When electromagnetic waves impinge on objects with complex geometries and/or internal structure, we can observe scattering that is distributed in time rather than instantaneous. To detect and characterize such targets, we build the coordinate‐delay synthetic aperture radar (cdSAR) images by adding a delay term to the standard SAR matched filter. In order to apply this approach to the case of extended targets where the image intensity and phase are subject to strong and rapid variations (the phenomenon called speckle), we sample the cdSAR image at several coordinate‐delay “points” in the vicinity of the scatterer location. The discrimination between the instantaneous and delayed targets is realized through autocorrelation analysis of this sample. Because of the statistical properties of speckle, misclassification errors are inevitable. Hence, prediction of the error rate as a function of system and target parameters becomes an important problem. While Monte Carlo simulations can generate the ensembles of data for direct calculation of the error rate, this approach is computationally demanding because of its slow convergence. In order to simplify the prediction of the error rate, we employ statistical divergence measures, namely, the Hellinger distance and Kullback‐Leibler divergence. These divergence measures are calculated directly from the theoretical models of reflectivity of extended targets that we want to distinguish. We empirically establish a linear relation between the misclassification rate and the Hellinger distance for a certain class of simple target models. This relation allows us to make predictions of the error rate without performing the Monte Carlo simulations.

中文翻译：

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SAR分散目标的发散测度和检测性能。

当电磁波撞击具有复杂几何形状和/或内部结构的对象时，我们可以观察到散射是按时间而不是瞬时分布的。为了检测和表征此类目标，我们通过在标准SAR匹配滤波器中添加延迟项来构建坐标延迟合成孔径雷达（cdSAR）图像。为了将这种方法应用于图像强度和相位会发生强烈而快速变化（称为斑点的现象）的扩展目标，我们在cdSAR图像附近的几个坐标延迟“点”处进行采样散射体位置。瞬时目标和延迟目标之间的区别是通过对此样本进行自相关分析来实现的。由于斑点的统计特性，错误分类错误是不可避免的。因此，作为系统和目标参数的函数的错误率的预测成为重要的问题。尽管蒙特卡洛模拟可以生成数据集合以直接计算错误率，但由于其收敛速度较慢，因此该方法在计算上要求很高。为了简化错误率的预测，我们采用统计差异度量，即Hellinger距离和Kullback-Leibler差异。这些发散度量是直接根据我们要区分的扩展目标的反射率理论模型计算得出的。我们凭经验在特定类型的简单目标模型中建立了误分类率与Hellinger距离之间的线性关系。这种关系使我们无需执行蒙特卡洛模拟就可以预测错误率。