Correlated multi-paths may cause a biased bearing estimation in shallow water, so most existing methods make fully use of the multi-path nature and the underwater channel property to provide an unbiased bearing estimation. However, an imprecise knowledge of the underwater channel parameters or the array model mismatches will cause performance degradation, especially for the high-resolution methods. Therefore development of robust bearing estimation methods in shallow water is critically important. In this paper, a new approach to robust bearing estimation is proposed in the presence of underwater channel parameter uncertainties or array model mismatches. The proposed method is based on the convex optimization theory, exactly to say, the vector optimization theory, and can be derived by imposing a certain constraint on the Euclidean norm of the source vector. It is shown that the proposed method can be reformulated as a convex secondorder cone program (SOCP) problem and solved efficiently by the well-established interior point method, such as SEDUMI. Computer simulations and experiment analysis show that the proposed method is highly robust against the underwater channel parameter uncertainties and array model mismatches, moreover, demonstrates its excellent performance as compared with existing methods.

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