Adaptive Radar MIG Detectors based on the Total Bregman divergence for Sample-Starved Scenarios

Matrix information geometry (MIG) represents an interesting design tool allowing for the design of new detectors with a significant performance gains over the traditional methods. This superiority is due to the discriminative power of geometric measures that comes in handy especially in sample-starved scenarios. In this paper, we propose a class of adaptive MIG detctors based upon the total Bregman divergence (TBD), which removes redundant information in sample data through dimensionality reduction learning. Specifically, the clutter covariance matrix is estimated by the TBD mean of a set of Hermitian positive definite (HPD) matrices computed by means of secondary data samples. Then, the HPD matrices are projected onto a lower-dimensional manifold with an objective function that mazimizes inter-class distance while minimizing the intra-class distance. This operation can be transformed into an optimization problem on the Stiefel manifold and solved by the Riemannian trust-region Newton method. In this framework, three adaptive TBD-MIG detectors are designed. Numerical results confirm the advantage of the proposed detectors over the conventional TBD-MIG detectors that do not use this projection as well as the traditional detectors in sample-starved scenarios.