Optimal input signals for parameter estimation in dynamic systems--Survey and new results

Abstract

This paper surveys the field of optimal input design for parameter estimation as it has developed over the last two decades. Many of the developments covered are only recent and have not appeared in the open literature elsewhere. After a brief introduction, the paper discusses the historical background of the subject both in the engineering and in the statistical literature. The concepts of optimality and input design are then discussed, followed by a derivation of the Fisher information matrix for multiinput multioutput systems with process noise. The design procedures are divided into the categories of time-domain methods and frequency-domain methods, with the former being more general, but also more time consuming (computationally). Several extensions to state constraints, continuous-time systems, etc., are discussed. A number of examples are given to illustrate the nature of optimal inputs. The results on time-domain synthesis with state constraints and their relationship to "dual control" are new.