Robust source localization in shallow water based on vector optimization

Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the underwater environment and have poor robustness against the underwater channel uncertainty, which limit their further application in practical engineering. In this paper, a new method of source localization in shallow water, based on vector optimization concept, is described, which is highly robust against environmental factors affecting the localization, such as the channel depth, the bottom reflection coefficients, and so on. Through constructing the uncertainty set of the source vector errors and extracting the multi-path sound rays from the sea surface and bottom, the proposed method can accurately localize one or more sources in shallow water dominated by multipath propagation. It turns out that the natural formulation of our approach involves minimization of two quadratic functions subject to infinitely many nonconvex quadratic constraints. It shows that this problem (originally intractable) can be reformulated in a convex form as the so-called second-order cone program (SOCP) and solved efficiently by using the well-established interior point method, such as the software tool, SeDuMi. Computer simulations show better performance of the proposed method as compared with existing algorithms and establish a theoretical foundation for the practical engineering application.