Robust Localization Method Based on Non-Parametric Probability Density Estimation

Abstract

This paper presents robust localization techniques that calculate location using distance observations. In enclosed and heavily populated urban environments, the positive measurement bias introduced by a non-line-of-sight signal can have a considerable adverse impact on estimation performance. Therefore, to mitigate the detrimental effects of the multipath effect caused by the non-line-of-sight signal, robust localization techniques are considered. In particular, the ${k}$ -nearest neighbor (KNN)-based and orthogonal series (OSERIES)-based localization approaches are proposed. The difference from conventional probability density estimation (PDF) estimation methods is that the proposed methods use the first-peak information of the estimated PDF to obtain the actual distance information, not just the PDF shape estimation. More specifically, the proposed methods use the mean calculated from observations selected by statistical testing because the mean estimate generally outperforms the mode estimate. In addition, the Rao test in the context of the two-mode Gaussian mixture model (GMM) is demonstrated to be uniformly most powerful (UMP) test. Furthermore, the conditional variance of the range measurement is derived. Also, the proposed techniques outperforms that of competing algorithms in terms of localization accuracy.

Keywords

• First peak
• Gaussian mixture model
• k-nearest neighbor
• localization
• non-line-of-sight
• orthogonal series