A sensor quantization algorithm for best linear estimation fusion in bandwidth-constrained systems

In this paper, we consider the design problem of optimal sensor quantization rules (quantizers) and an optimal linear estimation fusion rule in bandwidth-constrained decentralized random signal estimation fusion systems. First, we derive a fixed point type necessary condition for both optimal sensor quantization rules and an optimal linear estimation fusion rule, which character the structure of the optimal solutions-a fixed point of a integral operation of sensor quantization rules and a linear estimation fusion rule. To facilitate computer implementation, we also present the discretized necessary condition for the both. Then, we can motivate an iterative Gauss-Seidel algorithm to simultaneously search for both optimal sensor quantization rules and an optimal linear estimation fusion rule. We then prove that the algorithm converges to an optimal solution of sensor quantization rules and a linear estimation fusion rule in the discretized scheme after a finite number of iterations. Finally, several numerical examples demonstrate the efficiency of our method, and provide some reasonable and meaningful observations how the estimation performance is influenced by the observation noise power and numbers of sensors or quantization levels.