# Robust Kalman Filter Aided GEO/IGSO/GPS Raw-PPP/INS Tight Integration
Accordingly, the visible satellite number may be reduced to under four, which is not sufficient for PPP computation, even when using GPS and BDS together [20; 21]. In order to bridge PPP solutions during those signal outages, the inertial navigation system (INS) [22; 23] is utilized. INS is an autonomous positioning technique and can provide continuous positioning solutions by processing the specific force measurements from triaxial accelerometers and the angular increments from triaxial gyroscopes [24; 25]. Meanwhile, INS solutions are accurate in the short term and it is hardly influenced by surrounding environments [24]. Thus, PPP's performance in challenging conditions can be bridged by adopting the integration of PPP and INS. As such, according to [26], two integration modes can be used, namely loose integration and tight integration. 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]. Accordingly, the tight integration mode can also work in the case that the observed satellite number is inadequate for PPP's calculation. Therefore, the tight integration model between GPS/BDS and INS is adopted in this paper. Nevertheless, there are only four MEO satellites in BDS and the time in view is hours. Hence, usually only GEOs and IGSOs are visible in most of the dynamic applications. According to the BDS quality analysis works in [27; 28; 29], the qualities of BDS GEO, IGSO, and MEO are different from each other due to the different orbit accuracy, observation noise, and multipath. Particularly, the quality of GEO is proven to be several times lower than that of IGSO and MEO. However, 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. In this paper, the famous robust extended Kalman filter (R-EKF) [30; 31] that is based on equivalent weight function is employed to reduce the impact of the inappropriate priori weight of BDS GEO. Besides, according to the works in [32], the un-differenced un-combined PPP (i.e., raw PPP) is more powerful than the ionosphere-free combination PPP (i.e., IF PPP). Therefore, the raw PPP mode is adopted in this paper. Compared to previous works, 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. (2) To discriminate the different qualities of BDS GEO and IGSO satellites, this paper introduces the equivalent weight function based R-EKF, instead of the empirical satellite elevation angle weight function based EKF, to distinguish the real contributions from IGSO and GEO in GEO/IGSO/GPS PPP/INS tight integration. To validate the proposed method, a set of land-borne vehicle GPS/BDS data and two groups of INS data were processed and analyzed. The paper is organized as follows: The mathematical models of BDS GEO/IGSO enhanced PPP, INS update, and R-EKF based PPP/INS tight integration are described in Section 2. The tests and results are presented in Section 3, which is followed by the conclusions in Section 4.