Robust localisation methods based on modified skipped filter weighted least squares algorithm

Abstract

Robust localisation techniques that utilise distance observations to determine the location are focused upon. In urban environments with limited visibility and high population density, the presence of non-line-of-sight signals can introduce a positive measurement bias, negatively affecting the accuracy of estimation. To resolve this problem caused by multipath effects, robust localisation techniques have been explored, specifically the skipped filter weighted least squares (WLS) method for localisation. However, the squared estimation bias of the transformed distance estimate of the existing skipped filter WLS method is high in the low signal-to-noise ratio condition owing to the second-order noise terms. Therefore, the modified skipped filter WLS methods are proposed to reduce the squared estimation bias of transformed distance estimate. First, the closed-form modified skipped filter WLS method uses the maximum likelihood estimate (MLE) to reduce the squared estimation bias of the transformed distance estimate. In addition, the modified skipped filter WLS method using the online ML and online expectation maximisation (EM) algorithms are introduced whose advantage is that they do not require the number of Gaussian components unlike the existing Gaussian mixture model EM algorithm. The mean square error analysis of proposed closed-form skipped filter WLS and existing skipped filter WLS methods is performed. Furthermore, the localisation accuracy of the proposed techniques is found to outperform that of competing algorithms via simulation results.