Multi-Class Random Matrix Filtering for Adaptive Learning

Covariance matrix estimation is a crucial task in adaptive signal processing applied to several surveillance systems, including radar and sonar. In this paper we propose a dynamic learning strategy to track both the covariance matrix of data and its structure (class). We assume that, given the class, the posterior distribution of the covariance is described through a mixture of inverse Wishart distributions, while the class evolves according to a Markov chain. Hence, we devise a novel and general filtering strategy, called multi-class inverse Wishart mixture filter, able to capitalize on previous observations so as to accurately track and estimate the covariance. Some case studies are provided to highlight the effectiveness of the proposed technique, which is shown to outperform alternative methods in terms of both covariance estimation accuracy and probability of correct model selection. Specifically, the proposed filter is compared with class-clairvoyant covariance estimators, e.g., the maximum likelihood and the knowledge-based recursive least square filter, and with the model order selection method based on the Bayesian information criterion.