Journal of Radio Electronics. eISSN 1684-1719. 2026. №7

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DOI: https://doi.org/10.30898/1684-1719.2026.7.7

 

 

 

STOCHASTIC MODEL

OF A ONE-DIMENSIONAL POSITIONING SYSTEM

IN LONG UNDERGROUND STRUCTURES

 

D.V. Fedosov, A.V. Kolesnikov

 

HF-Communication, 644012, Omsk, Akademika Koroleva ave., 32.

 

The paper was received May 29, 2026.

 

Abstract. The article is devoted to phase radio ranging in the medium-wave range in quasi-one-dimensional underground structures (mines). The errors arising from lateral displacement, vertical orientation of the subscriber's receiver, noise, and synchronization with the base station's generator are considered. A model of a receiving dipole in the field of a single-wire transmission line above a homogeneous half-space is used for signal analysis. It is shown that a magnetic dipole is the most suitable for use in subscriber devices. A stochastic model with a Gaussian distribution for the dipole's tilt, a Rayleigh distribution for radial displacement, and white noise is used. At low signal-to-noise ratios (below 30 dB), the error in determining coordinates is determined by the noise level and approaches 15 m at 10 dB. At signal-to-noise ratios exceeding 35 dB, the graphs approach a horizontal line, indicating that the error is determined by the physical characteristics of signal reception, regardless of the signal-to-noise ratio, and the accuracy is approximately 4 meters.

Key words: underground communication, underground navigation, positioning, phase-based radio-altimetry, positioning error.

Corresponding author: Kolesnikov Andrey Viktorovich, kolesnikov.radio@yandex.ru

 

References

1. Fedosov D.V., al. Current state of microwave radionavigation systems in underground structures // Journal Achievements of Modern Radioelectronics. 2025. Vol. 79. No 4. P. 48-63. https://doi.org/10.18127/j20700784-202504-05

2. Patent RU 2797240. Method of navigation and distance measurement in extended objects / Fedosov D.V., 06/01/2023. Application No. 2022112599 dated 05.05.2022

3. Fedosov D.V., Kolesnikov A.V. Substantiation of the concept of a communication system in the range of medium waves in underground quasi-one-dimensional structures // Physics of Wave Processes and Radio Systems. 2023. Vol. 26(3). P. 89-97. https://doi.org/10.18469/1810-3189.2023.26.3.89-97

4. Wait J.R. The eccentrically located wire in a cylindrical cavity in a conducting medium and the limit of a planar boundary // Radio Science. 1976. Vol.11 (11), pp. 897-899.

5. Pettersson P. Image representation of wave propagation on wires above, on and under ground // IEEE Trans. Power Delivery. 1994. Vol. 9, No. 2. Pp. 1049–1055.

6. Pettersson P. Propagation of waves on a wire above a lossy ground – different formulations with approximations // IEEE Transactions on power delivery. 1999. Vol. 14. No. 3. P. 1173-80.

7. Papadopoulos T.A., Chrysochos A.I., Traianos Ch. K., Papagiannis G. Closed-form expressions for the analysis of wave propagation in overhead distribution lines // Energies. 2020. №13, pp. 4519. https://doi.org/10.3390/en13174519

8. Tikhonov V.I. Statisticheskaya radiotekhnika. – M.: Radio i svyazʹ, 1982. – 624 p.

 

For citation:

Fedosov D.V., Kolesnikov A.V. Stochastic model of a one-dimensional positioning system in long underground structures // Journal of Radio Electronics. – 2026. – №. 7. https://doi.org/10.30898/1684-1719.2026.7.7 (In Russian)