In this paper, nonlinear Bayesian filtering techniques are applied to the localization of mobile radio communication devices. The application of this approach is demonstrated for the localization of DECT mobile telephones in a scenario with several base stations and a mobile handset. The received signal power, measured by the mobile
handsets, is related to their position by nonlinear measurement equations. These consist of a deterministic part, modeling the received signal power as a function of the position, and a stochastic part, describing model errors and measurement noise. Additionally, user models are considered, which express knowledge about the motion
of the user of the handset. The new Prior Density Splitting Mixture Estimator (PDSME), a Gaussian mixture filtering algorithm, significantly improves the localization quality compared to standard filtering techniques as the Extended Kalman Filter (EKF).
This paper is concerned with recursively estimating the internal
state of a nonlinear dynamic system by processing noisy measurements and the known system input. In the case of continuous states, an exact analytic representation of the probability
density characterizing the estimate is generally too complex for
recursive estimation or even impossible to obtain. Hence, it is replaced by a convenient type of approximate density characterized by a finite set of parameters. Of course, parameters are desired that systematically minimize a given measure of deviation between
the (often unknown) exact density and its approximation, which in general leads to a complicated optimization problem. Here, a new framework for state estimation based on progressive processing is proposed. Rather than trying to solve the original problem, it is exactly converted into a corresponding system of explicit ordinary first-order differential equations. Solving this system over a finite "time" interval yields the desired optimal density