Simple recursive algorithm for linear-in-the-parameters nonlinear model identification

This paper introduces a simple recursive algorithm for nonlinear dynamic system identification using linear-in-the-parameters models for NARX or RBF network where both the structure and parameters can be obtained simultaneously and recursively. The main objective is to improve the numerical stability when the model terms are highly correlated. This is based on the ＂innovation＂ idea and net contribution criteria. Using the recursive formulae for the computation of the Moore-Penrose inverse of matrices and the net contribution of model terms, it is possible to combine the structure term determination and parameters estimation within one framework by adding and deleting an item in the selected candidate model. The formulae for enhancing and reducing a matrix are given. Simulation results show the proposed method is numerically more stable than existing approaches.