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This paper presents several methods based on signal strength and wave scattering models for tracking a user. The received-signal level method is first used in combination with maximum likelihood (ML) estimation and triangulation to obtain an estimate of the location of the mobile. Due to nonline-of-sight conditions and multipath propagation environments, this estimate lacks acceptable accuracy for demanding services, as the numerical results reveal. The 3-D wave scattering multipath channel model of Aulin is employed, together with the recursive nonlinear Bayesian estimation algorithms to obtain improved location estimates with high accuracy. Several Bayesian estimation algorithms are considered, such as the extended Kalman filter (EKF), the particle filter (PF), and the unscented PF (UPF). These algorithms cope with nonlinearities in order to estimate mobile location and velocity. Since the EKF is very sensitive to the initial state, we propose the use of the ML estimate as the initial state of the EKE In contrast to the EKF tracking approach, the PF and UPF approaches do not rely on linearized motion models, measurement relations, and Gaussian assumptions. Numerical results are presented to evaluate the performance of the proposed algorithms when the measurement data do not correspond to the ones generated by the model. This shows the robustness of the algorithm based on modeling inaccuracies. Index Terms--Kalman filtering, location tracking, maximum likelihood estimation (MLE), multipath fading channels, particle filtering.

A new time-varying (TV) long-term fading (LTF) channel model which captures both the space and time variations of wireless systems is developed. The proposed TV LTF model is based on a stochastic differential equation driven by Brownian motion. This model is more realistic than the static models usually encountered in the literature. It allows viewing the wireless channel as a dynamical system, thus enabling well-developed tools of adaptive and nonadaptive estimation and identification techniques to be applied to this class of problems. In contrast with the traditional models, the statistics of the proposed model are shown to be TV, but converge in steady state to their static counterparts. Moreover, optimal power control algorithms (PCAs) based on the new model are proposed. A centralized PCA is shown to reduce to a simple linear programming problem if predictable power control strategies (PPCS) are used. In addition, an iterative distributed stochastic PCA is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal-to-interference ratio. Generalizations of the power control problem based on convex optimization techniques are provided if PPCS are not assumed. Numerical results show that there are potentially large gains to be achieved by using TV stochastic models, and the distributed stochastic PCA provides better power stability and consumption than the distributed deterministic PCA.