Search

The estimation of mean matrix for a set of Hermitian positive definite (HPD) matrices can be considered based on a geometric framework. This kind of estimator is closely related to geometric measures, which can be established to measure the dissimilarity between two matrices on the matrix manifold. In this paper, the matrix spectral norm is exploited to derive a new geometric measure on the matrix manifold consisting of all HPD matrices. Correspondingly, the mean matrix associated with the new geometric measure on the matrix manifold is considered via two effective solution techniques. More specifically, the first method transforms the mean matrix estimation into a semidefinite programming problem solved by the interior point method; the second method exploits joint approximate diagonalization to diagonalize the given covariance matrices and then recasts the mean matrix estimation into an optimization problem with linear inequality constraints. Furthermore, two matrix detectors employing the proposed mean matrix estimators are designed for target detection using pulse Doppler radar with a small bunch of pulses. At the analysis stage, we show that the proposed matrix detector can guarantee the bounded constant false alarm rate property in terms of the clutter covariance matrix. Finally, numerical experiments based on simulated clutter data and real sea clutter data are performed to verify the effectiveness and robustness of the proposed matrix detectors. [ABSTRACT FROM AUTHOR]

A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distributionfree estimators shares a shrinkage-type form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed-form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable signal-to-interference-plus-noise ratio (SINR) both for spatial and Doppler processing scenarios assuming different data statistical characterizations. The results show that interesting SINR improvementswith respect to some counterparts available in the open literature can be achieved especially in training starved regimes. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications, when a limited number of training data is present. We determine the maximum likelihood (ML) estimator of the covariance matrix starting from a set of secondary data, assuming a special covariance structure (i.e., the sum of a positive semi-definite matrix plus a term proportional to the identity), and a condition number upper-bound constraint. We show that the formulated constrained optimization problem falls within the class of MAXDET problems and develop an efficient procedure for its solution in closed form. Remarkably, the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix. At the analysis stage, we assess the performance of the proposed algorithm in terms of achievable signal-to-interference-plus-noise ratio (SINR) both for a spatial and a Doppler processing. The results show that interesting SINR improvements, with respect to some existing covariance matrix estimation techniques, can be achieved. [ABSTRACT FROM AUTHOR]