Robust Covariance Estimation under Imperfect Constraints using an Expected Likelihood Approach

We address the problem of structured covariance matrix estimation for radar space-time adaptive processing (STAP). A priori knowledge of the interference environment has been exploited in many previous works to enable accurate estimators even when training is not generous. Specifically, recent work has shown that employing practical constraints such as the rank of clutter subspace and the condition number of disturbance covariance leads to powerful estimators that have closed form solutions. While rank and the condition number are very effective constraints, often practical non-idealities makes it difficult for them to be known precisely using physical models. Therefore, we propose a robust covariance estimation method for radar STAP via an expected likelihood (EL) approach. We analyze covariance estimation algorithms under three cases of imperfect constraints: 1) a rank constraint, 2) both rank and noise power constraints, and 3) condition number constraint. In each case, we formulate precise constraint determination as an optimization problem using the EL criterion. For each of the three cases, we derive new analytical results which allow for computationally efficient, practical ways of setting these constraints. In particular, we prove formally that both the rank and condition number as determined by the EL criterion are unique. Through experimental results from a simulation model and the KASSPER data set, we show the estimator with optimal constraints obtained by the EL approach outperforms state of the art alternatives.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0506

Robust Covariance Matrix Estimation for Radar Space-Time Adaptive Processing (STAP)

Estimating the disturbance or clutter covariance is a centrally important problem in radar space time adaptive processing (STAP). The disturbance covariance matrix should be inferred from training sample observations in practice. Large number of homogeneous training samples are generally not available because of difficulty of guaranteeing target free disturbance observation, practical limitations imposed by the spatio-temporal nonstationarity, and system considerations. In this dissertation, we look to address the aforementioned challenges by exploiting physically inspired constraints into ML estimation. While adding constraints is beneficial to achieve satisfactory performance in the practical regime of limited training, it leads to a challenging problem. We focus on breaking this classical trade-off between computational tractability and desirable performance measures, particularly in training starved regimes. In particular, we exploit both the structure of the disturbance covariance and importantly the knowledge of the clutter rank to yield a new rank constrained maximum likelihood (RCML) estimator. In addition, we derive a new covariance estimator for STAP that jointly considers a Toeplitz structure and a rank constraint on the clutter component. Finally, we address the problem of working with inexact physical radar parameters under a practical radar environment. We propose a robust covariance estimation method via an expected likelihood (EL) approach. We analyze covariance estimation algorithms under three different cases of imperfect constraints: 1) only rank constraint, 2) both rank and noise power constraint, and 3) condition number constraint. For each case, we formulate estimation of the constraint as an optimization problem with the EL criterion and formally derive and prove a significant analytical result such as uniqueness of the solution