Modeling regional ionospheric delay with ground-based BeiDou and GPS observations in China

Transcription

1 GPS Solut (2015) 19: DOI /s z ORIGINAL ARTICLE Modeling regional ionospheric delay with ground-based BeiDou and GPS observations in China Rui Zhang Wei-wei Song Yi-bin Yao Chuang Shi Yi-dong Lou Wen-ting Yi Received: 5 September 2013 / Accepted: 15 October 2014 / Published online: 19 November 2014 Springer-Verlag Berlin Heidelberg 2014 Abstract The Compass/BeiDou system is currently being built as a navigation constellation consisting of 16 navigation satellites. Construction of these satellites will significantly increase the number of visible satellites over the Chinese mainland and improve the geometry of satellite positioning. We obtained data by simulation and measurements to analyze the influence of BeiDou regarding the longest observation arc and the ionosphere piercing point distribution. A regional ionosphere delay model is built using data measured by BeiDou only, global positioning system (GPS) only, and the dual-satellite system. The results show that the model accuracy for BeiDou only is as accurate as the single GPS system in the middle and lower latitudes, while a deviation becomes noticeable at high latitudes and over marginal areas where observations are fewer due to lack of BeiDou satellites. With the current distribution of the satellites and tracking stations, it appears that the dual-satellite system could significantly improve the ionospheric model in China and the accuracy of differential code bias (DCB) determination. The experimental results also show that the BeiDou satellite DCB is quite stable, with a monthly maximum change of 1.8 ns. R. Zhang College of Informatics, South China Agricultural University, Guangzhou , China R. Zhang Y. Yao School of Geodesy and Geomatics, Wuhan University, Wuhan , China W. Song (&) C. Shi Y. Lou W. Yi Research Center of GNSS, Wuhan University, Wuhan , China SWW@whu.edu.cn Keywords BeiDou satellite navigation system GPS Regional ionospheric model DCB Introduction Ionospheric total electron content (TEC) and other ionospheric phenomena are not only important information in studies of the ionosphere, but also provide important ionospheric correction parameters for navigation and precise positioning. To investigate the physical characteristics of ionospheric structures and apply such attributes in the positioning process, there are different approaches for ionosphere modeling. Some models use physical aspects, e.g., the Global Assimilative Ionospheric Model (GAIM) (Schunk et al. 2004); others are empirical models, e.g., the International Reference Ionosphere (IRI) (Bilitza and Reinisch 2008), Klobuchar model broadcast by GPS satellites (Klobuchar 1987), or the NeQuick (Hochegger et al. 2000). It is effective to monitor ionospheric changes by extracting the ionospheric delay and building an ionospheric model from dual-frequency global navigation satellite system (GNSS) observations. After Lanyi and Roth (1988) used a third-order polynomial model to model regional ionospheric delay with GPS data, various studies and applications in this area were carried out (Enge et al. 1996; Mannucci et al. 1998; Schaer 1999; Hernández-Pajares et al. 1999). The International GNSS Service (IGS) has been contributing to reliable IGS combined vertical total electron content (VTEC) maps in both rapid and final schedules since 1998 (Hernández-Pajares et al. 2009). Several efforts have been made to use GPS observations to establish a Chinese regional ionospheric model (Yuan and Ou 2002; Zhang 2006). In order to improve the autonomy and security of satellite navigation and positioning, China is launching the

2 650 GPS Solut (2015) 19: BeiDou system. Because of the compatibility and interoperability between the BeiDou system and other systems, users can use multi-system observational data simultaneously to greatly improve data availability, accuracy, integrity, and reliability (Yang et al. 2011). The latest BeiDou satellite was launched into its preset orbit on October 25, It is a geostationary satellite (GEO) that operates in conjunction with the fifteen BeiDou navigation satellites already in orbit. Although the complete constellation of the BeiDou system has not been deployed, it already has the capabilities of providing positioning, navigation, and timing services for the entire Asia Pacific region (BeiDou 2012). The initial deployment of the Bei- Dou system will increase the number of available satellites in China significantly, improve the geometry of satellite observations, and play an important role in regional ionospheric delay modeling. Simulations and measured data are used to analyze the influence of BeiDou on the length of arc and the IPP distribution. Then, the regional ionosphere delay model is built using observation of the BeiDou system, GPS, and the dual-satellite system. The IGS analysis center for Orbit Determination in Europe (CODE) provides daily global ionosphere map (GIM) model (CODE 2012), which corresponds to the middle day of a 3-day combination analysis (Alizadeh et al. 2011) using both GPS and GLONASS observations (Hernández-Pajares et al. 2009). According to information about the accuracy of IGS products ( the GIM errors are within the range of ±2 to ±8 TECU. We analyze the accuracy and stability of the regional model and the DCB estimates for the three different modes by comparing with the CODE product and processing standard single-point positioning (SPP). Algorithm of modeling a regional ionospheric area with BeiDou and GPS observations The anisotropic ionospheric plasma effects in phase and code delays at high frequencies can be represented as a rapidly decreasing series in inverse powers of frequency (Bassiri and Hajj 1993; Kim and Tinin 2011). Using different frequency observations from the same satellites, we are able to obtain the relevant ionospheric delay measurement: P i k;4 ¼ Pi k;1 Pi k;2 ¼ A f1 2 A f2 2 b i 1 bk 1 b i 2 b k 2 ð1þ where i and k represent satellite and station, P and L represent the code and phase measurements, f is the carrier frequency, subscripts 1 and 2 denote L1 and L2 frequencies, A represents the ionospheric delay, b r and b s are the receiver and transmitter inter-frequency DCBs, and N represents carrier phase ambiguity in cycles (including the integer ambiguity and float-phase instrumental delay). The ionospheric TEC can be calculated directly using pseudorange or phase observations. However, the pseudorange observations are significantly influenced by measurement noise, and the phase observation method will introduce ambiguous parameters, which cause high computational complexity. So TEC is usually calculated using the phase-smoothing pseudorange algorithm (Hatch 1982; Lachapelle et al. 1986), whose formula is as follows: A ¼ P^i k;4 þðb i 1 bk 2 Þ ðbi 1 bk 2 Þ 1 where P^i k;4 f f 2 2 ð3þ represents the phase-smoothed pseudorange observations. This approach is simple and widely used, but sensitive to the length of the continuous satellite arc and receiver-related model errors, e.g., multi-path effects and observational noise. To balance of precision and efficiency, different approaches have been proposed to extract ionospheric delay from the dual-frequency pseudorange and phase observations. Zhang et al. (2012) used precise point positioning (PPP) to extract ionospheric delay. Hernández-Pajares et al. (2011) adopted the decomposition combination of observations method, which can cause less computation and maintain a high accuracy at the same time. We chose this method, and the realization steps are as follows: In our method, there are three combinations of carrier phase observations involved, including the ionospheric combination, ionosphere-free combination, and wide-lane combinations. The ionospheric combination and its ambiguity are (all units are m): L I ¼ L 1 L 2 N I ¼ N 1 N 2 ¼ k 1k 2 k m k n ðn w N c Þ ð4þ where k w is the wide-lane wavelength, and k n is the narrow-lane wavelength. The ionosphere-free combination and its ambiguity are as follows: L c ¼ f 2 1 L 1 f 2 2 L 2 f 2 1 f 2 2 N c ¼ f 2 1 N 1 f 2 2 N 2 f 2 1 f 2 2 ð5þ L i k;4 ¼ Li k;1 Li k;2 ¼ A f 2 2 A f 2 1 ðn 2 N 1 Þ ð2þ and the wide-lane combination and its ambiguity are as follows:

3 GPS Solut (2015) 19: L w ¼ f 1L 1 f 2 L 2 f 1 f 2 N w ¼ f 1N 1 f 2 N 2 f 1 f 2 ð6þ At a single station, the known coordinates of the tracking station are fixed; the satellites errors are corrected by using precise ephemeris and clock products. So we can only estimate the receiver clock and tropospheric delay through PPP and obtain N c for each satellite easily. At the same time, by averaging several epochs, we can obtain the M w functions: M w ¼ L w P n ð7þ where P n represents the narrow-lane pseudorange observation P n ¼ f 1 P 1 þf 2 P 2 f 1 þf 2. Since N w ¼ M w k wk n k 1 k 2 ððb s 1 br 2 Þ ðbs 1 br 2ÞÞ, the ionospheric combination can also be stated as: N I ¼ k 1k 2 k w k n ðm w N c Þ ððb s 1 br 2 Þ ðbs 1 br 2 ÞÞ L I k 1k 2 k w k n ðm w N c Þ¼aA ððb s 1 br 2 Þ ðbs 1 br 2 ÞÞ ð8þ ð9þ where a represents the proportion of ionospheric delay in L 1 and L 2. According to (9), once M w, N c, and L I are correctly estimated, the STEC can be obtained with a high accuracy together with the satellite and receiver DCB parameters. In order to simplify the description of ionospheric distribution, it is often assumed that the ionospheric delay is concentrated at an infinitely thin layer at a certain height above the earth, so that total electron content can be seen as a physical quantity with location and time distribution characteristics. An ionospheric model can then be described as a function with location and time as its independent variables. There are several fitting functions available, such as polynomials and triangular interpolation (Wild 1994; Mannucci and Wilson 1993). Among these, the spherical harmonic function model can use a limited number of parameters to represent the global TEC well (Schaer 1999). The slant ionospheric delay information obtained from GNSS observations is modeled as: STECðb; sþ ¼ Xnmax X n n¼0 m¼0 ~P nm ðsin bþða nm cos ms þ b nm sin msþ=m þ b s þ b r ð10þ where b and s represent the geomagnetic latitude and sunfixed longitude of the user IPP, ~P nm is the regular Legendre series, a nm and b nm are coefficients to be estimated, n max is the maximum degree of the spherical harmonic expansion, and M represents the mapping function. The number of parameters to be estimated is (n max? 1) 2. The low-order spherical harmonic function model is also well suited for a regional area (Schaer et al. 1996; Weimer 2001; Venkataratnam and Sarma 2012). During parameters estimation, there must be enough redundant observations relative to the number of parameters. So the selection of the order mainly depends on the size and location of the fitting area. We chose a spherical harmonic function of order four for all modeling experiments (Liu et al. 2008). In (10), the station and the satellite DCB parameters are strongly correlated and cannot be isolated directly. So we add constraints for both GPS and BeiDou satellites to force the sum of all satellite DCBs equal to zero, as done by IGS, since such constraints do not affect the relative DCB values for each satellite system, X n GPS n¼0 X n BD n¼0 b s G ¼ 0 b s B ¼ 0 ð11þ In the ionosphere modeling process, there are many DCB parameters, and the design matrix is a sparse matrix. We explore respective patterns to achieve calculation efficiency. Experimental analyses We analyzed the impact of the BeiDou satellite system on the ionosphere modeling with data from simulations and dual-mode measured data and built the ionospheric delay model for the region of China. First, the sources of the experimental data and the status of the BeiDou satellite system are introduced. Data sources and the status of the BeiDou satellite system Wuhan University began establishing BeiDou Experimental Tracking Stations (BETS) in the Asia Pacific region in early 2011, which are equipped with BeiDou/GPS dualmode receivers UR240-CORS (Shi et al. 2012). This study uses observation taken from April 2 to June 27, 2012 (DoY , a total of 87 days). At the end of June 2012, a total of 13 BeiDou navigation satellites had been launched that include five GEO, five inclined geosynchronous orbit (IGSO) satellites, and three medium orbit (MEO) satellites (Table 1). Among these satellites, the clock of satellite M1 experiences

4 652 GPS Solut (2015) 19: Table 1 BeiDou navigation system state (June 30, 2012) PRN Type Longitude Working conditions PRN Type Longitude Working conditions C01 GEO 140 E Normal C02 GEO 23 Abnormal 124 E C03 GEO 84 E Normal C04 GEO 160 E Normal C05 GEO E Normal C06 IGSO 122 E Normal C07 IGSO 119 E Normal C08 IGSO 120 E Normal C09 IGSO 96.5 E Normal C10 IGSO 92.5 E Normal C11 MEO Normal C12 MEO Normal M1(C30) MEO Abnormal satellite clock abnormalities, satellite C2 cannot transmit signals (Hauschild et al. 2012) and also vibrates uncontrollably near its nominal orbit around 75 E (Flohrer et al. 2012). All other BeiDou satellites operate normal and can be positioned independently and combined with GPS or GLONASS. Shi et al. (2013) and Montenbruck et al. (2013) performed research on PPP with BeiDou satellites. Their research indicates that the current BeiDou system relative positioning accuracy is able to achieve millimeter-level and that static PPP can achieve centimeter-level accuracy. The distribution of satellites and tracking stations used in our experiment is shown in Fig. 1. Impact analysis of the BeiDou satellite system on ionospheric modeling The BeiDou satellite system contains multiple GEO and IGSO satellites, which is different from existing GPS. Next, the observation arc length and the IPP distribution were analyzed. Longest observation arc The observations of June 18, 2012 from station CENT were used to statistically analyze the longest observation arc of the BeiDou and GPS system in 1 day. Figure 2 shows the results of PRN1 PRN12 satellites for each system (the observations end due to cycle slips occurring or losing track of satellite signals). The data of the PRN2 BeiDou are ignored due to its abnormal clock. As can be seen from the figure, the GPS satellite observation arcs last approximately 6 h, and the longest arc can reach 8 h; the observation arcs of the BeiDou GEO and IGSO satellites are obviously longer than the GPS or BeiDou MEO satellites. Benefitting from stable GEO satellites, the observations can essentially be continuously carried out throughout the entire day; the observation time of IGSO is slightly shorter Fig. 1 Map of satellite tracking stations (Montenbruck et al. 2013)

5 GPS Solut (2015) 19: than that of the GEO satellites, and some satellites exhibit a segmented observation arc in 1 day, which may be due to weak signal strength resulting in loss of tracking at low elevation angles. Distribution of IPP The number and distribution of the IPP are the major factors that affect modeling accuracy. In general, the fitting accuracy is better in high IPP density areas and lower in the sparse areas. In the following section, the measured and simulated data of BeiDou/GPS dual-mode, including all satellites (5 GEO, 5 IGSO, and 27 MEO), were used to analyze the IPP distribution. The ionospheric model coefficients are often estimated with a specific period of data. Therefore, the IPP distribution during 2 h is given below. The tracking stations were chosen as seen in Fig. 1. In Figs. 3 and 4, the blue dots represent GPS IPP and red dots represent BeiDou IPP. Because the tracking stations were mainly located in the eastern region of China, the IPPs are also concentrated in this region. The figures show that for a fully capable BeiDou system, there are more IPPs than in case of GPS, especially in the mid-latitude areas. The GEO satellites can provide continuous observations, but the IPP distribution does almost not change. Figure 4 shows that due to the current number of BeiDou MEO satellites, the measured number of IPP is less than that of GPS, and the distribution is much poorer, especially for the high latitude and peripheral areas. The analysis shows that compared to single GPS or single BeiDou system, the dual system combination increased the number of observations and improved the IPP distribution effectively. Meanwhile, the synchronous satellites can provide longer continuous observation to increase the extraction accuracy and thus further improve the ionospheric modeling accuracy. Ionospheric delay modeling and accuracy analysis Three different experimental strategies were taken for regional ionospheric modeling: (1) only BeiDou observations (SMB), (2) only GPS observations (SMG), and (3) BeiDou/GPS dual-mode observations (DM). A set of ionospheric model coefficients was estimated every 2 h, and the standard IONEX files were produced with the a grid range in latitude N and longitude E. The DCB parameters for both satellites and receivers were considered constant and estimated every day. The satellite orbit and clock errors were corrected by BEIDOU Obs Time(H) GPS Obs Time(H) Total Longest Arcs Satellite PRN Fig. 2 Length of observation span for BeiDou and GPS satellites at station CENT, Wuhan, with coordinates XYZ (-2,267, , 5,009, , 3,220, ) Fig. 3 IPP distributions of simulated data. The data interval is set to 300 s Fig. 4 IPP distributions of measured data of DoY 175, The data interval is set to 300 s

6 654 GPS Solut (2015) 19: the BeiDou precise orbit clock correction provided by Wuhan University and the GPS precise product provided by IGS. Because there were no P1 observations in the measured data, we used the P1C1 DCB products from CODE to correct the GPS observations and used the BeiDou C1 and P2 observations for ionospheric delay extraction, and ultimately, we could obtain the GPS satellite P1P2 DCB and BeiDou satellite C1P2 DCB. During the experiment, the solar activity was stable; the monthly average of solar 10.7 cm flux was about There were rarely any big geomagnetic changes or ionospheric anomalies in these days. Analysis of ionospheric model accuracy by comparing with CODE Figure 5 shows the model differences between SMB, SMG, DM, and CODE on June 23, 2012 (DoY 175) at local time 14:00 (UTC time 6:00, when the ionospheric density may be close to the daily peak). Since the tracking stations distribution was uneven, the model accuracy in the western region was lower than that of the eastern region, and there were obvious edge effects in the high- and low-latitude areas. IPP analysis showed that the BeiDou system had fewer IPPs at higher latitudes, and SMB deviation from CODE was significantly greater than that of SMG and DM in this area. The SMB deviation could be about -6 to-10 TECU, while it was about -5 to -8 TECU for the other two models. In the mid-latitude region, the SMB model fitting accuracy was good and the deviation was about -3 to-4 TECU; the correction accuracy relative to the total amount of electronic was about %. In the lower-latitude peak regions, the deviation was in the range of -5 to-8 TECU with the correction accuracy being %. Due to the larger number and well-distributed GPS observations in this area, the SMG model was superior to the SMB model, and its difference from CODE was about -2 to-4 TECU in mid-latitude areas, the correction accuracy was 8 14 %, and approximately -3to-6 TECU in lower-latitude areas, and the correction accuracy was 8 16 %. The difference of the DM model was roughly equal to the SMG model; in the mid-latitude regions, it was larger than SMG (by about 1 TECU); but for the low latitudes, DM model edge effects decreased significantly. To further illustrate the accuracy of the ionospheric model under the three strategies, full-time ionospheric grid products and CODE differences from DoY 093 to DoY 179 were statistically analyzed. Figures 6 and 7 show the average and the standard deviation (STD) differences of SMB, SMG, and DM from CODE products. Similar to the analysis of 1-day variation, due to the tracking station distribution, the difference of the western region was greater than in the eastern region, and edge effects were seen in high and low latitude. The SMB model had larger deviations; in the mid-latitudes, its deviation was approximately -4 to-6 TECU, and at low latitudes, it could reach -8 TECU. The SMB STD was generally 3 5 TECU. The correction accuracy was about %. The SMG bias was significantly less than that of SMB, normally in the -2 to-4 TECU range and reached -6 TECU in low-latitude areas when the ionosphere was active; the SMG STD was generally 2 4 TECU in these areas. The correction accuracy was about 8 15 %. Average deviation of all grids for the DM model was -2.9 TECU and was slightly less than for the SMG model. At low latitudes, the DM system deviation and STD statistics were significantly less than the SMG model, but at high latitudes, the DM STD statistics were slightly greater than the SMG model. Ionospheric model accuracy analysis by SPP As mentioned above, the accuracy of the CODE product is about several TECU and mainly depends on the GPS observations. The position accuracy of single-frequency SPP is susceptible to ionospheric error, which allows SPP to be used as a means of assessing the accuracy of ionospheric models (Øvstedal 2002; Le and Tiberius 2007). Next, we selected three rover stations with different latitudes to process SPP. The selected stations are as in Table 2. For all three stations, SPP was processed with four Fig. 5 Difference between estimated models and CODE products at 6:00 of DoY 175, From left to right: SMB, SMG, and DM

7 GPS Solut (2015) 19: Fig. 6 Average differences from CODE products from DoY 093 to DoY 179. From left to right: SMB, SMG, and DM Fig. 7 STD from CODE products from DoY 093 to DoY 179. From left to right: SMB, SMG, and DM Table 2 Rover stations coordinate information Name Longitude ( ) Latitude ( ) Height (m) HRBN WUHN KMIN , different kinds of ionospheric products, including CODE, SMB, SMG, and DM. During the experiment, only GPS observations were available and used for all rover stations, and IGS final orbit and clock products were used to correct the satellite orbit and clock error. Figure 8 shows the average RMS of three rover stations from DoY 093 to DoY 179, and for north, east, up, and 3D. The figure shows that DM positioning results were slightly better than those of SMG; the average 3D improvement was 5.83 %. Both DM and SMG performed better than CODE, especially in middle and low latitude; the 3D improvement is up to approximately 30 %. The SMB positioning results were worse for the high-latitude HRBN station, but slightly better than SMG for the middle and low-latitude stations. Based on the above discussion, it can be seen due to the current low number of BeiDou MEO satellites, satellite distribution conditions were poor in certain areas. The ionospheric modeling precision of single BeiDou system was low for the high- and low-latitude areas and was of the same accuracy as single GPS system in mid-latitude RMS(m) RMS(m) RMS(m) HRBN CODE SMB SMG DM N E U 3D WUHN N E U 3D KMIN N E U 3D Direction Fig. 8 Average RMS of three rovers from DoY 093 to DoY 179 regions. Under the current situation where few tracking stations can be used and observation distribution is uneven, using the dual-mode system could help to improve model accuracy and reduce the edge effects in China. DCB accuracy analysis of satellite systems As a by-product of the ionospheric modeling, we can obtain new satellite and receiver DCB estimates per day. Their accuracy and stability reflect the ionospheric model

8 656 GPS Solut (2015) 19: Fig. 9 RMS statistics of GPS only and DM GPS satellite DCB compared with CODE products during DoY BeiDou&GPS 0.44ns GPS only 0.5ns RMS(ns) Satellite PRN accuracy to some extent. Figure 9 shows the RMS of the difference between estimated GPS satellite DCB and CODE products during DoY Since PRN24 GPS malfunctioned during this period, there were no results for it shown. The figure shows that the RMS of most satellites estimated by DM model was obviously lower than that of SMG model, where the average RMS decreased from 0.5 to 0.44 ns. Currently, there is no agency providing BeiDou satellite DCB values, so we can only assess the inner precision of the BeiDou satellite DCB. During the estimation process, we set the benchmark constraint that the sum of satellite DCB is 0 as defined in (11), but two of the MEO satellites were launched in April 30, leading to different constraint benchmarks for April, May, and June. The estimated DCB results contain systematic bias difference, so we calculate the STD of all satellites within the 3 months and average their STD values. Figure 10 shows that the STD of GEO and IGSO satellites were significantly smaller than that of the MEO satellites for both of the modeling strategies due to the longer observation period and greater number of observations. The STD was approximately ns, while the MEO STD was in the range of ns. The STD for PRN4 and PRN5 satellites was significantly larger than that of other IGSO satellites. This is probably because the two satellites operated at longitudes 160 E and E, respectively. They were located at the eastern-most and western-most points in China, with observation elevation angles that may be too low. The accuracy of SMB and DM models was nearly identical for good distribution of GEO and IGSO satellites. The use of dual-mode data can significantly improve the accuracy of MEO and edge region GEO satellites. The average STD for all satellites decreased from 0.66 to 0.61 ns. For both the GPS and BeiDou systems, the accuracy improvement of satellite DCBs was about 10 %. Because of the different benchmark constraints for 3 months, we set PRN1 satellite as the reference satellite. Figure 11 shows monthly DCB values (daily averaged STD(ns) results) of BeiDou satellites PRN3 PRN12 in the 3 months estimated with DM model. As can be seen from the figure, the differences of DCB between different satellites were large, and the biggest difference was approximately 20 ns; the DCBs of individual satellites remained relatively stable, and their monthly variation was generally \0.5 ns. Although the DCB of certain GEO and MEO satellites exhibited larger changes, their maximum variation was no more than 1.8 ns. The monthly variation may be caused by satellite hardware changes or the accuracy of estimation method; a longer period of observations will be necessary for further analysis. Conclusion E160 BEIDOU&GPS 0.61ns GEO E58.75 BEIDOU only 0.66ns IGSO MEO Satellite PRN Fig. 10 STD statistics results of BeiDou only and DM BeiDou satellite DCB during DoY We used the BETS BeiDou/GPS dual-model measured data to analyze regional ionospheric model of China based on three different strategies. Experimental results showed that ionosphere modeling accuracy using the single-mode Bei- Dou system was high in the low- and middle-latitude regions. Because the BeiDou satellites had not yet been fully deployed, there are large edge effects at high latitudes. Under the current conditions of few tracking stations and uneven observations distribution, the modeling accuracy of dual-mode satellite system is significantly higher,

9 GPS Solut (2015) 19: Differences(ns) -9 GEO IGSO MEO and the DCB accuracy can also be improved. With the continuous improvement of the BeiDou satellite system, the regional ionospheric model and satellite DCB accuracy can be further improved, which can be beneficial for monitoring ionospheric changes in China and implementing single-frequency positioning. Acknowledgements Thanks for the GPS satellite products offered by IGS, ionospheric and DCB products offered by CODE. This study was supported by the National Natural Science Foundation of China ( and ), the National High Technology Research and Development Program of China (2013AA122502). References Apr. May. Jun Satellite PRN Fig. 11 Monthly variation of BeiDou satellite DCB for April, May, and June, 2012 Alizadeh MM, Schuh H, Todorova S, Schmidt M (2011) Global ionosphere maps of VTEC from GNSS, satellite altimetry, and formosat-3/cosmic data. J Geod 85(12): Bassiri S, Hajj GA (1993) Higher-order ionospheric effects on the global positioning system observables and means of modeling them. Manuscripta Geodaetica 18(6): BeiDou (2012) BeiDou satellite navigation system network. Bilitza D, Reinisch BW (2008) International reference ionosphere 2007: improvements and new parameters. Adv Space Res 42(4): CODE (2012) Center for Orbit Determination in Europe. Astronomy Institute, University of Berne. Enge P, Walter T, Pullen S, Kee C, Chao YC, Tsai YJ (1996) Wide area augmentation of the global positioning system. Proc IEEE 84(8): Flohrer T, Choc R, Bastida B (2012) Classification of geosynchronous objects. GEN-DBLOG OPS-GR, issue 14, Feb., European Space Agency, ESA/ESOC, Darmstadt Hatch R (1982) The synergism of GPS code and carrier measurements. Proceeding third international symposium on satellite Doppler positioning, New Mexico State University, Feb 8 12, 2: Hauschild A, Montenbruck O, Sleewaegen JM, Huisman L, Teunissen P (2012) Characterization of compass M-1 signals. GPS Solut 16(1): Hernández-Pajares M, Juan JM, Sanz J (1999) New approaches in global ionospheric determination using ground GPS data. J Atmos Solar Terr Phys 61(16): Hernández-Pajares M, Juan JM, Sanz J, Orús R, Garcia-Rigo A, Feltens J, Komjathy A, Schaer S, Krankowski A (2009) The IGS VTEC maps: a reliable source of ionospheric information since J Geod 83(3 4): Hernández-Pajares M, Juan JM, Sanz J, Aragón-Ángel A, García- Rigo A, Salazar D, Escudero M (2011) The ionosphere: effects, GPS modeling and the benefits for space geodetic techniques. J Geod 85(12): Hochegger G, Nava B, Radicella SM, Leitinger R (2000) A family of ionospheric models for different uses. Phys Chem Earth Part C 25(4): Kim BC, Tinin MV (2011) Potentialities of multifrequency ionospheric correction in global navigation satellite systems. J Geod 85(3): Klobuchar J (1987) Ionospheric time-delay algorithm for single frequency GPS users. In: IEEE transactions on aerospace and electronic systems, AES 23(3): Lachapelle G, Hagglund J, Falkenberg W, Bellemare P, Casey M, Eaton M (1986) GPS land kinematic positioning experiments. Proceeding fourth international geodetic symposium on satellite positioning, Austin, Texas, April 28 May 2, 2: Lanyi GE, Roth T (1988) A comparison of mapped and measured total ionospheric electron content using global positioning system and beacon satellite observations. Radio Sci 23(4): Le AQ, Tiberius C (2007) Single-frequency precise point positioning with optimal filtering. GPS Solut 11(1):61 69 Liu JB, Wang ZM, Zhang HP, Zhu WY (2008) Comparison and consistency research of regional ionospheric TEC models based on GPS measurements. J Wuhan Univ (Inf Sci) 33(5): (In Chinese) Mannucci AJ, Wilson BD, Edwards CD (1993) A new method for monitoring the earth s ionospheric total electron content using the GPS global network. Proceedings ION-GPS-1993, Institute of Navigation, Salt Lake City, Mannucci AJ, Wilson BD, Yuan DN, Ho CH, Lindqwister UJ, Runge TF (1998) A global mapping technique for GPS derived ionospheric total electron content measurements. Radio Sci 33(3): Montenbruck O, Hauschild A, Steigenberger P, Hugentobler U, Teunissen P, Nakamura S (2013) Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system. GPS Solut 17(2): Øvstedal O (2002) Absolute positioning with single frequency GPS receivers. GPS Solut 5(4):33 44 Schaer S (1999) Mapping and predicting the earth s ionosphere using the global positioning system. Ph.D. dissertation, Bern: The University of Bern Schaer S, Beutler G, Rothacher M (1996) Daily global ionosphere maps based on GPS carrier phase data routinely produced by the CODE analysis center. Proceedings of the IGS AC Workshop, Silver Spring, MD, USA, Schunk RW, Scherliess L, Sojka JJ et al (2004) Global assimilation of ionospheric measurements (GAIM). Radio Sci, 39: RS1S02. doi: /2002rs Shi C, Zhao Q, Li M, Tang W, Hu Z, Lou Y, Zhang H, Niu X, Liu J (2012) Precise orbit determination of BeiDou satellites with precise positioning. Sci China Earth Sci 55(7):

10 658 GPS Solut (2015) 19: Shi C, Zhao Q, Hu Z, Liu J (2013) Precise relative positioning using real tracking data from COMPASS GEO and IGSO satellites. GPS Solut 17(1): Venkataratnam D, Sarma AD (2012) Modeling of low latitude ionosphere using GPS data with SHF model. Geosci Remote Sens IEEE Trans 50(3): Weimer DR (2001) An improved model of ionospheric electric potentials including substorm perturbations and application to the geospace environment modeling November 24, 1996, event. J Geophys Res: Space Phys ( ), 106(A1): Wild U (1994) Ionosphere and satellite systems: permanent GPS tracking data for modelling and monitoring. Geodätisch-geophysikalische Arbeiten in der Schweiz, Band 48 Yang Y, Li J, Xu J, Tang J, Guo H, He H (2011) Contribution of the COMPASS satellite navigation system to global PNT users. Chin Sci Bull 56(26): Yuan Y, Ou J (2002) Differential areas for differential stations (DADS): a new method of establishing grid ionospheric model. Chin Sci Bull 47(12): Zhang HP (2006) Monitoring and research on ionosphere using Chinese ground based GPS network. Chinese Academy of Sciences, Beijing Zhang BC, Ou JK, Yuan YB, Li ZS (2012) Extraction of line-of-sight ionospheric observables from GPS data using precise point positioning. Sci China Earth Sci 55(11): Rui Zhang is a lecturer in South China Agricultural University. She obtained her Ph.D. degree with distinction in Geodesy and Surveying Engineering in Wuhan University in Her current research focuses mainly involve GNSS precise positioning technology and GNSS meteorology, etc. Weiwei Song is a lecturer in Wuhan University. He obtained his Ph.D. degree with distinction in Geodesy and Surveying Engineering in Wuhan University in His current research interests mainly focus on real-time GNSS precise positioning technology. Yibin Yao is a professor in Wuhan University. He obtained his Ph.D. degree with distinction in Geodesy and Surveying Engineering in Wuhan University in His main research interests include GPS/MET and high-precision GNSS data processing. Chuang Shi is the head of GNSS Research Center in Wuhan University. He obtained his Ph.D. degree with distinction in Geodesy and Surveying Engineering in Wuhan University in His research interests include network adjustment and precise orbit determination of GNSS, LEO satellites. Yidong Lou is an associate professor at GNSS Research Center, Wuhan University. He obtained his Ph.D. degree with distinction in Geodesy and Surveying Engineering in Wuhan University in His current research interests include realtime precise GNSS Orbit determination and GNSS precise point positioning. Wenting Yi is a Ph.D. student. He has obtained his Bachelor s degree in Wuhan University, P.R.C. in His current research focuses mainly involve GNSS precise positioning technology, etc.