Robust Linear Decentralized Tracking of a Time-Varying Sparse Parameter Relying on Imperfect CSI

Robust linear decentralized tracking of a time-varying sparse parameter is studied in a multiple-input-multiple-output (MIMO) wireless sensor network (WSN) under channel state information (CSI) uncertainty. Initially, assuming perfect CSI availability, a novel sparse Bayesian learning-based Kalman filtering (SBL-KF) framework is developed in order to track the time-varying sparse parameter. Subsequently, an optimization problem is formulated to minimize the mean-square error (MSE) in each time slot (TS), followed by the design of a fast block coordinate descent (FBCD)-based iterative algorithm. A unique aspect of the proposed technique is that it requires only a single iteration per TS to obtain the transmit precoder (TPC) matrices for all the sensor nodes (SNs) and the receiver combiner (RC) matrix for the fusion center (FC) in an online fashion. The recursive Bayesian Cramer-Rao bound (BCRB) is also derived for benchmarking the performance of the proposed linear decentralized estimation (LDE) scheme. Furthermore, for considering a practical scenario having CSI uncertainty, a robust SBL-KF (RSBL-KF) is derived for tracking the unknown parameter vector of interest followed by the conception of a robust transceiver design. Our simulation results show that the schemes designed outperform both the traditional sparsity-agnostic Kalman filter and the state-of-the-art sparse reconstruction methods. Furthermore, as compared to the uncertainty-agnostic design, the robust transceiver architecture conceived is shown to provide improved estimation performance, making it eminently suitable for practical applications.