输入输出端存在噪声时系统的无偏辨识

Unbiased Identification of Linear Systems in the Presence of Input-Output Measurement Noises

在实际辨识中，观测到的系统输入输出数据往往被噪声所污染，这给无偏辨识系统带来困难．基于和文［６］中相同的原理，本文提出了一种递推的偏差补偿最小二乘法（ＲＢＥＬＳ）．它通过在系统输入端引入已知滤波器，将已知零点嵌入被辨识系统中，然后利用这些零点所提供的信息在线估计辨识偏差，并将偏差加以补偿，从而实现系统的无偏估计．尤其，在没有任何有关噪声先验信息的情形下，利用此方法可获得满意的辨识结果．

In practical identification the observed input-output data are usually polluted by measurement noises. The main problem in such identification is how to remove the estimation bias induced by the measurement noises. Based on the principle in [51,a recursive bias-eliminated least-squares method (RBELS) is developed in this paper. A known pre filter is ar'tificially inserted into the identified system so that the augmented system has a known zero. Using this known zero, the noise-induced bias can be calculated recursively. With the bias removed, the consistent parameter estimates are obtained.