Skew-t inference with improved covariance matrix approximation

TL;DR

This paper introduces improved filtering and smoothing algorithms for linear state-space models with skew-t measurement noise, utilizing a refined variational Bayes approach for better covariance estimation and enhanced accuracy and speed.

Contribution

It presents novel algorithms that outperform previous methods and conventional approaches by improving covariance matrix approximation in skew-t noise models.

Findings

More accurate posterior covariance estimation.

Enhanced filtering and smoothing accuracy.

Faster computational performance.

Abstract

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t distributed measurement noise are presented. The proposed algorithms improve upon our earlier proposed filter and smoother using the mean field variational Bayes approximation of the posterior distribution to a skew-t likelihood and normal prior. Our simulations show that the proposed variational Bayes approximation gives a more accurate approximation of the posterior covariance matrix than our earlier proposed method. Furthermore, the novel filter and smoother outperform our earlier proposed methods and conventional low complexity alternatives in accuracy and speed.