Statistically Optimal Structured Additive MIMO Continuous-time System Identification

TL;DR

This paper presents a two-stage method for accurately estimating structured additive MIMO models in continuous-time systems, ensuring consistency and efficiency even in closed-loop conditions, validated through extensive simulations.

Contribution

It introduces a novel two-stage estimation procedure that enforces structural constraints via weighted nonlinear least-squares, improving accuracy and efficiency over existing methods.

Findings

Method is consistent and asymptotically efficient in open-loop scenarios.

Achieves minimum covariance among instrumental variable estimators in closed-loop settings.

Validated through extensive simulation studies.

Abstract

Many applications in mechanical, acoustic, and electronic engineering require estimating complex dynamical models, often represented as additive multi-input multi-output (MIMO) transfer functions with structural constraints. This paper introduces a two-stage procedure for estimating structured additive MIMO models, where structural constraints are enforced through a weighted nonlinear least-squares projection of the parameter vector initially estimated using a recently developed refined instrumental variables algorithm. The proposed approach is shown to be consistent and asymptotically efficient in open-loop scenarios. In closed-loop settings, it remains consistent despite potential noise model misspecification and achieves minimum covariance among all instrumental variable estimators. Extensive simulations are performed to validate the theoretical findings, and to show the efficacy of the proposed approach.