Efficient Gaussian mixture filter for hybrid positioning

This paper presents a new way to apply Gaussian mixture filter (GMF) to hybrid positioning. The idea of this new GMF (efficient Gaussian mixture filter, EGMF) is to split the state space into pieces using parallel planes and approximate posterior in every piece as Gaussian. EGMF outperforms the traditional single-component positioning filters, for example the extended Kalman filter and the unscented Kalman filter, in nonlinear hybrid positioning. Furthermore, EGMF has some advantages with respect to other GMF variants, for example EGMF gives the same or better performance than the sigma point Gaussian mixture (SPGM) [1] with a smaller number of mixture components, i.e. smaller computational and memory requirements. If we consider only one time step, EGMF gives optimal results in the linear case, in the sense of mean and covariance, whereas other GMFs gives suboptimal results.