By Paolo Franchi In Formal Reports
Adaptive sequential learning of time-varying structured random matrices. Braca, Paolo; Aubry, Augusto; Millefiori, Leonardo; De Maio, Antonio; Marano, Stefano. CMRE-FR-2019-003. December 2020.
Covariance matrix estimation is a crucial task in adaptive signal processing applied to several surveillance systems, including radar and sonar. This report proposes a time-varying learning strategy to track both the covariance matrix of data and its structure (class). Assuming that, given the class, the posterior distribution of the covariance is described through a mixture of inverse Wishart distributions, while the posterior distribution of 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.