Outlier-Robust Unscented RTS Smoothing for Independent Sensing Data

Abstract

In this letter, we propose a version of the unscented Rauch–Tung–Striebel (RTS) smoother robust to outliers in the observations. We consider a common case where data are collected from independent sensors with additive white Gaussian noise. Our method is primarily motivated by recent arguments and results presented in favor of learning-based outlier-robust state estimators, which assume adaptive residual cost functions in their formulation. We resort to the variational Bayesian (VB) theory to design an algorithm that selectively discards the corrupted measurements unlike other learning-based methods. Moreover, with the assumption that data are obtained from independent sensors, we are able to leverage computational results from advances in the unscented filtering theory that exploit the sparsity in the measurement covariance. For performance bench-marking, we present the Bayesian Cramér–Rao bound for a smoother with perfect outliers detection and rejection capabilities. Numerical experiments under different scenarios showcase performance gains in comparison with similar learning-based smoothers derived with the VB approach.