有色噪声系统的迭代辨识与递推辨识方法仿真比较研究

Comparison of Iterative and Recursive Identification for Systems with Colored Noises

针对ARARX模型(即动态调节模型),提出了分别辨识系统模型参数向量和噪声模型参数向量的新型最小二乘迭代辨识方法。其基本思想是:通过极小化一个信息矩阵中含噪声项的准则函数,导出两个参数向量的最小二乘估计式,进一步将估计式中信息矩阵所含的未知噪声项用其迭代估计代替,而其迭代估计又用前一次迭代的参数估计进行计算。在每步迭代计算中,二者执行了一个递阶计算过程。与滤波式递推广义最小二乘算法相比,提出的迭代算法也可用于在线辨识,而且在每一步迭代计算中,反复利用了系统可测数据信息,因而能够获得高精度参数估计。仿真例子证实了理论研究结果。

For stochastic systems described by the controlled ARAR models （CARAR models）, namely, dynamical adjusting models, a new-type least-squares-iterative algorithm of identifying the system parameter vector and noise parameter vector was proposed respectively. The basic idea is to derive the least squares estimation of the these two parameter vectors by minimizing the criterion function with the information matrix containing unknown noise terms, which are replaced with their corresponding iterative estimation computed by using the preceding parameter estimates. They perform a hierarchical computational process. Comparing with the recursive generalized least squares algorithms with data filtered by using the estimated noise models, the proposed iterative algorithms are also suitable for on-line identification and make full use of all data at each iteration and thus highly accurate parameter estimates can be obtained. Simulation example confirms the theoretical results.