An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models

Zhu, Quanmin; Yu, Dingli; Zhao, Dongya

Abstract

© 2016 Informa UK Limited, trading as Taylor & Francis Group. In this study, an enhanced Kalman Filter formulation for linear in the parameters models with inherent correlated errors is proposed to build up a new framework for nonlinear rational model parameter estimation. The mechanism of linear Kalman filter (LKF) with point data processing is adopted to develop a new recursive algorithm. The novelty of the enhanced linear Kalman filter (EnLKF in short and distinguished from extended Kalman filter (EKF)) is that it is not formulated from the routes of extended Kalman Filters (to approximate nonlinear models by linear approximation around operating points through Taylor expansion) and also it includes LKF as its subset while linear models have no correlated errors in regressor terms. No matter linear or nonlinear models in representing a system from measured data, it is very common to have correlated errors between measurement noise and regression terms, the EnLKF provides a general solution for unbiased model parameter estimation without extra cost to convert model structure. The associated convergence is analysed to provide a quantitative indicator for applications and reference for further research. Three simulated examples are selected to bench-test the performance of the algorithm. In addition, the style of conducting numerical simulation studies provides a user-friendly step by step procedure for the readers/users with interest in their ad hoc applications. It should be noted that this approach is fundamentally different from those using linearisation to approximate nonlinear models and then conduct state/parameter estimate.

• Journal Article Type: Article
• Acceptance Date: Apr 22, 2016
• Online Publication Date: May 19, 2016
• Publication Date: Feb 17, 2017
• Deposit Date: Jun 1, 2016
• Publicly Available Date: Oct 21, 2016
• Journal: International Journal of Systems Science
• Print ISSN: 0020-7721
• Electronic ISSN: 1464-5319
• Publisher: Taylor & Francis
• Peer Reviewed: Peer Reviewed
• Volume: 48
• Issue: 3
• Pages: 451-461
• DOI: https://doi.org/10.1080/00207721.2016.1186243
• Keywords: nonlinear rational models, NARMAX models, parameter estimation, Kalman filter, recursive algorithms, data driven modelling, simulations
• Public URL: https://uwe-repository.worktribe.com/output/899244
• Publisher URL: http://dx.doi.org/10.1080/00207721.2016.1186243
• Additional Information: Additional Information : This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Systems Science on 19 May 2016, available online: http://www.tandfonline.com/10.1080/00207721.2016.1186243
• Contract Date: Jun 1, 2016