Weighted Least-Squares PARSIM

TL;DR

This paper introduces PARSIM extsubscript{opt}, an improved subspace identification method using weighted least-squares to achieve optimal unbiased estimates of the system's observability space.

Contribution

It proposes a novel weighted least-squares version of PARSIM that enhances estimation accuracy and derives consistent estimates for the weighting matrix.

Findings

PARSIM extsubscript{opt} outperforms classical SIMs in simulations.

The method achieves the best linear unbiased estimator for the observability matrix.

Simulated comparisons demonstrate improved accuracy over existing algorithms.

Abstract

Subspace identification methods (SIMs) have proven very powerful for estimating linear state-space models. To overcome the deficiencies of classical SIMs, a significant number of algorithms has appeared over the last two decades, where most of them involve a common intermediate step, that is to estimate the range space of the extended observability matrix. In this contribution, an optimized version of the parallel and parsimonious SIM (PARSIM), PARSIM\textsubscript{opt}, is proposed by using weighted least-squares. It not only inherits all the benefits of PARSIM but also attains the best linear unbiased estimator for the above intermediate step. Furthermore, inspired by SIMs based on the predictor form, consistent estimates of the optimal weighting matrix for weighted least-squares are derived. Essential similarities, differences and simulated comparisons of some key SIMs related to our method are also presented.