On Initialization of Iterative Algorithms For Nonlinear ARX Models

Abstract

A challenging issue with parameter estimation for models that are nonlinear in parameters, is that in excess to the global minimum they may have local minima as well. As iterative algorithms are commonly used for identification of such models, finding proper initial values for these algorithms decreases the risk of ending up in local minima.In this contribution an algorithm to obtain a suitable candidate for initial values of an iterative algorithm when the model is nonlinear autoregressive model with exogenous (NARX model) is suggested. The algorithm is based on linearizing the nonlinear model structure and solving the mapping equations between the parameters of the corresponding linear model and nonlinear model. Note that since the method relies on the identification of a linearized model, the data must be selected so that a linear approximation works. In this way, an estimation of the unknown parameters of the nonlinear model can be obtained.The mapping between the linear and the nonlinear models may have one unique solution, no solution, or multiple solutions, and the paper explains and investigates these possible outcomes.