OPTIMAL MEASUREMENT SCHEDULING FOR STATE ESTIMATION

In this paper, we consider the problem of optimal allocation of measur ement resources, when: 1) the total measurement budget and time durati on of measurements are fixed, and 2) the cost of an individual measure ment varies inversely with the (controllable) measurement accuracy. Th e objective is to determine the time-distribution of measurement varia nces that minimizes a measure of error in estimating a discrete-time, vector stochastic process with known auto-correlation matrix using a l inear estimator. The metric of estimation error is the trace of weight ed sum of estimation error covariance matrices at various time indices . We show that this problem reduces to a nonlinear optimization proble m with linear equality and inequality constraints. The solution to thi s problem is obtained via a variation of the projected Newton method. For the special case when the vector stochastic process is the state o f a linear, finite-dimensional stochastic system, the problem reduces to the solution of a nonlinear optimal control problem In this case, t he gradient and Hessian with respect to the measurement costs are obta ined via the solution of a two-point boundary value problem and the re sulting optimization problem is solved via a variation of the projecte d Newton method. The proposed method is illustrated using four example s.