  In this paper, we consider the problem of sensor selection for parameter
estimation with correlated measurement noise. We seek optimal sensor
activations by formulating an optimization problem, in which the estimation
error, given by the trace of the inverse of the Bayesian Fisher information
matrix, is minimized subject to energy constraints. Fisher information has been
widely used as an effective sensor selection criterion. However, existing
information-based sensor selection methods are limited to the case of
uncorrelated noise or weakly correlated noise due to the use of approximate
metrics. By contrast, here we derive the closed form of the Fisher information
matrix with respect to sensor selection variables that is valid for any
arbitrary noise correlation regime, and develop both a convex relaxation
approach and a greedy algorithm to find near-optimal solutions. We further
extend our framework of sensor selection to solve the problem of sensor
scheduling, where a greedy algorithm is proposed to determine non-myopic
(multi-time step ahead) sensor schedules. Lastly, numerical results are
provided to illustrate the effectiveness of our approach, and to reveal the
effect of noise correlation on estimation performance.
