Sensor Location for Parameter Estimation of Spatiotemporal Systems with Correlated Observations

Abstract

The problem of sensor selection for parameter estimation of spatiotemporal systems with correlated measurement noise is considered. Since in the examined setting the correlation structure of the noise is not known exactly, the ordinary least squares method is supposed to be used for estimation and the determinant of the covariance matrix of the resulting estimator is adopted as the measure of estimation accuracy. This design criterion is to be minimized by choosing a set of spatiotemporal measurement locations from among a given finite set of candidate locations. To make the problem computationally tractable for large sensor networks, its relaxed formulation is considered. As the resulting problem is nonconvex, a majorization-minimization algorithmic framework is employed. Thus, at each iteration, a convex tangent surrogate function that majorizes the original nonconvex design criterion is minimized using simplicial decomposition. This results in a sequence of iterates which monotonically reduce the value of the original nonconvex design criterion. A computational experiment is reported to illustrate the proposed technique.