Journal of Radio Electronics. eISSN 1684-1719. 2025. №5
Full text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2025.5.4
FILTERING OF NAVIGATION SIGNALS
IN RADIO NAVIGATION SYSTEMS
E.I. Glushankov 1, Z.K. Kondrashov 2, V.YA. Kontorovich 3, A.V. Sudenkova 1
1 The Bonch-Bruevich Saint Petersburg State University of Telecommunications,
193232, Saint-Petersburg, Bolshevikov Av., 22, bldg. 1, lit. A2 Progress Microelectronic Research Institute (JSC Progress MRI),
125183, Moscow, Cherepanov Av., 543 Center for Research and Advanced Studies of the National Polytechnic Institute
(CINVESTAV-IPN), 07360, Mexico City, Av. IPN 2508, Col. San Pedro Zacatenco
The paper was received February 13, 2025.
Abstract. The primary quality indicator of global satellite and local radio navigation systems is the positioning accuracy they provide. This is determined by the measurement errors of the radio navigation parameters, i.e. the radio signal parameters that carry information about the coordinates or speed of an object. The design of the radio navigation system dictates the inclusion of certain parameters within the radio navigation signals. These include the time, frequency or phase shift of the oscillations of the received signal relative to the reference signal, the angle between the direction to the object and the reference direction, the Doppler shift of the frequency and other relevant variables. Based on the Rao-Kramer inequality, the measurement errors of radio navigation parameters are inversely proportional to the signal-to-noise ratio at the input of the navigation receiver of consumer navigation equipment. The development of noise-immune navigation equipment for consumers has necessitated the implementation of filtering methods at the input of the navigation receiver. These methods are designed to segregate a useful signal from the mixture of noise and interference, thereby enhancing the signal-to-noise ratio and, consequently, the accuracy of positioning. The radio navigation parameters at the receiver input, influenced by the radio wave propagation medium, thermal and atmospheric noise, can be modeled as random processes. The dynamic models of random processes are described through their representation in the form of stochastic differential equations. Stochastic differential equations have been synthesized for different types of random processes, which include a uniform distribution to represent the time delay of the radio navigation signal, a Gaussian and uniform distribution for the Doppler frequency shift, and a Gaussian, uniform and von Mises-Tikhonov distribution for the phase of the radio signal. The coefficients of stochastic differential equations that describe dynamic non-stationary models are determined for all types of random process distributions. The equation of state models of noise at the input of navigation receivers are represented by white Gaussian and non-white noise. Linear and nonlinear filtering algorithms are synthesized for stochastic differential equations of state of radio navigation signal parameters and models of the equation of state of signals at the input of receivers.
Key words: GNSS signals, stochastic differential equations, Kalman filter, nonlinear filter, MAP, colored noise
Corresponding author: Glushankov Evgeniy Ivanovich, glushankov57@gmail.com
Dedicated to the memory of Valery Yakovlevich Kontorovich
References
1. Кловский Д.Д., Конторович В.Я., Широков С.М. Модели непрерывных каналов связи на основе стохастических дифференциальных уравнений. [Models of continuous communication channels on the basis of stochastic differential equations.] – Радио и связь, 1984.
2. Глушанков Е.И., Конторович В.Я. Математическое моделирование сигналов различной пространственной когерентности в системах радиосвязи [Mathematical Modelling of Signals of Different Spatial Coherence in Radio Communication Systems] // Адаптивные радиотехнические системы с антенными решетками. Л.: Издательство Ленинградского университета. – 1991. – С. 432-466.
3. Primak S., Kontorovich V., Lyandres V. Stochastic methods and their applications to communications: stochastic differential equations approach. – John Wiley & Sons, 2005.
4. Глушанков Е.И., Конторович В.Я., Караваев Д.А. Математическое моделирование сигналов в непрерывных каналах связи в форме стохастических дифференциальных уравнений [Mathematical modelling of signals in continuous communication channels in the form of stochastic differential equations] // Системы управления, связи и безопасности. – 2023. – №. 4. – С. 1-35.
5. Перов А.И. и др. ГЛОНАСС. Модернизация и перспективы развития [GLONASS. Modernisation and development prospects] // Радиотехника. – 2020.
6. Ярлыков М.С. Статистическая теория радионавигации. [Statistical theory of radio navigation.] – 1985.
7. Stage P., Melsa J.L. Estimation Theory with Application to Communication and Control // McGrav-Hill, New York. – 1971.
8. Лемешко Б.Ю. Непараметрические критерии согласия: Руководство по применению [Nonparametric criteria of agreement: Guide to application] // М.: ИНФРА-М. – 2014.
For citation:
Glushankov E.I., Kondrashov Z.K., Kontorovich V.YA., Sudenkova A.V. Filtering of navigation signals in radio navigation systems // Journal of Radio Electronics. – 2025 – №.5. https://doi.org/10.30898/1684-1719.2025.5.4 (In Russian)