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

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 dev...

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Bibliographic Details
Published in:International journal of systems science 2017-02, Vol.48 (3), p.451-461
Main Authors: Zhu, Quanmin, Yu, Dingli, Zhao, Dongya
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Correlation analysis
Cost analysis
data driven modelling
Data processing
Error analysis
Extended Kalman filter
Kalman Filter
Kalman filters
Mathematical models
NARMAX models
Noise measurement
Nonlinear rational models
Nonlinearity
Parameter estimation
Readers
recursive algorithms
Regression analysis
simulations
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Summary: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.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2016.1186243