基于自然梯度的非线性变分贝叶斯滤波算法

In statistical manifold space, the essence of nonlinear state posterior distribution approximation from the perspective of information geometry is minimizing Kullback-Leibler (KL) divergence between posterior distribution and the corresponding approximated distribution; Meanwhile, it is equivalent to maximizing evidence low bound. Aiming at the problem of improving the estimation accuracy of nonlinear system state, the natural gradient of evidence lower bound is derived under Gaussian system assumption by combining with Fisher information matrix and variational Bayesian (VB) inference, which produces a faster movement direction to the posterior distribution, and realizing a close approximation between variational distribution and the posterior. On this basis, a variational Bayesian Kalman filtering algorithm using natural gradient is proposed for updating the variational hyperparameters of state estimation and the associated error covariance. Simulations in low earth orbit target tracking system with space-based optical sensors and bearing-only target tracking system are presented verifying that the proposed algorithm has higher accuracy than the comparison algorithms.