雷达空时自适应处理中的抗差协方差阵估计（STAP）
Robust Covariance Matrix Estimation for Radar Space-Time Adaptive Processing (STAP)
摘要：
估计干扰或杂波协方差是雷达空时自适应处理（STAP）中的一个重要问题。在实际应用中，需要从训练样本观测值中推导出干扰协方差阵。由于难以保证目标无干扰观测、时空非平稳性带来的实际限制以及系统考虑因素，通常无法获得大量同质训练样本。在本论文中，我们希望通过利用ML估计中的物理约束来解决上述挑战。虽然增加约束有利于在有限训练的实际制度中实现令人满意的性能，但它导致了一个具有挑战性的问题。我们专注于打破这种经典的计算易处理性和理想的性能指标之间的权衡，特别是在训练饥饿的制度。特别是，我们利用结构的干扰协方差和重要的知识的杂波秩产生一个新的秩约束极大似然（RCML）估计。此外，我们推导出一个新的协方差估计STAP联合考虑Toeplitz结构和杂波分量的秩约束。最后，我们解决了在实际雷达环境下使用不精确的物理雷达参数的问题。我们提出了一个强大的协方差估计方法通过期望似然（EL）的方法。本文分析了三种不同约束条件下的协方差估计算法：1）仅秩约束，2）秩和噪声功率约束，3）条件数约束。对于每一种情况下，我们制定的约束作为一个优化问题的EL标准的估计，并正式推导和证明一个重要的分析结果，如唯一的解决方案。
英文摘要：
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.
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