Modeling and Identification of Low Rank Vector Processes

TL;DR

This paper addresses the challenge of modeling low-rank vector processes by introducing a feedback-based identification method that decomposes the problem into two manageable steps, enabling effective estimation despite the reduced innovation dimension.

Contribution

It proposes a novel feedback structure for low-rank vector process identification, facilitating the use of standard algorithms in a two-step approach.

Findings

The feedback structure enables separation of the identification problem.

Standard algorithms can be applied in the first step of the method.

The second step involves a deterministic least squares fit for the reduced dimension innovation.

Abstract

We study modeling and identification of 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.