SCIENCE CHINA Physics, Mechanics & Astronomy. Analysis of RDSS positioning accuracy based on RNSS wide area differential technique

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1 SCIENCE CHINA Physics, Mechanics & Astronomy Article October 2013 Vol.56 No.10: doi: /s z Analysis of RDSS positioning accuracy based on RNSS wide area differential technique XING Nan 1,2*, SU RanRan 3, ZHOU JianHua 3*, HU XiaoGong 1, GONG XiuQiang 1, LIU Li 3, HE Feng 3, GUO Rui 3, REN Hui 3, HU GuangMing 3 & ZHANG Lei 3 1 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai , China; 2 Graduate University of Chinese Academy of Sciences, Beijing , China; 3 Beijing Satellite Navigation Center, Beijing , China Received May 21, 2013; accepted July 4, 2013; published online August 8, 2013 The BeiDou Navigation Satellite System (BDS) provides Radio Navigation Service System (RNSS) as well as Radio Determination Service System (RDSS). RDSS users can obtain positioning by responding the Master Control Center (MCC) inquiries to signal transmitted via GEO satellite transponder. The positioning result can be calculated with elevation constraint by MCC. The primary error sources affecting the RDSS positioning accuracy are the RDSS signal transceiver delay, atmospheric trans-mission delay and GEO satellite position error. During GEO orbit maneuver, poor orbit forecast accuracy significantly impacts RDSS services. A real-time 3-D orbital correction method based on wide-area differential technique is raised to correct the orbital error. Results from the observation shows that the method can successfully improve positioning precision during orbital maneuver, independent from the RDSS reference station. This improvement can reach 50% in maximum. Accurate calibration of the RDSS signal transceiver delay precision and digital elevation map may have a critical role in high precise RDSS positioning services. BeiDou Navigation Satellite System (BDS), RDSS, RNSS, wide-area differential technique PACS number(s): Eg, s Citation: Xing N, Su R R, Zhou J H, et al. Analysis of RDSS positioning accuracy based on RNSS wide area differential technique. Sci China-Phys Mech Astron, 2013, 56: , doi: /s z 1 Introduction The Chinese regional satellite navigation system, known as the BeiDou Navigation Satellite System (BDS), encompasses proposed a three-step strategy: experimental, regional and global system [1]. Recently with the completion of 5 Geostationary Earth Orbit (GEO), 5 Inclined Geostationary Earth Orbit (IGSO) and 4 Medium Earth Orbit (MEO) mixed Constellation, as the second milestone, has implied that BDS can now provide users both active service *Corresponding author (XING Nan, nanx@shao.ac.cn; ZHOU JianHua, yishu-zhou@263.net) and passive service by Radio Determination Service System (RDSS) and Radio Navigation Service System (RNSS), respectively. Unlike other Global Navigation Service Systems (GNSS), BDS adopts a unique system architectural design, which may possibly take the advantages of combining RDSS and RNSS resources to supply users with a greater variety, higher precision positioning and timing as well as information reporting services. For the RDSS users, Master Control Center (MCC) will firstly send inquiries signal via GEO. If needed, the users can respond those signals and send a positioning request back to MCC via more than 2 GEO, so that a four-course ranging measurement is fulfilled. Based on Science China Press and Springer-Verlag Berlin Heidelberg 2013 phys.scichina.com

2 Table 1 Differences between RDSS and RNSS a) RDSS RNSS 1996 Xing N, et al. Sci China-Phys Mech Astron October (2013) Vol. 56 No. 10 such measurements from multiple, MCC can calculate the position of the user with the high-precision Digital Elevation Model (DEM) database as well as providing it to the required users. Since RDSS service only uses GEO, the ranging error, such as the orbital error and ionospheric delay, cannot be accurately estimated. Before RNSS was adopted, such errors were corrected using Local Area Augment System (LAAS) by differencing data collected at reference stations with high-precision known coordinates. The 3-D positioning error is approximately several tens of meters [2,3]. Ulike RDSS, RNSS operates in traditional passive mode similar with GNSS. Recently BDS already has 14 navigation in service, which extends service coverage over 50 E 160 E. In addition, more than 30 monitoring stations were built in China to provide RNSS data support and implement orbit determination, time synchronization, ionospheric delay modeling and wide-area differential correction information calculating. The primary differences between the RDSS and RNSS are summarized in Table 1. In an optimal condition, namely where all 5 GEOs are available, Horizontal Dilution of Precision (HDOP) of RDSS could be 1.3, which indicates that the RDSS horizontal positioning accuracy is approximately 1.3 times of ranging error, that is, 9 13 m. However, if there is no reference station within the required coverage area of the user, since the ranging systematic errors can not be corrected, the user equivalent range error (UERE) would be of approximately 20 m. Consequently, the positioning accuracy may be seriously degraded to a few tens of meters. Moreover, GEO need to maneuver frequently in order to maintain the longitude of the ascending node. During orbital maneuver phase, even though the availability of the satellite can be maintained by changing the orbit determination methods, the orbit precision will greatly attenuated so that the corresponding user range error can be raised to 50 m. In order to expand the RDSS system service area and improve RDSS continuity, availability and positioning accuracy, herein we propose to apply precise orbit, ionospheric model and the wide area differential information produced by RNSS to correct RDSS systematic error. We first analyze the RDSS measurement error and the accuracy after corrected with RNSS service information, particularly the RNSS wide area differential information. Secondly, we propose an improved approach to decrease the orbital error during orbital maneuver by using 3-D wide area differential corrections. Finally, the RDSS observation is used to estimate the active positioning accuracy based on the RNSS wide area differential information. 2 The RDSS positioning principle and error analysis RDSS broadcasts inquiry signal 32 times per second through GEO (that is, C-band outbound signal). Users receive the strongest S-band signal from one GEO and immediately forward the frame number of the signal back to more than two GEO in the L-band, requesting for positioning. Those GEO will immediately transfer the request of the user to MCC by C-band inbound signal. By synthesizing the return moments and return frame number, MCC can calculate the four-course ranging of the user and the position based on the DEM database, with a resolution of 5 5 and with an accuracy of 10 m. Ultimately, MCC can inform the required users the positioning results through the GEO satellite. The positioning observation equation of the user is as follows: Constellation in service 5 GEOs 5GEOs/5IGSOs/4MEOs Positioning principle Four-course combinations ranging Triple frequency pseudorange and carrier phase in L-band Positioning methods Dilution of Precision (DOP)* Error correction method Horizontal positioning by MCC based on DEM database. No need to estimate the parameters of the user clock error 2 GEOs: ~4 3 GEOs: ~2 4 GEOs: ~1.5 5 GEOs: ~1.3 LAAS based on RDSS reference stations; the sources of errors are not distinguished 3-D positioning and timing by receiver based on navigation messages 4 GEOs/3 IGSOs: ~6 4 GEOs/5 IGSOs/2 MEOs: ~2.5 5 GEOs/5 IGSOs/4 MEOs: ~2 Ionospheric delay: ionospheric model (open service) or ionospheric grid (authorized service); Troposphere delay: BLACK model [4], meteorological parameter is collected from monitoring station; Orbital error: pseudorange differential corrections (authorized service) User equivalent ranging 7 10 m 2 m (open service), m (authorized service) accuracy 3-D positioning accuracy Tens of meters 5 10 m (open service), 2 4 m (authorized service) 50 o E 160 o E, service area covering the northern and southern Availability Limited by RDSS reference station hemispheres a) DOP listed in this table are HDOP for RDSS, which is calculated with elevation constraint, and Position DOP (PDOP) for RNSS.

3 Xing N, et al. Sci China-Phys Mech Astron October (2013) Vol. 56 No S D D D D t c t c t c i Co S L Ci MCC so si t c ( i 1,..., N, 2 N 5), (1) r i H H h (2) 0, ( t ) d d, (3) Co sat 1 MCC 0 Co, ion Co, trop Co, orb ( t ) d d, (4) S usr 2 sat 1 S, ion S, trop S, orb ( t ) d d, (5) L sat 3 usr 2 L, ion L, trop L, orb ( t ) d d. (6) Ci MCC 4 sat 3 Ci, ion Ci, trop Ci, orb Since users can send requests back to MCC via more than 2 GEO, we use eq. (1) to describe the observation equation of the four-course ranging for each satellite. The values of D S, D L, D Co and D Ci represent the ranging in S-band, L-band, outbound C-band and inbound C-band, respectively; t MCC, t so, t Si and t r represent the hardware delay of MCC, satellite outbound, satellite inbound and user receiver respectively; i is the measurement noise and c is the light velocity. Eq. (2) is constraint equation for elevation H, where H 0 is the theoretical value from DEM database and h is elevation error. Eqs. (3) (6) are specific observation equations for D Co, D S, D L and D Ci, including geometric distance, ionospheric delay d Co,ion, d S,ion, d L,ion, d Ci,ion, tropospheric delay d Co,trop, d S,trop, d L,trop, d Ci,trop, and the orbital error Co,orb, S,orb, L,orb, Ci,orb. Specifically, geometric distance is calculated with the position of MCC, satellite or user, that is, r MCC, r sat or r usr ; and t 0 t 4 represent the moments when MCC sends out inquiry signal, satellite sends out inquiry signal, the user sends out request signal, satellite sends out request signal and MCC receives request signal. Overall there are five main components that contribute to the systematic error: ionospheric delay, tropospheric delay, orbital error, hardware delay caused by MCC and satellite as well as measurement noise. The RDSS measurement noise is approximately 4 m (see Figure 1), which cannot be eliminated. In general, the former four errors can be corrected with regional differential method, that is, interpolating user ranging errors with 3 4 strictly calibrated reference stations near users [5]. Table 2 shows the positioning error of 2 users where the distance from the nearest reference station is less than 100 km. Systematic error of users can be well eliminated and the positioning error is approximately 10 m. This method could comprehensively treat all error instead of distinguishing the source of error. However, it severely depends on reference station. In order to elimimate such dependence, we suggest obtaining corrections with the Table 2 Horizontal positioning error of RDSS based on reference station Receiver Average of positioning error Standard deviation of positioning error (m) (m) A B Figure 1 Probability distribution of RDSS measurement noise. 1-h observations from 2 RDSS receivers were collected. Receiver A was located in northwestern China while Receiver B was located in northeastern China. Compared with 4th order polynomial fitting the observation, the residuals can be studied as the RDSS noise. Black, dark blue and light blue lines represent the measurement noise of three visible GEO collected from receiver A. The noise is approximately 3 4 m. Cyan, green, yellow and red lines represent the measurement noise of four visible GEO collected from receiver B. The magnitude is approximately 4 5 m. aid of RNSS service. Ionospheric delay magnitude is approximately 10 m, and it is proportional to Total Electron Content (TEC) and inversely proportional to the square of the signal propagation frequency. With L-band dual-frequency observations, RNSS system firstly models TEC and then broadcasts both Klobuchar parameters and ionospheric grid parameters to public users and authorized users respectively. The accuracy of the former two models is approximately 1 m and 0.5 m for L-band signals [6,7]. As mentioned above, unlike RNSS system measurements, RDSS adopts four-course ranging signals in C, S, and L-band respectively. With higher frequency, two courses ranging in C-band has less ionospheric delay, and so the correction error is rendered negligible. The correction error in S-band and L-band ranging is of similar magnitude to the RNSS system. Thus the total ionospheric delay correction accuracy in RDSS system should be twice that of RNSS, namely 1 2 m. The tropospheric delay magnitude is approximately 1 m, far less than the ionospheric delay. This delay can be calculated by interpolation of tropospheric delay of the RNSS stations near the user, which is estimated with meteorological parameters reported by RNSS stations according to the Black model [4]. The correction accuracy is several tens of centimeters. Orbital error is related to orbit determination methods. During coasting phase, multiple joint dynamic orbit determination method was adopted, which could simultaneously solve orbit elements of all in the constellation together with satellite clocks, RNSS station clocks

4 1998 Xing N, et al. Sci China-Phys Mech Astron October (2013) Vol. 56 No. 10 and other dynamic parameters. This can provide relevant orbit information to both RDSS and RNSS. Assessed with laser ranging, the orbit forecast radial precision is approximately 1 m [8,9]. During GEO maneuver phase, the orbit was determined by kinetic method based on fixing of receiver clocks with time synchronization technology which is only provided to RDSS. The radial orbit forecast precision is better than 20 m. Because of limited domestic stations and satellite geometry, tangential and normal precision is of several hundred meters (see Figure 2). After orbit maneuver was completed 4 72 h (referred as fast recovery phase hereafter), dynamics method was adopted. The advantage of fixing of satellite clock with time synchronization technology was taken to determine and forecast only the maneuvered satellite orbit. The orbit forecast radial precision is approximately 1.5 m [10]. Hardware delays included MCC transceiver delay, satellite transponder delay and response delay of the user. MCC transceiver delay and satellite transponder delay for each satellite and signal beam have been calibrated in the laboratory. The calibration error caused inconsistency among the. User response delay was calibrated as a constant for all the satellite and signal beams. When a receiver was registered, the calibrated value was recorded in the MCC database. Total calibration error of hardware delay is approximately 5 m, and none of the with no delays being corrected by the RNSS systems services information. 3 Application of RNSS wide area differential information to RDSS positioning Satellite-based augmentation system (SBAS) is an important complement to satellite navigation service system. In general, such system will comprise multiple ground stations locating at accurately-surveyed points, so that it can create additional correction messages to improve user positioning precision. On the other hand, SBAS uses GEO to broadcast the complementary differential information to users. With extensive use of GEO in BDS, RNSS degenerate one SBAS, which imitated the algorithm of Wide Area Augment System (WAAS) [11 13]. Atmospheric delay, orbital errors and clock error are the primary source of error in RNSS. The RNSS broadcasts a set of ionospheric grid every 3 min with satellite pseudorange differential corrections every 18 s to authorized users for precise ionospheric delay, orbital error and clock error corrections. These two types of information, known as wide area differential information, can significantly improve RNSS positioning accuracy from 5 m for public users to 2 m for authorized users [14 16]. Pseudo-range differential corrections (referred as pcor hereafter) can be calculated with RNSS pseudo-range whose observation equation is as follows: k k Pi j tj c t c dion dtrop k k ji, i c e j orb clk i, (7), (8) e k j orb R Rorb T Torb N Norb Figure 2 (Color online) Orbit forecast precision with kinetic method. From top to bottom, the radial, tangential and normal orbital error in sequence is given. For every minute, the current orbit is determined and the orbit for the following minute is forecast. where P i is denoted to pseudorange of the i th frequency, k j is the geometric distance between the k th satellite and the j th receiver, t j and t k are the receiver and satellite clock error, d ion is ionosphere delay, d trop is troposphere delay, and j,i and k i are hardware delay for the i th frequency of the receiver and the satellite. orb is orbital error, and e k j orb is the projection in line of sight. It can also be decomposed into radial, tangential and normal components in the orbital coordinate system (eq. (8)). The value of clk is clock error and i is other errors including multipath error, measurement noise, etc. The angle between orbital radial direction and line-of-sight direction of the user within BDS regional service area is less than 10. Thus for GEO and IGSO, R >0.989; for MEO, R > The values of T and N are far smaller so that when orbital total error is in the magnitude of sub-meter, the distinction of projection in different line-of-sight direction of the user is in the range of several millimeters. Therefore, pcos ( = Rorb + clk ) for a certain satellite can be computed by averaging the UERE of all stations. After corrected by pcor, UERE of RNSS is approximately 0.5 m, which is 50% more accurate compared to 1 2 m before being corrected.

5 Xing N, et al. Sci China-Phys Mech Astron October (2013) Vol. 56 No The value of pcor is applicable to coasting phase and fast recovery phase when orbital error is not so large. However, during orbital maneuver phase, orbital error will be increased to 10 m or even 100 m. As shown in Figure 2, compared with precise orbit, orbital forecast radial error with kinetic method is up to 30 m. The tangential as well as normal error could be several hundreds of meters. Consequently, distinction of UERE for different users caused by orbital error cannot be ignored, thus simply using pcor is not sufficient for this situation. Since the geometric method does not take into account any orbit kinetic factors, orbit precision only depends on stations distribution. To remedy this error, we suggest that 3-D orbital corrections (referred as 3doc hereafter) should be effectively be [,, ]. (9) Rorb clk Torb Norb We find both pcor and 3doc can lower UERE. Before orbital maneuver starts, UERE can be corrected by two methods which are in the similar level. However, when kinetic method was used after orbital maneuver starting, 3doc are more effective and significant to improve UERE than the other method (see Figure 3). Note that pcor cannot be applied directly to correcting RDSS four-course ranging. Since the satellite clock error is much smaller than orbital error, the value of pcor can be seen as radial orbital correction. As a vector, 3doc can directly correct orbit being used by RDSS. Figure 3 RNSS user equivalent range error corrected with different method. Black stars indicate UERE without any differential correction. Green crosses indicate UERE corrected by pcor and the red dots indicate UERE after 3doc. Dynamic orbit determination method is used before orbital maneuver time, while kinetic method is adopted thereafter. 4 RDSS positioning results with observational data 4.1 Coasting phase and fast recovery phase During coasting phase and fast recovery phase, since dynamic method produces high precision of orbit, pcor is suficiently to correct the user range error. Here observations of RDSS receivers located at northern China are used to test different correction methods. Using coasting phase data on July 30, 2012, we calculated the user position with and without pcor. As shown in Figure 4, pcor only slightly improved the positioning accuracy, which is already better than 15 m even without applying pcor. On the other hand, we find error in east-west direction is greater than in north-south regardless of pcor. This phenomenon is related to the constellation geometry so that it can be demonstrated by EDOP and NDOP list in Table 3. Special constellation of BDS gives a strong correlation between north-south component error and elevation component error [15]. With increasing visible number, the strict elevation constraint will narrow the error space in north-south direction so that NDOP and corresponding error will significantly decrease. During fast recovery phase, pcor has a similar effect as in Figure 4 Positioning accuracy with and without pcor during coasting phase. Black hexagons represent positioning results without pcor, whose RMS is 3.9 m and green squares represent the results with pcor, whose RMS is 3.4 m. Table 3 DOP of the receiver used in the test with different visible satellite number 2 GEOs 3 GEOs 4 GEOs EDOP NDOP coasting phase. After orbital maneuver 4 12 h on July 18, 2012, observations of two receivers were gathered. The positioning results are list in Table 4. The value of pcor improved the positioning accuracy by approximately 0.4 m. 4.2 Orbital maneuver phase The pcor and 3doc are both applied to orbital maneuver

6 2000 Xing N, et al. Sci China-Phys Mech Astron October (2013) Vol. 56 No. 10 phase data. We gathered data on July 12, 18 and 25, 2012, when GEO 3, 1 and 4 was maneuvered, respectively. From Table 5, we can find that pcor can lower orbits error brought by kinetic method somewhat, but 3doc results in significantly more accuracy. Specifically the result of July 18, 2012 (in Figure 5) shows that the improvement of the positioning accuracy with pcor could be up to 11%, while 3doc is close to 50%. Table 4 Comparison of different methods of positioning errors during fast recovery With or without Receiver A Receiver B differential corrections 4 visible 3 visible 4 visible 3 visible Without With Table 5 Positioning accuracy of 3 data sets corrected with different methods CASE Without any correction With pcor With 3doc 7.12 (4 visible ) (4 visible ) (2 visible ) Figure 5 Results of positioning accuracy of July 18, 2012, when GEO 1 was maneuvered. The black dots represent results without any correction while the green dots represent results with pcor. The pink dots represent results with 3doc. As mentioned above, kinetic method introduces tangential and normal orbital error with a magnitude of several hundred meters. Therefore, the distinction of UERE for different users within China is approximately several meters. With ability to correct tangential and normal orbital error, 3doc are more suitable during orbit maneuver phase than pcor. For RNSS, the pseudo-range noise is merely 0.3 m. The primary sources of error affecting positioning accuracy are orbital error and other errors of the correction models. Both pcor and 3doc bring about significant improvement. However, the RDSS system measurement noise is approximately 4 m, which is the primary reason of the dispersion with several meters as seen in every positioning result in this section. This sort of error can only be suppressed by means of filtering, which is difficult to put in real-time discontinuous use in MCC. Thus for RDSS, both improvements from pcor and 3doc are relatively small comparing with RNSS. After using 3doc, radial and tangential orbital errors can reach the magnitude of decimeters or meters. However, orbital normal error is restricted to tens of meters. Because of the lack of stations in the southern hemisphere, observations were unable to constrain the orbital normal error of GEO, which is in the northerly direction. 4.3 Other error sources of RDSS positioning accuracy Excluding orbital error, the elevation error and hardware delay calibration error can also affect the RDSS positioning accuracy. Analysis of the above data was based on accurate elevation and strictly calibrated hardware delay. In the following, we discuss the influence on RDSS positioning accuracy raised by these two errors. As a consequence of involving GEO in the constellation, there is strong correlation between north-south component and elevation component of error. We list positioning errors of a receiver located in Northern China with three situations of different elevation errors as recorded in Table 6. Note that two factors are relevant for determining elevation error, namely DEM database accuracy and the interpolation method accuracy. Currently the DEM database accuracy is approximately 10 m and the normal space resolution is given as 5 5. Such resolution would lead the interpolation error of the elevation to be around several decimeters. Consequently, the final elevation error should be in the order of 10 m, which is the maximum value adopted in our samples. As expected, elevation error is proportional to the north-south component error and has slight impact on the east-west component. The entire 9 data sets we used herein were are collected from 3 RDSS receivers in 5 d. Hardware delay could be calculated on the basis of these data (see Figure 6), which primarily contains the user receiver delay and the satellite transponder delay. In order to calculate how these hardware delay influence positioning, we have recalculated all the results in sects. 4.1 and 4.2 without calibrating them. We find that the user receiver delay calibration error affects the user timing accuracy and positioning accuracy in the north-south direction, while the satellite transponder delay calibration error influences the east-west component of positioning accuracy. Positioning errors caused by the delay Table 6 RDSS positioning errors caused by different elevation errors Elevation error (m) East-west component error (m) North-south component error (m)

7 Xing N, et al. Sci China-Phys Mech Astron October (2013) Vol. 56 No both of them influence positioning accuracy in some extent: elevation error is proportional to north-south component error, while the user receiver part of hardware delay calibration error primarily affects timing and positioning accuracy in north-south direction. The satellite transponder impacts positioning accuracy in the east-west direction. These results show the improvement of the accuracy of calibration for RDSS signal transceivers and digital elevation maps which may have a critical role in high precise RDSS positioning services. Figure 6 Hardware delay calibration error of 9 data sets, which are collected from 3 RDSS receivers in 5 d. Every buddle of histogram represents a set of data, named after collected date and receiver serials. As shown, calibration errors of receivers A, B and C were approximately 10, 20 and 12 m, respectively. The error of GEO4 is smaller while GEO5 is larger than others. calibration error r can be estimated with the product of geometric factor HDOP and the delay error (see eq. (10)). Thus hardware delay needs to be updated regularly in order to improve accuracy. 5 Discussion and conclusions r HDOP. (10) We firstly demonstrated the RDSS Positioning Principle and investigated how each error sources can affect the positioning accuracy in detail. We then proposed a new method to enhance RDSS Positioning accuracy based on RNSS wide area differential information. Finally, we use 9 data sets covering coasting phase, fast recovery phase and orbital maneuver phase to test the improvement in positioning accuracy brought by such method. The results show that during coasting phase and fast recovery phase, the value of pcor can markedly improve positioning accuracy. Taking the results of July 30, 2012 (coasting phase) and July 18, 2012 (fast recovery phase) as examples, the improvement of positioning accuracy is approximately 0.5 and 0.4 m (RMS), respectively. During orbital maneuver phase, kinetic orbit determination method is adopted, which causes larger tangential and normal orbital error. In order to correct these errors, 3doc were designed. Through analysis of 3 data sets covering orbital maneuver phase, we find that pcor could improve positioning accuracy by 11%, which is much lower than the improvement given by 3doc, that is, 50%. We note here that 3doc could effectively correct the radial and tangential orbital errors, however, it can hardly correct the normal error because of the lack of stations in the southern hemisphere. Finally we analyzed another two errors types that cannot be corrected with wide area differential information, namely altitude error and hardware delay calibration. 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