Fitting of experimental data using a fractional Kalman-like observer

J E Solís-Pérez; J F Gómez-Aguilar; L Torres; R F Escobar-Jiménez; J Reyes-Reyes

doi:10.1016/j.isatra.2018.11.036

Fitting of experimental data using a fractional Kalman-like observer

ISA Trans. 2019 May:88:153-169. doi: 10.1016/j.isatra.2018.11.036. Epub 2018 Dec 5.

Authors

J E Solís-Pérez¹, J F Gómez-Aguilar², L Torres³, R F Escobar-Jiménez¹, J Reyes-Reyes¹

Affiliations

¹ Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira. C.P. 62490, Cuernavaca, Morelos, Mexico.
² CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira. C.P. 62490, Cuernavaca, Morelos, Mexico. Electronic address: jgomez@cenidet.edu.mx.
³ CONACyT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Circuito Escolar s/n, Ciudad Universitaria, Coyoacán, Mexico City 04510, Mexico.

PMID: 30545766
DOI: 10.1016/j.isatra.2018.11.036

Abstract

In this paper, a fractional order Kalman filter (FOKF) is presented, this is based on a system expressed by fractional differential equations according to the Riemann-Liouville definition. In order to get the best fitting of the FOKF, the cuckoo search optimization algorithm (CS) was used. The purpose of using the CS algorithm is to optimize the order of the observer, the fractional Riccati equation and the FOKF tuning parameters. The Grünwald-Letnikov approximation was used to compute the numerical solution of the FOKF. To show the effectiveness of the proposed FOKF, four examples are presented, the brain activity, the cutaneous potential recordings of a pregnant woman, the earthquake acceleration, and the Chua's circuit response.

Keywords: Cuckoo search optimization algorithm; Fourier series; Fractional order Kalman filter; Grünwald–Letnikov approximation; Riemann–Liouville derivative.