Regularization Features in the System Identification Toolbox. Issue 28 (2015) - Ljung, Lennart; Singh, Rajiv; Chen, Tianshi
Abstract: Regularization is a well known technique in estimation methodology. Its usefulness to assure well conditioned calculations and to handle reliable prior information about partly known parameters is a classical theme in statistics. Recently some deeper understanding about the advantages for general estimation and identification methods has been found and discussed. This is often done using the term "kernel methods". It has some links to machine learning and statistical function learning as well as to reproducing kernel Hilbert spaces. But algorithmically, it is all a question of regularization with an appropriate (quadratic norm) regularization matrix. Regularization was introduced into the MATLAB System Identification Toolbox in the 2013a version. It is a general option for all linear and nonlinear model estimation. Several specialized commands for estimation impulse responses (impulseest), tuning of kernels for ARX models (arxRegul), and general linear state space models with regularization (ssregest) have also been implemented. The paper describes and illustrates the used of these new features in the toolbox.