  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.
