Synthesis of Input Signals in Parameter Estimation Problems.

摘要

Design of input signals to enhance the estimation on unknown parameters in discrete time dynamics is considered. The system identification problem can be considered as the initial phase of a stochastic control problem of a dynamic system. In such a situation it is desirable to estimate the parameters as rapidly as possible without disturbing the normal operation of the process. The problem is represented in a Baysian framework. The optimality criterion for the synthesis problem is defined in terms of the statistical distance measure between distributions characterized by distinct parameter values. In this dissertation we define this quantity in terms of the pairwise Bhattacharyya distance. The distance measure has the desirable property of ordering the Bayes'probability of error as a function of two experimental design programs. The statistical distance measures have been successfully used in studying taxonomy and characterization of racial distributions. It is shown that such an approach is also feasible in applications to more general dynamic situation.