A novel multivariate Laplace distribution-based Gaussian approximate filter with colored heavy-tailed measurement noise

Abstract This work presents a novel multivariate Laplace distribution (MLD)-based Gaussian approximate filter (GAF) developed to address the estimation problem in a nonlinear system subject to colored heavy-tailed measurement noise (CHTMN). Initially, through the application of measurement difference and state extension methods, the estimation challenge featuring CHTMN is converted into a filtering issue with white heavy-tailed measurement noise (WHTMN); subsequently, the MLD is introduced to characterize the WHTMN, and the formulation of a novel state space model is thereby established. Moreover, the system state vector and MLD covariance matrix are jointly inferred through the application of variational Bayesian inference methodology and a novel MLD-based GAF is designed. Ultimately, the superiority of the proposed MLD-based GAF in the scenario of CHTMN is demonstrated by two simulation models.