Bayesian Positioning Using Gaussian Mixture Models with Time-varying Component Weights

Gaussian mixture models are often used in target tracking applications to take into account maneuvers in state dynamics or changing levels of observation noise. In this study it is assumed that the measurement or the state transition model can have two plausible candidates, as for example in positioning with line-of-sight or non-line-sight-signals. The plausibility described by the mixture component weight is modeled as a time-dependent random variable and is formulated as a Markov process with a heuristic model based on the Beta distribution. The proposed system can be used to approximate some well-known multiple model systems by tuning the parameter of the state transition distribution for the component weight. The posterior distribution of the state can be solved approximately using a Rao-Blackwellized particle filter. Simulations of GPS pedestrian tracking are used to test the proposed method. The results indicate that the new system is able to find the true models and its root mean square error-performance is comparable to filters that know the true models.