A novel nonlinear filter through constructing the parametric Gaussian regression process

In this paper, a new variational Gaussian regression filter (VGRF) is proposed by constructing the linear parametric Gaussian regression (LPGR) process including variational parameters. Through modeling the measurement likelihood by LPGR to implement the Bayesian update, the nonlinear measurement function will not be directly involved in the state estimation. The complex Monte Carlo computation used in traditional methods is also avoided well. Hence, in PVFF, the inference of state posteriori and variational parameters can be achieved tractably and simply by using variational Bayesian inference approach. Secondly, a filtering evidence lower bound (F-ELBO) is proposed as a quantitative evaluation rule of different filters. Compared with traditional methods, the higher estimation accuracy of VGRF can be explained by the F-ELBO. Thirdly, a relationship between F-ELBO and the monitored ELBO (M-ELBO) is found, i.e., F-ELBO is always larger than M-ELBO. Based on this finding, the accuracy performance improvement of VGRF can be theoretically explained. Finally, three numerical examples are employed to illustrate the effectiveness of VGRF.