In order to address the problem of 3-D localization of an underwater target using a 2-D active sonar with unknown oceanographic factors in a multipath environment with heavy clutter, a novel iterative framework based on Maximum Likelihood Probabilistic Data Association (ML-PDA), which considers ocean sound speed profile (SSP) uncertainty and utilizes multiple detections to realize 3-D position estimation with only bearing and time of flight (ToF) measurements, is proposed. ML-PDA is highly effective in low SNR target detection. However, it is limited by its assumption of at most one target-originated detection within a scan. To estimate the 3-D target state with multipath detections under weak observability conditions, we first extend the ML-PDA into a multipath ML-PDA by enumerating the combined association events formed from multiple detection patterns. In contrast to the situation in air target tracking, the water column is nonhomogeneous and the underwater sound speed profile varies, influenced by uncertain ocean factors, e.g., temperature, salinity, and pressure. The resultant acoustic signal travels in a curvilinear path instead of a straight line. In this article, an SSP-dependent ToF measurement model is derived for both the direct path and the surface-reflected path between two remote nodes, so that the SSP uncertainty can be addressed systematically. By adopting an iterative prediction-update methodology, we first propagate the SSP uncertainty into the modified measurement covariance with the help of the unscented sampling technique. Then, we formulate a new joint likelihood ratio (JLLR) function based on the modified measurement covariance within the multidetection ML-PDA framework. A hybrid optimization method with grid search and particle swarm optimization is applied to solve the complex JLLR objective function and to find the optimal target state estimate from a large surveillance region. Finally, a sequential update technique is used to update the SSP state with the estimated target state and sensor measurements. In subsequent iterations, a more accurate JLLR can be rebuilt based on the updated SSP state, which can help find a better parameter estimate eventually. In addition, the Cramér-Rao lower bound, which quantifies the best possible accuracy in the presence of SSP uncertainties, is derived and analyzed. Numerical simulations confirm the underwater target localization performance of the proposed method in the presence of heavy clutter in an unknown ocean environment with a realistic sound propagation model.

中文翻译：

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不确定多路径海洋环境中的水下目标跟踪


为了解决在重杂波多径环境下使用具有未知海洋因素的二维主动声纳对水下目标进行3D定位的问题，提出了一种基于最大似然概率数据关联（ML-PDA）的新型迭代框架提出了考虑海洋声速剖面 (SSP) 不确定性并利用多重检测仅通过方位和飞行时间 (ToF) 测量来实现 3D 位置估计。 ML-PDA 在低信噪比目标检测中非常有效。然而，它受到一次扫描中至多一个目标发起的检测的假设的限制。为了在弱可观测性条件下通过多路径检测来估计 3D 目标状态，我们首先通过枚举由多个检测模式形成的组合关联事件将 ML-PDA 扩展为多路径 ML-PDA。与空中目标跟踪的情况相反，水柱是不均匀的，水下声速剖面变化，受到不确定的海洋因素（例如温度、盐度和压力）的影响。由此产生的声信号沿曲线路径而不是直线传播。本文针对两个远程节点之间的直接路径和表面反射路径推导了依赖于 SSP 的 ToF 测量模型，从而可以系统地解决 SSP 不确定性。通过采用迭代预测更新方法，我们首先借助无迹采样技术将 SSP 不确定性传播到修改后的测量协方差中。然后，我们基于多重检测 ML-PDA 框架内修改的测量协方差制定了新的联合似然比 (JLLR) 函数。 应用网格搜索和粒子群优化的混合优化方法来求解复杂的 JLLR 目标函数，并从大监视区域中找到最佳目标状态估计。最后，使用顺序更新技术根据估计的目标状态和传感器测量值更新 SSP 状态。在后续迭代中，可以根据更新的SSP状态重建更准确的JLLR，这有助于最终找到更好的参数估计。此外，还导出并分析了 Cramér-Rao 下限，该下限量化了存在 SSP 不确定性的情况下的最佳可能精度。数值模拟通过真实的声音传播模型证实了该方法在未知海洋环境中存在重杂波的情况下的水下目标定位性能。