A-optimal sensor location subject to correlated observations via a fast exchange algorithm

A powerful computational technique is exposed for sensor selection maximizing the parameter estimation accuracy for spatiotemporal processes in the presence of correlated measurement noise. The trace of the posterior covariance matrix is employed as the design criterion. A best subset of a given number of candidate sites is constructed by iteratively improving its initial guess through greedy exchanges in which gauged sites are replaced by those selected from a list of ungauged sites. To make this inherently combinatorial problem more tractable, a novel equivalent form of the optimality criterion is employed to drastically simplify the exchanges. It heavily relies on the decomposition of the noise into uncorrelated and correlated components. The enhanced exchanges are then incorporated into a local search procedure with random multistart. Simulation experiments for two environmental monitoring networks demonstrate that the speedup can reach up to 100 times that of a state-of-the-art exchange algorithm.