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Distributed Estimation in Sensor Networks with Modeling Uncertainty
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A major issue in distributed wireless sensor networks (WSNs) is the design of efficient distributed algorithms for network-wide dissemination of information acquired by individual sensors, where each sensor, by itself, is unable to access enough data for reliable decision making. Without a centralized fusion center, network-wide reliable inferencing can be accomplished by recovering meaningful global statistics at each sensor through iterative inter-sensor message passing. In this dissertation, we first consider the problem of distributed estimation of an unknown deterministic scalar parameter (the target signal) in a WSN, where each sensor receives a single snapshot of the field. An iterative distributed least-squares (DLS) algorithm is investigated with and without the consideration of node failures. In particular, without sensor node failures it is shown that every instantiation of the DLS algorithm converges, i.e., consensus is reached among the sensors, with the limiting agreement value being the centralized least-squares estimate. With node failures during the iterative exchange process, the convergence of the DLS algorithm is still guaranteed; however, an error exists be- tween the limiting agreement value and the centralized least-squares estimate. In order to reduce this error, a modified DLS scheme, the M-DLS, is provided. The M-DLS algorithm involves an additional weight compensation step, in which a sensor performs a one-time weight compensation procedure whenever it detects the failure of a neighbor. Through analytical arguments and simulations, it is shown that the M-DLS algorithm leads to a smaller error than the DLS algorithm, where the magnitude of the improvement dependents on the network topology. We then investigate the case when the observation or sensing mode is only partially known at the corresponding nodes, perhaps, due to their limited sensing capabilities or other unpredictable physical factors. Specifically, it is assumed that the observation validity at a node switches stochastically between two modes, with mode I corresponding to the desired signal plus noise observation mode (a valid observation), and mode II corresponding to pure noise with no signal information (an invalid observation). With no prior information on the local sensing modes (valid or invalid), we introduce a learning-based distributed estimation procedure, the mixed detection-estimation (MDE) algorithm, based on closed-loop interactions between the iterative distributed mode learning and the target estimation. The online learning (or sensing mode detection) step re-assesses the validity of the local observations at each iteration, thus refining the ongoing estimation update process. The convergence of the MDE algorithm is established analytically, and the asymptotic performance analysis studies shows that, in the high signal-to-noise ratio (SNR) regime, the MDE estimation error converges to that of an ideal (centralized) estimator with perfect information about the node sensing modes. This is in contrast with the estimation performance of a naive average consensus based distributed estimator (with no mode learning), whose estimation error blows up with an increasing SNR.
Zhou, Qing (2013). Distributed Estimation in Sensor Networks with Modeling Uncertainty. Doctoral dissertation, Texas A&M University. Available electronically from