An application of the least-squares method to system parameters extraction from experimental data

We explore the possibility and the limits of extracting the parameters of the model from simulated logistic and Henon time series. For the models considered, the least-squares approach provides accurate values of the recurrence order and polynomial degree along with the model parameters. We found that the number of data points increases the accuracy of the estimation only for noise-free data. With the white noise added to the data, the accuracy could not be improved above a certain threshold that is almost independent of the number of data points. The additive noise flattened the global minimum of the least-squares function such that above a noise threshold it is no longer possible to discern the optimum values of the recurrence order and/or polynomial degree. (c) 2002 American Institute of Physics.