Constrained Mobile Sensor Routing for Parameter Estimation of Spatiotemporal Processes

Abstract

An approach is proposed to joint activation of stationary sensor nodes and design of mobile sensor trajectories in a hybrid sensor network collecting measurements for parameter estimation of a process described by a partial differential equation. The ultimate objective is maximization of the log-determinant of the information matrix associated with the estimated parameters. The search for the optimal solution is performed using the branch-and-bound method in which a block coordinate ascent method is employed to produce an upper bound to the maximum objective function. It alternates between solving a relaxed combinatorial problem for the selection of active stationary nodes and a relaxed optimal control problem for the design of sensor trajectories. The former is achieved using a simplicial decomposition algorithm in which the restricted master problem is solved using a multiplicative algorithm for optimal design. In turn, the latter is solved by another algorithm for optimal design, namely the Wynn-Fedorov algorithm, which is capable of finding an optimal element in the convex hull of the set of attainable information matrices and can be easily implemented by using a standard optimal control solver as its component.