Knowledge-Aided Covariance Matrix Estimation via Kronecker Product Expansions for Airborne STAP
This letter proposes a new approach for knowledge-aided estimation of structured clutter covariance matrices (CCMs) in airborne radar systems with limited training data. First, we model the CCM in space–time adaptive processing (STAP) as a sum of low-rank Kronecker products. We then apply a permutation operation to convert the Kronecker factors into linear structures and propose a novel CCM estimation method under the maximum-likelihood framework. Employing a proximal gradient algorithm, the proposed method simultaneously exploits the knowledge about the clutter and the Kronecker structure of the CCM. We finally evaluate the performance of the proposed method using real data from airborne STAP.
Robust Kronecker Product PCA for Spatio-Temporal Covariance Estimation
Kronecker PCA involves the use of a space versus time Kronecker product decomposition to estimate spatio-temporal covariances. In this paper, the addition of a sparse correction factor is considered, which corresponds to a model of the covariance as a sum of Kronecker products of low (separation) rank and a sparse matrix. This sparse correction extends the diagonally corrected Kronecker PCA of [Greenewald, and Hero, 2014] to allow for sparse unstructured “outliers” anywhere in the covariance matrix, e.g., arising from variables or correlations that do not fit the Kronecker model well, or from sources such as sensor noise or sensor failure. We introduce a robust PCA-based algorithm to estimate the covariance under this model. An extension to Toeplitz temporal factors is also provided, producing a parameter reduction for temporally stationary measurement modeling. High dimensional MSE performance bounds are given for these extensions. Finally, the proposed extension of KronPCA is evaluated on both simulated and real data coming from yeast cell cycle experiments. This establishes the practical utility of robust Kronecker PCA in biological and other applications.
Symptomatic Trans-sexualism
A 24-year-old male schizophrenic had a delusion that he was female and had lived his life as a woman for almost two years. Unlike the only other reported case, his ‘symptomatic transsexualism’ responded to the effective treatment of his schizophrenia.