Improving GLONASS System Efficiency Using Non-Multiple Phase Scale Technology

Introduction. This article analyzes the possibility of implementing highly efficient fault-tolerant algorithms for resolving the ambiguity of phase measurements in Russian and foreign global navigation satellite systems. Nominal values of the GLONASS carrier frequencies with code division of signals are proposed, which ensure an increase in its efficiency by implementing the technology of non-multiple scales. Algorithms for resolving the ambiguity of phase measurements are considered. These algorithms are based on a system of residual classes to calculate the integer value of the number of phase cycles of carrier frequencies in the obtained unambiguity range. The simulation results are presented, and the stability of the proposed algorithms to systematic and random errors of phase measurements is shown.

Aim. To improve the efficiency of global navigation satellite systems in determining the position of consumer navigation equipment using phase measurements.

Materials and methods. The MATLAB modeling environment was used to process phase measurements from RINEX files. This environment has proven efficient in resolving a wide range of scientific problems of varying complexity in industrial and research settings. To achieve the research aim, the mathematical apparatus of number theory and the system of residual classes were employed.

Results. For the GLONASS system with code division of signals, new nominal values of carrier frequencies are proposed; a highly efficient fault-tolerant algorithm for resolving the ambiguity of phase measurements is developed and simulated. The stability of non-multiple scales to systematic errors causing a shift of scales relative to each other is shown, and the operability and reliability of ambiguity resolution algorithms in the presence of random errors not exceeding the value of the specified limiting error of phase measurements is confirmed.

Conclusion. The conducted analysis has shown the possibility of forming non-multiple phase metric scales in consumer navigation equipment using signals with code division of GLONASS, GPS, Galileo, and BeiDou systems.

1. Zabelin A. V. Mathematical Model of the Exact Fraction Method for the Order of Interference. Measurement Techniques. 2011, vol. 54, no. 7. pp. 750–757. doi: 10.1007/s11018-011-9799-4

2. Kukushkin S. S. Constructive Theory of Finite Fields – The Basis of an Algorithmic Solution to Problems of Radio Engineering Measurements. Dual technologies. 2007, no. 3 (40), pp. 67–73. (In Russ.)

3. GLONASS. Modernizatsiya i perspektivy razvitiya [GLONASS. Modernization and Development Prospects]. Ed. by A. I. Perov. Moscow, Radio Engineering, 2020, 1072 p. (In Russ.)

4. Global'naya navigatsionnaya sputnikovaya sistema. Interfeisnyi kontrol'nyi dokument. Obshchee opisanie sistemy s kodovym razdeleniem signalov [Global Navigation Satellite System. Interface Control Document. General Description of the Code Division Multiple Access System]. Ed. 1.0. Moscow, JSC RKS, 2016, 133 p. (In Russ.)

5. Shikhanovich Yu. A. Vvedenie v sovremennuyu matematiku [Introduction to Modern Mathematics]. Moscow, Nauka, 1965, 375 p. (In Russ.)

6. Mikhelovich Sh. M. Teoriya chisel [Number Theory]. Moscow, Vysshaya shkola, 1967, 336 p. (In Russ.)

7. Bakholdin V. S. Non Reboric Method of Resolution of Ambiguity of Phase Measurements in System GLONASS. Radio Engineering. 2015, no. 11, pp. 105–111. (In Russ.)

8. Pat. RF no. 2157547. Ponomarev V. A., Bakholdin V. S. A Method for Resolving the Ambiguity of Phase Measurements. Publ. 10.10.2000. (In Russ.)

9. Tyapkin V. N. Metody opredeleniya navigatsionnykh parametrov podvizhnykh sredstv s ispol'zovaniem sputnikovoi radionavigatsionnoi sistemy GLONASS [Methods for Determining Navigation Parameters of Mobile Facilities Using the GLONASS Satellite Radio Navigation System]. Krasnoyarsk, Sib. Federal University, 2012, 260 p. (In Russ.)

10. Pat. RF, no. 2591953. Dai L. L., Hatch R. R., Zhang Yu., Wang M. Navigation System and Method for Resolving Integer Ambiguities Using the Double-Difference Ambiguity Constraint. Publ. 20.07.2016. (In Russ.)

11. Pat. RF, no. 2213979. Ponomarev V. A., Bakholdin V. S. Method for Resolving Ambiguity of Phase Measurementsin the GPS System. Publ. 10.10.2003. (In Russ.)

12. Karutin S. N. Differentsial'naya korrektsiya i monitoring global'nykh navigatsionnykh sputnikovykh sistem [Differential Correction and Monitoring of Global Navigation Satellite Systems]. Moscow, Moscow University Publishing House GALLERY, 2014, 464 p. (In Russ.)

13. Bakholdin V. S., Lekontsev D. A. Conceptual Model of Radio Engineering System of Trajectory Measurements Based on Technology of Formation of Continuous Measuring Scales. Questions Of Radio Electronics. 2020, no. 11, pp. 14–21. doi:10.21778/2218-5453-2020-11-14-21

14. Global'naya navigatsionnaya sputnikovaya sistema. Interfeisnyi kontrol'nyi dokument. Navigatsionnyi radiosignal otkrytogo dostupa s kodovym razdeleniem v diapazone L1 [Global Navigation Satellite System. Interface Control Document. Open-Access Code Division Multiple Access Navigation Radio Signal in the L1 Band]. Ed. 1.0. Moscow,JSC RKS, 2016, 64 p. (In Russ.)

15. Global'naya navigatsionnaya sputnikovaya sistema. Interfeisnyi kontrol'nyi dokument. Navigatsionnyi radiosignal otkrytogo dostupa s kodovym razdeleniem v diapazone L2 [Global Navigation Satellite System. Interface Control Document. Open-Access Code Division Multiple Access Navigation Radio Signal in the L2 Band]. Ed. 1.0. Moscow,JSC RKS, 2016, 15 p. (In Russ.)

16. Ponomarev V. A., Ponomarev A. V., Ponomareva T. M., Bakholdin V. S. Razreshenie neodnoznachnosti v informatsionno-izmeritel'nykh mnogoshkal'nykh priborakh i sistemakh [Ambiguity Resolution in Multiscale Information-Measuring Instruments and Systems]. SPb., VIKU, 2001, 164 p. (In Russ.)

17. Bakholdin V. S., Lekontsev D. A. Results of Modeling and Experimental Processing of Phase Measurements of the GPS System Using Exhaustive Search Algorithms for Ambiguity Resolution. Navigation and Hydrography. 2023, no. 71, pp. 34–46. (In Russ.)

18. Vlasov I. B., Karutin S. N. Method of Removal of Phase Measurement Ambiguity in Angle-Metering Navigational Apparatus of Global Positioning System. Herald of the Bauman Moscow State Technical University. Series Instrument Engineering. 2004, no. 3, pp. 62–75. (In Russ.)

19. Bakholdin V. S., Lekontsev D. A. Results of experimental processing of phase measurements of the GLONASS system using an exhaustive integer ambiguity resolution algorithm for high-precision absolute positioning. Journal of Instrument Engineering. 2024, vol. 67, no. 2, pp. 162–170. doi: 10.17586/0021-3454-2024-67-2-162-170

20. Dyakonov V. P. MATLAB: obrabotka signalov i izobrazhenii [MATLAB. Signal and image processing]. St Petersburg, Piter, 2002, 608 p. (In Russ.)