A New Adaptive Kalman Filter with Inaccurate Noise Statistics

Abstract

In this paper, a new adaptive Kalman filter is proposed for a linear Gaussian state-space model with inaccurate noise statistics based on the variational Bayesian (VB) approach. Both the prior joint probability density function (PDF) of the one-step prediction and corresponding prediction error covariance matrix and the joint PDF of the mean vector and covariance matrix of measurement noise are selected as Normal-inverse-Wishart (NIW), from which a new NIW-based hierarchical Gaussian state-space model is constructed. The state vector, the one-step prediction and corresponding prediction error covariance matrix, and the mean vector and covariance matrix of measurement noise are jointly estimated based on the constructed hierarchical Gaussian state-space model using the VB approach. Simulation results show that the proposed filter has better estimation accuracy than existing state-of-the-art adaptive Kalman filters.