M. A. Shugurova¹, A. V. Tsyganov¹, Yu. V. Tsyganova²

¹Ulyanovsk State Pedagogical University named after I.N. Ulyanov (Ulyanovsk, Russian Federation)

²Ulyanovsk State University (Ulyanovsk, Russian Federation)

Abstract. Mathematical and computer modeling of daily thermometry allows to study processes of human thermal homeostasis more deeply. In practice, thermometry data is obtained using a digital thermometer, which autonomously reads the temperature of human skin in certain time intervals. The aim of present work is to analyse the methods of modeling and processing of human daily thermometry data. The first method consists in applying linear discrete stochastic models in the state space with Gaussian noises and known vector of input actions, while the estimation of the state vector is performed by discrete covariance Kalman filter. The second method assumes that the vector of input actions is unknown, and the S. Gillijns and B.D. Moor algorithm is used to process daily thermometry data. An alternative option is to use a model with an extended state vector and a Kalman filtering algorithm. The third method takes into account the presence of anomalous measurements (outliers) in the measurement data, and correntropy filter is proposed for their effective filtering. Numerical experiments for modeling and processing of daily thermometry data in MATLAB were carried out in order to compare the quality of discrete filtering algorithms. Modeling of thermometry data was carried out using a three-dimensional model 3dDRCM (3-dimension Discrete-time Real-valued Canonical Model). The results obtained can be used in the study of human daily thermometry processes, for example, to study the reaction of the athlete’s body to the received load.

Key Words: daily thermometry, thermal homeostasis, linear discrete stochastic systems, discrete filtration, Kalman filter

For citation: M. A. Shugurova, A. V. Tsyganov, Yu. V. Tsyganova. Analysis of methods for modeling human daily thermometry data. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 24:4(2022), 469–484. DOI: https://doi.org/10.15507/2079-6900.24.202204.469-484

Information about the authors:

Marina A. Shugurova, PhD Student, School of Higher Mathematics, Ulyanovsk State Pedagogical University named after I. N. Ulyanov, (4/5 Lenin Sq., Ulyanovsk 432011, Russia), ORCID: https://orcid.org/0000-0001-9697-3816, m.a.shugurova@gmail.com

Andrey V. Tsyganov, Professor, School of Higher Mathematics, Ulyanovsk State Pedagogical University named after I. N. Ulyanov, (4/5 Lenin Sq., Ulyanovsk 432011, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-4173-5199, andrew.tsyganov@gmail.com

Yulia V. Tsyganova, Professor, School of Information Technology, Faculty of Mathematics, Information and Aviation Technologies, Ulyanovsk State University, (42 Leo Tolstoy St., Ulyanovsk 432017, Russia), Dr.Sci. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-8812-6035, tsyganovajv@gmail.com