Integer GLONASS phase ambiguity estimation methods

DOI: 10.34759/trd-2023-130-16

Аuthors

Baburin A. A.

Joint Stock Company “Russian Space Systems”, JSC “RSS”, 53, Aviamotornaya str., Moscow, 111250, Russia

e-mail: contact@spacecorp.ru

Abstract

The article considers integer estimator methods for GLONASS phase ambiguities necessary in the problems of high accuracy absolute and relative positioning for GLONASS signals measurement with integer ambiguity resolution. Accounting for the integer properties of pseudo-phase ambiguities allows significant reduction in solution convergence time up to the centimeter accuracy level. With a view to frequency division of satellites signals, adopted for GLONASS signals, two problems arise while solving the problems high-precise positioning. They are the difference in the hardware delays of the receiver while measuring pseudo-distances of various GLONASS satellites, and the difference between wavelengths of the signals carrier frequency of various GLONASS satellites. These specifics do not allow integer estimation of the GLONASS pseudo-phase ambiguities. Thus, the known methods developed for the systems with code division, such as GPS, cannot be employed for GLONASS. The presented article deals with the second said problem. Two methods of strict and non-strict integer estimation based on solution of the uncertain system of the linear equations by the S-transform theory are being suggested. The strict integer method is based on integer unimodular transformto the system of linear equations prior to its solution, and does not require the presence of GLONASS satellites with neighboring characters in the visibility zone of the receiver. The non-strict method is simpler in application, but integer estimations may be obtained only observing certain conditions. Conditions at which the difference from the integers may be neglected with the non-strict estimation were analyzed. Both strict and non-strict methods do not require engaging direct measurements of pseudo-distances and pseudo-phases processing. Linear approximation of the receiver phase-frequency characteristic is being used for the pseudo-phase measurements model (linear dependence of the phase delays on the frequency in the receiver is being accepted). The analysis is being conducted on the example of the first differences of real navigation receivers of the IGS network processing, which confirms correctness of the suggested methods and adequacy of the mathematical models being used to the real measurements.

Keywords:

GLONASS, integer ambiguity resolution, carrier phase measurements

References

1. Povalyaev A.A. Sputnikovye radionavigatsionnye sistemy. Vremya, pokazaniya chasov, formirovanie izmerenii i opredelenie otnositel’nykh koordinat (Navigation satellite systems. Time, clock, measurements and relative positioning), Moscow, Radiotekhnika, 2008, 328 p.
2. Teunissen P.J.G. The least-squares ambiguity decorrelation adjustment: A method for fast GPS integer ambiguity estimation, Journal of Geodesy, 1995, no. 70, pp. 65-82. DOI: 10.1007/BF00863419
3. Collins P. Isolating and Estimating Undifferenced GPS Integer Ambiguities, Proceedings of the National Technical Meeting of the Institute of Navigation, San Diego, California, January 28-30, 2008, pp. 720-732.
4. Laurichesse D., Mercier F. Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and its Application to PPP, Proceedings of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2007). Fort Worth, TX, September 2007, pp. 839-848.
5. Podkorytov A.N. Trudy MAI, 2012, no. 59. URL: https://trudymai.ru/eng/published.php?ID=34845
6. Povalyaev A.A., Podkorytov A.N., Nikitin C.A., Filimonova D.V. Raketno-kosmicheskoe priborostroenie i informatsionnye sistemy, 2019, vol. 6, no. 1, pp. 4-16. DOI: 10.30894/issn2409-0239.2019.6.1.4.16
7. Povalyaev A.A., Baburin A.A., Podkorytov A.N. Raketno-kosmicheskoe priborostroenie i informatsionnye sistemy, 2021, vol. 8, no. 2, pp. 51-61. DOI: 10.30894/issn2409-0239.2021.8.2.51.61
8. Povalyaev A.A., Baburin A.A., Podkorytov A.N. Raketno-kosmicheskoe priborostroenie i informatsionnye sistemy, 2021, vol. 8, no. 3, pp. 48-62. DOI: 10.30894/issn2409-0239.2021.8.3.48.62
9. Skakun I.O. Trudy MAI, 2014, no. 73. URL: https://trudymai.ru/eng/published.php?ID=48570
10. Banville S., Collins P., Lahaye F. Concepts for Undifferenced GLONASS Ambiguity Resolution, Proceedings of the 26th International Technical Meeting of the ION Satellite Division, ION GNSS- 2013, Nashville, Tennessee, September 16-20, 2013, pp. 1186-1197.
11. Wanninger L. Carrier-phase inter-frequency biases of GLONASS receivers, Journal of Geodesy, 2012, vol. 86, no. 2, pp. 139-148. DOI:10.1007/s00190-011-0502-y
12. Sleewaegen J-M., Simsky A., De Wild W., Boon F., Willems T. Digital vs analog. Demystifying GLONASS inter-frequency carrier phase biases, Inside GNSS, 2012, vol. 7 (3), pp. 57–61.
13. Kouba J. A guide to using international GNSS service (IGS) products, Geodetic Survey Division, Natural Resources Canada, September 2015.
    14. Hofmann-Wellenhof B., Lichtenegger H., Wasle E. GNSS — Global Navigation Satellite Systems: GPS, GLONASS, Galileo, and more, Springer, Wien-NewYork, 2008, 548 p.
14. Podkorytov A.N. Trudy MAI, 2012, no. 50. URL: https://trudymai.ru/eng/published.php?ID=28680
15. Teunissen P.J.G. Generalized Inverses, Adjustment the Datum Problem and S-transformations. Preprint. Delft University of Technology. Reports of the Department of Geodesy Mathematical and Physical Geodesy, 1984, 47 p. DOI:10.1007/978-3-642-70659-2_3
16. P.J. Jonge. A processing Strategy for the Application of the GPS in Networks. Publications on Geodesy 46. Delft, August 1998, 225 p.
17. Podkorytov A.N. Vysokotochnoe mestoopredelenie v global’nykh navigatsionnykh sputnikovykh sistemakh v absolyutnom rezhime za schet razresheniya neodnoznachnosti psevdofazovykh izmerenii (Precise point positioning with phase ambiguity resolution in global navigation satellite systems). Doctor’s thesis... Moscow, 2014, 195 p.
18. Baburin A.A. Raketno-kosmicheskoe priborostroenie i informatsionnye sistemy, 2022, vol. 9, no. 4, pp. 47–58. DOI: 10.30894/issn2409-0239.2022.9.4.47.58
19. Baburin A.A. Raketno-kosmicheskoe priborostroenie i informatsionnye sistemy, 2023, vol. 10, no. 1, pp. 63–77. DOI 10.30894/issn2409-0239.2019.6.2.3.16

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