Dimensionality reduction with automatic dimension assignment for distributed estimation

We consider distributed estimation of a random vector parameter by a wireless sensor network (WSN). To meet stringent power and bandwidth budgets in WSN, local data compression is performed at each sensor to reduce the number of messages sent to a fusion center (FC). Under the constraint of a given total number of messages, our problem is to jointly determine the number of messages sent by each senor (a.k.a. dimension assignment) and design the corresponding compression matrix. The problem is formulated as a constrained optimization problem that minimizes the estimation mean-square error (MSE) at the FC. We analyze the problem using a subspace projection technique, which yields an efficient iterative solution. Numerical results are presented to illustrate the effectiveness of the proposed algorithm.