Modified MM Algorithm and Bayesian Expectation Maximization-Based Robust Localization Under NLOS Contaminated Environments

Robust localization methods that employ distance measurements to predict the position of an emitter are proposed in this paper. The occurrence of outliers due to the non-line-of sight (NLOS) propagation of signals can drastically degrade the localization performance in crowded urban areas and indoor situations. Hence, robust positioning methods are considered to mitigate the effects of outliers. Specifically, localization methods based on robust statistics are considered. Modified multi-stage ML-type method (MM) based weighted least squares (WLS), maximum a posteriori (MAP) expectation maximization (EM) WLS and variational Bayes (VB) EM WLS algorithms are developed under various outlier-contaminated environments. Simulation results show that the position estimation accuracy of the proposed modified MM WLS method, which uses the novel weight, is higher than that of the other methods under most outlier-contaminated conditions. Furthermore, the MAP-EM WLS and VB-EM WLS methods are the most accurate among algorithms that do not require statistical testing. Additionally, the mean square error (MSE) and asymptotic unbiasedness of the proposed algorithms are analyzed.