Model structure selection in LTI MISO system identification

In the paper a problem of model structure determination for linear time-invariant (LTI) multiinput-single-output (MISO) system identification is considered. The main formulas for discrete-time linear models and the estimation of their parameters based on prediction error minimisation are given. Then the problem of a model form is discussed and some practical advices based on the author's experience are given. The next problem is related to the model structure determination. The approach is based on the previous estimation of the parameters of tentative models with different structures, and the selection of the model according to the assumed criterion. The criteria for model selection are proposed and a new algorithm for automatic model structure searching is described. The proposed heuristic algorithm enables for obtaining a (sub)optimal model (in the sense of the chosen criterion) in a small number of steps. A simulation example is presented and conclusions about the effectiveness of the proposed approach are drawn.