Maximum a posteriori vs maximum probability recursive sparse estimation

Abstract

Recursive sparse parameter estimates obtained using the author's recent maximum a posteriori (MAP) approach, where the sparse parameter estimates are determined as the a posteriori mode of a Gaussian sum filter, are compared with a new maximum probability (MP) methodology, where the sparse parameter estimates are determined as the component of a Gaussian sum filter with the highest a posteriori weighting. We show how the performance of the MP estimator approach to sparse parameter estimates, in both sparsity and mean square error senses, depends on the parameters that characterize each multivariate Gaussian in the Gaussian sum filter. Through this work we also provide additional performance analysis for the MP estimator and suggest possible areas of future work that will further improve its performance.