Robust subspace intersection method for source bearing estimation in uncertain shallow water

Traditional bearing estimation methods assuming plane wave propagation suffer significant measurement errors due to multi-modal propagation in ocean waveguides, particularly for sources near the endfire of a horizontal line array (HLA). The HLA signal wavefront is a linear combination of modal steering vectors, characterized by modal horizontal wavenumbers, spanning the modal subspace. The subspace intersection (SI) method matches this signal subspace with replica modal subspaces for measuring source bearing but requires precise wavenumber knowledge. Uncertainty in environmental parameters renders wavenumbers unknown, causing SI performance degradation. In this work, we propose a robust SI method for uncertain shallow water. We suggest to incorporate the value range of modal horizontal wavenumbers resulting from the uncertain environment to construct a high-dimensional modal subspace. By using an optimization criterion derived from minimizing global bearing errors, we present a simple metric to truncate redundant dimensions to achieve the effective modal span. The resulting processor, termed the effective-modal-subspace-based SI (EM-SI), exhibits better performance than the SI. Simulations in a benchmark uncertain waveguide confirm that the EM-SI outperforms the SI and traditional methods in bearing measurement errors and resolution. Real data from the SWellEx96 sea trial further demonstrates its effectiveness.