Student's <inline-formula> <tex-math notation="LaTeX">$t$</tex-math> </inline-formula>-Filters for Noise Scale Estimation

Abstract

In this letter, we analyze certain student's $t$ -filters for linear Gaussian systems with misspecified noise covariances. It is shown that under appropriate conditions, the filter both estimates the state and re-scales the noise covariance matrices in a Kullback–Leibler optimal fashion. If the noise covariances are misscaled by a common scalar, then the re-scaling is asymptotically exact. We also compare the student's $t$ -filter scale estimates to the maximum-likelihood estimates. Simulations demonstrating the results on the Wiener velocity model are provided.