Distributed parameter estimation in unreliable WSNs: Quantized communication and asynchronous intermittent observation

Motivated by the application of wireless sensor networks, we study a class of distributed learning algorithms for estimating an unknown deterministic parameter. In such networks, each sensor activates in an unreliable network environment which admits new nodes joining and old nodes leaving the network, and can tolerate link failures and noisy interference. Additionally, sensors operate under limited computational, bandwidth and energy resources. In order to overcome these constraints, we propose a novel algorithm to reliably estimate the unknown parameter associated with a linear measurement function based on its noisy samples occasionally made at local sensors. Each local sensor processes its observation, updates its estimate through local information exchange and sends its quantized estimate to its one-hop neighbors. Based on the theory of matrix decomposition and stochastic approximation, we show that the studied algorithm converges almost surely to the unknown parameter with probability one, and the sensor estimate is, in expectation, equal to the unknown parameter. Specifically, we further provide the upper bounds on the mean square error and ∊∊-convergence time. Finally, we present a numerical example to assess and compare the communication cost with several similar scheme algorithms to achieve a given performance.