3D passive localization in shallow water using bearing and multipath time-delay measurements

In the passive underwater context the presence of two bounding surfaces (i.e., sea surface and seabed) results in several paths between the receiver and the source. In this paper we propose a novel closed-form least-squares (LS) solution by combining the time-delay information with angle measurements. Despite its simplicity, the LS estimator exhibits poor localization performance as a result of ignoring the dependence between the entries of the unknown parameter vector. To overcome this, we develop a constrained LS (CLS) estimator which not only outperforms the LS estimator, but also provides a bias and variance performance comparable to that of the computationally demanding maximum likelihood estimator (MLE). The LS and CLS estimators developed in the paper are computationally much less expensive than MLE and do not require any initialization or prior knowledge of the measurement noise covariance. The performance of the proposed LS and CLS estimators and MLE is illustrated with simulation examples.