Revisiting Skipped Filter and Development of Robust Localization Method Based on Variational Bayesian Gaussian Mixture Algorithm

This paper presents robust positioning methods that use distance observations to estimate location parameters. The propagation of a non-line-of-sight (NLOS) signal can significantly affect the estimation performance in indoor and densely populated urban areas. Hence, robust localization algorithms are considered for alleviating the adverse effects of the NLOS signal. In particular, the skipped filter is derived theoretically and a robust localization method based on the variational Bayesian Gaussian mixture model (VB GMM) is proposed. The skipped filter has been introduced in the existing literature; however, the derivation of the skipped filter has not been addressed in the previous study. Therefore, we construct the mathematical derivation of the skipped filter in the formulation of the maximum likelihood estimation (MLE). In addition, the VB GMM weighted least squares (WLS) method is presented, wherein the VB GMM WLS method is based on the two-mode GMM. Furthermore, the localization accuracies of the proposed methods are found to be superior to those of the other algorithms. However, it is not guaranteed that NLOS error is necessarily a two-mode GMM. Therefore, we investigate the robustness of the proposed methods against modeling errors using the other state-of-the-art NLOS error distributions, such as the skew-t and Gaussian-uniform mixture models.