A Quantized Order Estimator

TL;DR

This paper introduces a new criterion for accurately estimating the order of ARX systems using quantized data, ensuring consistency under certain conditions and providing practical guidelines for parameter selection.

Contribution

It proposes a novel order estimation criterion based on least squares and CIC for quantized ARX systems, with proven consistency and practical quantization parameter selection methods.

Findings

The proposed criterion achieves consistent order estimation with small quantization steps.

The method is effective when system orders are known and persistent excitation condition holds.

Numerical examples validate the theoretical results.

Abstract

This paper considers the order estimation problem of stochastic autoregressive exogenous input (ARX) systems by using quantized data. Based on the least squares algorithm and inspired by the control systems information criterion (CIC), a new kind of criterion aimed at addressing the inaccuracy of quantized data is proposed for ARX systems with quantized data. When the upper bounds of the system orders are known and the persistent excitation condition is satisfied, the system order estimates are shown to be consistent for small quantization step. Furthermore, a concrete method is given for choosing quantization parameters to ensure that the system order estimates are consistent. A numerical example is given to demonstrate the effectiveness of the theoretical results of the paper.