Gaussian Mixture Filter for Multipath Assisted Positioning

Navigation in global navigation satellite system denied areas such as urban canyons or indoors has aroused large interest due to the recent growth of location aware services. In these scenarios, multipath-assisted positioning schemes are promising due to a rich multipath propagation. Instead of trying to combat multipath, multipath-assisted positioning approaches make use of multipath components arriving at a receiver that is to be located. In more detail, multipath components arriving at the receiver via different paths are regarded as pure line-of-sight signals from virtual transmitters. In general, the number of transmitters might be large, and their location may be unknown. The underlying estimation problem, i.e., estimating the positions of the receiver and the physical and virtual transmitters, tends to be very costly in computational terms. Within this paper, we present a Rao-Blackwellization approach to tackle the computational burden. The receiver location is tracked using a particle filter, while the probability density functions of the transmitter states are represented by Gaussian mixture models, whose parameters are estimated using cubature Kalman filters.