Robust LMedS-Based WLS and Tukey-Based EKF Algorithms Under LOS/NLOS Mixture Conditions

Joon-Hyuk Chang,Chee-Hyun Park

doi:10.1109/access.2019.2946376

Abstract

In this paper, we present robust localization algorithms that use range measurements. The least median of squares (LMedS)-weighted least squares (WLS), LMedS-spherical simplex unscented transform (SSUT) based WLS and Tukey-based extended Kalman filter (EKF) algorithms are proposed for line-of-sight (LOS)/non-line-of-sight (NLOS) mixture environments. First, the LMedS solution is obtained, and then sensors are predicted to be LOS or LOS/NLOS mixture sensors. The range observation predicted as an outlier is replaced with the estimated distance obtained using the LMedS algorithm. Subsequently, the two-step WLS method is executed using these new distance measurements. In the Tukey-based EKF method, Tukey's risk function and the 3-σ edit rule are employed in the innovation step. Furthermore, the mean square error (MSE) analysis of the proposed algorithms is performed. We demonstrate that the positioning accuracy of the proposed methods is higher than that of conventional methods through extensive simulation.

Highlights

Source localization is a technique in which the coordinates of the source are determined by utilizing measurements from each sensor, including the time difference of arrival (TDOA), the time of arrival (TOA), the received signal strength (RSS), or the angle of arrival (AOA)
We develop robust closed-form localization methods, i.e., least median of squares (LMedS)-weighted least squares (WLS) and LMedS-spherical simplex unscented transform (SSUT) WLS, where the LMedS algorithm is adopted as an initial solution to estimate the outlier-resistant distance
SIMULATION RESULTS We compared the performance of the proposed LOS/NLOS mixed emitter positioning methods with those of a robust LMedS method [16], a bi-section estimator [39] and a maximum correntropy criterion (MCC)-extended Kalman filter (EKF) technique [40]

Summary

INTRODUCTION

Source localization is a technique in which the coordinates of the source are determined by utilizing measurements from each sensor, including the time difference of arrival (TDOA), the time of arrival (TOA), the received signal strength (RSS), or the angle of arrival (AOA). We utilize the LMedS estimation to eliminate the adverse effects of outliers in the context of LOS/NLOS mixture localization and to obtain an initial solution. Chang: Robust LMedS-Based WLS and Tukey-Based EKF Algorithms Under LOS/NLOS Mixture Conditions the proposed LMedS-weighted least squares (WLS) method employing the newly updated distances and the extended Kalman filter (EKF) using Tukey’s cost function and 3-σ edit rule are implemented. Accurate positioning is infeasible in the LOS/NLOS mixture environments; we develop the Tukey-based EKF, in which the LMedS solution is used as the initial state vector and Tukey’s risk function is utilized in the innovation computation step. The EKF-based robust localization method combining Tukey’s risk function and the 3-σ edit rule has not been studied.

PROBLEM FORMULATION

Choose the weight

THE LMedS-WLS ALGORITHM

Calculate the Kalman gain

SIMULATION RESULTS

CONCLUSION