Prediction and simulation errors in parameter estimation for nonlinear systems

Abstract

This article compares the pros and cons of using prediction error and simulation error to define cost functions for parameter estimation in the context of nonlinear system identification. To avoid being influenced by estimators of the least squares family (e.g. prediction error methods), and in order to be able to solve non-convex optimisation problems (e.g. minimisation of some norm of the free-run simulation error), evolutionary algorithms were used. Simulated examples which include polynomial, rational and neural network models are discussed. Our results—obtained using different model classes—show that, in general the use of simulation error is preferable to prediction error. An interesting exception to this rule seems to be the equation error case when the model structure includes the true model. In the case of error-in-variables, although parameter estimation is biased in both cases, the algorithm based on simulation error is more robust.