Journal of Radio Electronics. eISSN 1684-1719. 2025. ¹3

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DOI: https://doi.org/10.30898/1684-1719.2025.3.15

 

 

 

MATHEMATICAL MODEL

FOR DETERMINING THE TIME DELAY

OF A RADIO SIGNAL RELAYED

BY THE MAIN AND ADJACENT SPACE VEHICLES

 

V.V. Sevidov

 

Military Orders of Zhukov and Lenin Red Banner Academy of Communications

named after Marshal of the Soviet Union S.M. Budyonny

194064, St. Petersburg, Tikhoretsky pr. 3

 

The paper was received December 20, 2024.

 

Abstract. Currently, methods of coordinate measurement of earth stations operating via spacecraft are being intensively developed. The specified methods are based on the reception and processing of radio signals of earth stations after their retransmission by spacecraft. In this case, in the ground-based coordinate measurement complex, time delays of the same realizations of radio signals caused by different trajectories are estimated. The accuracy of determining the coordinates of earth stations largely depends on the accuracy of estimating these time delays. Theorems and their consequences are formulated and proven, which together ensure an increase in the accuracy of estimating the time delays of a radio signal retransmitted by the main and adjacent spacecraft. As an illustration of the developed model, a difference-range method for estimating the coordinates of earth stations based on four small spacecraft is presented. The scientific novelty of the developed technical solution lies in expanding the theory of spline-algebraic harmonic analysis and extending it to the spaces of derivatives of radio signals, derivatives of correlation functions of radio signals. Moreover, special cases of the extended theory of spline-algebraic harmonic analysis coincide with the results obtained earlier.

Key words: spacecraft, earth station, bases of spline character functions, spline algebraic harmonic analysis, interpolation, difference-range method,

Corresponding author: Sevidov Vladimir Vitalievich, v-v-sevido@mail.ru

 

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For citation:

Sevidov V.V. Mathematical model for determining the time delay of a radio signal relayed by the main and adjacent space vehicles // Journal of Radio Electronics. – 2025. – ¹. 3. https://doi.org/10.30898/1684-1719.2025.3.15 (In Russian)