Information Flow Optimization for Estimation in Linear Models Using a Sensor Network

The problem considered is one of maximizing the information flow through a sensor network tasked with estimating, at a fusion center, an underlying parameter in a linear observation model. The sensor nodes take observations, quantize them, and send them to the fusion center through a network of relay nodes. The links in the network are assumed to satisfy certain capacity constraints in terms of the maximum number of bits that can be transmitted on the links. Furthermore, the relay nodes are assumed to satisfy flow conservation constraints, i.e., the number of bits flowing into a relay node is equal to the number of bits flowing out of it. It is shown that this flow optimization problem for estimation can be cast as a Network Utility Maximization (NUM) problem by suitably defining the utility functions at the sensors. The inference problem considered is one of parameter estimation with a linear observation model, which is studied in both Bayesian and non-Bayesian settings. Upper bounds on the mean-squared error (MSE) of optimal linear estimators are obtained in both settings, and these bounds are used to construct utility functions for the corresponding NUM problems. It is verified via simulations that the bit assignments at the sensors obtained through the solutions to the NUM problems, in both the Bayesian and non-Bayesian settings, yield considerably better estimation performance than the Max-Flow solution that simply assigns bits to the sensors in such a way as to maximize the total bits transmitted to the fusion center.