This paper deals with measurement extraction, from an optical sensor's Focal Plane Array (FPA), of a streaking target. We use a model that assumes pixels are separated by dead zones and model the streaking target's point spread function (PSF) as a Gaussian PSF that moves during the optical sensor's integration time. We make an assumption that the target has a constant velocity over the sampling interval and parametrize its motion with a starting and ending position. The noise model for a single pixel has variance proportional to its area, consistent with a Poisson model of the number of nontarget originated photons. We develop a maximum likelihood (ML) method of estimating the target motion parameter vector based on the set of pixel measurements from the optical sensor. This paper then derives the Cramer–Rao lower bound (CRLB) on the estimation error of the target motion parameter. We then present a matched filter (MF) based definition of the signal-to-noise ratio (SNR) to use as a basis for comparison of Monte Carlo simulation based location estimates to the calculated CRLB. It is shown that the ML estimator for the starting and ending positions of a streak in the FPA is efficient for MFSNR $\geq 12$ dB. We then provide a test statistic for target detection and propose approximate distributions to set the detection threshold for specific detection ($P_D$) and false alarm probabilities ($P_{\text{FA}}$), which are then verified via simulations. This paper's major contributions are the proposal of an ML/MF method for measurement extraction of streaking targets, confirmation that this method achieves the best accuracy possible for realistic FPA sensors, i.e., it attains the CRLB, the introduction of a statistically supported definition of SNR for these measurements, and an evaluation of the target measurement detection performance. Furthermore, this paper shows that, given our MFSNR definition, the streak length and direction of motion in the FPA have a negligible effect on performance compared to the SNR where we show that with a 4-dB change, the detection performance increases dramatically.

中文翻译：

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使用泊松模型对 FPA 中的裸奔目标进行检测、位置估计和 CRLB

本文涉及从光学传感器的焦平面阵列 (FPA) 中提取条纹目标的测量值。我们使用假设像素被死区分隔的模型，并将裸奔目标的点扩散函数 (PSF) 建模为在光学传感器的积分时间内移动的高斯 PSF。我们假设目标在采样间隔内具有恒定速度，并使用起始位置和结束位置对其运动进行参数化。单个像素的噪声模型的方差与其面积成正比，这与非目标源光子数量的泊松模型一致。我们开发了一种最大似然 (ML) 方法，该方法基于来自光学传感器的像素测量集来估计目标运动参数向量。然后，本文推导出了目标运动参数估计误差的 Cramer-Rao 下界（CRLB）。然后，我们提出了一个基于匹配滤波器 (MF) 的信噪比 (SNR) 定义，用作将基于蒙特卡罗模拟的位置估计与计算出的 CRLB 进行比较的基础。结果表明，对于 FPA 中条纹的开始和结束位置的 ML 估计器对于 MFSNR $\geq 12 $ dB 是有效的。然后我们提供目标检测的测试统计量，并提出近似分布来设置特定检测的检测阈值（$P_D$）和误报概率（$P_{\text{FA}}$），然后通过模拟进行验证。本文的主要贡献是提出了一种用于裸奔目标测量提取的 ML/MF 方法，确认该方法实现了现实 FPA 传感器可能的最佳精度，即它达到了 CRLB，为这些测量引入了统计支持的 SNR 定义，以及对目标测量检测性能的评估。此外，本文表明，根据我们的 MFSNR 定义，与 SNR 相比，FPA 中的条纹长度和运动方向对性能的影响可以忽略不计，其中我们表明，随着 4-dB 的变化，检测性能显着提高。