Robust Inference for State-Space Models with Skewed Measurement Noise

TL;DR

This paper introduces robust filtering and smoothing algorithms for linear state-space models with skewed, heavy-tailed measurement noise, using variational Bayes approximation to improve accuracy over traditional methods.

Contribution

The paper develops novel variational Bayes-based algorithms for state estimation in models with skewed measurement noise, outperforming conventional approaches in accuracy.

Findings

Proposed methods achieve better accuracy than traditional filters.

Computational complexity is 5 to 10 times that of the Kalman filter.

Algorithms are validated in a simulated pseudorange positioning scenario.

Abstract

Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew-t-distributed measurement noise. The proposed filter and smoother are compared with conventional low-complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.