Multi-Normal-Inverse Wishart mixture distribution based nonlinear filter with applications

Abstract

In Kalman filter-based spacecraft autonomous celestial navigation, Inertial/Celestial integrated navigation system and asynchronous multi-sensor data fusion, complex environments and sensor alignment errors are likely to lead to inaccurate statistical priors for the noise covariance matrices and the non-zero measurement noise mean vector (MNMV). To address this issue, this paper firstly proposes a Multi-Normal-Inverse Wishart (MNIW) mixture distribution modelling the joint probability density function (PDF) for one-step prediction and measure likelihood, then the MNIW mixture distribution is decomposed into a Gaussian hierarchy, and finally the posterior estimates of the state and variables are obtained using variational Bayesian technique. In this paper, a Multi-Normal-Inverse Wishart mixture distribution-based variational Bayesian extended Kalman filter (VB-EKF) is proposed, in which a first-order Taylor expansion is used to address the non-linear problem. The proposed filter can be used to address non-linear filtering problem with inaccurate noise covariance matrices and measurement bias. Simulations of spacecraft autonomous celestial navigation validate the effectiveness and superiority of the proposed filter.