PARAMETRIC IDENTIFICATION OF DIFFUSION-ADVECTION-REACTION SYSTEMS USING THE EXTENDED KALMAN FILTER

Abstract

The article considers the problem of parametric identification of partial differential equations (PDE) from noisy observational data. The relevance of the study is due to the widespread use of PDE in modeling physical, chemical and engineering processes, where accurate parameter estimates are critical for adequate prediction of system dynamics. A combined method is proposed that combines the least squares method and an extended Kalman filter based on the Crank-Nicolson scheme. This approach allows minimizing the bias of estimates arising from errors in regressors and increasing resistance to noise. Numerical modeling is carried out for a one-dimensional diffusion-advection-reaction equation with Gaussian noise. The results are compared with the integral and Bayesian methods. The analysis showed that the proposed method provides small biases and low standard deviations, demonstrating better balance compared to alternative methods. The Bayesian approach, although robust to uncertainty, produces a larger bias, while the integral method is comparable in accuracy but less adaptive. Thus, the combination of the least squares method and the extended Kalman filter based on the Crank-Nicholson scheme is an effective solution for parametric identification of PDEs, especially at moderate noise levels. Future work includes extending the method to nonlinear equations and taking into account the spatio-temporal correlation of errors.