The Sensitivity analysis of Box Gaussian Mixture Filter

In this paper, we study the sensitivity of the Box Gaussian Mixture Filter (BGMF) in hybrid positioning. The idea of BGMF is to split the state space into pieces using parallel planes when necessary and approximate the restriction of a Gaussian component in each piece as a Gaussian. In the sensitivity analysis, we change the distance between the parallel planes and examine how that affects the filter accuracy in hybrid positioning. We see that BGMF is not very sensitive to the distance between the parallel planes. 1 Hybrid positioning Hybrid positioning means that measurements used in positioning come from different sources e.g. Global Navigation Satellite System, Inertial Measurement Unit, barometer, or local wireless networks such as a cellular network. Range, pseudorange, deltarange, altitude and restrictive [4] measurements are examples of typical measurements in hybrid positioning. In the hybrid positioning case, it is common that the measurements are nonlinear and thus the posterior density may have multiple peaks (multiple positioning solutions). In these cases, traditional single-component positioning filters, such as Extended Kalman Filter (EKF), perform poorly [5]. This is the reason for developing Gaussian Mixture Filter (GMF) for hybrid positioning [2]. GMF (also called Gaussian Sum Filter [6]) is an approximation of the Bayesian filter when prior and posterior densities are Gaussian mixtures, i.e. convex combinations of normal density functions. An other possibility is to use the general nonlinear Bayesian filter, which is usually implemented as a particle filter or a point mass filter. These filters usually work correctly and give good positioning accuracy but require a lot of computation time and memory. Digest of TISE Seminar 2009, Editor Pertti Koivisto, pages 70-75