Recursive prediction error parameter estimator for non-linear models

A recursive prediction error parameter estimation algorithm is derived for systems which can be represented by the NARMAX (non-linear ARMAX) model. A convergence analysis is presented using the differential equation approach, and the new concept of m-invertibility is introduced. The analysis shows that while a highly non-linear process model may be used to capture the non-linearity of the system it is advisable to fit a simple noise model. The results of applying the algorithm to both simulated and real data are included.