基于输出累积量的 ARMA(AR)系统的一致性阶次递推辩识(英文)

Consistent Order-recursive Identification of ARMA(AR) Systems with Noisy Output Cumulants

本文提出了一种根据系统输出的观测数据对ARMA（AR）系统进行盲识别的新算法。该模型由独立同分布非高斯随机序列驱动，其输出序列中含方差未知的加性高斯噪声。通过求解基于三阶累积量谱的代价函数，该算法以模型阶次递推形式同时辩识ARMA的系统阶次和估计出系统参数。文章给出了该算法一致收敛性的证明，并对两类不同阶次的最小及非最小相位ARMA系统的AR参数及阶次辩识进行了数字仿真，结果令人满意。

In this paper the problem of determining the AR order and parameters of a nonminimum phase ARMA system from its output observation corrupted by additive Gaussian noise of unknown covariance is considered. The system is driven by a sequence of i. i. d. non- Gaussian random variables which is assumed unobservable. A novel consistent algorithm based on the third-order cumulants of output sequences is introduced. It is performed recursively by minimizing a well-defined cost function. Strong convergence and consistency of the algorithm are proved. Theoretical analysis and numerical simulation show that this order-recursive algorithm is satisfactory for both order and parameter identification of a non-minimum phase AR system which is subordinated to the ARMA system.