Generalized Multivariate Laplace Filtering Algorithm Supresses Process and Measurement Noise Outliers

Abstract

This article proposes a state estimation algorithm designed to effectively suppress process and measurement noise outliers and enhance the precision of state estimation. To accurately model heavy-tailed noise contaminated by outliers, we adopt a generalized multivariate Laplace (GML) distribution. Through a rigorous analysis of its statistical properties, we identify a specific parameterization of the GML distribution (the rate parameter of the exponential distribution in the hierarchical model is determined to be 0.2, departing from the conventional setting of 1) that accurately captures the characteristics of the nonstationary noise. Based on this, a state-space model is formulated within a hierarchical Bayesian framework. This model separately accounts for the uncertain noise covariance matrices and the heavy-tailed factors. Given the non-Gaussian nature and analytical intractability of the joint posterior distribution, we employ a fixed-point variational Bayesian (VB) approach to derive variational distributions for both noise parameters and the state vector. The superiority of the algorithm is confirmed through a real-world quadrotor unmanned aerial vehicle (UAV) tracking experiment and numerical simulations. Results show significant improvements in estimation accuracy and robustness over existing filtering techniques.