Ambiguity Resolution for GPS/GNSS Network Solution Implemented in SPODS

Ambiguity resolution plays an essential role in global GPS/GNSS network solution. In order to fix as many double-difference(DD) ambiguities to the nearest integers as possible, a set of "most-easy-to-fix" independent DD-ambiguities has to be defined. The most usable state-of-art method (the "traditional" method)at present is to make the independency checking on two levels firstly on the baseline level and then the network level, in which the DD-ambiguity candidates are sorted by their fixing probabilities on both levels. Considering the fact that, in general global network solution, the number of stations involved is usual times larger than that of satellites, a new approach for independent DD-ambiguities selection was presented, which makes the independency checking in an analogous two-level way firstly on the constellation level and then the network level. Together with a new procedure for sequential ambiguity fixing base on updating the upper triangular square root of covariance matrix, the new approach is implemented in the satellite positioning and orbit determination system (SPODS) software which is designed and developed at Xi'an Research Institute of Surveying & Mapping. Validation experiment with GPS observation data collected from about 64 IGS stations was carried out, which demonstrate that 1D RMSs for daily orbit solution, compared with IGS final combined solution, are about 0.012 m, and about 92% of DD-ambiguities were fixed, with only neglectable tiny difference for both the new and traditional method. Another experiment with varied number of stations indicates that the ratio of the number of DD-ambiguities candidates to be checked for independency on the network level between the new and the traditional approach is nearly equal to the ratio of satellites to stations involved. For the cases that more stations are involved than satellites, which are common in actual GPS/GNSS network solution, the computation time for independent DD-ambiguities selection is reduced with the new approach, the more stations involved, the greater advantage is exhibited

Generating Carrier Range with Between-satellite Single-difference Phase Ambiguity Resolution

Data processing for large-scale GNSS network is faced with increasing challenges as both the number of tracking stations and navigation satellites continuously increases. It has been shown that converting original carrier phase observations to carrier range observations is one of the valid approaches to improve the computing efficiency of data processing. In this paper, a new method to generate the carrier range observation is presented,correcting the ionosphere-free combination of carrier phase using the estimation of un-difference ambiguities obtained in the PPP solution with fixing between-satellite single difference ambiguities. Experiments with GPS data from the crustal movement observation network of China (CMONOC) during day 1-30 of year 2017 are conducted to validate the proposed approach. It is demonstrated that, using the carrier range observation, the computation time for the network with 252 stations is less than 20 minutes. If the original phase observations are used, it takes about 11 hours, nearly half of which is spent for resolving integer double difference ambiguities. Excluding the 12 abnormal stations, the monthly coordinate repeatability of the 240 stations are 0.74, 0.85 and 2.53 mm on average respectively in the directions of N, E and U, which are slightly better than those with original phase data. We also discuss the difference of integrated network solutions with original phase and carrier range. Using the concept of adjustment model with constrain condition, a unified formula of observation model is presented to interpret the principle of integrated network solution with carrier range generated with various integer ambiguity resolution strategies, i.e. resolving zero-difference, double-difference and between-satellite single-difference integer ambiguities. It is concluded that the effect of network solution with carrier range observation is theoretically equivalent with the traditional approach with original phase data

BDS-3 satellite orbit and clock determination with one-way inter-satellite pseudorange and monitoring station data

In this paper,BDS-3 satellite orbits and clock offsets are determined by using the original one-way inter-satellite-link (ISL) pseudorange data together with the carrier phase and pseudorange data of ground monitoring stations. The satellite clock offsets are expressed by piecewise polynomial with appropriate piecewise intervals (e.g. 1 min), thus the non-simultaneously observed one-way ISL pseudorange data can be processed directly. Experiments of orbit determination and clock estimation for BDS-3 satellites with observation data from 6 iGMAS stations in China and ISL pseudorange data are carried out. The results show that the RMS of the overlapping orbit differences in R, T and N directions are 0.078, 0.321 and 0.375 m, respectively. The RMS and STD of the overlapping clock differences of satellite are 0.589 and 0.519 ns, respectively. Compared with the results obtained with only data from monitoring stations, the improvements of orbit and clock exceed 80% and 60% respectively. The average RMS of one-way ISL pseudo-range residuals is 0.083 m, and the stability of estimated hardware delay bias for transmitting and receiving ISL equipment is 0.53 and 0.72 ns on average, respectively

Satellite Clock Estimation with Between-satellite Single Difference Phase Ambiguity Fixing

A large number of researches suggest that integer ambiguity resolution(IAR) significantly improve the precision and reliability of precise point positioning (PPP) and providing “integer” satellite clock corrections is one of the available approaches proposed in the past ten years. In this paper, we propose a novel approach to estimate integer satellite clock corrections to support IAR for PPP application, Our approach is based on between-satellite single difference (BSSD) ambiguity fixing which contains two key steps, namely to estimate wide-lane fractional cycle bias (FCB) for satellites and to select and fix the BSSD ambiguity datum, which would recover the integer property of the wide- and narrow-lane BSSD ambiguities, respectively. This approach has been implemented in the SPODS software developed at Xi'an Research Institute of Surveying and Mapping. Experiments for clock estimation with data collected at about 66 IGS stations have been carried out to validate the proposed approach. It is demonstrated that, in the clock estimation, 73%, on average, of the independent BSSD ambiguities were successfully fixed to integers and the mean RMS and STD of differences between our clocks and the IGS final clocks are 0.170 ns and 0.012 ns respectively. The fractional parts of the wide-lane and narrow-lane BSSD ambiguities from about 448 IGS stations were analyzed, which proves that the obtained satellite clocks together with the wide-lane FCB products have the ability to support IAR in PPP. Using our products, experiments for simulated kinematic PPP with data collected at 20 IGS stations were carried out. It is shown that, with IAR, the positioning accuracy (RMS) in N, E, U and 3D are 0.009, 0.010, 0.023 and 0.027 m, corresponding to improvements of 30.8%, 61.5%, 23.3% and 37.2%, respectively, compared with that without IAR or with IGS final clocks

Analysis on BDS Satellite Internal Multipath and Its Impact on Wide-lane FCB Estimation

To the issue of the satellite internal multipath (SIMP) of BeiDou satellites, it proposed and emphasized that the SIMP model should be established as a function of the nadir angle with respect to the observed satellite rather than the elevation of the measurement, so that it can be used for receivers at various altitude. BDS data from global distributed stations operated by the International Monitoring and Assessment System (iGMAS) and the Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS) are collected and a new SIMP model as a piece-wise linear function of the nadir angle is released for the IGSO-and MEO-satellite groups and for B1, B2 and B3 frequency band individually. The SIMP of GEO,IGSO and MEO satellites is further analyzed with B1/B2 dual-frequency data onboard the FengYun-3 C(FY3C) satellite at an altitude of~830 km, and it showed that, for nadir angles smaller than 7°, the SIMP values for GEO is quite close to the IGSO's, especially for B2, which may suggest that the SIMP model for IGSO satellites possibly also works for GEO satellites. It also demonstrated that, when the nadir angle is smaller than 12°for the MEO and 7°for the IGSO, the estimated SIMP model with data from FY3C is considerable consistent with that estimated with data collected at ground stations. Experiments are carried out to investigate the impacts of the SIMP on wide-lane fractional cycle bias (FCB) estimation for BDS satellites. The result indicates that, with the correction of the estimated SIMP, the repeatability of the FCB series is significantly improved by more than 60% for all satellites. Specifically, for the MEO and IGSO satellites, the repeatability is smaller than 0.05 cycle; the repeatability of 0.023 and 0.068 cycles achieved for GEO satellites C01 and C02 respectively with the estimated SIMP model for IGSO satellites

Analysis about Parameters Selection Strategy of ECOM Solar Radiation Pressure Model for BeiDou Satellites

In this paper,the variations of ECOM solar radiation pressure model parameters were analyzed for BeiDou satellites through orbit fitting using 3 years precise ephemeris data. The ECOM parameter selection strategies for the three types of BeiDou satellites were confirmed. Based on the satellite attitude control modes,satellite illumination was theoretically analyzed. We pointed out that solar panels are perpendicular illuminated,and then solar radiation pressure has the periodic component associated with the orbital period when satellite is at orbit-normal attitude control mode. Periodic parameters of D direction need to be added to enhance the ECOM 5 parameters. Orbit determination tests were carried out using MGEX global network data. Tests prove that using ECOM 7 parameters the orbit overlap accuracy improvement could reach up to 50%~80%

Satellite precise orbit determination with ionospheric-free strategy using triple-frequency observations

As the development of global navigation satellite system (GNSS), GNSS satellites transmitting multi-frequency signals has become a prevailing trend. However, recently the international GNSS service (IGS) analysis centers still use dual-frequency (DF) observations to derive the orbits, clocks and other products. The additional observations from the third frequency are not considered. We use two DF ionospheric-free (IF) combinations as the observation model, the improvements from the third frequency on orbits, clocks and station positions are assessed. In the carrier phase observation model, the satellite-dependent time-invariant and time-variant components are introduced. The two DF IF observation equations are re-parameterized to make the clock parameter aligned to the IGS clock products, and then the full-rank TF observation model is derived. Based on the strategy of building up extra wide lane, wide lane and narrow lane double-differenced ambiguities, the TF ambiguity resolution (AR) method is deduced. First taking 12 GPS Block IIF satellites as example, three precise orbit determination (POD) schemes, the L1/L2 DF IF POD (denoting as S1), the L1/L5 DF IF POD (denoting as S2), the L1/L2 and L1/L5 TF IF POD (denoting as S3), are processed in two station layouts. Results show that the S3 scheme in two station layouts can obtain the optimal precision. The orbit improvements of S3 with respect to S1 in cases of even and uneven distribution are within 10% and about 10%, respectively. The improvement of clocks RMS is slight, while STD is improved by 6.4% and 10.0%. The improved percentages of S3 vs. S2 are about less one times than that of S3 vs. S1, with the improved percentage of about 5%. Then the BDS-only POD test is processed and the orbits are validated by satellite laser ranging residuals. Results show that comparing with B1/B3 POD, the orbit and clock accuracy of TF POD can be improved. However, the improvement of TF POD comparing to B1/B2 POD is slight or even worse. The possible reason is the inaccuracy antenna phase values

GPS/BDS/Galileo precise orbit determination using triple-frequency uncombined observation model

The navigation satellite of the four global navigation satellite system (GNSS) transmitting multi-frequency signals becomes a prevailing trend. In this contribution, a triple-frequency (TF) uncombined (UC) precise orbit determination (POD) method based on IGS clock datum is developed and its ambiguity resolution strategy is proposed. The hardware delay of carrier phase is divided by time-invariant and variant components. Then the UC observation model is given by re-parameterizing the unknown parameters. The step-by-step ambiguity fixing method, i.e. the extra-wide-lane, wide-lane and narrow-lane ambiguities fixed in sequence, is deduced by using double-differenced ambiguities in a network. With the GPS ⅡF, BDS-2 and Galileo being able to transmit triple-frequency signals, the four POD tests are conducted: ionospheric-free (IF) POD of frequency 1/2, IF POD of frequency 1/3, UC POD of frequency 1/2, UC POD of TF signals. The three metrics of external orbit product, day boundary discontinuities and satellite laser ranging are used to validate the POD product accuracy. Results show that a subtle improvement are received with the addition of the third frequency observations. However, the improvement of GPS TF POD results with respect to L1/L2 POD is about 10%, which may be the signal power of L5 is stronger than that of L2

The PPP Precision Analysis Based on BDS Regional Navigation System

BeiDou navigation satellite system(BDS) has opened service in most of the Asia-Pacific region, it offers the possibility to break the technological monopoly of GPS in the field of high-precision applications, so its performance of precise point positioning (PPP) has been a great concern. Firstly, the constellation of BeiDou regional navigation system and BDS/GPS tracking network is introduced. Secondly, the precise ephemeris and clock offset accuracy of BeiDou satellite based on domestic tracking network is analyzed. Finally, the static and kinematic PPP accuracy is studied, and compared with the GPS. The actual measured numerical example shows that the static and kinematic PPP based on BDS can achieve centimeter-level and decimeter-level respectively, reaching the current level of GPS precise point positioning

Satellite Positioning and Orbit Determination System SPODS:Theory and Test

The Satellite Positioning and Orbit Determination System(SPODS)is a software package for GNSS positioning/orbit determination,developed by the Xi'an Research Institute of Surveying and Mapping.So far it has been able to treat GPS data and has the capability of high precision GPS positioning and orbit determination.The underlying theory and the performance test are briefly addressed.The test utilizes the GPS data collected from some 127IGS stations during days 4~10of 2009.The results show that the rms 1D difference is 1.1cm between SPODS orbits and final IGS combined orbits,and that the repeatability of daily solutions of station coordinates is 1.5mm for horizontal components,and 4.5mm for height component,and that the consistency of ERP solutions with final IGS values is 0.025mas,0.093mas and 0.013ms/d respectively for pole coordinates and changes in length of day