Robust Linear Filter with Parameter Estimation Under Student-t Measurement Distribution

In this paper, we propose an approximate Kalman filter of measurements following Student's t-distribution by using the variational Bayes approach. This approach can decompose the estimation of multivariate parameters into a univariate estimation. The recursive formula for the approximate posterior densities of parameters and states is derived in detail. Then, the asymptotic Bayesian Cramer-Rao lower bounds are derived for the proposed filter. Numerical simulations verify both the performance of the proposed filter and the variance lower bounds under time-varying noise. The efficiency of the proposed filter is also demonstrated in a real application, namely an integrated strapdown inertial navigation system/Doppler velocity log shipborne test for navigation.