Minimum determinant estimate for source bearing estimation in shallow-water waveguides

Most prevalent source bearing estimation methods are based on the plane-wave assumption, which might lead to biases in the estimates due to multimode propagation in waveguide channels, especially when the source is near the endfire direction of the sensor array. While the environment-dependent method, such as matched field processing (MFP), can provide unbiased estimates, it requires either a computationally expensive 3-D search over range, depth and bearing or prior knowledge of the source range and depth. The recently-developed subspace intersection method (SIM) circumvents these limitations by exploiting the alignment between the signal vector and the modal subspace, enabling accurate bearing estimation via a 1-D search. However, it requires prior knowledge of the number of sources. This work reformulates source bearing estimation as a matrix similarity measurement problem. It is demonstrated that the maximum likelihood estimate (MLE) for the source bearing can be derived by minimizing a tailored Euclidean distance between the sampled covariance matrix and the modal subspace projection matrix. Furthermore, a novel minimum determinant estimate (MDE) is proposed based on the Jensen-Bregman LogDet divergence, which minimizes the determinant of the sum of the data sampled covariance matrix and the modal subspace projection matrix. Numerical simulations in a shallow water waveguide demonstrate that the MDE achieves accurate bearing estimation of multiple sources without requiring information on the number of sources, and produces ambiguity surfaces with a clean background. The proposed method is also validated using experimental data from the SWellEx-96 trial.