Optimal Sensor Location in a Linear Distributed Parameter System

Abstract In this paper, we treat the optimal sensor location problem by using functional analysis. Thus, the partial differential equations are embedded into the ordinary differential equations in Hilbert spaces. It is assumed that a criterion for the sensor location is to minimize the trace of the estimation error covariance operator described by the operator-valued differential equations of Riccati type plus the measurement cost. We prove the existence and uniqueness theorem concerning the solution of the estimation error covariance operator by using the theory of the evolution operator and Picard's method. Furthermore, we prove the comparison theorem for the operator-valued differential equations. Based on the theorems, we derive the sufficient condition for the optimal sensor location and then derive the necessary condition. Finally, some numerical examples for the optimal sensor locations are shown.