Input selection for parameter identification in discrete systems

In this paper the problem of selecting an optimal input for identifying an unknown parameter of a known discrete system by observing its output in the presence of Gaussian noise is considered. The system is assumed to be a generalized discrete system in which the inputs and possible parameter values are members of a finite set. The criterion for the optimal input is defined as that which maximizes the probability of correctly determining the true parameter value from a multiple hypothesis test. Although the above criterion totally orders the set of inputs, it is a difficult task to select the best inputs. Some theorems are presented which yield a partial ordering whose extension is the desired total ordering. In the special case of strong noise, it is shown that the ordering of inputs can be related to the perimeter in the output vector space. The results of the paper are applicable to the selection of preset input lengths or to adaptive identification.