Resistant to Correlated Noise and Outliers Discrete Identification of Continuous Non-linear Non-stationary Dynamic Objects

Abstract

In the article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and non-linear ordinary differential equations. The necessary discrete-time approximation of the base models is achieved by appropriately tuned linear FIR “integrating filters”. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical least squares procedure. Since in the presence of correlated noise, the obtained parameter estimates are biased by an unavoidable asymptotic systematic error (bias), the instrumental variable method is used here to significantly improve the consistency of estimates. The finally applied algorithm based on the criterion of the lowest sum of absolute values is used to identify linear and non-linear models in the presence of sporadic measurement errors. In conclusion, the effectiveness of the proposed solutions is demonstrated using numerical simulations.