Underwater Target Tracking in Uncertain Multipath Ocean Environments

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.