Sequential Channel State Tracking & SpatioTemporal Channel Prediction in Mobile Wireless Sensor Networks

We propose a nonlinear filtering framework for approaching the problems of channel state tracking and spatiotemporal channel gain prediction in mobile wireless sensor networks, in a Bayesian setting. We assume that the wireless channel constitutes an observable (by the sensors/network nodes), spatiotemporal, conditionally Gaussian stochastic process, which is statistically dependent on a set of hidden channel parameters, called the channel state. The channel state evolves in time according to a known, non stationary, nonlinear and/or non Gaussian Markov stochastic kernel. Recognizing the intractability of general nonlinear state estimation, we advocate the use of grid based approximate filters as an effective and robust means for recursive tracking of the channel state. We propose a sequential spatiotemporal predictor for tracking the channel gains at any point in time and space, providing real time sequential estimates for the respective channel gain map, for each sensor in the network. Non trivial, real time recursive estimators of the variance of the channel gain map predictions are also developed. Additionally, we show that all three estimators converge towards the true respective MMSE optimal estimators, in a common, relatively strong sense. Numerical simulations corroborate the effectiveness of the proposed approach.