Joint Optimization of Dimension Assignment and Compression in Distributed Estimation Fusion

This paper studies linear distributed estimation of an unknown random parameter vector in a bandwidth-constrained multisensor network. To meet the bandwidth limitations, each sensor converts its observation into a low-dimensional datum via a suitable linear transformation. Then, the fusion center estimates the parameter vector by linearly combining all the received low-dimensional data, aiming at minimizing the estimation mean square error. The main purpose of this paper is to jointly determine the compression dimension of each sensor (referred to as dimension assignment) and design the corresponding compression matrix when the total compression dimensions is limited. Such a joint design problem can be formulated as a rank-constrained optimization problem and it is shown to be NP-hard for the first time. In addition, successive quadratic upper-bound minimization (SQUM), SQUM-block coordinate descent (SQUM-BCD) and nuclear norm regularization (NNR) methods are developed to solve it approximately. Furthermore, we show that any accumulation point of the sequence generated by the SQUM method satisfies the Karush-Kuhn-Tucker conditions of the rank-constrained optimization problem, and the Phase II algorithm of the SQUM-BCD and NNR methods (both are two-phase algorithms and have the same Phase II algorithm) guarantees convergence at least to a stationary point. Numerical experiments illustrate the advantages of the proposed methods compared with the existing method.