Abstract
Reliable and continuous navigation solutions are essential for high-accuracy location-based services. Currently, the real-time kinematic (RTK) based Global Positioning System (GPS) is widely utilized to satisfy such requirements. However, RTK’s accuracy and continuity are limited by the insufficient number of the visible satellites and the increasing length of base-lines between reference-stations and rovers. Recently, benefiting from the development of precise point positioning (PPP) and BeiDou satellite navigation systems (BDS), the issues existing in GPS RTK can be mitigated by using GPS and BDS together. However, the visible satellite number of GPS + BDS may decrease in dynamic environments. Therefore, the inertial navigation system (INS) is adopted to bridge GPS + BDS PPP solutions during signal outage periods. Meanwhile, because the quality of BDS geosynchronous Earth orbit (GEO) satellites is much lower than that of inclined geo-synchronous orbit (IGSO) satellites, the predicted observation residual based robust extended Kalman filter (R-EKF) is adopted to adjust the weight of GEO and IGSO data. In this paper, the mathematical model of the R-EKF aided GEO/IGSO/GPS PPP/INS tight integration, which uses the raw observations of GPS + BDS, is presented. Then, the influences of GEO, IGSO, INS, and R-EKF on PPP are evaluated by processing land-borne vehicle data. Results indicate that (1) both GEO and IGSO can provide accuracy improvement on GPS PPP; however, the contribution of IGSO is much more visible than that of GEO; (2) PPP’s accuracy and stability can be further improved by using INS; (3) the R-EKF is helpful to adjust the weight of GEO and IGSO in the GEO/IGSO/GPS PPP/INS tight integration and provide significantly higher positioning accuracy.
Highlights
Precise point positioning (PPP) [1], which is based on the ionosphere-free combination of dual-frequency (L1: 1575.42 MHz and L2: 1227.6MHz) Global Positioning System (GPS) phase and code observations [2], was proposed two decades ago and has been adopted for static positioningSensors 2019, 19, 417; doi:10.3390/s19020417 www.mdpi.com/journal/sensorsSensors 2019, 19 FOR PEER REVIEW applicationsThis phenomenon is mainly dueortoeven the two advantages ofabsoluteprecise point positioning (PPP)
The undulant test area could improve the observability for gyro estimation and further improve the performance of Figure is error estimation and further improve the performance of PPP/inertial navigation system (INS) tight integration
According to the results above, it can be concluded that geosynchronous Earth orbit (GEO) and inclined geo-synchronous orbit (IGSO) have different influences on improving PPP performance and the robust extended Kalman filter (R-EKF) that is based on posteriori residuals can effectively adjust the optimal weight for GPS + BeiDou satellite navigation systems (BDS) data processing
Summary
Precise point positioning (PPP) [1], which is based on the ionosphere-free combination of dual-frequency (L1: 1575.42 MHz and L2: 1227.6MHz) Global Positioning System (GPS) phase and code observations [2], was proposed two decades ago and has been adopted for static positioning. The tight integration mode is based on the raw GPS/BDS phase/code observations and the INS predicted phase/code values [20,21], while the loose integration mode is based on PPP position and velocity solutions and that of the INS updated ones [25,26]. Usually the elevation dependent weight function [6] is used to present satellite quality Such a method is not significantly rigorous for real observed data, especially for BDS. This paper’s contributions are: (1) The impacts of BDS GEO satellites and IGSO satellites on GPS + BDS PPP and GPS + BDS PPP/INS tight integration are analyzed and evaluated.
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