Comparison of Regressor Selection Methods in System Identification

In non-linear system identification the set of non-linear modelsis very rich and the number of parameters usually grows very rapidlywith the number of regressors. In order to reduce the large variety ofpossible models as well as the number of parameters, it is of greatinterest to exclude irrelevant regressors before estimating any model.In this work, three existing approaches for regressor selection, basedon theGamma test, Lipschitz numbers, and on linear regression solved witha forward orthogonal least squares algorithm, wereevaluated by the means of Monte Carlo simulations. The data weregenerated by NFIR models, both with a uniform and a non-uniformsampling distribution. All methods performed well in selecting theregressors for both sampling distributions, provided that thedata's underlying relationship was sufficiently smooth and we hadenough data. The orthogonal regression approachand the Gamma test appeared robust to noise and were easy to apply.If there are not too many potential regressors, we suggest to use theorthogonal regression. Otherwise, the Gamma test should be used, as with thenumber of regressors the number of cross-bilinear terms in the linearregression grows very rapidly