Robust EKF Based on Shape Parameter Mixture Distribution for Wireless Localization With Time-Varying Skewness Measurement Noise

In this article, we explore the state estimation challenge in wireless localization (WL) when faced with the time-varying skewness measurement noise arising from the variable nonline-of-sight (NLOS) and imperfect synchronization. To model this kind of noise, we employ a shape parameter mixture (SPM) distribution, which is obtained by mixing the shape parameters of a Gaussian scale mixture (GSM) distribution and is structured in a hierarchical Gaussian form. We then develop an extended Kalman filter (KF) based on the SPM distribution, which can adjust the skewness parameters adaptively by employing the variational Bayesian approach to approximate the exact joint posterior probability density functions of the system state and measurement noise parameters. Several existing works are special cases of our generalized estimation algorithms by choosing different hyperparameters. Extensive simulations and experiments demonstrate that the proposed algorithm surpasses the existing counterparts in the presence of the time-varying skewness noise.