Optimal Regularization for System Identification from Noisy Input and Output Signals

Jingmin XIN  Hiromitsu OHMORI  Akira SANO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A   No.12   pp.1805-1815
Publication Date: 1995/12/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
regularization,  system identification,  least squares estimation,  corrected least squares estimation,  eigenvalue decomposition,  

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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) method become often numerically unstable, when the true input signal to the system is strongly correlated. To overcome this ill-conditioned problem, we propose a regularized CLS estimation method by introducing multiple regularization parameters to minimize the mean squares error (MSE) of the regularized CLS estimate of the FIR model. The asymptotic MSE can be evaluated by considering the third and fourth order cross moments of the input and output measurement noises, and an analytical expression of the optimal regularization parameters minimizing the MSE is also clarified. Furthermore, an effective regularization algorithm is given by using the only accessible input-output data without using any true unknown parameters. The effectiveness of the proposed data-based regularization algorithm is demonstrated and compared with the ordinary LS, CLS and TLS estimates through numerical examples.