A. V. Tsyganov¹, J. V. Tsyganova^{1, 2}

¹Ulyanovsk State Pedagogical University (Ulyanovsk, Russian Federation)

²Innopolis University (Innopolis, Russian Federation)

Abstract. The paper considers the problem of automatic optimality control of a distributed discrete information Kalman filter in multisensory networks. The aim of the study is to develop a new method for detecting the loss of optimality of a distributed discrete filter caused by an ubrupt change in the parameters of a dynamic system with a distributed network of sensors. A network with a fully connected topology is considered. A new approach is proposed based on the analysis of the gradient of the negative log likelihood function calculated in terms of a distributed information filter. The method uses sensitivity equations that allow decentralized calculation of the optimality criterion and its gradient in each node of the network, which ensures scalability and fault tolerance of the multisensory system. The main theoretical result is expressions for calculating the optimality criterion in the form of a negative logarithmic likelihood function and its gradient in terms of a distributed discrete filter. The results of computer modeling conducted in MATLAB validate the proposed approach. The developed method can be used in monitoring, motion control and tracking systems using distributed sensor networks. The results obtained show that the proposed approach makes it possible to control the optimality of a discrete filter and, therefore, can be integrated into adaptive algorithms for automatically reconfiguring the parameters of a dynamic system model with a distributed network of sensors.

Key Words: automatic optimality control, discrete-time linear stochastic system, distributed measurements, distributed Kalman filter, gradient of optimality criterion

For citation: A. V. Tsyganov, J. V. Tsyganova. automatic optimality control, discrete-time linear stochastic system, distributed measurements, distributed Kalman filter, gradient of optimality criterion. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 28:1(2026), 79–95. DOI: https://doi.org/10.15507/2079-6900.28.202601.79-95

Information about the authors:

Andrey V. Tsyganov, Ph. D. (Phys. and Math.), Professor, Department of Higher Mathematics, Ulyanovsk State Pedagogical University (4/5 Lenin Square, Ulyanovsk, 432071, Russia), ORCID: https://orcid.org/0000-0002-4173-5199, andrew.tsyganov@gmail.com

Julia V. Tsyganova, D. Sci. (Phys. and Math.), Professor, Institute of Data Science and Artificial intelligence, Innopolis University (1 Universitetskaya Str., Innopolis, 420500, Russia), ORCID: http://orcid.org/0000-0001-8812-6035, tsyganovajv@gmail.com