Efficient Estimation of Kronecker Product of Linear Structured Scatter Matrices under t-distribution

This paper addresses structured scatter matrix estimation within the non convex set of Kronecker product structure. The latter model usually involves two matrices , which can be themselves linearly constrained, and arises in many applications, such as MIMO communication , MEG/EEG data analysis. Taking this prior knowledge into account generally improves estimation accuracy. In the framework of robust estimation, the t-distribution is particularly suited to model heavy-tailed data. In this context, we introduce an estimator of the scatter matrix, having a Kronecker product structure and potential linear structured factors. In addition, we show that the proposed method yields a consistent and efficient estimate.