Joint Collaboration and Compression Design for Distributed Sequential Estimation in a Wireless Sensor Network

In this work, we propose a joint collaboration-compression framework for sequential estimation of a random vector parameter in a resource constrained wireless sensor network (WSN). Specifically, we propose a framework where the local sensors first collaborate (via a collaboration matrix) with each other. Then a subset of sensors selected to communicate with the FC linearly compress their observations before transmission. We design near-optimal collaboration and linear compression strategies under power constraints via alternating minimization of the sequential minimum mean square error. We show that the objective function for collaboration design can be non-convex depending on the network topology. We reformulate and solve the collaboration design problem using quadratically constrained quadratic program (QCQP). Moreover, the compression design problem is also formulated as a QCQP. We propose two versions of compression design, one centralized where the compression strategies are derived at the FC and the other decentralized, where the local sensors compute their individual compression matrices independently. It is noted that the design of decentralized compression strategy is a non-convex problem. We obtain a near-optimal solution by using the bisection method. In contrast to the one-shot estimator, our proposed algorithm is capable of handling dynamic system parameters such as channel gains and energy constraints. Importantly, we show that the proposed methods can also be used for estimating time-varying random vector parameters. Finally, numerical results are provided to demonstrate the effectiveness of the proposed framework.