部分均匀环境下基于几何中心的扩展目标检测

Adaptive detection for distributed targets based on geometric median in partially homogeneous environment

摘要:

针对部分均匀环境中样本数有限以及样本中包含异常值时的扩展目标检测问题，设计了一类基于几何中心的自适应检测器，其包含两个步骤，第一步，构建基于几何中心广义内积的数据选择器，用以剔除包含异常值的样本数据；第二步，利用基于几何中心的协方差矩阵估计量，构建广义自适应子空间检测器的检测统计量。所设计的检测器利用正定矩阵空间中的几何中心特性，无需获得样本数据的先验概率分布。在分析阶段，根据异常值正确剔除概率、恒虚警特性和检测概率，评估检测器的性能。通过仿真数据和实测数据验证，相比传统检测器，本文提出的检测器具有更好的性能。

Abstract:

To solve the problem of adaptive detection for distributed targets in partially homogeneous environment with outliers and limited samples, a class of adaptive detectors are designed based on geometric median in this paper. The first step is to construct a data selector based on geometric median generalized inner product and eliminate sample data containing outliers. The second step is to construct detection statistics of the generalized adaptive subspace detector using covariance matrix estimators, which are based on geometric median. The detectors utilize geometric median of the positive definite matrix space without any knowledge of prior probability distribution of sample data. The performance of the proposed two-step detectors is evaluated in terms of the probabilities of correct outliers excision, false alarm, and detection. Experiment results based on simulated and real data show that the proposed approach has better detection performance than the existing ones based on traditional covariance estimator.