Optimal sensor selection in sequential estimation problems

Abstract

The optimal selection of measurements in finite and infinite dimensional filtering systems is considered. The function space approach is followed and an optimization procedure, in a general operator formulation, is established for systems with continuous dynamics and continuous-time or intermittent measurements. The optimality index follows from the functional properties of the covariance operator and it is deduced to be the trace of the operator at the system terminal time. For computational purposes, orthogonal collocation is used to transform the infinite dimensional systems into finite dimensional ones, and the conditions under which minimizing the trace of the covariance operator is equivalent to minimizing the trace of the resulting covariance matrix are established. The kernel representation of the optimization procedure for the tubular-flow reactor system with intermittent, point-value measurements is presented. The optimal locations of sensors placed either simultaneously or sequentially in the s...