Track-before-detect (TkBD) algorithms have been shown to greatly abate measurement-to-track association (MTA) challenges. These simplifications are aptly relevant for reducing operator workload in deployed sonar systems that require a human “in-the-loop.” In a prior manuscript a case study of a passive bearings-only target motion analysis TkBD algorithm was demonstrated in complex sonar scenarios relevant to advanced fielded sonar systems. In this manuscript, a Cramer-Rao Lower Bound (CRLB) is derived for the algorithm previously developed. The approximations used in developing the CRLB are validated with a real data set. The CRLB itself, as a predictor of state estimation error performance, is validated with single- and multi-contact simulated data scenarios. The prior algorithm and CRLB derived herein is applicable to passive sonar, active sonar, radar, and optical applications through a change of point spread functions and Jacobians. The CRLB derived is simple to implement, requires minimal statistical assumptions, and is applicable to similarly implemented TkBD algorithms.

中文翻译：

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被动声纳检测前跟踪算法的 Cramemer-Rao 下界推导


检测前跟踪 (TkBD) 算法已被证明可以极大地减轻测量与跟踪关联 (MTA) 的挑战。这些简化非常适合减少需要人工“在环”的已部署声纳系统中操作员的工作量。在之前的手稿中，在与先进现场声纳系统相关的复杂声纳场景中演示了仅被动轴承目标运动分析 TkBD 算法的案例研究。在本手稿中，为先前开发的算法推导了 Cramer-Rao 下界 (CRLB)。开发 CRLB 时使用的近似值已通过真实数据集进行了验证。 CRLB 本身作为状态估计误差性能的预测器，通过单接触和多接触模拟数据场景进行了验证。本文导出的现有算法和 CRLB 通过点扩散函数和雅可比行列式的改变适用于无源声纳、有源声纳、雷达和光学应用。导出的 CRLB 实现起来很简单，需要最少的统计假设，并且适用于类似实现的 TkBD 算法。