A Sliding Window Based Adaptive Progressive Gaussian Approximate Filter

Progressive Gaussian approximate filter (PGAF) provides an efficient way for estimating the states of nonlinear systems with large prior errors and accurate measurements. However, its performance declines when an inaccurate measurement noise covariance matrix (MNCM) is applied, which makes it even more challenging when the MNCM is coupled with progression step size in the measurement update step. To solve this problem, we adopt the sliding window method to accurately estimate the MNCM within the variational Bayesian framework adaptively. In the proposed algorithm, the system state’s posterior distribution is obtained through PGAF for forward filtering and Gaussian approximation smoother for backward smoothing within the sliding window. The proposed sliding window based adaptive PGAF outperforms existing nonlinear Gaussian filters as demonstrated using the target tracking examples.