Identification of Low Rank Vector Processes

TL;DR

This paper addresses the modeling and identification of stationary low-rank spectral density processes, proposing a two-step method leveraging a feedback structure to improve identification accuracy.

Contribution

It introduces a novel two-step identification procedure for low-rank processes using a feedback structure, with analysis of identifiability and simulation validation.

Findings

The proposed method effectively identifies low-rank processes in simple examples.

A feedback-based structure allows splitting the identification into manageable steps.

Simulations demonstrate the approach's practical viability.

Abstract

We study modeling and identification of stationary processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly applicable. We show that these processes admit a special feedback structure with a deterministic feedback channel which can be used to split the identification in two steps, one of which can be based on standard algorithms while the other is based on a deterministic least squares fit. Identifiability of the feedback system is analyzed and a unique identifiable structure is characterized. Simulations show that the proposed procedure works well in some simple examples.