Comparison of Regressor Selection Methods in System Identification, Report no. LiTH-ISY-R-2730

In non-linear system identification the set of non-linear models is very rich and the number of parameters usually grows very rapidly with the number of regressors. In order to reduce the large variety of possible models as well as the number of parameters, it is of great interest to exclude irrelevant regressors before estimating any model. In this work, three existing approaches for regressor selection, based on the Gamma test, Lipschitz numbers, and on linear regression solved with a forward orthogonal least squares algorithm, were evaluated by the means of Monte Carlo simulations. The data were generated by NFIR models, both with a uniform and a non-uniform sampling distribution. All methods performed well in selecting the regressors for both sampling distributions, provided that the data’s underlying relationship was sufficiently smooth and we had enough data. The orthogonal regression approach and the Gamma test appeared robust to noise and were easy to apply. If there are not too many potential regressors, we suggest to use the orthogonal regression. Otherwise, the Gamma test should be used, as with the number of regressors the number of cross-bilinear terms in the linear regression grows very rapidly.