Frequency-Domain Synthesis of Optimal Inputs for Linear System Parameter Estimation

Abstract

This paper formulates the problem of estimating parameters in linear single-input multi-output dynamic systems as a regression problem in frequency domain. An expression for the information matrix is derived and its properties are studied. A frequency domain condition on the input for the nonsingularity of the information matrix is obtained. It is shown that a deterministic input with a point spectrum can always be found for single input multi-output systems such that it has the same information matrix as a mixed input (stochastic and deterministic) whose spectrum contains both continuous and discrete parts. A number of different criteria used in the design of regression experiments are stated and their relevance to input design is examined. Convergent numerical algorithms are obtained for globally minimizing the determinant or a suitable linear norm of the dispersion matrix (the inverse of the information matrix) with respect to the input spectrum. The algorithms are based on equivalence properties between criteria in the parameter space and criteria in the sample space.