Mathematics > Statistics Theory
[Submitted on 1 Jun 2025
]
Title: A Quantized Order Estimator
Title: 量化阶数估计器
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.
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