A Sequential Student’s t-Based Robust Kalman Filter for Multi-GNSS PPP/INS Tightly Coupled Model in the Urban Environment

Abstract

The proper stochastic model of a global navigation satellite system (GNSS) makes a significant difference on the precise point positioning (PPP)/inertial navigation system (INS) tightly coupled solutions. The empirical Gaussian stochastic model is easily biased by massive gross errors, deteriorating the positioning precisions, especially in the severe GNSS blockage urban environment. In this paper, the distributional characteristics of the gross-error-contaminated observation noise are analyzed by the epoch-differenced (ED) geometry-free (GF) model. The Student’s t distribution is used to express the heavy tails of the gross-error-contaminated observation noise. Consequently, a novel sequential Student’s t-based robust Kalman filter (SSTRKF) is put forward to adjust the GNSS stochastic model in the urban environment. The proposed method pre-weights all the observations with the a priori residual-derived robust factors. The chi-square test is adopted to distinguish the unreasonable variances. The proposed sequential Student’s t-based Kalman filter is conducted for the PPP/INS solutions instead of the standard Kalman filter (KF) when the null hypothesis of the chi-square test is rejected. The results of the road experiments with urban environment simulations reveal that the SSTRKF improves the horizontal and vertical positioning precisions by 57.5% and 62.0% on average compared with the robust Kalman filter (RKF).