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

TLDR

Optimal input design for parameter estimation has evolved rapidly over the past two decades, with many recent developments not yet published elsewhere. This paper surveys the field of optimal input design for parameter estimation as it has developed over the last two decades. The authors review the literature, derive the Fisher information matrix for multi‑input multi‑output systems with process noise, and categorize design procedures into time‑domain and frequency‑domain methods, including extensions to state constraints and continuous‑time systems, illustrated by examples. New results on time‑domain synthesis with state constraints and their link to dual control are presented.

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.