This paper considers the problem of robust bearing-only source localization in impulsive noise with symmetric α-stable distribution based on the Lp-norm minimization criterion. The existing Iteratively Reweighted Pseudolinear Least-Squares (IRPLS) method can be used to solve the least LP-norm optimization problem. However, the IRPLS algorithm cannot reduce the bias attributed to the correlation between system matrices and noise vectors. To reduce this kind of bias, a Total Lp-norm Optimization (TLPO) method is proposed by minimizing the errors in all elements of system matrix and data vector based on the minimum dispersion criterion. Subsequently, an equivalent form of TLPO is obtained, and two algorithms are developed to solve the TLPO problem by using Iterative Generalized Eigenvalue Decomposition (IGED) and Generalized Lagrange Multiplier (GLM), respectively. Numerical examples demonstrate the performance advantage of the IGED and GLM algorithms over the IRPLS algorithm.

Robust techniques critically improve bearing-only target localization when the relevant measurements are being corrupted by impulsive noise. Resistance to isolated gross errors refers to the conventional least absolute residual (LAR) method, and its estimate can be determined by linear programming when pseudolinear equations are set. The LAR approach, however, cannot reduce the bias attributed to the correlation between system matrices and noise vectors. In the present study, perturbations are introduced into the elements of the system matrix and the data vector simultaneously, and the total optimization problem is formulated based on least absolute deviations. Subsequently, an equivalent form of total least absolute residuals (TLAR) is obtained, and an algorithm is developed to calculate the robust estimate by dual ascent algorithms. Moreover, the performance of the proposed method is verified through the numerical simulations by using two types of localization geometries, i.e., random and linear. As revealed from the results, the TLAR algorithm is capable of exhibiting significantly higher localization accuracy as compared with the LAR method.