Improved parameter estimates for non-linear dynamical models using a bootstrap method

Abstract

It is known that the least-squares (LS) class of algorithms produce unbiased estimates providing certain assumptions are met. There are many practical problems, however, where the required assumptions are violated. Typical examples include non-linear dynamical system identification problems, where the input and output observations are affected by measurement uncertainty and possibly correlated noise. This will result in biased LS estimates and the identified model will exhibit poor generalisation properties. Model estimation for this type of error-in-variables problem is investigated in this study, and a new identification scheme based on a bootstrap algorithm is proposed to improve the model estimates for non-linear dynamical system identification.

Keywords:

• bootstrap
• error-in-variables
• measurement uncertainty
• NARX and NARMAX models
• non-linear systems identification
• orthogonal least-squares
• parameter estimation

Acknowledgements

The authors gratefully acknowledge that this work was supported by EPSRC (UK), and the data given in this article is taken from http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/.