Inter-system biases solution strategies in multi-GNSS kinematic precise point positioning

Estimating inter-system biases (ISBs) is important in multi-constellation Global Navigation Satellite System (GNSS) processing. The present study aims to evaluate and screen out an optimal estimation strategy of ISB for multi-GNSS kinematic precise point positioning (PPP). The candidate strategies considered for ISB estimation are white noise process (ISB-WN), random walk process (ISB-RW), constant (ISB-CT) and eliminated by between-satellite single-differenced observations (ISB-SD). We first present the mathematical model of ISB derived from the observation combination among different GNSSs, and we demonstrate the equivalence between ISB-WN and ISB-SD in the Kalman filter. In order to evaluate the performance of these four ISB solution strategies, we implement kinematic PPP with 1-month static data from 112 International GNSS service stations and two-hour dynamic vehicular data collected in an urban case. For comparison, precise orbit and clock products from the Center for Orbit Determination in Europe (CODE), GeoForschungsZentrum in Germany (GFZ) and Wuhan University (WHU) are employed in our experiments. The results of static tests show that the positioning accuracy is comparable among the four strategies, but ISB-CT performs slightly better in convergence time. In the kinematic test, there are more cycle slips than static test, and the ISB-CT improves the positioning accuracy by 15.7%, 38.9% and 63.2% in east, north and up components, and reduces the convergence time by 60.1% comparing with the other strategies. Moreover, both the static and kinematic tests prove the consistence among CODE, GFZ and WHU precise products and the equivalence between ISB-WN and ISB-SD strategies. Finally, more, i.e., the same amount of cycle slips as for the dynamic data, are artificially added to the static data to conduct the pseudo-kinematic test. The result shows that ISB-CT improves the positioning accuracy and convergence time by 19.2% and 24.4%, respectively.The study is funded by Laoshan Laboratory (LSKJ202205104, LSKJ202205104_01), National Key Research and Development Program of China (2020YFB0505800, 2020YFB0505804), National Natural Science Foundation of China (42004012), Natural Science Foundation of Shandong Province, China (ZR2020QD048) and by the project RTI2018-094295-B-I00 funded by the MCIN/AEI 1013039/501100011033 which is co-funded by the FEDER program.Peer ReviewedPostprint (published version

Assessment of Different Stochastic Models for Inter-System Bias between GPS and BDS

Inter-system bias (ISB) will affect accuracy and processing time in integrated precise point positioning (PPP), and ISB stochastic models will largely determine the quality of ISB estimation. Thus, the impacts of four different stochastic models of ISB processing will be assessed and studied in detail to further reveal the influence of ISB in positioning. They are ISB-PW considering ISB as a piece-wise constant, ISB-RW considering ISB as random walk, ISB-AD considering ISB as an arc-dependent constant, and ISB-WN considering ISB as white noise. Together with the model without introducing ISB called ISB-OFF, i.e., five different schemes, ISB-OFF, ISB-PW, ISB-RW, ISB-AD, and ISB-WN, will be designed and tested in this study. From the results of pseudorange residuals, it can be noticed that when considering ISB, the Root-Mean-Square (RMS) of ionosphere-free combined pseudorange residuals are much smaller than without ISB (ISB-OFF). The results of convergence time and positioning accuracy analysis show that PPP performance with ISB-AD is even worse than ISB-OFF, when using the precise products from the German Research Centre for Geosciences (GFZ) named as GBM products here; while the strategies of ISB-RW, and ISB-WN achieve the best results. For the products from Wuhan University called WUM products, a completely different result is achieved. PPP with the stochastic models of ISB-PW and ISB-AD perform best. The most likely reason is the ISB stochastic models applied by the analysis centers are consistent with those used in the PPP on the user side. So, ISB-RW, or ISB-WN is recommended when GBM products are used, and for the WUM products, ISB-PW, or ISB-AD is chosen. From the statistics of PPP precision during the convergence period, it can be concluded that considering ISB also has a great improvement on combined PPP accuracy during the initialization phase