Skew-t Filter and Smoother with Improved Covariance Matrix Approximation

TL;DR

This paper introduces a new skew-t filter and smoother that improve covariance matrix approximation accuracy in linear state-space models with skew-t measurement noise, outperforming previous methods in simulations and real-world GPS data.

Contribution

The paper proposes a novel variational Bayes-based filter and smoother with coupled variables, enhancing covariance approximation and robustness in skew-t noise scenarios.

Findings

More accurate posterior covariance matrix approximation

Outperforms existing filters and smoothers in accuracy and speed

Demonstrated effectiveness on real-world GPS navigation data

Abstract

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness variables to reduce the error caused by the variational approximation. Although the variational update is done suboptimally using an expectation propagation algorithm, our simulations show that the proposed method gives a more accurate approximation of the posterior covariance matrix than an earlier proposed variational algorithm. Consequently, the novel filter and smoother outperform the earlier proposed robust filter and smoother and other existing low-complexity alternatives in accuracy and speed. We present both simulations and tests based on real-world navigation data, in particular GPS data in an urban area, to demonstrate the performance of the novel methods. Moreover, the extension of the proposed algorithms to cover the case where the distribution of the measurement noise is multivariate skew-$t$ is outlined. Finally, the paper presents a study of theoretical performance bounds for the proposed algorithms.