Fast and optimal joint decision and estimation by quantized data via noisy channels of sensor networks

Abstract

Joint decision and estimation (JDE) problems arise in a wide range of practical applications. This work addresses the JDE problem in a distributed scenario using quantized data from noisy channels to achieve optimized decision and estimation at fusion center. Most previous works mainly focus on JDE from measurement acquired by single sensor, and certain class of JDE algorithms suffer from the high computational complexity for involving numerical search. To address these issues, we first propose a distributed JDE model incorporating the essential factors, e.g., spatial correlation of measurement noise between neighboring nodes, information loss due to necessary quantization for limited bandwidth, and unavoidable transmission errors caused by noisy channels. Secondly, we theoretically investigate the distributed JDE model, then propose an optimal JDE algorithm. Thirdly, we propose an equality constrained linear programming (ECLP) algorithm for solving optimal decision rule. The core idea is using the equality constraints of detection error probabilities to simplify the decision-dependent estimation cost, such that the expensive numerical search can be eliminated. Extensive simulations verify that, the proposed distributed JDE algorithm along with ECLP achieves a lower cost and more stable estimation in terms of worst-case mean square error, and faster than the state-of-the-art JDE algorithms.