Robust DRSS Based Localization in Sensor Networks With Generalized Gaussian Noise

Abstract

This letter addresses the problem of robust differential received signal strength (DRSS) based localization in the presence of generalized Gaussian noise. Instead of transforming the nonlinear equation into a pseudo-linear equation, we develop a maximum likelihood (ML) estimator which is based on the unconstrained <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{p}$ </tex-math></inline-formula> -norm optimization problem for highly nonlinear cost functions. A non-iterative Monte Carlo importance sampling (MCIS) method is proposed to solve the optimization problem. To obtain the global optimal solution using relatively a fair number of random particles, a robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -norm based estimator for initial position is developed by solving the linear programming problem. The MCIS- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> method can yield a nearly unbiased estimate and avoid derivation or matrix multiplication operations compared to these algorithms that are based on pseudo-linear measurement equations. Simulation shows that the localization algorithm proposed in this letter achieves significant performance improvement in wireless sensor network localization with generalized Gaussian noise.