Weighted Null-Space Fitting for Identification of Cascade Networks

TL;DR

This paper introduces a novel weighted null-space fitting algorithm for the simultaneous identification of cascade network modules, achieving asymptotic efficiency without solving non-convex optimization problems.

Contribution

It extends Weighted Null-Space Fitting (WNSF) to cascade networks with sensor noise, enabling efficient simultaneous module estimation without non-convex optimization.

Findings

Simulation results suggest network WNSF is asymptotically efficient.

The method avoids non-convex cost function minimization.

Potential extension to more general networks discussed.

Abstract

For identification of systems embedded in dynamic networks, applying the prediction error method (PEM) to a correct tailor-made parametrization of the complete network provided asymptotically efficient estimates. However, the network complexity often hinders a successful application of PEM, which requires minimizing a non-convex cost function that in general becomes more difficult for more complex networks. For this reason, identification in dynamic networks often focuses in obtaining consistent estimates of particular network modules of interest. A downside of such approaches is that splitting the network in several modules for identification often costs asymptotic efficiency. In this paper, we consider the particular case of a dynamic network with the individual systems connected in a serial cascaded manner, with measurements affected by sensor noise. We propose an algorithm that estimates all the modules in the network simultaneously without requiring the minimization of a non-convex cost function. This algorithm is an extension of Weighted Null-Space Fitting (WNSF), a weighted least-squares method that provides asymptotically efficient estimates for single-input single-output systems. We illustrate the performance of the algorithm with simulation studies, which suggest that a network WNSF may also be asymptotically efficient estimates when applied to cascade networks, and discuss the possibility of extension to more general networks affected by sensor noise.