Linear Gaussian Regression Filter Based on Variational Bayes

In this paper, a novel nonlinear filter method named linear Gaussian regression filter (LG RF) is proposed. The LG RF utilizes the Variational Bayes (VB) to indirectly approximate the posterior probability density function (PDF) for state estimation. The core of the LG RF is to use a linear Gaussian distribution with a set of compensating parameters (CPs) to characterize the likelihood probability (LP) for maximizing the lower bound. Through iteratively and alternatively achieving the state estimation and CPs identification, the estimation accuracy can be improved gradually. In addition, compared with point-based filters, there is no decomposition of the covariance matrix in the LG RF so that the inborn defect of numerical instability is avoided. The superior performance of the LGRF is demonstrated in the simulation of maneuvering target tracking.