An Adaptive Combined Filtering Algorithm for Non-Holonomic Constraints with Time-Varying and Thick-Tailed Measurement Noise

Abstract

Aiming at the problem that the pseudo-velocity measurement noise of non-holonomic constraints (NHCs) in the integrated navigation of vehicle-mounted a global navigation satellite system/inertial navigation system (GNSS/INS) is time-varying and thick-tailed in complex road conditions (turning, sideslip, etc.) and cannot be accurately predicted, an adaptive estimation method for the initial value of NHC lateral velocity noise based on multiple linear regression is proposed. On the basis of this method, a Gaussian Student’s T distribution variational Bayesian filtering algorithm (Ga-St VBAKF) based on NHC pseudo-velocity measurement noise modeling is proposed through modeling and analysis of pseudo-velocity measurement noise. Firstly, in order to adaptively adjust the initial value of NHC lateral velocity noise, a vehicle turning detection algorithm is used to detect whether the vehicle is turning. Secondly, based on the vehicle motion state, the variational Bayesian method is used to adaptively estimate the statistical characteristics of the measurement noise in real time based on modeling of the lateral velocity noise as Gaussian white noise or Student’s T distribution thick-tail noise. The test results show that compared to the traditional Kalman filtering algorithm with fixed noise, the Ga-St VBAKF algorithm with noise adaptation reduces the maximum horizontal position error by 65.9% in the GNSS/NHC/OD/INS (where OD stands for odometer and INS stands for inertial measurement unit) system when the vehicle is in a turning state, and by 42.3% in the NHC/OD/INS system. This indicates that the algorithm can effectively suppress the divergence of positioning errors during turning and improve the performance of integrated navigation.