论文标题
使用广义光谱分解的ARX模型识别
ARX Model Identification using Generalized Spectral Decomposition
论文作者
论文摘要
本文涉及通过外源输入（ARX）模型鉴定自回归的鉴定。大多数现有方法（例如预测误差最小化和状态空间框架）被广泛接受并用于估计ARX模型，但已知可以为正确提供的输入输出订单和延迟提供无偏见且一致的参数估计。 在本文中，我们提出了一个新型的自动框架，该框架可以恢复订单，延迟，输出噪声分布以及参数估计。提出的框架中使用的主要工具是普遍的光谱分解。所提出的算法系统地估算了两个步骤的所有参数。第一步通过检查广义特征值来利用顺序的估计，第二步是从广义特征向量估算参数。提出了模拟研究以证明该方法的疗效，并观察到即使在低信号与噪声比（SNR）下，也可以提供一致的估计。
This article is concerned with the identification of autoregressive with exogenous inputs (ARX) models. Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized for the estimation of ARX models but are known to deliver unbiased and consistent parameter estimates for a correctly supplied guess of input-output orders and delay. In this paper, we propose a novel automated framework which recovers orders, delay, output noise distribution along with parameter estimates. The primary tool utilized in the proposed framework is generalized spectral decomposition. The proposed algorithm systematically estimates all the parameters in two steps. The first step utilizes estimates of the order by examining the generalized eigenvalues, and the second step estimates the parameter from the generalized eigenvectors. Simulation studies are presented to demonstrate the efficacy of the proposed method and are observed to deliver consistent estimates even at low signal to noise ratio (SNR).
