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Asymptotically Optimal Discrete Time Nonlinear Filters From Stochastically Convergent State Process Approximations
"... We consider the problem of approximating optimal in the MMSE sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More specifically, we consider a class of nonlinear, partially observable stochastic systems, comprised b ..."
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We consider the problem of approximating optimal in the MMSE sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More specifically, we consider a class of nonlinear, partially observable stochastic systems, comprised by a (possibly nonstationary) hidden stochastic process (the state), observed through another conditionally Gaussian stochastic process (the observations). Under general assumptions, we show that, given an approximating process which, for each time step, is stochastically convergent to the state process in some appropriate sense, an approximate filtering operator can be defined, which converges to the true optimal nonlinear filter of the state in a strong and well defined sense, i.e., compactly in time and uniformly in a completely characterized measurable set of probability measure almost unity, also providing a purely quantitative justification of Egoroff’s Theorem for the problem at hand. The results presented in this paper can form a common basis for the analysis and characterization of a number of heuristic approaches for approximating a large class of optimal nonlinear filters, such as approximate grid based techniques, known to perform well in a variety of applications.
Sequential channel state tracking & spatiotemporal channel prediction in mobile wireless sensor networks
 IEEE Transactions on Signal and Information Processing over Networks, submitted in 2015. Available at: http://arxiv.org/pdf/1502.01780v1.pdf
"... 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), spatio ..."
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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. This formulation results in a partially observable system, with a temporally varying global state and spatiotemporally varying observations. 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 also 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. Additionally, we show that both estimators converge towards the true respective MMSE optimal estimators, in a common, relatively strong sense. Numerical simulations corroborate the practical effectiveness of the proposed approach.