Parametric Identification Using Weighted Null-Space Fitting

TL;DR

Weighted null-space fitting (WNSF) is a three-step method for system identification that offers asymptotic efficiency comparable to prediction error methods, with flexibility and suitability for various data conditions.

Contribution

This paper demonstrates that WNSF achieves asymptotic properties similar to PEM and shows its competitiveness through simulation studies.

Findings

WNSF provides asymptotically efficient estimates.

WNSF is flexible and suitable for open- and closed-loop data.

Simulation results indicate competitive performance.

Abstract

In identification of dynamical systems, the prediction error method using a quadratic cost function provides asymptotically efficient estimates under Gaussian noise and additional mild assumptions, but in general it requires solving a non-convex optimization problem. An alternative class of methods uses a non-parametric model as intermediate step to obtain the model of interest. Weighted null-space fitting (WNSF) belongs to this class. It is a weighted least-squares method consisting of three steps. In the first step, a high-order ARX model is estimated. In a second least-squares step, this high-order estimate is reduced to a parametric estimate. In the third step, weighted least squares is used to reduce the variance of the estimates. The method is flexible in parametrization and suitable for both open- and closed-loop data. In this paper, we show that WNSF provides estimates with the same asymptotic properties as PEM with a quadratic cost function when the model orders are chosen according to the true system. Also, simulation studies indicate that WNSF may be competitive with state-of-the-art methods.