GNSS integrity enhancement for urban transport applications by error characterization and fault detection and exclusion (FDE)
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Résumé
Auteurs
Marion Berbineau |
David Bétaille |
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REE N°5/2018 Z107 JOURNÉES SCIENTIFIQUES URSI 2018 DOSSIER 2 In the past decades, more and more Global Navigation Satellite Systems (GNSS)- based urban transport applications emerged. Among these applications, the lia- bility critical ones, such as Electronic Toll Collection (ETC) and Pay as you Drive insurance, have high requirements for positioning accuracy as well as integrity since large errors can lead to serious consequences. Yet urban environments present great challenges for GNSS positioning due to the existence of multipath effects and None-Line-of-Sight (NLOS) receptions. This article presents a com- plete integrity monitoring scheme for urban transport applications. This scheme is realized in several levels. Firstly, measurement errors are better characte- rized by using weighting models with the help of an Urban Multipath Mode- ling (UMM). Secondly, several Fault Detection and Exclusion (FDE) methods are applied in order to detect and exclude erroneous measurements. Finally, Hori- zontal Protection Levels (HPLs) are computed and the probability of Misleading Information (MI) is analyzed. Au cours des dernières décennies, de plus en plus d’applications de transport urbain basées sur les systèmes de positionnement par satellites (GNSS) ont vu le jour. Des applications exigent une ﬁabilité critique comme le télépéage basé sur l’utilisation du GNSS, pour lesquelles des erreurs de positionnement peuvent entraîner de graves conséquences. Pourtant, les environnements urbains pré- sentent de grands déﬁs pour le positionnement GNSS en raison de l’existence des trajets multiples et de signaux NLOS (None-Line-of-Sight). Cet article pré- sente un système complet de surveillance de l’intégrité pour les applications de transport urbain. Tout d’abord, les erreurs de mesure sont mieux caractérisées en utilisant des modèles de pondération tirant parti d’un modèle de multi-trajet urbain (UMM). Deuxièmement, différentes méthodes de détection et d’exclu- sion de défauts (FDE) sont appliquées aﬁn de détecter et d’exclure des mesures erronées. Enﬁn, les niveaux de protection horizontale (HPL) sont calculés et la probabilité d’événements redoutés (MI) est analysée. Ni Zhu Univ Lille Nord de France, IFSTTAR, COSYS, LEOST, F-59650 Villeneuve d’Ascq, France, {ni.zhu, juliette.marais, marion.berbineau}@ifsttar.fr David Bétaille IFSTTAR, COSYS, SII, F-44344 Bouguenais, France, david. betaille@ifsttar.fr Juliette Marais Univ Lille Nord de France, IFSTTAR, COSYS, LEOST, F-59650 Villeneuve d’Ascq, France, {ni.zhu, juliette.marais, marion.berbineau}@ifsttar.fr Marion Berbineau Univ Lille Nord de France, IFSTTAR, COSYS, LEOST, F-59650 Villeneuve d’Ascq, France, {ni.zhu, juliette.marais, marion.berbineau}@ifsttar.fr GNSS Integrity Enhancement for Urban Transport Applications by Error Characterization and Fault Detection and Exclusion (FDE) Introduction GNSS integrity is one criterion to evaluate GNSS perfor- mance, which was ﬁrst introduced in the aviation ﬁeld. It is deﬁned as a measure of trust, which can be placed in the correctness of the information supplied by the total sys- tem [1]. The Radio communication Sector of International Telecommunication Union (ITU-R) has also attached impor- tance on this issue in their recommendation documents such as [2]. Due to the complexity of urban environments, GNSS performance could be severely degraded if no special mea- sures are taken. At the same time, the algorithms developed for the aerospace domain cannot be introduced directly to the GNSS land applications. This is because a high data re- dundancy exists in the aviation domain and the hypothesis that only one failure occurs at a time is made, which is not the case for urban users [3]. The main objective of this ar- ticle is to present a complete integrity monitoring scheme for GNSS-based urban transport applications. On the one hand, the measurement errors will be better characterized and re- duced by different approaches. On the other hand, several FDE methods will be used in order to detect and exclude the faults. Finally, the HPL is calculated so as to provide a statisti- cal position error bound. The paper is organized as follows: after the introduction, two weighting models will be introduced: the C/N0 (carrier- power-to-noise-density ratio) weighting model [4] and a new Hybrid model [5], which combines the C/N0, the satellite elevation and an Urban Multipath Model (UMM), which is an 108 Z REE N°5/2018 DOSSIER 2 JOURNÉES SCIENTIFIQUES URSI 2018 improved version of the Urban Trench Model (UTM) described in [6]. In the next section, ﬁve different FDE methods will be described brieﬂy, including the Subset Test (ST) (also named exhaustive search), the Local Test (LT), the Forward-Backward (FB) Test, the Danish method as well as the Classic Test [7] [8]. Then, several HPLs will be discussed in order to choose the one which can better ﬁt the urban canyons. The next section will present the real GPS data set as well as the evaluation of the accuracy performance with the Weighted Least Square (WLS) estimator compared to the Ordinary Least Square (OLS) estimator. Finally, ﬁve FDE algorithms will be applied with each WLS estimator and HPL will be calculated. The integrity perfor- r r mance will be analyzed from different aspects. Error Characterizations: Signal Weighting GNSS signals are often inﬂuenced by different error sources during the transmission in the propagation channels. Distributing different weights to each pseudo-range measu- rement according to the severity of its contamination is often an economic way to enhance the accuracy of positioning for the commercial GNSS receivers. This approach can be highly efﬁcient if the propagation errors can be properly characte- rized. Conventional weighting models are often determined by signal transmission delay, such as ionospheric, troposphe- ric delay, etc., far from considering the real-time local effects, such as the multipath and NLOS reception. In fact, these lo- cal effects are predominant in the total GNSS measurement error budget for urban transport applications, since they can lead up to a measurement error of several kilometers. In this paper, we will design the weighting matrix according to the real-time signal reception states. Generally, the linearized GNSS pseudo-range observation equation can be written as: (1) where, sbl is the deviation between the actually measured pseu l - do-ranges and the predicted noiseless pseudo-ranges with a speciﬁed initial user state; s ( denotes the geometry matrix which describes the satel- lite-receiver relative position information; %b x represents the offset vector of the user states ( x XYZ ( ( b t with the initial states; ¡ denotes the measurement error vector. ¡ The Weighted Least Square (WLS) solution of b Xis ex- pressed as: (2) here, W represents the measurement weighting matrix. W In fact, the weighting matrix 7is a diagonal matrix, whose diagonal elements are the reciprocal of each variance of mea- surement. That is to say, measurements with smaller error variances will contribute to large weights in the estimation. On the contrary, measurements with large error variances, such as NLOS signals, will get small weights or even be ap- proximately canceled from the measurement set by nearly zero weights. Thus, in the following sections, error variance estimation according to different error models will be imple- mented in this matrix and the navigation solutions will be estimated with the WLS according to Eq. (2). C/N0 -based Weighting model The carrier-power-to-noise-density ratio, i.e., C/N0 repre- sents the ratio of signal power and noise power per unit of bandwidth. It can be seen as an indicator of the signal quality. Several weighting models exist in the literature using C/N0 as a criterion [4] [9] [10]. In this paper, we will choose the C/ N0 model proposed in [4], which was ﬁrstly built for geodetic receivers. The following formula of variance estimation was proposed for all types of receivers: (3) where, a (in m2 ), b (in m2 (Z) are model parameters. Z The two model parameters, i.e., a and b, strongly relate to the receiver characteristics and signal reception environ- ments. Calibrations are needed according to speciﬁc datasets and receivers. A new Hybrid model: Contribution of the Urban Multipath Modeling (UMM) Despite its non-complicated implementation, the C/N0 weighting model presents some drawbacks especially in dense urban canyons. On the one hand, constructive mul- tipath interference leads to an increase in C/N0 , while de- structive multipath interference leads to a decrease. Thus all signals with high C/N0 do not possess high quality but they all contribute to a larger weight in the C/N0 weighting model when calculating a position. Thus, we propose here a new hybrid model, which is in- spired by [5]. This model takes into consideration not only the C/N0 , but also the satellite elevation e and a LOS/NLOS indicator k from the UMM. This model of measurement error variance can be written as: (4) REE N°5/2018 Z 109 GNSS Integrity Enhancement for Urban Transport Applications by Error Characterization and Fault Detection and Exclusion (FDE) where, m is a multiplier for model calibration, which depends on receivers and environments. The UMM is an improved version of the Urban Trench Model (UTM) described in [6]. Based on 2D+1 (2D building features and building heights) map data, the UTM calculates the mask of satellite visibility and the additional pseudo-range distances due to signal reﬂections. An important hypothesis of UTM is that the length of the streets is inﬁnite. In fact, this hypothesis is an approximation of the map geometry which ﬁts well the reality when the vehicle is inside the homoge- neous streets which have approximately the same geometric features as an example of a typical urban trench shown in the ﬁgure 1(a). However, this assumption is no longer true espe- cially in the no-homogeneous streets or the intersections as shown in the ﬁgure 1(b). In order to avoid the drawback of the UTM, the UMM is proposed while getting rid of the inﬁnite length street assumption. The process is ﬁrst to detect if any facade exists in every satellite azimuth, which is high enough to occult the corresponding satellite elevation. This initial step will identify LOS/NLOS satellites. The ﬁgure 2 shows an example of this step at a crossroad in the Chaussée de la Madeleine of Nantes: the ﬁgure 2(a) is an illustration with the information of digital map, where the polygons represent upside view of buildings. The red lines repre- sent the directions of each received satellite azimuth. The ﬁgure 2(b) is the street view of the same location provided by Google Earth. The next step is to examine every facade locally, to detect whether it could make a specular reﬂection with the occulted satellite previously identiﬁed. In this case, the ﬁnal step is to check that no other facade may occult the reﬂected ray, either in between the antenna and the impact point, or in between the impact point and the satellite. In case several facades exist with reﬂected rays, the one with the largest gra- Figure 1 : Examples of two kinds of streets. (a) Inside a homogeneous street: a typical urban trench. (b) At an intersection area. Figure 2 : An illustration of the ﬁrst step of the UMM (a) (b) 110 Z REE N°5/2018 DOSSIER 2 JOURNÉES SCIENTIFIQUES URSI 2018 zing angle (i.e., the smallest angle of incidence) is preferred. Facades are regarded as vertical planes, with the height of the polygon they belong to. The ﬁgure 3 shows an illustra- tion of this step provided respectively by digital map (ﬁgure 3(a)) and the same location provided by Google Earth (ﬁ- gure 3(b)). The green line represents a NLOS satellite signal, which is reﬂected by a facade (in blue) and then received by the receiver. Finally, the additional distances will be calculated for all the NLOS receptions according to the geometrical rules of spe- cular reﬂection. These additional distances will be corrected when applying the hybrid error model. Fault Detection and Exclusion (FDE) Algorithms Fault Detection and Exclusion (FDE) algorithms are gen- erally based on the consistency check of the difference between the measured pseudorange l and the predicted l pseudorange based on the estimated solution , which is called residuals. The WLS residual vector can be written as: (5) Two principle hypothesis tests exist in FDE algorithms: the Global Test (GT) and the Local Test (LT). The GT is generally implemented at the primary stage in order to detect whether faulty measurements exist. If a fault exists, the LT is able to further identify the faulty measurement. Global Test (GT) In the framework of the residual-based FDE, the test sta- tistic t used in the GT is called Normalized Sum of Squared t Error (NSSE), which can be expressed as: (6) where, the matrix Y denotes Variance Covariance Matrix (VCM) of the measurement errors, which is also the inverse of the weighting matrix W mentioned previously. W Figure 3 : An illustration of the second step of the UMM. (a) (b) Figure 4 : Global Test (GT) and Local Test (LT). (a) Global Test (b) Local Test (LT) REE N°5/2018 Z 111 GNSS Integrity Enhancement for Urban Transport Applications by Error Characterization and Fault Detection and Exclusion (FDE) Under fault-free conditions, the test statistic t follows a central distribution; under faulty conditions, t follows a non-central distribution [11] [12], which is illustrated in the ﬁgure 4(a). With the pre-deﬁned probability of false alarm Pfa and the probability of missed detection PMD P , a threshold Th can be deduced and the statistical hypothesis test can be conducted as follows: (0 : (fault-free conditions) t )4H (7) (a : (fauly conditions) t Th If the null hypothesis (0 is rejected and the alternative hypothesis (0 is accepted, an inconsistency of the total measurement set is detected. Then, the fault identiﬁcation procedure is needed to isolate and exclude the faulty mea- surement. The LT is one of methods to realize the fault iden- tiﬁcation. Local Test (LT) If a fault is detected with GT, that means an outlier does exist in one or several measurements. LT can be carried out so as to identify the outlier. The LT uses the normalized resi- duals as test statistic, which can be written as follows: (8) where, represents the ith diagonal element of the covariance matrix of the residuals . If the ith measurement is not an outlier, Wi W is supposed to i follow a standard normal distribution, which is the local null hypothesis (0,i . Otherwise, WI W follows a biased normal distri- bution, which corresponds to the local alternative hypothesis (a,i as shown in the ﬁgure 4(b). In that ﬁgure, th denotes the i local threshold, which can be calculated with the predeter- r r mined local signiﬁcance level Pfa0 . As a result, the local test is realized as follows: (0,i 0 : ( i i ( ( th measurement not outlier) wi w )TH (9) (a,i : ( i i ( ( th measurement an outlier) wi w )TH This procedure can be repeated several times in a loop until no outlier exists in current measurement set. Different Fault Detection and Exclusion (FDE) Schemes Different FDE methods exist by combining the GT and LT in different ways. In this paper, we will implement ﬁve FDE techniques which allow eliminating multiple faults. Most of them are explained in detail in our previous work [7]. So they will be brieﬂy described here. In case of GT failure, the fol- lowing FDE techniques can be carried out: s3UBSET4ESTING34 EACHSUBSETNUMBEROFSATELLITES 4) of the initial measurement set will be used to calculate an user position solution, among which the ST with the maximum of satellites and the smallest test statistic which passes the GT will be chosen; s3EQUENTIAL,OCAL4EST,4 EACHMEASUREMENTWILLBEEXA- mined by LT. In each iteration, the measurement with the biggest local test statistic exceeding the threshold will be eliminated as outlier. The procedure stops until no outlier exists or lack of redundancy; s&ORWARD
"ACKWARD &" 4EST THE FORWARD LOOP WILL BE conducted as the sequential LT described previously. Then in the backward loop, the eliminated satellites in the forward loop will be reintroduced with all the possible combinations until the optimal measurement set is found. The main advantage of the FB technique is, on the one hand, to avoid the erroneous rejection of a good measu- rement since a huge measurement error can sometimes distribute and hide in other measurements’ residuals due to special satellite geometry. On the other hand, the effect of re-introduction of a previously excluded satellite can enhance the satellite geometry, which is usually poor in urban canyon. s$ANISHMETHOD$!. ANITERATIVELYREWEIGHTINGPROCEDURE on the pre-estimated measurement variance will be carried out according to the ratio between local test statistic and the local threshold th. What should be highlighted is that there is no exclusion step in this method, which can well keep the initial satellite geometry. If the algorithm cannot converge after several iterations (here, we ﬁx it as 10), the solution will be declared as unreliable. s4HE#LASSIC4EST#4 THEMEASUREMENTWITHLARGESTNOR- R R malized residual will be excluded in one iteration. The pro- cedure stops until the GT passes or lacks of redundancy. During all the FDE procedures, if there is not enough re- dundancy to realize the FDE or the FDE cannot successfully identify the outliers, the position solution will be declared as unreliable. Horizontal Protection Level (HPL) Estimation Protection Level (PL) is a statistical error bound computed so as to guarantee that the probability of the absolute posi- tion error exceeding the said number is smaller than or equal to the target integrity risk [3] [13]. Several methods of HPL computation exist in the literature especially for aviation utili- ty. Generally speaking, a “complete” HPL is composed of two 112 Z REE N°5/2018 DOSSIER 2 JOURNÉES SCIENTIFIQUES URSI 2018 terms: the impact of measurement noise on user position and the impact of measurement bias on user position. The noise term (0,n is calculated according to the error propaga- tion, which is deﬁned in [13] as the HPL for Satellite-Based Augmentation System (SBAS): (10) where, dmajor d corresponds to the error uncertainty along the r semi-major axis of the error ellipse. K is an inﬂation factor in K order to meet speciﬁed integrity risk, which is usually obtained in the corresponding table with 4 degrees of freedom for conservative purpose. More details can be found in [13] [14]. The noise term of HPL in Eq. (10) is often not big enough to bound the position errors especially in the presence of bias in one or several measurements. Thus, the bias term of HPL should be added. The bias term (0,b generally consists of in- formation of satellite geometry and the detectable bias in the domain of test statistic, which can be expressed as follows: (11) where, 3,/0%i % represents the sensibility of HPE to the bias of ith i satellite [14]; mi m represents the standard deviation of the i ith measure- ment; Pbias P denotes the bias in the domain of test statistic which can take different values according to the degree of conser- vative. In this paper, we will take . In fact, the satellite with the largest 3,/0% is the most % difﬁcult to detect because given the same HPE, it yields the smallest test statistic. Also, given a test statistic, the satellite with the highest 3,/0% produces the largest position error. % Finally, the complete HPL can be obtained as the sum of the noise term and the bias term: (12) The size of HPL is also an important issue for urban trans- port applications since it will be less effective if the size of HPL is too big compared to the size of the current road where the vehicle user is situated. Thus, a compromise should be made between the efﬁciency of the HPL (i.e ( ( ., HPL well bound the HPE) and its size. Application of the Complete Integrity Monitoring Scheme Description of System and Dataset The complete framework consists of two modules: an ac- curacy enhancement module and an integrity enhancement module as shown in the ﬁgure 5. In the accuracy enhance- ment module, measurement errors will be characterized with error models described previously. They will be compared with the results obtained from the Ordinary Least Square (OLS) estimator, in which, all the measurements have the same weight. Then, in the integrity enhancement module, ﬁve FDE methods mentioned in the previous section will be implemented and evaluated. In this paper, we ﬁx Pmd P 0 d fa = 10-2 . Finally, the HPL will be calculated according to Eq. (12). Figure 5 : The ﬂowchart of the complete integrity monitoring scheme. REE N°5/2018 Z 113 GNSS Integrity Enhancement for Urban Transport Applications by Error Characterization and Fault Detection and Exclusion (FDE) The GPS data used to test the complete system was col- lected in the city center of Nantes, France. Two kinds of recei- vers are used: an Ublox-LEA-6T, which is a typical equipment used in car navigation systems and a dual-frequency Novatel- DLV3 receiver, which is a high precision receiver used to pro- vide the reference trajectory. The total trajectory have 17903 epochs that take about one hour at 5(Z. The ﬁgure 6 shows an overview of this trajectory with Google Earth. We can see that the traveled streets are in deep urban canyons with dif- ferent heights of buildings. Experimental Validation and Performance Analysis Performance of accuracy In this sub-section, only the error models are applied (wit- hout FDEs). The ﬁgure 7 shows the reference trajectory (in green) together with the trajectories estimated respectively by OLS (in blue), by WLS with C/N0 model (in red on the ﬁgure 7a) and by WLS with hybrid model (in red on the ﬁgure 7b). Then the ﬁgure 8 presents the Cumulative Distribution Function (CDF) of the HPE. We can see that with the two error models, the accuracy is well improved compared to the OLS, especially with the hybrid model. Figure 6 : An overview of the trajectory in the city center of Nantes, France. Horizontal Position Error [m] Mean Median 95% std OLS 10.14 5.66 30.74 77.39 WLS C/N0 4.81 2.64 13.78 26.79 WLS Hybrid 3.61 2.33 10.83 4.43 Table 1 : WLS Accuracy Comparison (without applying FDE). Figure 7 : Comparison of Estimated Trajectories (a) C/N0 model (b) Hybrid model 114 ZREE N°5/2018 DOSSIER 2 JOURNÉES SCIENTIFIQUES URSI 2018 The table 1 makes a summary about the HPE in terms of mean, median (50th percentile), 95th percentile and standard deviation (std), which is used to evaluate the dispersion of HPE. We can see obviously that the WLS with hybrid model has the best performance concerning the accuracy. The main advantage of the hybrid model compared to the C/N0 model is the capability of reducing huge errors since the 95th percentile of HPE passes from 13.78 m to 10.83 m and the std passes from 26.79 m to 4.43 m. Performance of integrity After the accuracy enhancement, the integrity module is implemented and the HPL is calculated in this section. The main performance evaluated after application of FDE are main- ly the accuracy, the size of HPL as well as the efﬁciency of HPL. The last one is assessed by the probability of misleading infor- mation Pmi, which represents the probability of HPE exceeding HPL whose value indicates that the position solution is reliable. The table 2 gives a summary about the WLS with C/N0 model with different FDE methods. We can see that the ac- curacy performance is again improved in that huge errors are removed since the standard deviations of HPE are much reduced. Among all the FDE methods, the FB has the best global performance and the ﬁgure 9 presents some details. It shows the reference trajectory (in green), the trajectory es- timated with C/N0 WLS (in sky blue) as well as the trajectory estimated with WLS C/N0 and FB (the reliable positions are in magenta and unreliable positions are in black). Especially in the red circles, we can see that the majority of huge HPEs are either reduced or ﬂagged as unreliable. The Pmi, are all smaller than 1%. The CDF curves of the ﬁgure 10 can prove the same conclusions. The table 3 reports the performance of each FDE method with hybrid model. Accuracy can be improved by LT, FB and DAN compared to the one without applying FDE. Unfortunately, with ST and CT, the accuracy is slightly de- graded. This is due to the user/satellite geometry degradation after satellite exclusion. In fact, the GNSS positioning accuracy depends not only on the range measurement quality but also on the user/ Figure 8 : Cumulative Distribution Function (CDF) of the HPE. Accuracy Performance: HPE [m] Integrity Performance mean medi- an 95% std median( HPL) [m] Pmi [%] ST 4.61 2.45 14.44 8.02 18.26 0.76 LT 3.56 2.38 9.56 4.41 17.76 0.11 FB 3.43 2.32 9.90 4.36 17.46 0.14 DAN 4.13 2.50 11.18 6.17 19.21 0.28 CT 4.55 2.46 13.61 8.07 18.29 0.75 Table 2 : Performance summary of C/N0 model with FDE. Accuracy Performance: HPE [m] Integrity Performance mean median 95% std median (HPL)[m] Pmi [%] ST 4.07 2.39 12.59 6.34 12.50 0.95 LT 3.42 2.29 10.59 3.94 12.36 0.42 FB 3.48 2.28 10.76 4.03 12.50 0.48 DAN 3.55 2.30 10.81 4.67 13.28 0.21 CT 4.01 2.39 11.96 7.16 12.45 0.80 Table 3 : Performance summary of Hybrid model with FDE. REE N°5/2018 Z 115 GNSS Integrity Enhancement for Urban Transport Applications by Error Characterization and Fault Detection and Exclusion (FDE) satellite geometry, i.e., Dilution of Precision (DOP). The smal- ler the value of DOP, the better the user/satellite geometry quality. For a FDE method, correct exclusions of faulty mea- surements will ameliorate the range measurement quality but could potentially degrade the satellite geometry due to a decrease of available satellite measurements. The ﬁgure 11 shows an example of Position Dilution of Precision (PDOP) increments after applying ST, which is a proof of severe satel- lite degradation. Additional measures should be taken in the following research, such as special control of satellite geo- metry, in order to avoid this degradation. Compared to the performance of total integrity scheme with C/N0 model, the sizes of HPL calculated with hybrid model are smaller. And all the Pmi can be guaranteed smaller than 1%. Figure 9 : Zoomed trajectories. Figure 10 : CDF of HPE before and after applying FB with C/N0 model. Figure 11 : Position Dilution of Position (PDOP) Increments After Subset Test. 116 ZREE N°5/2018 DOSSIER 2 JOURNÉES SCIENTIFIQUES URSI 2018 As mentioned in the section concerning the FDE tech- niques, the FDE algorithms are not all the time available. When there is not enough redundancy to check the consis- tency or when the FDE algorithms are not able to identify the outlier, the system will be declared as non available. These positions will be ﬂagged as unreliable. The table 4 reports the availabilities of each scheme. Thus, how to enhance the availability is also an issue for future research. Conclusions In this paper, we propose a complete integrity monito- ring scheme for urban transport applications. This framework consists of two modules: one for accuracy enhancement, inside which a new error model with the contribution of map information is proposed; the other for integrity enhancement, inside which ﬁve FDE methods are implemented. The validation with real GPS data collected in urban ca- nyons shows that accuracy can be signiﬁcantly improved by two error models compared to the classic Ordinary Least Square method, especially the new hybrid model. All the FDE algorithms are able to help improve the accuracy of C/N0 model but for hybrid model, only the Local Test, Forward- Backward Test and the Danish method can improve accuracy while the Subset Testing and the Classic method cannot due to satellite geometry degradation. Thus, special measures may be taken in order to avoid this degradation for future work. The HPL is able to well bound the HPE with Pmi smaller than 1%. HPLs still have a median value above 10 m in size (for HPE of 2 m in median), which is an issue to target for future research. Moreover, algorithms proposed in this paper are possibly to be applied with GNSS multi-constellations. This will no doubt improve the algorithm availability by bene- ﬁting from an increase of the number of visible satellites. Acknowledgment This work has been performed with the ﬁnancial support of CNES and the Hauts de France Region Council in the fra- mework of the SMARTIES project of the CPER ELSAT 2020 program which is co-ﬁnanced by the European Regional Development Fund, the French state and the Hauts de France Region Council. Bibliographie [1] P.B.Ober,“Integritypredictionandmonitoringofnavigation (%) ST LT FB DAN CT C/N0 98.58 93.55 95.01 94.81 98.57 Hybrid 98.08 89.53 91.22 96.39 97.98 Table 4 : FDE Availability. LES AUTEURS Ni ZHU received the B.Sc. degee in ﬂight vehicle propulsion en- gineering from the Civil Aviation University of China in 2013. She received the engineering degree in digital communications from Ecole Nationale de l’Aviation Civile (ENAC), France, in 2015. She is currently pursuing the Ph.D. degree with the Laboratoire Elec- tronique, Ondes et Signaux pour les Transports (LEOST) Labo- ratory, French Institute of Science and Technology for Transport, Development and Network (IFSTTAR). Her recent research is specialized in GNSS channel propagation modeling in urban environment and integrity monitoring for terrestrial vehicles. David Bétaille received the M.Sc. degree in robotics engi- neering from École Centrale de Nantes, France, in 1992, the Ph.D. degree in geodesy and navigation from University College London, U.K., in 2004, and Accreditation to supervise research (French HDR degree) from Nantes University in 2014. He is the Director of Research with the Components and Systems De- partment of the French Institute of science and technology for transport, development and networks (IFSTTAR). His research activities related to positioning and map-matching using satellite systems combined with dead reckoning and digital enhanced map data for applications to vehicles, intelligent transportation systems, multi-modal mobility. Juliette Marais received the engineering degree from Institut Supérieur de l’Electronique et du Numérique and Ph.D. de- gree in electronics from University of Lille, France, in 1998 and 2002, respectively. She received in 2017 her Accreditation to supervise research (French HDR degree) from Lille University. Since 2002, she has been a Researcher with the French Ins- titute of Science and Technology for Transport, Development and Networks. She is involved on GNSS performance analyses and enhancement in land transport environments. She is cur- rently involved in two projects: integrity monitoring for land transport applications and GNSS propagation characterization in railway environments. Her research interests principally include propagation phenomena, positioning error modeling, ﬁltering technics, and simulation. Marion Berbineau received the engineer degree in electrical engineering from PolytechLille, France, and the Ph.D. degree in electrical engineering from University of Lille Nord de France in 1986 and 1989, respectively. She is a Full Time Research Director Expert in the ﬁeld of radio wave propagation in trans- port environments (tunnels), channel characterization and modeling, MIMO, wireless systems for telecommunications, cognitive radio for railways, and GNSS localization-based for ITS, particularly for the rail domain. Since 2017, she has been in charge of coordination of Railway Research, (IFSTTAR). She is active as an expert for the GSM-R and future systems like LTE-A or 5G. She is author and co-author of several publica- tions and patents. 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