UWB Positioning with Generalized Gaussian Mixture Filters

Abstract

Low-complexity Bayesian filtering for nonlinear models is challenging. Approximative methods based on Gaussian mixtures (GM) and particle filters are able to capture multimodality, but suffer from high computational demand. In this paper, we provide an in-depth analysis of a generalized GM (GGM), which allows component weights to be negative, and requires significantly fewer components than the traditional GM for ranging models. Based on simulations and tests with real data from a network of UWB nodes, we show how the algorithm's accuracy depends on the uncertainty of the measurements. For nonlinear ranging the GGM filter outperforms the extended Kalman filter (EKF) in both positioning accuracy and consistency in environments with uncertain measurements, and requires only slightly higher computational effort when the number of measurement channels is small. In networks with highly reliable measurements, the GGM filter yields similar accuracy and better consistency than the EKF.