Using Grasp for Choosing Best Periodic Observation Strategy in Stochastic Systems Filtering

The problem of optimal periodic scheduling of single channel measures for the state estimation of a multi output discrete time stochastic system is considered. The optimality criterion chosen is the value of the trace of the error covariance matrix of Kalman filter in the periodic steady state, averaged over the observation period. Two interesting examples for practical applications, are studied. The first one considers the case of a number of independent single output subsystems observed by a single observation channel, while the second case deals with the optimization of measurement points and of the relative scanning sequence for the model of a parabolic distributed parameter system. Given the combinatorial nature of the resulting problem, an approximate global optimization method is used to solve it and heuristic rules are devised to overcome difficulties arising from possibly slow convergence in computation of objective function. Numerical examples are reported showing a great improvement with respect to the standard scanning policy.