemeris Weighted / Weighted Broadcast least least square square ephemeris / Weighted least square i clock treated further in in this work. WeWe focus onon thethe testtest statistic’s variation to to induced angle T : Troposphere delay error (m) fordue mitigating range measurement errors are summarized treated further this work. focus statistic’s induced angle statistic’s variation due to induced angle error resulting from variation due / Receiver Broadcast ephemeris / Weighted least square urther in this work. We focus on the test statistic’s variation dueSatellite to induced angle bclock clock error Table 1. (s) u : Receiver in broadcast ephemeris failure. The threshold for ephemeris failure detection is determined by the probability prop error resulting from broadcast ephemeris failure. error resulting from broadcast ephemeris failure. bi : Satellite clock TheThe threshold for ephemeris ephemeris failure detection is by the threshold failure detection is determined by the probability The threshold ephemeris failure detection is determined probability propp error (s) for for ulting from broadcast ephemeris failure.range measurement errors in the ephemeris However, i : Noise, multipath, etc. inufor determined by must the property of the test statistics The threshold ephemeris failure detection isisprobability determined by the probability property ofofof The threshold threshold for ephemeris ephemeris failure The failure threshold detection detection for ephemeris isbe determined determined failure byby the the detection probability probability is determined property property by the prop the test statistics and system continuity requirements. We assume thatprobability test statistics fo However, range measurement inThe the ephemeris under normal conditions under normal conditions musterrors be accounted forfor the However, range measurement errors in the ephemeris under normal conditions must be test statistics and system continuity requirements. We statistic the test statistics and system continuity requirements. Wetest assume thatthat testtest statistics fo ver, range measurement errors in the ephemeris under normal conditions must beforc :ephemeris The threshold failure detection is determined by the probability ofassume andthe system continuity requirements. We assumeproperty that Speed of light (m/s) test statistic’s accuracy. The range measurement errors are the test statistics and system continuity requirements. We assume that test statistics aa a thatrequirement the the test test statistics statistics and and system system continuity the continuity test statistics requirements. requirements. and system We We assume continuity assume that that requirements. test test statistics statistics follow follow assume test statistics fo Gaussian distribution [11] with a zero mean, and thatfollow the continuity (LA statistics follow a Gaussian distribution [11] with aWe zero accounted for range in in thethe testtest statistic’s accuracy. The range measurement errors are defined as accounted statistic’s accuracy. The measurement errors are defined as[11] ed for in the test statistic’s accuracy. measurement errors are defined asrange defined asThefor Gaussian distribution with a zero mean, that continuity requirement Gaussian distribution [11] with a zero mean, andand thatfollow the the continuity requirement (LA( the test statistics and system continuity requirements. We assume that test statistics a mean, and that the continuity requirement (LAAS CAT-I, distribution [11] with aazero mean, and that the continuity requirement (LAAS Gaussian Gaussian distribution distribution [11] [11] with with Gaussian azero zero mean, distribution mean, and and that that [11] the the with continuity continuity aofzero mean, requirement requirement that (LAAS (LAAS the continuity requirement (LA i i i i i i i iSeveral methods i i i i Gaussian CAT-I, which the probability false alarm in case of the first rising of the day) is are introduced to mitigate part of the error inis range measurement. First, a and i i i i (3) R I T c b b (3) (3) R I T c b b which is the probability of false alarm inalarm case of the first u u u u u u u (3)uGaussian distribution [11] withCAT-I, I T c bu b u CAT-I, which isthat the probability ofrequirement false in case of the rising of the which is the probability of false alarm in case of the firstfirst rising of the day)day) is a zero mean, and the continuity (LAAS -4 rising of the day) iscase 1.9×10 (K =3.73) [12]. The threshold 4 alarm CAT-I, which the probability ofofof false ofofof the first rising of the day) isis FFA CAT-I, CAT-I, which which isthe the probability probability CAT-I, false false which alarm alarm is in the incase in probability case the the first of first false rising rising alarm ofof the in the day) case day) ofisthe first rising of the day) is model-based mitigation method isisis proposed for ionosphere delay and troposphere delay error. (4K 1.9 10 FFA 3.73 ) [12]. The threshold (TH) is also designed with respect to sat 4 i i i KFFA 3.73 3.73 ( in ) [12]. (TH) is also respect to ( Kdesigned ) [12]. TheThe threshold isisalso designed withwith respect to sat 1.9 10is 10 range Ru R: uTrue True range range(m) (m) (TH) also with respect tothreshold satellite elevation for designed CAT-I, which isrange the(m) probability of 1.9 false alarm case of the first rising of the(TH) day) Ru : True : True (m) FFA 4444 4 K 3.73 ( ) [12]. The threshold (TH) is also designed with respect to satellite K K 3.73 3.73 K 3.73 1.9 10 ( ( ) [12]. ) [12]. The The threshold threshold ( (TH) (TH) is is ) also [12]. also designed designed The threshold with with respect respect (TH) is to to also satellite satellite designed with respect to sat 1.9 1.9 10 10 1.9 10 IIii :: Ionosphere delay error (m) The range differential method then estimates range errors by subtracting the true range from navigation integrity and continuity, according to equation FFA FFA FFA FFA FFA Ionosphere delay error (m) elevation for navigation integrity and continuity, according to equation (4). Because 4 i integrity and continuity, according to equation Becaut elevation for for navigation integrity and continuity, according (4).(4). Because threshold (TH) is also designed with respect to satellite T delayerror error(m) (m)1.9 10 ( KFFA 3.73 ) [12]. The (4).elevation Because testnavigation statistics are affected by corrected rangeto equation T :: Troposphere Troposphere delay 5 5 5 pseudorange correction). The receiver clock error is also the range measurements (also called elevation for navigation integrity and continuity, according to equation (4). Because test elevation elevation for for navigation navigation integrity integrity elevation and and continuity, for continuity, navigation according according integrity to to equation and equation continuity, (4). (4). Because Because according test test to equation (4). Because buu:: Receiver Receiverclock clockerror error(s) (s) statistics are affected by corrected measurements, measurements, the threshold hasrange a stringent boundarythe asthreshold has a stringentt statistics affected by corrected range measurements, threshold a string statistics are are affected by corrected range measurements, the the threshold has has a stringent i elevation for navigation integrity and continuity, according to equation (4). Because test i bb :: Satellite Satellite clock clock error error(s) (s) satellite elevation increases relative to the case of a satellite reduced by subtraction of range measurements between satellites on common RS (called the statistics are affected by corrected range measurements, the threshold aastringent statistics statistics are are affected affected byby corrected corrected statistics range range are measurements, affected measurements, by corrected the the threshold threshold rangehas measurements, has has astringent stringent the threshold hasata stringent boundary as satellite elevation increases relative to the case of a satellite low eleva Noise, multipath, multipath,etc. etc. ui :: Noise, at low elevation. boundary as satellite elevation increases to the a satellite at low el boundary as satellite elevation increases relative to the casecase of aofsatellite at low eleva statistics are affected by corrected range measurements, the threshold has a relative stringent (m/s) c : Speed Speed of of light light (m/s) double difference between satellites). Aselevation described above, the combination of subtraction of boundary asasas satellite increases relative to the case of a satellite at low elevation. boundary boundary satellite satellite elevation elevation boundary increases increases as relative satellite relative to elevation to the the case case increases of of a a satellite satellite relative at at low low to elevation. the elevation. case of a satellite at low eleva (4) THiTSi i iTSi i K FFA iTSi i (4) boundary as satellite elevation increases THTSrelative at low elevation. TH TS KFFAKofFFAasatellite TS toTSthe case (4) (4) TS TS receivers and satellites gives from perspective of relative range i ii i the best i ii performance i iii iithe i i i i : standard deviation of test statistics (m) : test statistics mean (m), Several methods toTH mitigate part of the K TS TSi(4) i i i TH TH K K TH K (4) (4) (4) (m)(m) al methods are introduced to mitigate part of the are errorintroduced in range measurement. First, a TSTS TSTS FFA TSTS TSTS TSTS FFA FFA FFA TSTS TS TS FFA : test statistics mean deviation of test statistics : test Test statistics mean (m)(m), statistics mean (m), deviation of test statistics TSTS : standard TS TS : standard i i i TS : TH K K error in range measurement. First, a model-based mitigation elevation angle (degrees), : sigma multiplier based on the continuity req (4) i TS ii:ii ii i i i FFA TS FFA TS measurement accuracy.TSTS Standard deviation of test : :test statistics mean (m), ::TS:standard deviation of test test : test statistics statistics mean mean (m), (m), test :elevation standard statistics deviation deviation mean (m), ofof test test statistics statistics :Kstandard (m) (m) deviation of test statistics (m) statistics KTS TSTS:TSTSelevation :standard angle (degrees), :(m) sigma multiplier based on the continuity angle (degrees), :FFA sigma multiplier based on the continuity requ TSTS FFA ased mitigation method is method proposedisforproposed ionosphere and troposphere delay error. i i fordelay ionosphere delay and troposphere : test statistics mean (m), : standard deviation of test statistics (m) TS : Elevation angle (degrees) TSK angle (degrees), : sigma multiplier based on the continuity requirement K K ::elevation K elevation : elevation angle angle (degrees), (degrees), :FFA elevation : sigma : sigma angle multiplier multiplier (degrees), based based on on the : the sigma continuity continuity multiplier requirement requirement based on the continuity requ FFA FFA FFA However, in this work, a model-based mitigation method is used to mitigate range FFA delay error. The range differential method then estimates : Sigma multiplier continuity requirement ge differential method then estimates range errors by subtracting the range from true : elevation angle (degrees),2.2KSensitivity multiplierbased basedononthe the continuity requirement FFA sigmaAnalysis range errors by subtracting the true range from the range Sensitivity Analysis 2.2 2.2 Sensitivity Analysis measurement errors arising from thealso ionosphere and troposphere. The receiver clock bias is e measurements (also called pseudorange correction). Thepseudorange receiver clock error is measurements (also called correction). The 2.2 Sensitivity Analysis 2.2 2.2 Sensitivity Sensitivity Analysis Analysis 2.2 Sensitivity Analysis 2.2 Sensitivity Analysis Various geometry conditions can be formed between ground baseline vectors and s Various geometry conditions be formed between ground baseline vectors Various geometry conditions cancan be formed between ground baseline vectors andan s receiver clock error is also reduced bySensitivity subtraction of range 2.2 Analysis estimated by computation of the user’s position in a process using the weighted least squares by subtraction of range measurements between satellites on common RS (called the Various geometry conditions can be formed between Various geometry can be formed between ground baseline vectors and satellites. Various Various geometry geometry conditions conditions Various can can be be formed geometry formed between between conditions ground ground can baseline baseline be formed vectors vectors between and and satellites. ground satellites. baseline vectors and measurements between satellites on common RS (calledconditions the Consequently, the detection performance of this algorithm depends on the geometrys Consequently, the detection of this depends on the geometc Consequently, the detection performance of this algorithm depends on the geometry Various geometry conditions can bemeasurements, formed between baseline andalgorithm satellites. baseline vectors andperformance satellites. Consequently, double difference between satellites). described method. the adverse effect on accuracy ofground range weground recognized thatvectors difference between satellites). As described above, theDespite combination ofAssubtraction ofabove, Consequently, the detection performance of this algorithm depends on the geometry condition. Consequently, Consequently, the the detection detection performance Consequently, performance of of the this this detection algorithm algorithm performance depends depends on on of the the this geometry geometry algorithm condition. condition. depends on the geometry In this section, we derive the relationship between satellite position error and the testc the detection performance of this algorithm depends on the combination of subtraction of receivers and satellites In this section, we derive the relationship between satellite position error In this section, wealgorithm derive thedepends relationship between satellite position error andand the the test Consequently, the detection performance of this on the geometry condition. s and satellites gives the best performance from the perspective of relative range combining single and double difference methods posed a contradiction in this algorithm the geometry condition. In this section, we derive the gives the best performance from the perspective of relative InInIn this section, we derive the relationship between satellite error and the test statistics this this section, section, we we derive derive the the In relationship relationship this section, between between we derive satellite satellite the relationship position position error error between and and the the satellite test test statistics position error and analyze the properties ofposition this algorithm with regard tostatistics geometry [14].and the test relationship between satellite error and the test range measurement accuracy. and analyze the properties ofposition this algorithm with regard to geometry [14]. and analyze the properties ofposition this algorithm with regard to geometry [14]. In this section, we derive the relationship between satellite error and the test statistics ment accuracy. because these methods use the broadcast ephemeris (to be validated by test statistics). The [14]. i ,regard statistics and analyze thetoof properties of this algorithm with However, in this work, a model-based mitigation method i , f with f and analyze the properties ofofof this algorithm with regard geometry [14]. and and analyze analyze the the properties properties and this this analyze algorithm algorithm the with properties with regard regard to to this geometry geometry algorithm [14]. to geometry [14]. In equation (5) and Fig. 2, we define eiA, f ,i , feiB, f toi , f be unit line-of-sight (LOS) vect Intoequation and Fig. 2, we define to unit be unit line-of-sight (LOS) v In equation (5) (5) and Fig.to 2,geometry we define line-of-sight (LOS) vecto eA e, A eB, etoB be regard geometry [14]. ver, in this work, a model-based method is measurement used to validated mitigate range and analyze the properties this algorithm with regard [14]. is usedmitigation to mitigate range errors arising frombeofindependent test statistics and ephemeris must for ephemeris fault i, ifi,,reliable i, f i, f ffi , f i, ifi ,, ffi , f InInIn equation (5) and Fig. 2,2,we define be unit line-of-sight from ee e,(5) e, eand equation equation (5) (5) and and Fig. Fig. 2,we we In define equation define ,(5) Fig. toFig. bebe 2, unit unit we line-of-sight line-of-sight define (LOS) , (LOS) to vectors vectors be from line-of-sight from (LOS) vecto eto eB vectors In equation 2, we define eA (LOS) to be unit unit i the ionosphere and troposphere. The receiver clock bias BBand B to ,Af AA A iB,(A, RS antennas B) to the satellite i when ephemeris failure occurs. eiAi and eiB , f ment errors arising from the ionosphere and troposphere. The receiver clock bias isand Fig. 2, wetwo i equation (5)range define , but tovectors beto unit line-of-sight (LOS) vectors eAiantennas eB(A, In addition, required value, an absolute measurement. two (A, B) to the satellite i when ephemeris occurs. and line-of-sight (LOS) from two RS antennas (A, B)from to failure two RS RS antennas B) the satellite i when ephemeris failure occurs. eA eand e is estimated bydetection. computation of theInthe user’s position inisanot a relative A B, i ii i i ii i i ii i i i the satellite i when ephemeris failure occurs. and , two RS antennas (A, B) to the satellite i when ephemeris failure occurs. and , is e e two two RS RS antennas antennas (A, (A, B) B) to to the the two satellite satellite RS antennas i when i when (A, ephemeris ephemeris B) to the failure failure satellite occurs. occurs. i when ephemeris failure occurs. and and , , is is and e e e e e e process using weighted squares least method. Despite d by computation of the user’s position in the a process usingleast the weighted squares B, A Bii i represents i A AAi A, and iBBBR geometry rangeephemeris between RS and the satellite the faulty vecto The methods for mitigating range measurement errors are summarized in Table 1. iis two RS antennas (A, B) to the satellite i when failure occurs. and , e e is geometry range between RS and and thesatellite satellite and the adverse effect on accuracy of range measurements, we represents faulty ve geometry range between RS i i,, and represents the the faulty vector geometry range between and the the satellite B R R A i , and RS i ii i i Despite the adverse effectrecognized on accuracy that of range measurements, we recognized that represents the faulty vector of satellite i [13]. combining singlegeometry and double difference range between RS and the satellite i , and R represents the faulty vector of R R represents represents the the faulty faulty vector vector R of represents of the faulty vector geometry geometry range range between between RS RS and geometry and the the satellite satellite range i between , i and , and RS and the satellite i , and satellite i [13]. satellite i [13]. satellite i [13]. geometry range between RS and the satellite i , and Ri represents the faulty vector of ng single and double difference methods posed a contradiction in this algorithm satellite i i[13]. satellite satellite [13]. i [13]. satellite 1. Mitigation methods for range measurement error.i [13]. Table 1. MitigationTable methods for range measurement error. 7 satellite i [13]. these methods use the broadcast ephemeris (to be validated by test statistics). The Error components Mitigation Methods 77 7 stics and validated ephemeris must be independent for reliable ephemeris fault Klobuchar model 7 Ionospheric delay (with GPS Navigation Message Iono. Parameters) n. In addition, the required range is not a relative value, but an absolute measurement. 6 Troposheric delay Sasstamonien model Satellite / Receiverinclock Broadcast ephemeris / Weighted least square hods for mitigating range measurement errors are summarized Table 1. Mitigation methods for range measurement error. The threshold for ephemeris failure detection is determined by the probability property of omponents 91 7 7 7 http://ijass.org Mitigation Methods the test statistics and system continuity requirements. We assume that test statistics follow a 6 (89~101)14-083.indd 91 Gaussian distribution [11] with a zero mean, and that the continuity requirement (LAAS CAT-I, which is the probability of false alarm in case of the first rising of the day) is 2015-03-30 오후 3:48:27 (7) eBi cos B cos B iˆ1 cos B sin B iˆ2 sin B iˆ3 Figure 3. Local coordinates. In local coordinates, eAi and eBi can be defined as in equation (7) with local elevation Inangle equation (7), the local elevation angles ( A , B ) from reference stations (A, B) c ( ) and local azimuth angle ( ). eAi cos A cos Aiˆ1 cos A sin Aiˆ2 sin Aiˆ3 assumed as similar ( B ), ˆbecause B i3 eBi cos B cos B iˆ1 cos B sinA B iˆ2 sin Int’l J. of Aeronautical & Space Sci. 16(1), 89–101 (2015) igure Figure2.2.Geometry Geometryofofephemeris ephemerisfault faultcondition. condition. Figure 2. Geometry of ephemeris fault condition. km) isIn equation quite (7), large relative to the baseline length between two reference stations. If this the local elevation angles ( , ) from reference stations (A, B) can be A f fault f i Figure 2. Geometry of ephemeris eAi , eAi condition. eAi , eBi , eB eBi B because range from GNSS satellite and reference (over 20,000 (5) range(reference from GNSS satellite (over 20,000can be assumed to be an assumed as similar ( A B ), because assumption is adopted, triangle A, and B, reference and satellite) km) is quite large relative to the baseline length between two km) is quite large relative to the baseline length between two reference stations. If this reference stations. If this assumption is adopted, triangle isosceles triangle. Using this geometry property the local elevation angles ( A , B ) ar assumption is adopted, triangle (reference A, B, and satellite) can be assumed to be an (reference A, B, and satellite) can be assumed to be an isosceles isosceles Using triangle. Using this geometry property the local angles ( A , Bangles ) are triangle. geometry property theelevation local elevation regardless of reference position. expressed as this regardless ofas (θAexpressed reference position. of reference position. , θB) areas expressed θ regardless i Using equation (7)ininequation equation (6), E AB becomes Using (6), becomes Using equation equation (7) in(7) equation (6), becomes E (6) i i ,T i (5) i I e e R e i Substituting equation (5)equation into equation Substituting Substitutingequation equation(5)(5)into into equation equation(2) yields equation (6). (6).(2) yields equation (6). (2)yields Substituting equation (5) into equation (2) yields equation (6). Substituting equation (5) into equation (2) yields equation (6). (7) GNSS satellite and reference (over range from i ,T i ,T i ,T i ,T i i i ,T i ,TTS i AB i iT T Ri ,T eAi ,T eAi eBi ,T eBi eAB i i TSTS R R e e e e e e e e A A A A BB BB T eABeAB AB AB (6) i T TS AB R i ,T eAi ,T eAi eBi ,T eBi eAB (6)(6) i eAB Ri ,T E AB i ,T i ,T i i T T (6) i TeABeAB R R i,TEAB E AB eAB R EAB eAB :Unit baseline vector ( xAB ) : Unit baseline vector ( ) eAB: Unit eAB : Unitbaseline baselinevector vector (i x( xeABi ,T) e i e i ,T e i E eAB :Unit baseline vector ( xABABAB ) A A B B i i i , T i ,T i i i , T i ,T i i EE E e e e e e e e e i i , T i i , T i AB AB e A A eA A e B B e B B AB A A B B Figure 3. Local coordinates. T i AB cos cos cos cos sin cos sin cos sin cos cos cos (8) 2 2 2 2 cos cos cos sin cos sin cos sin sin cos cos sin cos(8) cos sinAsin E sin cos sin B sin cos cos A cos B A cos B A B cos sin cos cos cos sin sin sin 0 T i 2 2 2 2 cos cos sin cos sin cos sin sin sin cos sin A sin B E AB A A B B A B cos sin cos A cos B cos sin sin A sin B 0 2 T i AB 2 2 A 2 A A 2 B B A B B A 2 A 2 B 2 A A B B A B A B B The baseline unit vector of equation (6) can be derived as The baseline baseline unit vector vector of of9equation equation (6) (6) can can be be derived derived as as equation equation (9) (9) [10], [10], The equation (9) [10], unit The baseline unit vector of equation (6) can be derived as equation (9) [10], Equation (6) can be simplified in local coordinates that use the baseline vector as the x-axis. baselineTTunit vector of equation (6) can be derived as (9) Equation (6) can be simplified in local coordinates that The The as equation equation (9) [10], [10], Figure Figure 3. 3. Local Local coordinates. coordinates. (9) [1 [1baseline 0] unit vector of equation (6) can be derived eeAB 00 0] (9) (9) AB Equation Equation (6)(6) can can bebe simplified simplified in local localcoordinates coordinates that that use use thebaseline baseline vector vector asx-axis. asthethex-axis. x-axis. Equation (6) can be simplified inin local coordinates that use thethe baseline vector as the T use the baseline vector as the x-axis. Fig. (3) shows the local Figure (3) shows the local coordinates i iand the geometry of the satellite. eAB [1 0 0]T (9) T andtheesatellite. In localand coordinates, eA of (9) [1 00 0] 9 B can be defined as in equatione AB coordinates the geometry (9) e(7) with [1 local 0]elevation ABand Figure (3) shows the local coordinates and the geometry of the satellite. substituting equation (9) into into equation equation (6) yields yields [18] igure Figure (3)(3) shows shows thethe local local coordinates coordinatesand and thethe geometry of of the the satellite. satellite. and substituting equation (9) (6) [18] geometry and substituting equation (9) into equation (6) yields [18] i i i i In local coordinates, and bebedefined asas inas equation andeB ecan can be defined defined in in equation equation (7)(7) with with local local elevation elevation InIn local local coordinates, coordinates, eA eAand Bcan and substituting equation (9) into equation (6) yields [18] ( 2.)Geometry and local angle azimuth ( ).azimuth and substituting (9) Figure of ephemeris fault condition. iequation and substituting equation (9) into into equation equation (6) (6) yields yields [18] [18] (7)angle with local elevation (θ) angle and local angle (ψ). TT i ii ii (10) (10) TSAB EAB (10) TS E R AB AB T R E i TLL Ri i angle angle ( ) and local local azimuth azimuth angle angle (( ). ). ()and TS AB (10) i iii eAi cos A cos Aiˆ1 cos A sin Aiˆ2 sin Aiˆ3 TS (10) EEABABABii EEABiABiLTLL TTT RReeii ABAB TS (10) EAB (11) E (11) AB AB (7) (7) AB i i i i i LL T e (11) ˆ ˆ ˆ E E ˆ ˆ ˆ ˆ ˆ ˆ (11) cos cos sin sin i i i i i cos cos cos cos sin sin sin sin eAeA cos ecos i i i i i i AB T AB EAB B A A B BA2Af 2 B TT A 1fA 1 Bi 1 A Ai 2 A 3A 3 B 3 i L i cos E 22e cos22 cos22 (11) EAB EAB (11) (7)(7) eAi , eA eA , eBi , eBi eBi T L AB (5) AB AB cos AA cos BB i i cos2eAB L 2 2 ˆ ˆ ˆ ˆ ˆ ˆ Substituting equation (5) into equation (2) yields equation (6). sin Bcos Bi1Bi1 cos Bisin i2 isin Bi3B i3 8 eB eB cos cos cos sin 22 cos 2 cos 2 A cos 2 B TT TT B cos ,B T i B i2B ii In equation i(7), Ithe angles (θA, θB) from e local e elevation R 2 2 cos cos cos cos sin2 AA cos cos sin BB cos EEiABAB TLL cos AA sin cos BBBBsin 2 cos cos A e 8 T E cos cos sin cos sin i 2 i reference stations (A, B) can be assumed as similar (θ ≈θ ), AB A A B B from reference (A,cos B) In equation (7), the local sin cos AA cos cos BB B elevation angles ( A , BA) can sin be cos cos cos cos EEABABi stations LTLL cos A B sin cos2cos cos AA sin sin cos BB A B sin sin cos cos 88 A B B)B) cos be ) from reference reference stations stations (A,(A, can can be cos InIn equation equation (7), thethe local elevation (7), T angles cos sin sin cos A cos BB cos local elevation angles ( (A, A,B)Bfrom i assumed asi ,Tsimilar (over 20,000 A eAB range from GNSS satellite and reference TS AB R eAi ,T (eAi A eBi,T B e),Bi because (6) (10) ( ( i T ), Equation (10)20,000 shows the sensitivity sensitivity relationship relationship between between test test statistics statistics and and the the fa f Equation shows ), because range range from from GNSS GNSS satellite satellite and and reference reference (over (over 20,000the assumed assumed asas similar B eBABbecause similar Ri ,T large EA ABArelative Equation (10)If shows thesensitivity sensitivityrelationship relationshipbetween between test statistics and the fa Equation (10) shows km) is quite to the baseline length between two reference stations. this the Equation (10) shows the sensitivity relationship between test statistics and fa Equation (10)the shows sensitivity relationship between statistics and the the is fa satellite location resulting from ephemeris failure. When thetest Schwarz inequality is test statistics and fault the in from satellite location resulting fromthe satellite location resulting ephemeris failure. When Schwarz inequality eAB : Unit baseline vector ( xreference ) ABreference km) km) is assumption is quite quite large large relative relative to to the the baseline baseline length length between between two two stations. stations. If If this this satellite location resulting from ephemeris failure. When the Schwarz inequality is is adopted, triangle (reference A, B, and satellite) can be assumed to be an i ephemeris failure. When thefrom Schwarz inequality is applied satellite location resulting ephemeris failure. When the Schwarz inequality is E AB eAi ,T eAi eBi ,T eBi satellite from Schwarz geometry inequalityco is equationlocation (10), we weresulting can derive theephemeris sensitivityfailure. relationWhen in the thethe worst-case equation (10), relation in inassumed equation (10), we can can derive derive the the sensitivity sensitivity relation in the worst-case geometry con assumption assumption is is adopted, adopted, triangle triangle (reference (reference A,A, B,B, and and satellite) satellite) can can bebe assumed to to be be an an equation (10), we can derive the sensitivity relation in the worst-case geometry con A , we isosceles triangle. Using this geometry property the local elevation angles ((10), are derive the sensitivity relation in the worst-case geometry con B ) can equation worst-case geometry condition. equation (10), we derive the sensitivity relation in the worst-case geometry con TT can ii ii (12) TS E Rii (12) TS E R AB AB , , T isosceles isosceles triangle. triangle. Using Using this this geometry geometry property property the the local local elevation elevation angles angles ( ( ) are ) are AB AB Equationas(6) can be simplified in localposition. coordinates that use the baseline i A A vector i i x-axis. LLas the regardless of reference expressed (12) TS AB BEBAB R i i T i i i LT R i (12) TS E AB (12) (12) TS AB R AB E AB L L Figure (3) shows the local coordinates and the geometry of the satellite. regardless regardless of of reference reference position. position. expressed expressed as as i Using equation (7) in equation (6), E AB becomes This shows shows that that the the sensitivity sensitivity increases increases when when the the local local elevation elevation angle angle and and the the This This shows that the sensitivity increases when the local elevation angle and the a i i This shows that the sensitivity increases when the local Using Using equation equation (7) (7) in in equation equation (6), (6), becomes becomes E AB E AB2 2 2 condition. Fig. 2. Geometry of 2ephemeris fault This that sensitivity increases when elevation angle and Figure the fault condition. cos 2. cosGeometry A cos Bof cos sin A cos A sin B cos B sin cos cosshows A cosand ephemeris B the This shows theand sensitivity increases whentothe the local elevation and the the elevation angle azimuth angle are close 0°local andgiven angle are closethat to 0° and 90°, respectively. respectively. Accordingly, given these angle properties, thi angle are close to 90°, Accordingly, these properties, thi (8) 0° T i 2 2 2 2 cos cos A sin A cos B sin B cos sin sin sin cos sin sin E AB cos angle are close to 0° and 90°, respectively. Accordingly, given these properties, thi A B A BAccordingly, given these properties, this 90°, respectively. 2 2 2 2 2 2 2 2 cos 0° and 90°, respectively. Accordingly, given these properties, thi cos cos AAcos B B coscos sin sinAcos AAsin sinBcos B B sinsin cos cos cos angle AAare cos close cos cos cos B to A cos B cos B angle are 90°, respectively. Accordingly, theseangle. properties, cos sin cos A cos B cos sin sin A sin B 0 close (8) (8)and for to 0° is sufficient sufficient for fault detection for rising risingfor satellites of low lowgiven elevation angle. From athi a lo l is fault detection for satellites of elevation From T T algorithm is sufficient fault detection rising satellites for 2 2 2 2 cos B cos 2 cos cos AsinA sinAAcos Bsin sinB coscos 2 sin sin 2AAsin B2 B sinsin cos cos sin sinAAsin sinB cos sin B E ABi EABi B is sufficient for fault detection for rising satellites of low elevation angle. From a lo of islow angle.detection From a local azimuth perspective, for satellites of angle. aa lo sin sin cos cos AAcos B coscos sin sin sin sinAAsin sinB 0 sufficient 0 elevation cos B B coscos for fault is sufficient for rising rising satellites of low low elevation elevation angle. From From lbb azimuth perspective, various baseline baseline vectors are required required using multiple multiple RS and and for fault detection azimuth perspective, various vectors are using RS Substituting equation (5) into equation (2) yields equation (6). baseline various vectors are required using multiple RS and azimuth perspective, various baseline vectors are required using multiple RS and b azimuth perspective, various baseline vectors are required using multiple RS b baseline should be extended to increase the azimuth perspective, various vectors aresatellite’s required using multiple RS and and length length should be extended extended to baseline increase the satellite’s satellite’s induced angle. This means means thab length should be to increase the induced angle. This tha 8 induced angle. be This meanstothat the algorithm above is angle. This means tha length should extended increase the satellite’s induced 9 length should be extended to the induced angle. This means tha i ,T i ,T i i ,T i T length should be is extended to increase increase the satellite’s satellite’s induced angle. Thissuch means tha algorithm above is applicable for wide-area implementations of GNSS GNSS such as Spa Spa applicable for wide-area implementations of GNSS such i algorithm above applicable for wide-area implementations of as TS AB R eA eA eB eB eAB 9 9 algorithm above is applicable for wide-area implementations of GNSS such as Spa as Space-Based Augmentation System (SBAS) and Ground (6) is applicable for wide-area implementations of GNSS such as Spa algorithm above T algorithm above is applicable for wide-area implementations of GNSS such as Spa i Augmentation System (SBAS)(GRAS) and Ground Regional Augmentation System (GRA Augmentation System (SBAS) and Ground Augmentation System (GRA eAB Ri ,T E AB Regional Augmentation System ratherRegional than narrowAugmentation System (SBAS) and Ground Regional Augmentation System (GRA Augmentation System (SBAS) and Ground Regional Augmentation System (GRA implementations. eAB : Unit baseline vector ( xABarea )than Augmentation System (SBAS) and Ground Regional Augmentation System (GRA than narrow-area implementations. narrow-area implementations. i i ,T i i ,T i than narrow-area implementations. E AB eA eA eB eB than narrow-area implementations. than narrow-area implementations. 2.3 Ephemeris Protection Level and MDE Fig. 3. Local coordinates. GNSS implementations conduct a two-step process 2.3 Ephemeris Protection Level and MDE MDE Equation (6) can be simplified in local coordinates that use the baseline vector as theLevel x-axis. 2.3 Ephemeris Protection and Figure 3. Local coordinates. 2.3 Ephemeris Protection Level and MDE 2.3 Ephemeris Protection Level and MDE Ephemeris Protection Level andaaMDE Figure (3) shows the local coordinates and the geometry of 2.3 theGNSS satellite. GNSS implementations conduct two-step process process to to ensure ensure navigation navigation integrit integri implementations conduct two-step i i GNSS implementations conduct a two-step process to ensure navigation integrit In local coordinates, and can be defined as in equation (7) with local elevation e e GNSS implementations conduct a two-step process to ensure navigation integrit B A DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.89 92 GNSS implementations conduct a two-step process to ensure navigation integrit angle ( ) and local azimuth angle ( ). (89~101)14-083.indd eAi cos A cos Aiˆ1 cos A sin Aiˆ2 sin Aiˆ3 e92Bi cos B cos B iˆ1 cos B sin B iˆ2 sin B iˆ3 10 10 10 10 10 (7) 2015-03-30 오후 3:48:28 When affection of zero nominal of test statistics is considered, equation (13) is distribution mean and standard with condition deviation TSi . nthe n TSi i KK TS i i i i i i others SSvertvert XX SS x xthat x x to Sa Svert the test statisticsT correspond Gaussian vert others EE i i EEi i T i i11 A ABi ABiL L A n distribution with zero standard deviation and TS . i i i FFA TS Kmean TS x S i i X vert S vert x S vert vert others i Ei T i Ei T i 1 L i A AB L A i AB n i i i i i i FFA FFA TSTS derived as equation (15). We assume vert vert vert vert i i i i T T AA ABAB L L i K FFA TS (1( (1 TS i i i third x on right xside side Svert Sof second Xsecond S and (15) The and terms on the hand equation (15)are are developedinto int The terms the hand of (15) developed vertequation others third right i 1 E E Jongsun Ahn Orbit Ephemeris Failure Detection in a GNSS Regional Application information of faulty satellites, identified using fault detection algorithms, is broadcast to the The second and third terms on the right hand side of equation (15) are developed into equation (16). equation (16). ormation of faulty satellites, identified usingsatellites, fault detection algorithms, is broadcast toalgorithms, theidentifiedisusing information of faulty identified using fault detection broadcast the information of faulty satellites, fault to detection algorithms, is ofbroadcast to the user within a limited time; then, an airborne user computes the protectionThe level corresponding second terms on the right hand side(16). equation (15) are developed into equation (15) arethird developed equation to information ensure navigation integrity.identified First, the information equation (16). of faulty satellites, using fault detection algorithms, is and broadcast to theinto 2 2 (16). i r within a limited time;user then, an airborne user computes protection level corresponding a limited time; then, anthe airborne user computes thethen, protection level corresponding n n of within faulty satellites, identified using fault detection equation user within a limited an airborne user computes corresponding 2 2 level 2 2 TSiprotection to the available satellites’ geometry used to compute thetime; navigation solution. 2 2 protection i i 2 2 The i i TS x2xthe S S user within a limited time; then, an airborne user computes the protection level corresponding Sn Sverti verti others vert others vert algorithms, is broadcast to the user within a limited time; i 2i EEi i Ti T i 1i 1 2 2 position LTSL the he available satellites’to geometry used to computegeometry the navigation The 2 theisavailable satellites’ used tosolution. compute theprotection navigation solution. protection A A compute ABAB i i tohypotheses the the available geometry used protection navigation toThe level computed baseduser on various andsatellites’ compared with the allowable then, an airborne computes protection level Svert x solution. Sverti The others T (16) (16) i i to the available satellites’ geometry used to compute the navigation solution. protection S The x S i 1 AE EAB L corresponding to the available satellites’ geometry usedwith the allowable el is computed based on various hypotheses andon compared with the allowable position level is computed based various hypotheses and compared position i i n nwith the allowable position (16) level is computed based on various ihypotheses and compared (16) 2 2 error bound, known as the alertsolution. limit (AL), to check GNSS implementation i availability. i i 2 2 i i (16) TSTS x x position to level compute the navigation The protection level SSvertvert with S Svert others is computed based on various hypotheses and compared the allowable vert others T iT n i i i i i EE 2 2 i 1i 1 i i or bound, known as theerror alert limit (AL), to as check GNSS implementation availability. is computed based on hypotheses and compared bound, known the various alert limit (AL), to check GNSS implementation availability. check LTSL GNSS AB error bound, known as the alert limit(AL), availability. x ximplementation S S vert others [12][16] SSvertAAto iAB T i E i 1 errorthe bound, known position as the alerterror limit (AL), to check with allowable bound, knownGNSS as implementation E ABL Aavailability. ][16] [12][16] [12][16] thethis alert limit tothe check GNSS implementation In section we (AL), derived vertical PL (VPL ), which estimates the impact of one He [12][16] i i i i availability. [12][16] i is i of thestandard standard deviation Equation (16)isinto issubstituted substituted intoeqe where others where deviation . .Equation (16) others where isis the standard deviation of . (16) Equation isthe the standard deviation of of is substituted equation into others others n this section we derivedIn thethis vertical PLwe (VPL estimates the impact of one section derived the vertical PL section (VPL ), estimates thewhere impact of one others others . Equation He), which Hean In facility) this wewhich derived the vertical PL (VPL i MDE, He), which estimates the impacti of one satellite failure (undetected at a ground on airborne user’s position, and where isinto the standard deviation ofapplying . Equation (16) is substituted into eq In In this section we derived the vertical PL (VPL ), which others others He (16) is substituted equation (15) and the K this section we derived the vertical PL (VPL ), which estimates the impact of one MD i vert i vert i A i AB T i AB T i others 2 i A L L 2 i vert i vert i TS 2 i A i TS i A i AB n 2 i AB T L n T L i vert 2 2 i others i 1 i 1 i vert 2 He KK (15) and applying the with with the probability of missed detection, thedetection, protection MD associated estimates the impact one satellite failure (undetected ellite failure (undetected at a ground facility) on of anat airborne user’s position, MDE, and applying the associated with theprobability probability ofmissed missed detection,the theprot pro and the the satellite (undetected a ground facility) on anand airborne position, and MDE, associated with the probability of position, missed detection, the MDassociated MD satellite failure (undetected atuser’s a(15) ground facility) on an Kairborne user’s and MDE, of based onfailure the proposed ephemeris fault detection algorithm. MDE is(15) used toapplying compute the K MD associated with the probability of missed detection, the prot (15) position, and applying the at satellite a ground facility) on an airborne user’s position, failure (undetected at a ground facility) on anand airborne protection user’s and MDE, levelasisequation derived level is derived (17)as equation (17) ed on the proposed ephemeris detection algorithm. MDE isonto used toalgorithm. compute the based onfault the proposed ephemeris fault detection MDE islevel used to compute the based the proposed ephemeris fault detection MDE is used to compute the isderived derived equation (17) MDE, based on as the proposed ephemeris fault detection level ispseudorange asasalgorithm. equation (17) P-Value, broadcast integrity parameters the user together with the is derived based on MDE the proposed ephemeris algorithm. MDE level is used to compute the i(17) as equation algorithm. is used to computefault the Pdetection Value, broadcast n 2 2 K FFA K MD TS i i i i Value, broadcast as integrity parameters to as theintegrity user together with the pseudorange P-Value, broadcast parameters to the user together with the pseudorange VPL S P-Value, broadcast as integrity parameters to the user together with (17) Svert others (17) He vert correction (PRC). To derive ato VPL an estimated position error bei T K MDpseudorange can i xi the He,user as integrity parameters the togetheruser’s withconservative the i i 1 n n E P-Value, broadcast as integrity parameters to the user together with the pseudorange K A AB L 22 i i 22 K K K i FFA MD TS i FFA MD TS i i i i i n K 2 2 K MD TSxxKKMDMD pseudorange correction (PRC). To derive a user’s VPL , can an beVPL VPLHeposition Svertverterror Sestimated SSvert (17) (17) Heconservative FFA i i rection (PRC). To derive a VPLHe(PRC). , an estimated user’s conservative position error correction derive VPL beconservative He others He, an estimated i can correction (PRC). To derive a VPL , aniHe user’s can beothers HeVPL S vert x K MDerror Svert shown in equation To (13) usinga the Cauchy-Schwarz inequality. [12] (17) i i i i T T T position vert others 1 i 1 i E E i i estimated user’s conservative can be shown correction (PRC). To derive aposition VPLHe, error an estimated user’s conservative position be error A A can ABAB 1 i E L algorithm, A LAB ofthe The the proposed equation L TheMDE MDE of algorithm, equation in (18), is defined in the first term on proposed in shown wn in equation (13) using inequality. [12] in equation shown inCauchy-Schwarz equation (13) using theCauchy-Schwarz Cauchy-Schwarz inequality. [12] inthe equation (13) inequality. shown (13) using the Cauchy-Schwarz inequality. [12] shown i using the n R (18), is defined in the first term on the right hand side of shown in equation (13) using the Cauchy-Schwarz inequality. [12] i i i i [12] S the(13) right hand side of equation (17). According to the integrity requirement, the MDE of the x Svertothers X vert vert i i equation (17). According to the integrity requirement, n i Ri R i n1 n A fault detection algorithm is a confidential value corresponding to probability of int R TheMDE MDE the proposed algorithm, shown equation (18), defined inthe thefirst first The ofofthe algorithm, shown ininin equation (18), in te i i i i i i i The MDE ofproposed the proposed shown equation (18),isis isdefined defined in the first te ii i (13) i fault i detection algorithm is algorithm, a confidential value corresponding to probability of int i x X X vert Svert Svert i Rxi Svert S (13) the MDE of the fault detection algorithm is a confidential n X x S vert vertothers others S vert (13) fault detection algorithm is a confidential value corresponding to probability of int fault detection algorithm is a confidential value corresponding to probability of integrity vert vert others i i i i 12 i 1 Xi A i 1 Svert A i x Svertothers A (13) i the 1 value corresponding (13) i vert to probability integrity The theright right hand side equation (17).According According tothe therisk. integrity requirement, theMDE MDE hand side of equation (17). tois integrity requirement, the Pof The P-Value (side ), derived using theofMDE, one of the integrity parameters broad the right hand Ai of equation (17). According to the integrity requirement, the MDE o A i 1 P The P-Value ( i ), derived using the MDE, is one of the integrity parameters broad i A i P , derived using the MDE, is one of the integrity P-Value The P-Value ( ), derived using the MDE, is one of the integrity parameters broad P ), MDE, is one of the integrity parameters broadcast to The P-Value ( A where Svert is the vertical component of the projection matrix of the range error source A parameters broadcast to the user. The P-Value represents the user. The P-Value represents the decorrelation due to ephemeris error between the i i irange is the verticalcomponent component of the user. The P-Value represents the decorrelation due to ephemeris error between the where Svert is the verticalwhere component ofthe thevertical projection matrix ofofthe error source is the projection matrixcomponent of theuser. range source Svert 12 where is projection the vertical of error the projection matrix oferror the range error source Svert 1212 i The P-Value the decorrelation due to ephemeris error between user. The(ionosphere, P-Value represents the decorrelation due to the ephemeris the RSthe and decorrelation due torepresents ephemeris between RS anderror between i error and is nominal range measurement error onto the position others component where is the vertical of the projection matrix of the range error source matrix of theSrange error source onto the position error and vert aircraft [19]. theaircraft aircraft[19]. [19]. i i i error is nominal range measurement error (ionosphere, o the position error andonto is nominal error (ionosphere, others is nominal range measurement (ionosphere, the position errorrange and measurement aircraft [19]. aircraft [19]. the position error and others onto others is nominal range measurement error (ionosphere, troposphere, multipath, receiver noise, etc.) i nominal range measurement errori (ionosphere, onto the position errorreceiver and noise, troposphere, multipath, K FFA K MD TSiii others isetc.) MDE i (18) i K FFA K MD T TS posphere, multipath, receiver noise, etc.) (18) K troposphere, multipath, receiver noise, etc.) K FFA K FFA i MD etc.) MDE (18) i TS troposphere, multipath, receiver noise, i MD TS T isisthe satellite position error due to the undetected E AB but i real MDE i MDE failure, R (18) the satellite position error due to the undetected ephemeris in a (18) T T L EiAB troposphere, multipath, receiver noise, etc.) i L EAB LinEABa real L i to the i failure, Ri is the satellite position duesatellite tobut the in undetected ephemeris inposition aephemeris real error Ri error isfailure, the position error due undetected MDEtoiibut isisfailure, hard to but figure ephemeris a real case, R the satellite the undetected ephemeris failure, but in a real (19) P i due i A MDE i PAi i MDE (19) i ephemeris Ri Risi hard MDE is the position due to the undetected failure, in a real TS i in case, to satellite figure out using error equation (2). So, we assume that worst case (19) iAAi but (19) (19) out using TSi in equation (2). So, we assume that worst case PA PA i A A i i i i i e, R is hard to figure intoequation (2). So, we assume that worst case using Ri isTS TS case, hard figure out using in has equation (2). So, weusing assumeTSthat case (2). So, we assume that worst case of out ephemeris failure detection processor occurred, R case, is hard to figure out inworst equation i i of the ephemeris failure detection processor has occurred, the same as algorithm threshold. Then, R TS case, is hard to figure out using in equation (2). So, we assume that worst case same as algorithm threshold. Then, equation (4) is AsAs shown (18), the MDE MDE of ofthe theproposed proposed shownininequation equation (18), the algorithm depends on the As shown in equation (18), the MDE of the proposed algorithm depends on the As shown in equation (18), the MDE of the proposed algorithm depends theo ephemeris failure detection processorfailure has occurred, same as algorithm threshold. Then, substituted into the worstthe case of equation (12), and the As shown in equation (18), the MDE of the proposed algorithm on the on norm of ephemeris detection processor has occurred, the same as algorithm threshold. Then, algorithm depends on the norm of the worst-case sensitivity ephemeris detection processor has occurred, the same as algorithm threshold. Then, depends equation (4) is substituted into the of worst case of failure equation (12), and the satellite position error sensitivity vector, which fluctuates with the geometry condition. Howe of ephemeris processor has (14). occurred, the samevector, asworst-case algorithm threshold. Then, which fluctuates with the geometry condition. satellite positionfailure error isdetection derived with equation worst-case sensitivity sensitivity vector, vector, which which fluctuates fluctuates with with the the geometry geometry condition. condition. Howev Howe worst-case ation (4) is substitutedequation into the worst case of equation (12), andcase the(4)satellite position error worst-case sensitivity vector, which fluctuates withposition the geometry However, the (4) is substituted into the worst ofisequation (12), and the satellite position erroralgorithms equation substituted into the worst case ofprevious equation (12), and the satellite However, the use a fixed MDE aserror the condition. i is derived with equation (14). i i previous algorithms useerror a fixed MDE as the P-Value. Equation (19) is substituted i FFA TS equation the satellite position (4) TS into the worst case of equation (12), and Ksubstituted TS is FFA , (14) P-Value. Equation (19) is substituted into as equation (17); then previous algorithms use a fixed MDE the P-Value. Equation (19) is substituted (14) equationT(14). , R i with T previous algorithms use a fixed as MDE as the P-Value. Equation is substituted erived with equation (14). previous algorithms use a fixed MDE the P-Value. Equation (19) is(19) substituted into i is derived (14) is derived with equation (14). i the EPL of the proposed algorithm is derived in equation B L Eequation AB L equation (17); then the EPL of the proposed algorithm is derived in equation (21). is derived with (14). equation (17); then then the the EPL EPL of of the the proposed proposed algorithm algorithm is is derived derived in in equation equation (21). (21). K (21). [17] then equation (17); equation (17); the EPL of the proposed algorithm is derived in equation (21). [17] , (14) R E n 2 2 When affection of nominal condition 11 of test statistics i i i n 2 VPLiHe Svert PAii x K (20) n S vert i i i 2 i n of nominal condition of test When statistics is considered, the equation (13) is n MD 2 2 Si i 2 2 others affection of nominal condition of test statistics is considered, (20) VPLi Hethe iequation Sivert PAi x(13) Kis (20) i i i is considered, the equation (13) is derived as equation MD vert others i 1 S VPL S P x K VPL S P x K S 11 (20) (20) 11 verti 1 vertothers others He vert A MD MD vert A 11 When affection of nominal condition of test statistics is considered, the equation (13) is He 1 i i 1 (15). assume that the to testGaussian statistics correspond to on (15). We assume that the testWe statistics correspond 11 statistics derived as equation (15). We aassume that the test correspond to a Gaussian i as equation (15). We assume that the test statistics correspond to a Gaussian a derived Gaussian distribution with zero mean and standard VPLA,eph max VPLiA,eph (21) VPLA,eph max (21) (21) i VPLi A , eph i VPL max VPL (21) VPL max VPL (21) i distribution with zero mean and standard deviation . deviation . zero mean and standard deviation A , eph A , eph A , eph A , eph TS with zero mean and standard deviation distribution TS . i TS FFA T i AB L i TS K FFA i A i TS i i TS T E i AB L x Si vert i A i i i X ivert S vert i Ki FFA in TST x Svert TS E i i A AB x i KLSFFA TSi i TS i i E i T AB L A n x S i i vert others i 1 TS i i The derived VPLHe applies the geometry condition and The derived VPLHe applies the geometry condition and is expected to ensure int The derived VPLHeintegrity applies the geometry condition and is expected to ensure int (15) (15) is derived expected to ensure and increase availability. n The The derived the geometry condition is expected to ensure int VPL applies the geometry condition and is and expected to ensure integrity He applies HeVPL i i (15) vert others x S S X S x T (15) Further and validation are described in the following i vert vert vert vert othersdetails increase availability. Further details and validation are described in the following s T T i 1 i E i i Ei E AB The increase availability. Further details and validation are described in the following s i 1 L Athird AB terms A hand AB L side increase availability. Further details and validation are described in the following s sections. increase availability. Further details and validation are described in the following section second and on the right of L The second and third terms on the right hand side of equation (15) are developed into equation (16). 3. Experiment and Results d third terms on the right handThe sidesecond of equation (15)terms are developed intohand side of equation (15) and third on the right are developed into 3. Experiment and Results http://ijass.org 93 3. Experiment and Results 3. Experiment and Results x S S In this section, we evaluate the proposed algorithm using real GPS data for mult E (16). equation In this section, we evaluate the proposed algorithm using real GPS data for mul (16) this section, we evaluate the proposed algorithm using realdata GPSfor data for mult In this In section, we evaluate the proposed algorithm using real GPS multiple reference stations. First, sensitivity equation (Section 2.1), is evaluated with respec 2 S x S2 reference stations. First, sensitivity equation (Section 2.1), is evaluated with respe E n reference stations. First, sensitivity equation (Section 2.1), is evaluated with respec reference stations. First, sensitivity equation (Section 2.1), is evaluated with respect to i 2 2 n x 2 S i i i 2 TS x 2 S i 2 i 2 geometry conditions (local elevation angle, local azimuth, baselines length), and th vert others S T vert vert others geometry conditions (local elevation angle, local azimuth, baselines length), and th i 1 i Ei T (89~101)14-083.indd 93 2015-03-30 오후length), 3:48:29 i 1 AB L geometry conditions (local elevation local azimuth, baselines andwe th geometry conditions (local elevation angle, angle, local azimuth, baselines length), and then AB deviation of where isAthestandard . Equation (16) is substituted into equation 2 i vert i vert i TS 2 i A 2 i AB i TS i A i AB i T L n T L n i vert 2 2 i others i others i 1 i 1 i vert 2 i 2 Int’l J. of Aeronautical & Space Sci. 16(1), 89–101 (2015) 3. Experiment and Results The distinct property is that the effect of the local elevation angle is different for the two algorithms. Both algorithms have a similar tendency at the local azimuth angle. However, the In this section, we evaluate the proposed algorithm using sensitivity of the proposed algorithm increases as elevation real GPS data for multiple reference stations. First, sensitivity angle decreases, in contrast with the comparison algorithm’s equation (Section 2.1), is evaluated with respect to geometry tendency. As described, the purpose of these algorithms conditions (local elevation angle, Evaluation local azimuth, baselines 3.1 Sensitivity Results is ephemeris failure detection in the absence of a verified length), and then we compute the threshold based on test ephemeris. Thisrespect case isto frequent for the first rising evaluate the sensitivity the proposed algorithm with ephemeris failure, we satellite of statistics. Finally, we To check the applicability of of algorithm the day. Thus, the proposed algorithm is better because of its using MDE and EPL in case of landing aircraft at Gimpo compare the norm of the worst-case sensitivityhigh vector with that of a similar algorithm based sensitivity for a rising satellite with a low elevation angle. International Airport. From a baseline length perspective, the proposed algorithm on short baseline vectors and range measurements. Using real GPS data, we present a has high sensitivity with respect to large induced angle 3.1 Sensitivity Evaluation Results resulting from baseline length. The comparison algorithm simulation for verification of sensitivity properties. To evaluate the sensitivity of the proposed algorithm with has a similar tendency with baseline length; however, it has respect to ephemeris failure, we compare thefor norm of the usesaalimit baseline of the basic assumption The relevant algorithm comparison shorton baseline andlength carrierbecause phase measurement. worst-case sensitivity vector with that of a similar algorithm that LOS vectors of two reference station about the target The reason its range selection is that its information (range baseline, broadcast based on short baseline vectorsforand measurements. satellite aremeasurement, quasi-parallel.[8] This means that the proposed Using real GPS data, we present a simulation for verification algorithm does not have to consider the baseline length ephemeris, etc.) for generation of test statistics is analogous to the proposed algorithm and its of sensitivity properties. limitation and is applicable to various GNSS augmentation The relevant algorithm comparison uses aonshort systems: not only the local system (GBAS) detectionfor properties also depend the geometry condition between the area baseline vector andbut also widebaseline and carrier phase measurement. The reason for area systems (e.g., GRAS, SBAS). The various long baseline its selection is thatthe itssatellites. information (range measurement, vectors, which can be implemented with the local azimuth baseline, broadcast ephemeris, etc.) for generation of test and local elevation angle, are required to improve detection Figure 4 shows the norm of the sensitivity vector of the proposed algorithm and the statistics is analogous to the proposed algorithm and its performance of the proposed algorithm. The geometry of detection propertiescomparison also dependalgorithm. on the geometry condition various azimuth angles canisbe implemented It can be see that the sensitivity of both algorithms affected by the by multiple between the baseline vector and the satellites. RSs that are not on the same line. However, this is difficult geometry condition. Figure 4 shows the norm of the sensitivity vector of the with baseline vector geometry for various local elevations, proposed algorithm and the comparison algorithm. It can be especially when based on long baseline length. Fortunately, see that the sensitivity of both algorithms is affected by the satellites at low elevation angles are more frequent than geometry condition. those with high elevation angles (close to 90°) over a 24-h Worst Case Sensitivity w.r.t Geometry (Proposed Algorithm) -8 -3 x 10 Magnitude of Sensicivity Vector (Dimensionless) EA =0 Deg 5 4 3 EA = 30 Deg 2 EA = 60 Deg 1 0 0 EA = 90 Deg 0.05 0.1 0.15 0.2 Induced Angle (Deg) 0.25 0.3 0 30 60 90 120 150 Local Azimuth Angle (Deg) 180 Magnitude of Sensitivity Vector (Dimensionless) 4.5 6 Worst Case Sensitivity w.r.t Geometry x 10 4 3.5 EA EA EA EA 3 2.5 = = = = 0 degee 30 degee 60 degee 90 degee 2 1.5 1 0.5 0 0 20 40 60 80 100 120 Local Azimuth(Degree) 140 160 180 Fig. 4. Magnitude of the sensitivity vector with respect to the geometry condition Figure 4. Magnitude of the sensitivity vector with respect to the geometry condition (The proposed algorithm (left) and the comparison algorithm (right)). (The proposed algorithm (left) and the comparison algorithm (right)). 2. Tendency ofcorresponding increasing sensitivity corresponding to geometry conditions. Table 2. Tendency Table of increasing sensitivity to geometry conditions. Geometry conditions Local elevation angle Local azimuth angle Baseline length Comparison algorithm 14 close to 90° close to 90° Increase (limited) Proposed algorithm close to 0° close to 90° Increase The distinct property is that the effect of the local elevation angle is different for the two 94 algorithms. Both algorithms have a similar tendency at the local azimuth angle. However, the DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.89 sensitivity of the proposed algorithm increases as elevation angle decreases, in contrast with the comparison algorithm’s tendency. As described, the purpose of these algorithms is (89~101)14-083.indd 94 2015-03-30 오후 3:48:32 Jongsun Ahn Orbit Ephemeris Failure Detection in a GNSS Regional Application angle, can be an important factor for detection performance, period. However, this is left to be considered in further work. as shown in both Figs. 5 and 6. Next, we tried to verify the sensitivity equation in equation (12) for the proposed algorithm. As shown in Table 3, the Next, we tried to verify the sensitivity equation in equation (12) for the proposed algorithm. various baseline vectors are composed with Suwon (SUWN), 3.2 Algorithm Realization and Availability Test using Tablefrom 3, theSeoul various baseline composed Nonsan (NONS), As andshown Jeju in (JEJU) (SOUL) in vectors areGPS Data with Suwon (SUWN), Korea, and we use error-free range measurement to examine Nonsan (NONS), and Jeju (JEJU) from Seoul (SOUL) in Korea, and we use error-free range In this section, we realized and evaluated the proposed the influence of the geometry condition. A satellite position algorithm using real GPS data of multiple fault (1 km, XYZ) ismeasurement imposed on all visible satellites for 24 h. thesensitivity influence of the geometry condition. A satellite position fault RSs. The main Next, we triedtotoexamine verify the equation in equation (12) for the proposed algorithm. items were evaluation of the correction result of the range Figure 5 shows the mean and standard deviation of test error.Suwon Then, (SUWN), we determined the threshold, statistics with local elevation angle. As various expected, the test km, XYZ) is imposed on all baseline visible satellites for 24 h. As(1shown in Table 3, the vectors measurement are composed with MDE, and conducted availability testing based on the EPL statistics show a decreasing tendency with respect to high at Gimpo International multiple baseline in Korea, and we use Airport error-freewith range elevation angle. Nonsan (NONS), and Jeju (JEJU) from Seoul (SOUL) conditions in Korea. Figure 6 shows the mean and standard deviation of test Table 3. Baseline lengths the simulated measurement examine theofinfluence thecondition. geometry condition. A satellite As shown in Fig. 7, the position multiplefault baseline conditions (6 statistics with local azimuth to angle. As expected, the oftest baselines) were deployed using four reference stations statistics show an From increasing as close to 90° local Seoultendency (1 km, XYZ) is imposedtoonSuwon all visible satellites for 24 h. (NONS) (SUWN) tooperated Nonsan to Jeju (JEJU)Information Institute by the National Geographic azimuth angle in similar elevation angle. (SOUL) (NGII) in Korea. Finally, long baseline length, which causes larger induced Baseline length 39.37km 160.18km 459.26km Table of3.the Baseline lengths of the simulated condition. Table 3. Baseline lengths simulated condition. From Seoul5 shows the mean and standard deviation of test statistics with local elevation angle. Figure to Suwon (SUWN) to Nonsan (NONS) to Jeju (JEJU) (SOUL) As expected, the test statistics show a decreasing tendency with respect to high elevation Baseline length 39.37km 160.18km 459.26km angle. Mean of TS w.r.t Elevation Angle Standard Deviation of TS w.r.t Elevation Angle 14 Figure 5 shows the mean and standard deviation 15of test statistics with local elevation angle. SOUL-SUWN (39.37km) SOUL-SUWN (39.37km) SOUL-NONS (160.18km) SOUL-JEJU (459.26km) 12 SOUL-NONS (160.18km) SOUL-JEJU (459.26km) As expected, the test statistics show a decreasing tendency with respect to high elevation 10 10 8 6 14 TS STD (m) TS Mean (m) angle. Mean of TS w.r.t Elevation Angle 4 15 12 2 SOUL-SUWN (39.37km) SOUL-NONS (160.18km) SOUL-JEJU (459.26km) 10 10 20 8 30 40 50 60 Elevation Angle (Degree) 70 80 10 90 0 0 10 20 TS STD (m) 0 0 TS Mean (m) Standard Deviation of TS w.r.t Elevation Angle 5 SOUL-SUWN (39.37km) SOUL-NONS (160.18km) SOUL-JEJU (459.26km) 30 40 50 60 Elevation Angle (Degree) 70 80 90 Figure 5. Variation of test statistics in the ephemeris failure condition with respect to local 6 Fig. 5. Variation of test statistics in the ephemeris failure condition with respect to local elevation angle and baseline length: mean (left) and stanelevation angle and baseline length: mean (left) 5and standard deviation (right). dard deviation (right). 4 2 30 30 of test statistics with local azimuth angle. Figure 6 shows the mean and standard deviation 0 0 Test Statistics w.r.t Local Azimuth Angle (Elevation Angle 30~40 Deg) 0 10 20 Test Statistics w.r.t Local Azimuth Angle (Elevation Angle 70~80 Deg) 30 40 50 60 70 80 90 Elevation Angle (Degree)SOUL-JEJU (459.26km) 0 10 20 30 40 50 60 Elevation Angle (Degree) 70 80 90 As expected, the test statistics show an increasing as closewith to 90° local azimuth Figure 5. Variation of test statistics in the ephemeris tendency failure condition respect SOUL-JEJU (459.26 km) to local 20 20 elevation angle and baseline length: mean (left) and standard deviation (right). angle in similar elevation angle. 15 SOUL-NONS (160.18km) 25 Test Statistics (m) Test Statistics (m) 25 15 10 10 test statistics with local azimuth angle. Figure 6 shows the mean and standard deviation of SOUL-NONS (160.18km) 16tendency as close SOUL-SUWN (39.37km) SOUL-SUWN As expected, the test statistics show an increasing to(39.37km) 90° local azimuth 5 0 5 0 20 40 60 80 100 120 Azimuth Angle (Degree) angle in similar elevation angle. 140 160 180 0 0 20 40 60 80 100 120 Azimuth Angle (Degree) 140 160 180 Fig. 6. Variation of test statistics in the ephemeris failure condition with respect to local azimuth angle and baseline length: in elevation angle 30Figure 6. Variation of test statistics in the ephemeris failure condition with respect to local 40° (left) and in elevation angle 70-80° (right). azimuth angle and baseline length: in elevation angle 30-40° (left) and in elevation angle 16 70-80° (right). http://ijass.org 95 Finally, long baseline length, which causes larger induced angle, can be an important factor for detection performance, as shown in both Figs. 5 and 6. (89~101)14-083.indd 95 2015-03-30 오후 3:48:35 are shown in Table 4. Int’l J. of Aeronautical & Space Sci. 16(1), 89–101 (2015) Prior to generating test statistics, we corrected the range measurement error sources, which include the ionosphere, troposphere, and satellite/receiver clock bias, as described in Section 1. Fig. 8 shows the resulting range correction error at four reference stations of all visible satellites based on 24-h data. It canare be shown seen that the ramifications of range error in Table 4. sources are reduced in all visible satellites. Statistical results (mean, standard deviation, and histogram) are shown in Table 4. To ensure reliability, many data samples are required are shown in Table 4. for analysis in terms of statistics for determination of the threshold. In the present work, the mean and standard deviation of test statistics are computed using 1-week data received from 2014.9.1 to 2014.9.7 (sampling period 30 s). The plot on the left hand side of Fig. 9 shows the test statistics mean (red lines with diamond markers) and standard deviation (blue lines with circular markers) with local elevation angle. A standard deviation model of test statistics is derived in equation (22). Shown in the plot on the right hand side of Fig. 9, the threshold with respect to local elevation angle is derived in equation (23), which uses the multiplier (KFFA) associated with for thethe false alarm rate of the Figure 7. Baseline construction simulation. CAT-I requirement.[12] To ensure reliability, many data samples are required for analysis in terms of statistics for determination of the threshold. In the present work, the mean and standard deviation of test statistics are computed using 1-week data received from 2014.9.1 to 2014.9.7 (sampling period 30 s). The plot on the left hand side of Fig. 9 shows the test statistics mean (red lines with diamond markers) and standard deviation (blue lines with circular markers) with local elevation angle. Aconstruction standard deviation of test statistics is derived in equation (22). Figure 7. Baseline for the model simulation. Shown in the plot on the right hand side of Fig. 9, the threshold with respect to local elevation angle is derived in equation (23), which uses the multiplier (KFFA) associated with the false alarm rate of the CAT-I requirement.[12] Fig. 7. Baseline construction for the simulation. Fig. 8. Range measurement mitigation results (24 h). Figure 7. Baseline construction for the simulation. Figure 8. Range measurement mitigation results (24 h). Test Statistics w.r.t Elevation Angle 4.5 4 Table 4. Range mitigation error (mean and standard deviation). 8 3.5 3 Statistics Mean (m) Standard deviati Before mitigation 10.24 4.78 After mitigation -0.56 2.97 7 2.5 Threshold (m) STD (m), Mean (m) Threshold w.r.t Elevation Angle 9 Exponential Curve Fitting of STD Mean 2 1.5 6 5 1 0.5 4 0 -0.5 0 10 20 30 40 50 Elev (Deg) 60 70 80 90 3 0 10 20 30 40 50 Elev (Deg) 60 70 80 90 Figure 8. Range measurement mitigation results (24 h). Figure 9. Daily variation of test statistics and threshold with respect to local elevation angle. Fig. 9. Daily variation of test statistics and threshold with respect to local elevation angle. 18 Table 4.error Range mitigation error (mean and standard deviation). Table 4. Range mitigation (mean and standard i 0.01149deviation). TS 2.431 e (22) i Statistics Thresh K FFA TSi Mean (m) (23)Standard deviation (m) Before : mitigation Elevation angle (degrees)10.24 4.78 After mitigation 2.97 Figure 8. Range measurement mitigation results (24 h). -0.56 Table 4. Range mitigation error (mean and standard deviation). 5.Table False alarm and according to the CAT-I requirement False probability alarm probability and multiplier according to the CAT-I requirement Table 5. False alarmTable probability and5.multiplier according to themultiplier CAT-I requirement Statistics Requirement Requirement CAT-I BeforeCAT-I mitigation Mean (m)Alarm False Alarm False Rate Rate 18 -4 4 10.241.9 10 1.9 x 10 Standard deviation (m) ) Multiplier Multiplier (KFFA)(KFFA 3.74 4.78 3.74 Table 6. Missed detection probability and multiplier according to the CAT-I requirement After mitigation -0.56 2.97 DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.89 Requirement CAT-I (89~101)14-083.indd 96 Probability of 96 missed detection Multiplier (Kmd) 1.0 x 10-3 18 19 3.1 2015-03-30 오후 3:48:35 1 1.5 0.5 1 0 0.5 -0.5 Threshold 2 5 -0.5 6 5 4 4 0 0 6 Threshold (m) STD (m), M STD (m), Mean ( 2.5 2 1.5 10 0 20 10 30 20 30 40 50 60 Elev (Deg) 40 50 Elev (Deg) 70 60 80 70 3 90 80 0 90 3 10 0 20 10 30 20 30 40 50 60 Elev (Deg) 40 50 Elev (Deg) 70 60 80 70 90 80 90 Jongsun Ahnrespect Orbit Ephemeris Failure Detection in a GNSS Regional Application Figure 9. Daily variation of test statistics and threshold with to local elevation angle. Figure 9. Daily variation of test statistics and threshold with respect to local elevation angle. TSi i 2.431 e0.01149 0.01149 2.431 e i Thresh TS K FFA TSi i i Thresh TS K FFA (degrees) : Elevation angle : Elevation angle (degrees) TS and Threshold (m) (22) (22) MDE corresponding to six baselines. It is clear that the MDE (22) of the proposed algorithm fluctuates with respect to time (23) (23) (23)because of the variable worst-case sensitivity vector related to geometry of the baseline and the satellite. Consequently, for detection performance the appropriate θ : Elevation angle (degrees) baseline is selected based on the least MDE value monitored Figure 10 shows an example of the test statistics and among the various RS geometries in real time. The right threshold on alarm PRN 11 of the test In according the nominal Table 5. False probability andperiod. multiplier to the CAT-I requirement Table 5. False alarm probability multiplier according CAT-Iside requirement of Fig. 11 shows the least MDE value of all visible condition, we can see that the testand statistic does not exceedto the hand satellites(K and conditions for a 24-h period. Requirement Alarm Rate Multiplier ) the threshold, but does trigger aFalse false alarm. FFAbaseline Requirement False Multiplier (K ) 4 Alarm Rate FFA CAT-I 3.74 However, the figure showed unexpected MDE 1.9 10 3.74 CAT-I 1.9 10 4 divergence, to be investigated further. The given satellites 3.3 MDE and Availability Testing (PRN 1, PRN 11, PRN 26, and PRN 27) are close to highThe MDE of all visible satellites (24 h) is computed with elevation-angle status. A satellite at a high elevation angle equation (3-4). The missed detection probability and degrades the sensitivity of the algorithm and leads to multiplier associated with the CAT-I requirement, as shown an increase in the MDE value. Once again, this satellite 19 in Table 6, are is used to compute the MDE [18]. condition is not frequent for a 1 day (24-h) period, and this 19 The left hand side of Fig. 11 shows an example of the PRN 5 algorithm focuses on rising satellites with low elevation angles. However, to ensure system integrity, the GNSS Test Statistics and Threshold (PRN 11, Normal Condition) augmentation system, which implements this algorithm, 8 TS should also use additional ephemeris fault detection 6 Threshold algorithms. 4 Next, we present the availability result based on the ephemeris protection level that uses the MDE value. The 2 basic simulation condition considers an aircraft trying 0 to land at Gimpo International Airport on runway 32R -2 (RWY 32R), located at a CAT-I decision height (DH) of 200 ft. The GPS constellation is based on 31 satellites. -4 The reason for availability analysis at the DH is that the -6 aircraft determines the requirement use of baseline the ground because of5.the variable vector related geometry of the and landing-aided Table False alarmworst-case probability sensitivity and multiplier according totothe CAT-I -8 facility at the DH (final location) associated with system 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Local Time (Hours) the satellite. The analysis Requirement False Alarmrequirements. Rate Multiplierperiod (KFFA) is 24 h, considering -4 constellation (approximately 3.74 Fig. 10. Test statistics of normal CAT-I condition with threshold (PRN 11) 1.9 x 10the repeatability of the GPS Figure 10. Test statistics of normal condition with threshold (PRN Consequently, for detection performance the11) appropriate baseline is selected based on the 6. Missed detectionaccording probability andCAT-I multiplier according to the CAT-I requirement Table 6. Missed detectionTable probability and multiplier to the requirement least MDE value monitored among the various RS geometries in real time. The right hand Figure 10 shows an example of the test statistics and threshold on PRN 11 of the test Multiplier (K ) Requirement Probability of missed detection md side of Fig. 11 shows the least MDE value of all visible satellites and baseline conditions for -3 period. In the nominal condition, does not exceed the 3.1 CAT-Iwe can see that the test statistic 1.0 x 10 a 24-h period. threshold, but does trigger a false alarm. 2000 Minimum Detectable Error (Single Baselines, PRN 5) 4500 1600 4000 3.3 MDE and Availability Testing 1400 INCH-JEJU Minimum Detectable Error (Multiple Baselines, 24h) 5000 1800 PRN 11 PRN 1 PUSN-JEJU 3500 3000 1200 MDE (m) MDE (m) INCH-KANR The MDE of all visible satellites (24 h)KANR-PUSN is computed with equation (3-4). The missed 1000 KANR-JEJU 800 PRN 27 2500 PRN 28 2000 detection probability and600multiplier associated with the CAT-I requirement, as shown in 1500 1000 400 Table 6, are is used to compute the MDE [18]. 200 0 10 500 INCH-PUSN 11 12 13 Local Time (hours) 14 15 0 0 4 8 12 Local Time (hours) 16 20 24 Figure 11. MDE according to baseline vectors (PRN 5) and minimum MDE result (24 h). Fig. 11. MDE according to baseline vectors (PRN 5) and minimum MDE result (24 h). Table 6. Missed detection probability and multiplier according to the CAT-I requirement Requirement CAT-I of missed However,Probability the figure showed unexpected MDE divergence, to be investigated further. The Multiplier (Kmd) detection http://ijass.org 97 given satellites (PRN 3 1, PRN 11, PRN 26, and PRN 27) are close to high-elevation-angle 3.1 1.0 10 status. A satellite at a high elevation angle degrades the sensitivity of the algorithm and leads increase in the value. Once again, this corresponding satellite condition is not frequent for a The left hand sidetoofanFig. 11 shows anMDE example of the PRN 5 MDE to six (89~101)14-083.indd 97 2015-03-30 오후 3:48:36 The estimated aircraft position error due to the P-value, which represents ephemer The estimated estimated aircraft position error to P-value, the P-value, represents ephemeri the DH is that the aircraft determines the use of the ground landing-aided facility at theposition DH aircraft error duedue to the whichwhich represents ephemeris failur The estimated aircraftisposition error the P-value, which ephemer detection performance, shown on thedue righttoside of Fig. 12. The represents result shown in Fig detection is is shown on on thethe right sideside of Fig. 12. The shownshown in Fig. in 12 Fig. detection performance, shown right of Fig. 12.result The result (final location) associated with system requirements. The analysis periodperformance, is 24 h, considering detection shown on to theP-Value right side of Fig. The result shown in Figt shows thatperformance, position errorisaccording is less than12. centimeter-scale because shows that position error according to P-Value is less than than centimeter-scale becausebecause the effect shows that position error according to P-Value is less centimeter-scale the repeatability of the GPS constellation (approximately 11 h 58 s) and the rotation of the Int’l J. of Aeronautical & Space Sci. 16(1), 89–101 (2015) shows that position accordingistosmall P-Value is lessthethan centimeter-scale because of ephemeris failureerror decorrelation between aircraft and the RS in the cast of ephemeris failure decorrelation is small between the aircraft and the RS in the case of ephemeris failure decorrelation is small between the aircraft and the RS in the case earth. This property is advantageous for shortening the analysisofperiod. The availability of failure(752.5 decorrelation smallif between the aircraft and thethan RS in in this the cas small displacement However, the displacement sim in ephemeris this simulation condition, theisproposed algorithm is is larger 11 h 58 s) and the rotation of the earth. This property is small displacement (752.5 m).m). However, if the displacement is larger than in this simulation small displacement (752.5 m). However, if the displacement is larger than in this sim analysis with EPL is conducted in comparison with the same algorithm used in the sensitivity more useful than the comparison algorithm because of advantageous for shortening the analysis period. The small displacement (752.5 m). However, ifuseful the displacement is larger than in thisbeca sim condition, theproposed proposed algorithm is more thancomparison the comparison algorithm condition, the is more useful algorithm because of the increasing of thealgorithm decorrelation effect,than as the shown in availability analysis with EPL is conducted in comparison condition, theisproposed analysis in Section 3.1 [9]. The P-value of the comparison algorithm, which used to algorithm is more useful than the comparison algorithm beca equation (24). with the same algorithm used in the sensitivity analysis in condition, theofproposed algorithm is more the (24). comparison increasing effect, as shown in than equation the increasing ofthe thedecorrelation decorrelation effect, asuseful shown in equation (24). algorithm beca The nominal error models due to airborne antenna Section 3.1 [9]. The P-value of the comparison algorithm, the increasing of the decorrelation effect, as shown in equation (24). compute the EPL, is shown in equation (24) [12]. The nominal models due to airborne antenna multipath/noise (equation 25), 25), the increasing oferror the decorrelation as shown inmultipath/noise equation The nominalerror models due toeffect, airborne antenna (equation multipath/noise (equation 25), ionosphere (equation 26), (24). which is used to compute the EPL, is shown in equation The nominal error models due to airborne antenna multipath/noise (equation 25), troposphere (equation 27), and RS(equation receivers27), (equation 28) (24) [12]. ionosphere (equation troposphere and RS receivers (equation 28) are25), The nominal error26), models due to airborne antenna multipath/noise (equation ionosphere (equation 26), troposphere (equation 27), and RS receivers (equation 28) are applied to compute the EPL together with ephemeris ionosphere (equation 26), troposphere (equation 27), and RS receivers (equation 28) P K FFA K MD / b (24) (24) applied to compute the EPL together with ephemeris failure-based position error. failure-based position error. ionosphere (equation troposphere (equation 27), failure-based and RS receivers (equation applied to compute the26), EPL together with ephemeris position error.28) : Standard deviation of the test statistics (double differential carrier: 0.3 cm) applied to compute the EPL together with ephemeris failure-based position error. σϕ : Standard deviation of the test statistics (double i i 10 i together applied to compute the ephemeris position error. multipath 0.13 0.53 e EPL (25) a0,with failure-based i (25) , b : Baseline length (200 m) AAD a1, AAD e noise i c , AAD i 10 differential carrier: 0.3 cm) i imultipath i 0.13 0.53e i , (25) a a e noise 0, AAD 1, AAD iono ( X 2 v ) (26) i Fpp vert _ iono _ gradient 10 i air a i c , AAD multipath , air (25) a0, AAD b : Baseline length (200 m) i i 0.13 0.53e i noise 1, AAD e i F iono (26) , AAD c(26) 2gradient 10 ( Xi air 2 vair ) vert _0.53 iono i _e 0.13 , (25) a a e ipp imultipath noise 0, AAD 1, AAD R cos( ) i Fiono (26) noise where is thelevel noiseoflevel of the double difference 2 ( X air 2 vair ) vert _ iono _ 1Fppi ecorresponding pp where σϕ is the the double difference carriercarrier measurement, i gradient i cos( _)gradient h_Iiono iono F RR vert (26) 2 ( X air 2 vair ) i Fppi 1 pp R e cos( measurement, corresponding to an integrated multipath ) 62 i e R h h i e b I10 1value Fi Rofcos( h to an integrated limiting usedoffor RS [8]. The limiting antenna multipath (IMLA) used for antenna RS [8]. (IMLA) The value i Fpp e h ) (27) tropo N h0 R e I 62 i 1 e h pp 1 sin ( ) hI 10 h0 i b represents the baseline length between multiple RS h Re0.002 6 1 e (27) h 0 tropo N the represents the baseline length between multiple RS antennas and is similar to RS of10 2 i antennas and is similar to the RS of Gimpo International sin ( i ) 1 e hh0 6 tropo N h0 0.00210 (27) i tropo N h0 0.002 sin 2 ( i ) 1 e h0 (27) (27) Airport. Gimpo International Airport. 0.002 sin 2 ( i ) i i c , AAD 0 The P-value variation over 24 h is shown in Fig. 12. It can 23 The that P-value h is shown in Fig. 12. It can be seen that the P-value of the be seen the variation P-value ofover the24 proposed algorithm varies 2 i 0 ,GAD with time due to the geometry condition, whereas that of the a a e (28) 23 2 i proposed algorithm varies with time due to the geometry condition, whereas that0,GAD of the 1,GAD (28) Pr_gnd a2,GAD comparison algorithm does not; additionally, the P-value 23 M 23 magnitude is generally foradditionally, the proposed comparison algorithmsmaller does not; thealgorithm. P-value magnitude is generally smaller for As shown on the left side of Fig. 12, pronounced ramifications The parameters of the given model are shown in Tables due high-elevation-angle observed 7, The 8, and 9. The airborne accuracy and parameters of thedue given are shown (AAD) in Tables 7, 8, and 9. The airborne a thetoproposed algorithm. As satellites shown onare thealso left side of Fig.in12, pronounced ramifications to modeldesignator the P-value, as expected. Fortunately, it is still within the ground accuracy designator (GAD) are related to antenna designator (AAD) andforground accuracystation designator high-elevation-angle are also observed in the as expected. Fortunately, it isairborne allowable value (CAT-I),satellites established in ICAO Annex 10, P-value, for performance index the and(GAD) the RS,are related to antenna perf landing aircraft. [19]. respectively. [19] index10, forfor thelanding airborneaircraft. station and the RS, respectively. [19] still within the allowable value (CAT-I), established in ICAO Annex The estimated aircraft position error due to the Figure 13 shows the EPL result according to both P-value, algorithms. The results show that EPL will meet the availability [19]. which represents ephemeris failure detection Table 7. Errorcalled modelthe parameters the normal condition. performance, is shown on the right side of Fig. 12. The requirement, alert limitin(AL), established in CAT-I result shown in Fig. 12 shows that position error according (10 m) and CAT-II/III (4.4 m). The effect of high elevation to P-Value is less than centimeter-scale because the effect angle on theContents proposed algorithm is expected to increaseValues 25.5×10-6 slant ( not of ephemeris failure decorrelation is small between the the EPL (redIonosphere line), but it does threaten vert _ iono _ gradient )to exceed the aircraft and the RS in the case of small displacement AL (which would Earthresult radiusin( Rae loss ) of availability) because of6378.1368 km (752.5 m). However, if the displacement is larger than considerable satellite geometry. 350 km Ionosphere thickness ( hI ) 22 -4 P-Value (Gimpo International Airport, 24h) x 10 0.16 0.14 Dimensionless PL (m) 0.12 0.1 0.08 1 100 s Vehicle velocity ( vair ) 39.02 m/s Troposphere scale height ( h0 ) 25,500 m Troposphere refractivity uncertainty ( N ) No. Reference station ( M ) 255 Comparsion algorithm Proposed algorithm 0.18 2 752.5 m Slant Range ( X air ) Time constant ( ) Estimated Position Error due to MDE (GMP RWY 32R DH, 24h) 0.2 Comparison Method Proposed Method 4 0.06 0.04 0 0.02 Table 8. Airborne accuracy designator. 0 5 10 15 Local Time (Hours) 20 25 0 0 5 10 15 Local Time (Hours) 20 a0, AAD AAD to P-Value (right). Figure 12. P-Value (left) and estimated position error with respect AAD-B 0.11 Fig. 12. P-Value (left) and estimated position error with respect to P-Value (right). 98 Table 9. Ground accuracy designator. The estimated aircraft position error due to the P-value, which represents ephemeris failure GAD a0,GAD detection performance, is shown on the right side of Fig. 12. The result shown in Fig. 12 0.15 i ≥ 35 GAD-C i shows that position error according to P-Value is less than centimeter-scalebecause effect < 35 the0.24 a1, AAD C , AAD 0.13 4.0 DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.89 (89~101)14-083.indd 98 a1,GAD a2,GAD 0,GAD 0.84 0 0.04 0.04 15.5 - 2015-03-30 오후 3:48:37 Jongsun Ahn Orbit Ephemeris Failure Detection in a GNSS Regional Application Despite the explicit distinctions between the two 4. Conclusions and Future Work algorithms, appreciable differences in EPL are not observed in Fig. 13. If the ephemeris failure decorrelation due to GNSS orbit ephemeris is broadcast to users for computing aircraft-RS displacement increases (as in a wide-area the position of a navigation satellite. The orbit ephemeris is implementation), then the EPL based on the proposed estimated by the ground facility, which is the operational algorithm is more relatively valuable for system availability segment (OCS) and CAT-II/III (4.4 m). The effect of high elevation angle on thecontrol proposed algorithm is of the GPS, and affects the accuracy than that of the comparison algorithm. These findings of the user’s navigation solution. Currently, estimated suggest that to the proposed will be to not performance tends to improve when using the differential expected increase the algorithm EPL (red line), butsuitable it does not threaten to exceed the AL (which only GBAS, but also SBAS and GRAS, which are implemented GNSS (DGNSS) implementation, so ramifications of result in a loss of availability) because of considerable satellite geometry. for would wide-area applications. ephemeris error to the user are very small in limiting cases. However, the integrity issue has been magnified recently along with user accuracy requirements. In particular, Comparsion algorithm Proposed algorithm integrity can determine system availability and any other 4 2 i requirements faced within the aviation community. a0,GAD a1,GAD e i 0 ,GAD 2 2 i 0 ,GAD 3.5 (28)a threat to integrity of the GNSS; thus, Pr_gnd a a0,GAD a1,GAD e i 2,GAD 2 Ephemeris constitutes 2 i 0 ,GAD we propose an ephemeris a0,GAD a1,M e (28) failure detection algorithm. Pr_gnd a GAD 2, GAD 2 i M 3 (28) Pr_gnd a2,GAD Basically, the proposed algorithm uses trigonometry M (the First Cosine Law) to estimate the baseline length of The parameters of the given model are shown in Tables 7, 8, and 9. The airborne accuracy 2.5 reference antennas andaccuracy compute the residual with The parameters of the given model are shown in Tables 7, 8,station and 9. The airborne The parameters of the givenaccuracy model aredesignator shown in (GAD) Tables 7, and 9. to The airborne accuracyIf this residual (from true baseline length surveyed precisely. designator (AAD) and ground are8,related antenna performance 2 designator (AAD) and ground accuracy designator (GAD) are related to antenna performance test statistics) exceeds a threshold value, then ephemeris designator (AAD) andstation groundand accuracy designator (GAD) are related to antenna performance 1.5 index for the airborne the RS, respectively. [19] failure is detected. 0 5 10 15 20 Time (Hours) index for the Local airborne station and the RS, respectively. [19] For detailed algorithm analysis, we introduce the index for the station and the RS, respectively. [19] EPL result at airborne Gimpo International Fig.Figure 13. EPL 13. result at Gimpo International Airport (24 h).Airport (24 h). generation of test statistics and a threshold value. An Table 7. Error model parameters in the normal condition. VPL (m) 4.5 Ephemeris VPL (GMP RWY 32R DH, 24h) Table 7. Error model parameters in the normal condition. Table 7. Error model parameters in the condition. Table 7. Error model parameters in the normal condition. Contents Values Despite the explicit distinctions between the twonormal algorithms, appreciable differences in Contents slant ( Values -6 25.5×10 Ionosphere vert _ iono _ gradient ) Contents Values -6 EPL are not observed inIonosphere Fig. 13. If the ephemeris failure decorrelation due to aircraft-RS 25.5×10 slant ( vert _ iono _ gradient ) 6378.1368 R Earth radius ( ) e 25.5×10-6 km Ionosphere slant ( vert _ iono _ gradient ) 6378.1368 km Earth ( Re ) implementation), displacement increases Ionosphere (as in aradius wide-area then the EPL based the 350 km onkm ( hI ) 6378.1368 Earth radiusthickness ( Re ) 350 km h Ionosphere ( I) 752.5 m of the Slant Rangethickness (X proposed algorithm is more relatively valuable system availability than that air ) 350 km Ionosphere thickness ( hfor I ) 752.5 X Slant Range ( ) 100 s m Time constant ( air ) 752.5 m X Slant Range ( ) air comparison algorithm. These findings suggest that the proposed algorithm 100 will s m/sbe suitable to Time constant ( v) 39.02 Vehicle velocity ( ) 100 s Time constant ( ) air 39.02 m/s Vehicle velocity ( vheight ) ( hare) implemented for25,500 airwhich m not only GBAS, but alsoTroposphere SBAS and GRAS, wide-area scale 0 39.02 m/s Vehicle velocity ( vair ) 25,500 m h Troposphere scale height ( ) 0 255 Troposphere ( N ) 25,500 m Troposphere refractivity scale heightuncertainty ( h0 ) applications. 255 Troposphere ( N ) No. Referencerefractivity station ( Muncertainty ) 4255 Troposphere refractivity uncertainty ( N ) No. Reference station ( M ) 4 No. Reference station ( M ) 4 4. Conclusions Future Work Table and 8. Airborne accuracy designator. Table 8. Airborne accuracy designator. Table 8. Airborne accuracy designator. GNSS orbit is broadcast usersa for computing thea position of a navigation Tableephemeris 8. Airborne accuracy to designator. C , AAD AAD 0, AAD 1, AAD a0, AAD a1, AAD C , AAD AAD AAD-B 0.11 ground facility, 0.13 4.0 satellite. The orbit ephemeris is the operational a1,which C , AAD AAD is estimated by athe 0, AAD AAD AAD-B 0.11 0.13 4.0 0.11 4.0solution. control segment (OCS) AAD-B of the GPS, and affects the accuracy of 0.13 the user’s navigation 9. Ground accuracy designator. Table 9. GroundTable accuracy designator. Currently, Table estimated performance tends to improve when using the differential GNSS 9. Ground accuracy designator. Table 9. Ground accuracy designator. a GAD a1,GAD a2,GAD 0,GAD 0,GAD GAD a a a 0,GAD i 0,GAD 1,GAD 2,GAD 0.84 0.04 15.5 ≥ 35 25 0.15 GAD a0,GAD a1,GAD a2,GAD 0,GAD i GAD-C 0.15 0.04 ≥ 35 35 0.24 00.84 0.04 -15.5 ii < GAD-C 0.15 0.84 0.04 15.5 i ≥ 35 0.24 0 0.04 < 35 GAD-C 0.24 0 0.04 i < 35 Figure 13 shows the EPL result according to both algorithms. The results show that EPL Figure 13 shows the EPL result according to both 99 algorithms. The results show that EPL the EPL result according results show that EPL willFigure meet 13 theshows availability requirement, called to theboth alertalgorithms. limit (AL),The established in CAT-I (10 m) will meet the availability requirement, called the alert limit (AL), established in CAT-I (10 m) will meet the availability requirement, called the alert limit (AL), established in CAT-I (10 m) (89~101)14-083.indd 99 24 24 24 http://ijass.org 2015-03-30 오후 3:48:37 Int’l J. of Aeronautical & Space Sci. 16(1), 89–101 (2015) Proceedings of the 23rd International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2010), Portland, OR, Sep 2010, pp. 3115–3122 [6] Haochen Tang, Sam Pullen, Per Enge, Livio Gratton, Boris Pervan, Mats Brenner, Joe Scheitlin, and Paul Kline, “Ephemeris Type A Fault Analysis and Mitigation for LAAS”, Proceedings of Position Location and Navigation Symposium (PLANS), 2010 IEEE/ION, 4-6 May 2010, pp. 654-666 [7] Gang Xie, Optimal On-airport Monitoring of the Integrity of GPS-Based Landing System, Ph.D Thesis, Stanford University, March 2004, pp. 39-43. [8] Boris Pervan, Livio Gratton, “Orbit Ephemeris Monitors for Local Area Differential GPS”, Journal of IEEE Transactions on Aerospace and Electronic Systems, Vol. 41, No. 2, April 2005. [9] Jiyun Lee, Sam Pullen, Boris Pervan, and Livio Gratton, “Monitoring Global Positioning Satellite Orbit Errors for Aircraft Landing System”, Journal of Aircraft, Vol. 43, No. 3, May-June 2006. [10] Boris Pervan, and Fang Cheng Chan, “Detecting Global Positioning System Orbit Errors Using Short-Baseline Carrier-Phase Measurements“ Journal of Guidance, Control , and Dynamics, Vol. 26, No. 1, January-February 2003. [11] Gang Xie, Optimal On-airport Monitoring of the Integrity of GPS-Based Landing System, Ph.D Thesis, Stanford University, March 2004, pp. 26-43. [12] Pullen S., Lee J, Luo, M., Pervan, B, Chan, F-C, and Gratton, L., “Ephemeris Protection Level Equation and Monitor Algorithm for GBAS”, Proceedings of the 14th International Technical Meeting of the Satellite Division of the Institute of Navigation, Salt Lak City, UT, Sept, 11-14, 2001. [13] Chan, F.C., Detection of Global Positioning Satellite Orbit Errors Using Short-Baseline Carrier Phase Measurements, M.S.Thesis, Dept. of Mechanical, Materials, and Aerospace Engineering, Illinois Inst. of Technology, Chicago, Aug. 2001, pp. 17-19. [14] Jongsun Ahn, Hyang-Sig Jun, Chan-Hong Yeom, Sangkyung Sung, and Young Jae Lee, “Sensitivity Analysis of Ephemeris Fault Detection Algorithm based on Baseline Length Estimation Method”, Proceeding of KGS 2014, Nov. 2014, pp. 693-696. [15] Jongsun Ahn, Eunsung Lee, Moon Beom Heo, Sangkyung Sung, and Young Jae Lee, “Research of MDE of for Baseline-based GPS Ephemeris Fault Detection Algorithm”, Proceeding of KSAS 2014, Nov. 2014, pp. 330-332. [16] Mastumoto, S, Pullen, S, Rotkowitz, M., and Pervan, B., “GPS Ephemeris Verification for Local Area Augmentation System (LAAS) Ground Station,” Proceedings of the 12th International Technical Meeting of the Satellite Division of the Institute of Navigation, Inst., of Navigation, Alexandria, VA, analysis is conducted on the test statistics’ sensitivity vector, corresponding to ephemeris failure, and on an availability test, based on the ephemeris protection level in Korea. The important feature is that the performance index (sensitivity and MDE) depends on geometric parameters including local elevation angle, local azimuth angle, and baseline length between the satellite and the baseline vectors. Consequently, this algorithm is more efficient for use with multiple reference stations that can generate various long baseline vectors, such as GRAS and SBAS. The availability test conducted for Gimpo International Airport in Korea was based on the EPL of a landing aircraft at CAT-I decision height. In some cases, concern is warranted by an increase in EPL (which threatens availability) because of increased MDE. However, this effect is still small enough to meet the stringent requirements (CAT-I and CAT-II/III) for precision approaches and landing. In future work, we will address the algorithm’s weakness at high elevation angles and validate it using numerous international GNSS reference data. Acknowledgement This work was supported partially by the Ministry of Land, Infrastructure and Transport (MOLIT) under Grant 10AVINAV01. References [1] B. Hoffmann-Wellenhof H. and Lichtenegger, E. Walse, 2008, GNSS; GPS, GLONASS, Galileo & more, springer Wien New York, pp. 269~273 [2] Jeong Hwan Yang, Chang Ho Kang, Sun Young Kim, and Chan Gook Park, “International GNSS Interference Detection and Characterization Algorithm uisng AGC and Adaptive IIR Notch Filter”, International Journal of Aeronautical and Space Sciences, Vol. 13, No. 4, 2012. 12, pp. 491-498 [3] Bradford W. Parkinson, et al., Global Positioning System : Theory and Applications Volume 1, AIAA, 1996, pp. 121-139 [4] Liang Heng, Grace Xingxin Gao, Todd Walter, and Per Enge, “GPS Ephemeris Error Screening and Results for 2006-2009”, Proceedings of the 2010 International Technical Meeting of the Institute of Navigation (ION ITM 2010), San Diego, CA, Jan 2010, pp. 1014–1022 [5] Liang Heng, Grace Xingxin Gao, Todd Walter, and Per Enge: “GPS signal-in-space anomalies in the last decade: Data mining of 400,000,000 GPS navigation messages,” DOI: http://dx.doi.org/10.5139/IJASS.2015.16.1.89 (89~101)14-083.indd 100 100 2015-03-30 오후 3:48:37 Jongsun Ahn Orbit Ephemeris Failure Detection in a GNSS Regional Application ephemeris faults”, Proceedings of the 14th International Technical Meeting of the Satellite Division of the Institute of Navigation, Salt Lake City, UT, Sept. 11-14, 2001. [19] Draft, ICAO Annex 10, GBAS CAT II/III Development Baseline SARPs, 17-29, May 2010 meeting of the Navigation System Panel (NSP) Working Group 1999. 691-703. [17] Specification Category 1 Local Area Augmentation System Non-Federal Ground Facility, U.S. Federal Aviation Administration, FAA/AND 710-2937, Washington, DC, May, 2001 [18] Shively. C, “LAAS Integrity Risk due to satellite 101 (89~101)14-083.indd 101 http://ijass.org 2015-03-30 오후 3:48:37
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