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Robust covariance matrix estimation for radar space-time adaptive processing (STAP).

机译：雷达时空自适应处理（STAP）的鲁棒协方差矩阵估计。

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摘要

Estimating the disturbance or clutter covariance is a centrally important problem in radar space time adaptive processing (STAP) since estimation of the disturbance or interference covariance matrix plays a central role on radar target detection in the presence of clutter, noise and a jammer. The disturbance covariance matrix should be inferred from training sample observations in practice. Traditional maximum likelihood (ML) estimators are effective when homogeneous (target free) training data is abundant but lead to poor estimates, degraded false alarm rates, and detection loss in the regime of limited training. However, 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. The problem has been exacerbated by recent advances that have led to more antenna elements (J) and higher temporal resolution (P) time epochs resulting in a large dimension (N = JP).;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. Unlike unconstrained estimators, a vast majority of constrained radar STAP estimators are iterative and expensive numerically, which prohibits practical deployment. 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 of clutter/disturbance covariance. We demonstrate that the rank-constrained estimation problem can in fact be cast in the framework of a tractable convex optimization problem, and derive closed form expressions for the estimated covariance matrix. In addition, we derive a new covariance estimator for STAP that jointly considers a Toeplitz structure and a rank constraint on the clutter component. Past work has shown that in the regime of low training, even handling each constraint individually is hard and techniques often resort to slow numerically based solutions. Our proposed solution leverages the rank constrained ML estimator (RCML) of structured covariances to build a computationally friendly approximation that involves a cascade of two closed form solutions. Performance analysis using the KASSPER data set (where ground truth covariance is made available) shows that the proposed RCML estimator vastly outperforms state-of-the art alternatives even for low training including the notoriously difficult regime of K ≤ N training regimes and for the experiments considering real-world scenarios such as target detection performance and the case that some of training samples are corrupted by target information.;Finally, we address the problem of working with inexact physical radar parameters under a practical radar environment. As shown in this dissertation, employing practical constraints such as a rank of the clutter subspace and a condition number of disturbance covariance leads to a practically powerful estimator as well as a closed form solution. While the rank and the condition number are very effective constraints, often practical non-ideality makes it difficult to be known precisely using physical models. 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 expected likelihood criterion and formally derive and prove a significant analytical result such as uniqueness of the solution. 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 alternatives in the sense of a normalized signal-to-interference and noise ratio (SINR).
机译：在雷达空时自适应处理（STAP）中，估计干扰或杂波协方差是一个中心重要的问题，因为在存在杂波，噪声和干扰的情况下，干扰或干扰协方差矩阵的估计在雷达目标检测中起着核心作用。干扰协方差矩阵应从实践中的训练样本观察中推导出来。当同类（无目标）训练数据丰富时，传统的最大似然（ML）估计器很有效，但会导致估计不足，错误警报率下降以及训练受限时的检测损失。然而，由于难以保证无目标干扰的观测，时空非平稳性强加的实际限制以及系统方面的考虑，通常无法获得大量的同类训练样本。最近的进展加剧了这个问题，导致出现了更多的天线元件（J）和更高的时间分辨率（P）时间历元，从而导致尺寸较大（N = JP）。在本文中，我们希望解决上述挑战通过将物理启发约束条件用于ML估计。尽管增加限制有利于在有限训练的实际情况下获得令人满意的表现，但它带来了一个具有挑战性的问题。与无约束估计器不同，绝大多数受约束雷达STAP估计器在数值上都是迭代且昂贵的，这阻碍了实际部署。我们专注于打破计算可处理性与理想性能指标之间的经典折衷，尤其是在缺乏训练的情况下。特别是，我们利用扰动协方差的结构以及重要的杂波等级知识来产生新的杂波/扰动协方差的等级受限最大似然（RCML）估计器。我们证明了秩约束估计问题实际上可以在易处理凸优化问题的框架内进行转换，并为估计的协方差矩阵导出闭合形式的表达式。另外，我们为STAP导出了一个新的协方差估计器，该估计器共同考虑了Toeplitz结构和杂波分量的秩约束。过去的工作表明，在训练不足的情况下，即使单独处理每个约束也很困难，并且技术通常会采用基于数字的慢速解决方案。我们提出的解决方案利用了结构协方差的秩约束ML估计器（RCML）来构建一个计算友好的近似值，其中包括两个闭合形式解的级联。使用KASSPER数据集（可提供地面实数协方差）的性能分析表明，即使对于低训练量（包括众所周知的K≤N训练量的困难训练方案）和实验而言，所提出的RCML估计器也大大优于最新的替代方案。考虑到现实世界中的场景，例如目标检测性能以及一些训练样本被目标信息破坏的情况。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。如本论文所示，采用诸如杂波子空间的秩和干扰协方差的条件数之类的实际约束条件会导致产生实用的估计器以及闭式解。尽管等级和条件数是非常有效的约束条件，但通常实际的非理想性使得很难使用物理模型精确知道。我们提出了一种通过期望似然（EL）方法的鲁棒协方差估计方法。我们分析了三种不同情况下不完全约束的协方差估计算法：1）仅秩约束，2）秩和噪声功率约束，以及3）条件数约束。对于每种情况，我们将约束的估计公式化为具有预期似然准则的优化问题，并正式得出并证明重要的分析结果，例如解的唯一性。通过仿真模型和KASSPER数据集的实验结果，我们显示了在归一化的信噪比和噪声比（SINR）的意义上，通过EL方法获得的具有最优约束的估计器优于其他方法。

著录项

  • 作者

    Kang, Bosung.;

  • 作者单位

    The Pennsylvania State University.;

  • 授予单位 The Pennsylvania State University.;
  • 学科 Electrical engineering.
  • 学位 Ph.D.
  • 年度 2015
  • 页码 130 p.
  • 总页数 130
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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