Parsimonious System Identification from Fragmented Quantized Measurements

TL;DR

This paper introduces a novel method for identifying low-order linear systems from fragmented, noisy, and quantized data using an ADMM-based approach to optimize a non-convex quasi-norm, improving sparsity over traditional methods.

Contribution

It presents a new algorithm for parsimonious system identification from quantized, fragmented measurements, leveraging a non-convex optimization approach with ADMM.

Findings

The proposed method outperforms $ ext{l}_1$ minimization in inducing sparser solutions.

Numerical experiments demonstrate effective system identification from limited, quantized data.

The approach successfully handles data fragmentation and noise in system identification.

Abstract

Quantization is the process of mapping an input signal from an infinite continuous set to a countable set with a finite number of elements. It is a non-linear irreversible process, which makes the traditional methods of system identification no longer applicable. In this work, we propose a method for parsimonious linear time invariant system identification when only quantized observations, discerned from noisy data, are available. More formally, given a priori information on the system, represented by a compact set containing the poles of the system, and quantized realizations, our algorithm aims at identifying the least order system that is compatible with the available information. The proposed approach takes also into account that the available data can be subject to fragmentation. Our proposed algorithm relies on an ADMM approach to solve a $\ell_{p},(0<p<1),$ quasi-norm objective problem. Numerical results highlight the performance of the proposed approach when compared to the $\ell_{1}$ minimization in terms of the sparsity of the induced solution.