A Total Lp-Norm Optimization for Bearing-Only Source Localization in Impulsive Noise with SαS Distribution

Ji-An Luo,Ying-Jiao Rong,Shen-Tu Han,Chang-Cheng Xue

doi:10.3390/s21196471

Abstract

This paper considers the problem of robust bearing-only source localization in impulsive noise with symmetric -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.

Highlights

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
Bearing-Only Source Localization (BOSL) using spatially distributed sensors can be widely applied in network localization [1], vehicle localization [2], gunshot localization [3], animal behavior monitoring [4] and rigid body localization [5], to name but a few
We focus on the problem of robust BOSL with impulsive noise modeled as Symmetric α-Stable (SαS) distribution

Summary

Introduction

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 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. The problem of BOSL is to estimate the source location from a set of noise-corrupted bearing measurements where its main challenge originates in the highly nonlinear nature of the angle observations with the true source position. It is necessary to develop new estimators that are robust to impulsive noise

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Conclusion