一种时变系统模型结构确定和参数估计新算法

A New Algorithm for Model Structure Determination and Parameter Estimation of Time-Varying Systems

将参数检测技术和辨识方法相结合、系统结构在线辨识和参数跟踪相结合，基于Ｕ—Ｄ分解技术，提出一种时变系统结构确定和参数估计的最小二乘辨识新算法（ＭＵＤＩ）．该算法不仅可实现系统阶次和参数的同时估计，而且通过对损失函数的实时监测，实现协方差阵的自适应调整，使辨识算法收敛速度快，对时变系统阶次和参数变化均有很强的跟踪能力．此外，由于采用Ｕ—Ｄ分解技术，与递推最小二乘法（ＲＬＳ）等相比，本文的算法不仅具有很好的数值稳定性和快速收敛性，而且计算量明显小于ＲＬＳ，仿真计算结果表明本文算法的有效性和优越性．

Existing algorithms for model structure identification and parameter estimation of time-invariant system, including that proposed by Niu et al in 1992161, can be further improved and extended to time-varying systems for model structure identification and for tracking rapidly varying paramters. In view of this, a new modified U-D factorization least-squares identification algorithm of the time-varying systems is proposed in this paper. The main features of the new algorithm are:(1) The model parameters and loss functions for all model orders from I to n can be obtained simultaneously in every recursion.(2) Through monitoring the loss function and the use of so called #local forgetting factor#, adaptive tuning of covariancc matrix can be achieved; so the proposed algorithm has always rapid convergency rate and is capable of tracking the changes of both the model order and the parameters.(3) The new algorithm proposed here has not only excellent numerical properties, rapid convergency rate, but also the computational burden is considerably less than that of recursive least-squares (RLS) identification algorithm.The results of simulation computations show that the new algorithm proposed is very efficient and effective.