Variational resampling-free cubature Kalman filter for GNSS/INS with measurement outlier detection

In the information fusion of GNSS/INS, the cubature Kalman filter (CKF) has been widely recognized for its ability to map the probability distributions more accurately than the extended Kalman filter. The resampling-free sigma-point update framework (SUF) propagates additional information based on the residuals of instantiated points from nonlinear transforms, which approximates the covariance of the posterior state more effectively than resampling-based SUF. Unfortunately, resampling-free SUF inherits the limitations of the KF framework, where measurement outliers caused by GNSS signal blocking and disturbances significantly degrade its performance. In this paper, a variational-based SUF is proposed for GNSS/INS information fusion, in which the measurement noise covariance and outlier indicator are iteratively updated using variational Bayesian inference. Consequently, an adaptive SUF is proposed based on outlier-dependent switching SUFs, leading to the development of a variational resampling-free CKF. Numerical simulations and a car-mounted GNSS/INS field test were conducted to demonstrate the effectiveness of the proposed algorithm. The results indicate that the proposed algorithm can efficiently address measurement outliers and time-varying measurement noise.