This paper follows a detection-theoretic approach for using synthetic-aperture measurements, made at multiple moving passive receivers, in order to form an image showing the locations of stationary sources that are radiating unknown electromagnetic or acoustic waves. The paper starts with a physics-based model for the propagating fields, and, following the general approach of McWhorter et al (2023 arXiv:2302.06816, IEEE Open J. Signal Process. 4 437–51), derives a detection statistic that is used for the image formation. This detection statistic is a quadratic function of the data. Each point in the scene is tested as a possible hypothesized location for a source, and the detection statistic is plotted as a function of location. Because this image formation process is nonlinear, the standard linear methods for determining resolution cannot be applied. This paper shows how to analyze the detection image by first writing the noiseless image as a coherent sum of shifted complex ambiguity functions of the source waveform. The paper then develops a technique for calculating image resolution; resolution is found to depend on the sensor-source geometry and also on the properties (bandwidth and temporal duration) of the source waveform. Optimal filtering of the image is given, but a simple example suggests that optimal filtering may have little effect. Analysis is also given for the case in which multiple sources are present.

中文翻译：

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基于检测的合成孔径被动源定位的图像分析和分辨率

本文遵循一种检测理论方法，使用在多个移动无源接收器上进行的合成孔径测量，以形成显示辐射未知电磁波或声波的固定源位置的图像。本文从传播场的基于物理的模型开始，并遵循 McWhorter 的一般方法等人（2023 年 arXiv：2302.06816,IEEE Open J. 信号处理。 4437-51），导出用于图像形成的检测统计量。该检测统计量是数据的二次函数。场景中的每个点都被测试为源的可能假设位置，并且检测统计数据被绘制为位置的函数。由于该图像形成过程是非线性的，因此无法应用用于确定分辨率的标准线性方法。本文展示了如何通过首先将无噪声图像写入源波形的移位复模糊函数的相干和来分析检测图像。然后，本文开发了一种计算图像分辨率的技术；研究发现分辨率取决于传感器源的几何形状以及源波形的属性（带宽和持续时间）。给出了图像的最佳过滤，但一个简单的例子表明最佳过滤可能效果不大。还对存在多个源的情况进行了分析。