Research of Signal-in-Space Integrity Monitoring Based on Inter-satellite Links

Transcription

1 Chinese Journal of Electronics Vol.4, No., Apr. 05 Research of Signal-in-Space Integrity Monitoring Based on Inter-satellite Links WANG Yuechen, LI Rui and ZHAO Ruibin (School of Electronic and Information Engineering, Beihang University, Beijing 009, China) Abstract Using the Inter-satellite links (ISLs) to enhance the GNSS s positioning accuracy and integrity is attracting much more attentions. In order to ensure the autonomous positioning accuracy and stability based on ISLs, a satellite and ground joint positioning mode is presented in this paper, which is constrained by quality grade of position error. Spatial error ellipsoid is applied to calculate parameters and achieve Signal-in-space (SIS) integrity monitoring. To check the accuracy of the mode and performance of monitoring, mixed constellation of Beidou system is simulated to support the analysis and investigate the impact of the high-low ISLs. The orbit determination results verify that the introduced integrity monitoring method can satisfy the integrity risk of 0 5 /h and achieve the SIS integrity monitoring. Key words Integrity, Inter-satellite links, Quality grade of position error, High-low links, Spatial error ellipsoid. simulated to verify that this method can achieve global SIS integrity monitoring in the condition of relying on ISLs solely. II. Satellite and Ground Joint Positioning Mode Constrained by Quality Grade of Position Error The structure of satellite and ground joint positioning mode constrained by quality grade is shown in Fig.. It mainly includes the global ISLs and regional Ground-satellite links (GSLs). I. Introduction With the development of satellite navigation, its accuracy, continuity and integrity have attracted more and more attentions. Especially in the context of aviation, integrity is particularly important [ 3]. The system must have the ability to alert users in time when it can t be used [4,5]. At the same time, the design of ISLs has become a hot spot in navigation systems [6]. The ISLs range information can not only improve the satellite s position accuracy but also ensure the satellite s autonomous position when control stations are unavailable, guarantee that system can operate normally. So far, the main research of ISLs focuses on autonomous positioning [7] and the study of integrity parameters calculation is not enough. The integrity monitoring depended on ISLs is in its infancy [6]. Therefore, this study has great significance. A satellite and ground joint positioning mode constrained by quality grade of position error is presented in this article. What s more, a method of calculating integrity parameters using the spatial error ellipsoid is proposed after analyzing the results of positioning. Finally, Beidou mixed constellation is Fig.. ISLs and SGLs The satellite s positioning mainly relies on the observations of ISLs: at each epoch, all visible satellites are pairwise coupled and each satellite has only one ISL at most. In addition, ISLs keep changing with epochs so that each epoch s ISLs are different in a period. Each satellite is positioned by such a relatively ranging mode. It results in that the relative accuracy can be promised and the constellation-level drift can t be excluded. To solve this problem, ground stations are introduced to provide a few GSLs. In certain region, 4 ground stations are laid out and transmit their position, time information to all visible satellites at each epoch. Satellites receive the information as additional measurement and combine with ISLs measurement to position. By this way, the problem of constellation drift is solved with little cost.. Quality grade of position error constraint Although ground stations can ensure satellite s position accuracy relative to earth, the error propagation among ISLs still Manuscript Received Sept. 03; Accepted May 04. This work is supported by the National Basic Research Program (973 Program) (No.00CB73805). c 05 Chinese Institute of Electronics. DOI:0.049/cje

2 440 Chinese Journal of Electronics 05 exists. Therefore, the following quality grade of position error constraint is employed: by the position accuracy comparison, only the higher accuracy satellites can be used to locate the others, which can control error propagation. The constraint of quality grade is achieved by the comparison between different satellites orbit covariance matrix s maximums or their multiple: if one satellite s value is less than the one to be localized, its position accuracy is higher and the link can be used to position. Otherwise, extrapolation model is used to get the next status. As for the ground stations, they can always be used for localization since their accuracy is the highest.. The sequential Kalman filter Kalman filter is used to achieve satellite s autonomous positioning in the Earth-centered inertial (ECI) coordinate. For any satellite j to be located and satellite u to be used to locate, the process is shown in Fig.. Fig.. The process of satellite positioning Kalman filter s state vector includes three-dimensional position, velocity, acceleration and clock error information, the observation is pseudo ranges. X =[x, ẋ, ẍ, y, ẏ, ÿ, z, ż, z, c Δt, c Δṫ, c Δẗ] () The observation equation is: 8 >< >: Z k = ρ u,j = HX + V () H =[a xj, 0, 0,a yj, 0, 0,a zj, 0, 0,, 0, 0] xj xu yj yu zj zu a xj =,a yj =,a zj = r ju r ju r ju (3) q r ju = (x j x u) +(y j y u) +(z j z u) The satellite s motion is described by acceleration model: 3 3 Φ t Φ Φ = Φ , Φ0 = t t Φ Before the extrapolation, velocity information in navigation message is extracted to update velocity-related state parameters for higher accuracy. By designing proper Q and R matrixes, satellite autonomous position can be achieved by sequential approach: at each epoch, the satellite receives information from ISLs and GSLs to calculate pseudo ranges one by one. System selects observations which satisfy the quality grade to filter and extrapolate to the next status. Then the process is repeated to achieve the continuous positioning. The Kalman filter equationsareshownasbelow: 8 K k = P k k Hk T (H k P k k Hk T + R k ) >< X k k = X k k + K k (Z k H k X k k ) P k =(I K k H k )P k k (4) X k k = Φ k k X k k >: P k k = Φ k k P k Φ T k k + Q k III. Calculation of SIS Integrity Monitoring Parameters GPS modernization introduces the concept of SIS integrity and plans to use User range accuracy (URA) as monitoring parameter [8]. URA is decomposed into URA oe and URA oc so that they can monitor ephemeris and clock respectively [9,0]. But system s interface specification doesn t mention how to calculate and use these two parameters. In addition, Galileo uses ground stations to monitor the errors and residuals in the direction of Worst user location (WUL) to ensure integrity []. It shows that both methods are high confidence description of the distribution of satellite s orbit and clock errors. Because this paper mainly focused on the global integrity monitoring based on ISLs, the orbit covariance matrix varies with the ISL s changing, which leads to the WUL is no longer towards earth, the assumptions and methods based on ground stations are inapplicable. Therefore a new method to calculate the integrity parameters using spatial error ellipsoid is proposed below. Before introducing the calculation process, it s necessary to discuss how to choose and use the SIS integrity risk.. The selection and application of SIS integrity risk According to the requirements of aerospace applications by International civil aviation organization s (ICAO) DO-9D, user s integrity risk must be less than 0 7 /h in Non-precision approach (NPA) []. SIS integrity risk can be obtained by the decomposition of user s integrity risk. GPS gives two kinds of SIS integrity risk assurance: 0 5 /h as legacy level and 0 8 /h as enhanced level [8]. Assuming that user can see at least 0 satellites each moment. In the legacy level, the SIS integrity risk that only one satellite breakdowns is 0 4 /h. So user must apply Receiver autonomous integrity monitoring (RAIM) to meet the integrity requirement of 0 7 /h. In the RAIM, false-alarm probability is 0 5 and missing rate is 0 3 [3]. In the enhanced level, the SIS integrity risk that only one satellite breakdowns is already less than 0 7 /h and satisfies the risk requirement. So user should calculate the Horizontal protection level (HPL) to satisfy the integrity alarm threshold of NPA. As shown in the DO-9D, the calculation process is [] :

3 Research of Signal-in-Space Integrity Monitoring Based on Inter-satellite Links 44 User can position by weighted least square, the weight matrix includes URA,whichis: 3 w w 0 0 W = , wi = (5) σi w N σi = σi,ura + σi,uire + σi,air + σi,tropo (6) where σi,ura is the URA of satellite i and others are the errors of atmosphere, multipath and so on. Then user can get the observation matrix in the coordinate of East-north-up (ENU) by the rotation matrix: G(j) =[ cos El j sin Az j, cos El j cos Az j, sin El j, ] (7) The Az j and El j are direction angle and elevation of the satellite i. So the covariance matrix in ENU is: 3 d E d EN d EU d ET D =(G T WG) d NE d N d NU d NT = 6 4 d UE d UN d 7 (8) U d UT 5 d TE d TN d TU d T Finally, the HPL can be calculated as below: HPL = K H,NPA d major (9) v s u t d E d major = + d N d E + + «d N + d EN (0) To meet the requirement of NPA, K H,NPA =6.8. Comparing the HPL with 556m: if HPL<556m, the integrity requirement is satisfied; otherwise, there is integrity risk and the navigation message should be abandoned. Here the legacy level s 0 5 /h integrity risk is chosen as the example to explain the parameter s calculation process because it makes simulation simple.. Parameter calculation of satellite clock Since the satellite clock error mainly has effect on the pseudo range direction [4], URA oc is analyzed in one-dimension. GPS uses the concept of bound when monitoring SIS integrity by URA. The bound means: when estimating URA, a zero-mean Gaussian is used to describe the error s distribution [8]. It mainly focuses on censored probability and guarantees that accident s missing rate is less than integrity risk at the threshold, which is related to URA. Assuming the clock error is Gaussian distribution [4] and its Probability distribution function (PDF) is: f(x) = «(x μ) exp () πσ σ where μ is mean, σ is standard deviation. For the integrity risk of 0 5 /h, its Gaussian quantile is K =4.4, so: ) μ > 0, Gaussian bound s threshold is selected as ( μ Kσ,μ + Kσ), and the missing rate is obtained by integrating SIS error s PDF with this threshold: P = = Z μ+kσ Z μ Kσ μ+kσ μ Kσ f(x)dx πσ exp «(x μ) dx σ () making t = x μ σ,so Z K «P = exp t μ σ K π Z K «= exp t μ π 0 5 σ Z K K μ σ K dt dt exp t π Z K K «dt «exp t dt π μ>0, so P<0 5, which satisfies the risk requirement. ) μ < 0, Gaussian s threshold is (μ Kσ, μ + Kσ), on the same principle, the missing rate is: Z μ P 0 5 σ +K «exp t dt (3) K π μ<0, so P<0 5, it satisfies the risk requirement. 3) μ =0, Gaussian s threshold is ( Kσ,Kσ). Obviously the missing rate is P 0 5 and satisfies integrity risk requirement. In summary, if the zero-mean Gaussian distribution s censored probability by the threshold is less than the integrity risk, real error s censored probability must satisfy. As shown in Fig.3, it s obviously that outside the threshold, the area of full line (bound s distribution) is bigger than the dotted line (error s distribution). So the URA can be calculated in one-dimension: expanding the SIS error s standard deviation in K times and adding to the mean. So the URA oc can be calculated as: URA oc = σ 0 = ( μ + Kσ) (4) K 3. Parameter calculation of satellite orbit In three-dimension, the above is extended to calculate URA oe by a geometric method using the spatial error ellipsoid [5]. The schematic diagram is shown in Fig.4. Fig. 3. Schematic diagram of PDF Fig. 4. Spatial error ellipsoid modal Satellite s real position is assumed in an error ellipsoid whose center is the positioning result. The axes are relevant with covariance and can be obtained by multiplying by quantile of integrity risk, which results in an equal probability error ellipsoid. Inscribing the ellipsoid by a bounding ball, the probability that ephemeris error falls outside the ball is less than the risk and the ball s radius is Gaussian threshold, so: URA oe = K OE (5)

4 44 Chinese Journal of Electronics 05 Here is the mathematical derivation. With orbit covariance matrix, the variance in the direction of user is u j user T P Au j user, u j user is the unit direction vector from user to satellite j and P A is symmetry position covariance matrix. Because there is a unit orthogonal matrix satisfies C T P AC = P Y = diag(λ λ λ 3)andC can convert vector from ECI coordinate to the satellite local coordinate centered satellite s position. By the use of this transformation and satellite s orbit error s mean μ oe =(dr, da, dc), the formula can be reached with the help of quantile K, making g j user = C T u j user: In the first case, satellite s position error will expand over time gradually: orbit s error may be kilometers and clock error can be tens of meters in hour; Secondly, when adding quality constraint without station, if satellite No.9 is set as the standard, it can curb error s propagation effectively, but the relative location by ISLs may lead that constellation drifts to the same orient relative to earth; Thirdly, adding ground stations and quality grade can constrain satellite s position and improve the absolute position s accuracy to meters. URA oe = μ + g j user T P Y g j user = μ T oep Y μ oe + guser j T P Y guser j (6) = Kλ (x u + dr) + Kλ (y u + da) + Kλ 3(z u + dc) It can be considered as the distance from point ( Kλ (x u + dr), Kλ (y u + da), Kλ 3(z u + dc)) to the coordinate origin O. Obviously it s on the surface of the ellipsoid (x Kλ dr) + (y KλdA) + (z Kλ3dC) = Kλ Kλ Kλ 3 Finding the maximum distance from origin to ellipsoid, it must be the point E. So the calculated URA is consistent with the previous physical interpretation. IV. Simulation and Verification According to the Beidou global navigation system s interface control document version.0, its constellation consists with 5GEOs, 7MEOs and 3IGSOs [6]. Satellite s type and height are more plentiful than other systems, so it is taken as an example to verify the design and algorithm above.. The impact of ground stations and quality grade of position error In order to ensure all satellites position accuracy, ground stations and quality grade of error are added in satellite autonomous positioning mode. Simulating for hour in three cases and the results are shown in Figs.5 7: Neither ground station nor quality constraint Only quality constraint without station Both stations and quality constraint Fig. 6. Only quality constraint without station. The impact of High-low ISLs (HLLs) The used ISLs include not only normal MEO-MEO links but also high-low GEO (IGSO)-MEO links. Since the difference in height, these links can improve the satellite s observation condition effectively. Its influence on positioning result will be discussed by the comparison below. Fig. 7. Both stations and quality constraint Fig. 5. Neither station nor quality constraint Itcanbeseeninthreefigures: No. (GEO) is selected to analyze for hour and results are shown in Fig.8. The results that satellite position with and without HLLs are shown in left and right, orbit and clock errors are shown from top to bottom. It can be seen that there is little different whether HLLs exists or not by the threshold of 5 times quality grade. Because GEOs can always be seen by stations and have high accuracy, ISLs have little help on GEO s position accuracy because of the quality grade constraint. In addition, No.7 (MEO) is used to test and results by 5 times threshold are shown in Fig.9. The same as Fig.8, it s visible that links work because the satellite is invisible to stations

5 Research of Signal-in-Space Integrity Monitoring Based on Inter-satellite Links 443 and its position accuracy is poor. But the result s improvement can be ignored the same. In summary, conclusions can be reached: Firstly, although ISLs can add observations, higher accurate information is provided by stations. HLLs are the reuse of the same information and make little sense on accuracy improvement; Secondly, ISLs quality grade constraint can be selected as 5 times. It can both satisfy the position accuracy and prevent the propagation of error. Fig. 8. (a) The GEO s result without HLLs; (b) The GEO s result after adding HLLs Fig. 9. (a) The MEO s result without HLLs; (b) The MEO s result after adding HLLs 3. The verification of URA s performance in integrity monitoring In the following section, the availability of calculating URA in geometric way will be verified and analyzed by the ISLs positioning results. When finding the tangent point of the ball and ellipsoid, an equation of high degree must be analyzed, but its analytical solution can t be obtained. The iterative solution has high demand on the initial value s accuracy. So URA oe is always not the ideal solution and can t achieve integrity monitoring. Therefore, ellipsoid model is converted to ball model, ensuring they are equal in volume to get a suboptimal URA oe. Comparing URA oe, URA oc with orbit, clock error to test whether it can meet the integrity requirement. At least 0 5 epochs are simulated to verify the integrity risk of 0 5 /h. Taking NO.7 (MEO) as example, the comparison between SIS error and 4.4 times URA is shown in Figs.0. It can be seen that the calculated URA oe and URA oc bound the SIS errors well and satisfy the integrity risk s requirement. Fig. 0. Verification of ephemeris error s integrity monitoring V. Conclusion By the simulation of Beidou s mixed constellation, it concludes that the satellite and ground joint position mode can prevent undesirable diffusion of errors and suppress overall

6 444 Chinese Journal of Electronics 05 drift caused by the relative positioning through selecting appropriate constraint. What s more, because the accurate information mainly provides by ground stations, so HLLs are the reuse and has little effect on improving the positioning results. Fig.. Verification of clock error s integrity monitoring The calculated integrity parameters by spatial error ellipsoid can monitor orbit, clock errors respectively and achieve the global SIS integrity monitoring under the risk of 0 5 /h. References [] R. Xue, J. Zhang and Y.B. Zhu, Cascade dual frequency smoothing for local area augmentation system, Chinese Journal of Aeronautics, Vol., No., pp.49 55, 008. [] T.M. Corrigan, J.F. Hartranft, L.J. Levy, et al., GPSriskassessment study final report, Johns Hopkins University Applied Physics Laboratory, VS , pp. 3, 999. [3] T. Walter and P. Enge, Modernizing WAAS, Proceedings of the 7th International Technical Meeting of the Satellite Division of the Institute of Navigation, Long Beach, California, USA, pp , 004. [4] D.Kaplan Elliott and J.Hegarty Christopher, Understanding GPS: Principles and Applications, Second Edition, KouYanhong translation, Beijing, China, pp.56 58, 00. (in Chinese) [5] Fan Meijun, Zhou Jianhua, Niu Fei and Chang Zhiqiao, Analysis for satellite navigation system basic integrity algorithm and performance,journal of Geomatics Science and Technology, Vol.8, No.6, pp , 0. (in Chinese) [6] Brain Bian, Daniel O Laughlin, Curtis A.Shively and Ronald Braff, Independent control segment URA monitor incorporating crosslink ranging measurements for meeting LPV00 integrity requirement, 4th International Technical Meeting of Satellite Division of The Institute of Navigation, Portland OR, USA, pp.696 7, 0. [7] Zou Decai, Lu Xiaochun, Wu Haitao and Han Tao, Research on Global navigation satellite system (GNSS) Autonomous Navigation Technology Based on Inter Satellite Links (ISL), nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, USA, pp.88 97, 009. [8] J.Dunn Michael, GPS directorate system engineering & integration interface specification, available at gov/technical/icwg/is-gps-00f.pdf, 0-5. [9] Michael J.Dunn, GPS directorate system engineering & integration interface specification, available at gov/technical/icwg/is-gps-00e.pdf, [0] Michael J.Dunn, GPS directorate system engineering & integration interface specification, available at gov/technical/icwg/is-gps-00d.pdf, [] Veit Oehler, et al., The Galileo integrity concept, ION GNSS 7th International Technical Meeting of the Satellite Division, Long Beach, California, USA, pp , 004. [] RTCA/DO-9D: 006, Minimum Aviation System Performance Standards for the Wide Area Augmentation System Airborne Equipment. [3] Todd Walter, Juan Blanch and Per Enge, Vertical protection level equations for dual frequency SBAS, 3rd International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, OR, USA, pp.03 04, 00. [4] Liang Heng, et al., Statistical characterization of GPS signalin-space errors, ION National Technical Meeting, San Diego, CA, USA, pp.3 39, 0. [5] Shao Bo, Liu Jiansheng, Zhao Ruibin, Huang Zhigang and Li Rui, A user differential range error calculating algorithm based on analytic method, Chinese Journal of Aeronautics, Vol.4, No.6, pp , 0. [6] Management office of Chinese satellite navigation system, Beidou navigation system interface control document Public service signal BI (v.0), available at pdf, 03-. WANG Yuechen is a M.S. candidate in the School of electronic and information engineering of BeiHang University, China. His research interests include integrity monitoring of satellite navigation and its augmentation system. ( wangyuechenpavel@6.com) LI Rui received Ph.D. degree in radio navigation from Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China. Now he is a lecturer of Electronic and Information Engineer School in BUAA. His main interests include TIS, INS, GNSS and their integration application. ( leeruin@63.net) ZHAO Ruibin received M.S. Degree in the Inner Mongolia University of Technology, Hohhot, China. Now he is a Ph.D. candidate in Beijing University of Aeronautics and Astronautics, Beijing, China. His research interests include integrity monitoring techniques of satellite based augmentation system. ( zhrbdove@foxmail.com)