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.