Grid Based Nonlinear Filtering Revisited: Recursive Estimation & Asymptotic Optimality
We propose a nonlinear filtering framework for channel state tracking and spatiotemporal channel gain prediction in mobile wireless sensor networks, in a Bayesian setting. Under common assumptions, 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 Gaussian Markov stochastic kernel. Advocating 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 respective channel gain map, for each sensor in the network. We also show that both estimators (state and gain map trackers) converge towards the true respective Minimum Mean Squared Error (MMSE) optimal estimators, in a common, relatively strong sense. Numerical simulations corroborate the practical effectiveness of the proposed approach.