OPTIMAL REGULARIZATION FOR SYSTEM-IDENTIFICATION FROM NOISY INPUT ANDOUTPUT SIGNALS

In identification of a finite impulse response (FIR) model using noise -corrupted input and output data, the least squares type of estimation schemes such as the ordinary least squares (LS), the corrected least squares (CLS) and the total least squares (TLS) methods become often n umerically unstable, when the true input signal to the system is stron gly correlated. To overcome this ill-conditioned problem, we propose a regularized CLS estimation method by introducing multiple regularizat ion parameters to minimize the mean squares error (MSE) of the regular ized CLS estimate of the FIR model. The asymptotic MSE can be evaluate d by considering the third and fourth order cross moments of the input and output measurement noises, and an analytical expression of the op timal regularization parameters minimizing the MSE is also clarified. Furthermore, an effective regularization algorithm is given bq using t he only accessible input-output data without using any true unknown pa rameters. The effectiveness of the proposed data-based regularization algorithm is demonstrated and compared with the ordinary LS, CLS and T LS estimates through numerical examples.