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

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.