A multi-frequency method to improve the long-term estimation of GNSS clock corrections and phase biases

A. Rovira-Garcia; J. M. Juan; J. Sanz; G. González-Casado; J. Ventura-Traveset; L. Cacciapuoti; E. Schoenemann

doi:10.1002/navi.453

REFERENCES

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1. Allan, D. W.
(1966). Statistics of atomic frequency standards. Proceedings of the IEEE, 54(2), 221–230. https://doi.org/10.1109/PROC.1966.4634
CrossRef
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1. Beutler, G.,
2. Gurtner, W.,
3. Rothacher, M.,
4. Schildknecht, T., &
5. Bauersima, I.
(1986). Determination of GPS orbits using double difference carrier phase observations from regional networks. Bulletin Géodésique, 60(3), 205–220. https://doi.org/10.1007/BF02521052
↵
1. Beutler, G.,
2. Rothacher, M.,
3. Schaer, S.,
4. Springer, T.,
5. Kouba, J., &
6. Neilan, R.
(1999). The International GPS Service (IGS): An interdisciplinary service in support of Earth sciences. Advances in Space Research, 23(4), 631–653. https://doi.org/10.1016/S0273-1177(99)00160-X
CrossRef GeoRef Web of Science
↵
1. Bock, H.,
2. Dach, R.,
3. Jäggi, A., &
4. Beutler, G.
(2009). High-rate GPS clock corrections from CODE: support of 1 Hz applications. Journal of Geodesy, 83(11), 1083–1094. https://doi.org/10.1007/s00190-009-0326-1
↵
1. Blewitt, G.
(1993). Advances in global positioning system technology for geodynamics investigations: 1978–1992. In D. E. Smith & D. L. Turcotte (Eds.), Contributions of space geodesy to geodynamics: Technology, Volume 25 (pp. 195–213).
↵
1. Collins, P.,
2. Bisnath, S.,
3. Lahaye, F., &
4. Hérroux, P.
(2010). Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing. NAVIGATION, 57(2), 123–135. https://www.doi.org/10.1002/j.2161-4296.2010.tb01772.x
↵
1. Dach, R.,
2. Schildknecht, T.,
3. Hugentobler, U.,
4. Bernier, L.-G., &
5. Dudle, G.
(2006). Continuous geodetic time-transfer analysis methods. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 53(7), 1250–1259. https://doi.org/10.1109/tuffc.2006.1665073
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8. Hees, A.,
9. Poncin-Lafitte, C.,
10. Meynadier, F.,
11. Prieto-Cerdeira, R.,
12. Sohet, B.,
13. Ventura-Traveset, J., &
14. Wolf, P.
(2018). Gravitational redshift test using eccentric galileo satellites, Physical Review Letters, 121(23). https://doi.org/10.1103/PhysRevLett.121.231101
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1. European Union for the Space Programme Agency
(2017). Notice Advisory to Galileo Users (NAGU) 2017012. https://www.gsc-europa.eu/notice-advisory-to-galileo-users-nagu-2017012
↵
1. Ge, M.,
2. Gendt, G.,
3. Rothacher, M.,
4. Shi, C. &
5. Liu, J.
(2008). Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. Journal of Geodesy, 82(7), 389–399. https://doi.org/10.1007/s00190-007-0187-4
↵
1. Hatch, R.
(1982). The synergism of GPS code and carrier measurements. Proc. of the 3rd International Geodetic Symposium on Satellite Doppler Positioning, Las Cruces, NM, 1213–1231.
↵
1. Herrmann, S.,
2. Finke, F.,
3. Lülf, M.,
4. Kichakova, O.,
5. Puetzfeld, D.,
6. Knickmann, D.,
7. List, M.,
8. Rievers, B.,
9. Giorgi, G.,
10. Günther, C.,
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12. Prieto-Cerdeira, R.,
13. Dilssner, F.,
14. Gonzalez, F.,
15. Schönemann, E.,
16. Ventura-Traveset, J., &
17. Lämmerzahl, C.
(2018). Test of the gravitational redshift with Galileo satellites in an eccentric orbit. Physical Review Letters, 121(23). https://doi.org/10.1103/PhysRevLett.121.231102
↵
1. Johnston, G.,
2. Riddell, A., &
3. Hausler, G.
(2017). The International GNSS Service. In P. Teunissen & O. Montenbruck (Eds.), Springer handbook of global navigation satellite systems (pp. 967–982). Springer International Publishing. https://doi.org/10.1007/978-3-319-42928-1_33
↵
1. Juan, J. M.,
2. Sanz, J.,
3. Rovira-Garcia, A.,
4. González-Casado, G.,
5. Ventura-Traveset, J.,
6. Cacciapuoti, L. &
7. Schoenemann, E.
(2020). A new approach to improve satellite clock estimates, removing the Inter-day jumps. Proc. of the 51st Annual Precise Time and Time Interval Systems and Applications Meeting, San Diego, CA, 279–301. https://doi.org/10.33012/2020.17306
↵
1. Laurichesse, F. &
2. Mercier, D.
(2007) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP. Proc. of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2007), Fort Worth, TX, 839–848. https://www.ion.org/publications/abstract.cfm?articleID=7584
↵
1. Li, P.,
2. Jiang, X.,
3. Zhang, X.,
4. Ge, M., &
5. Schuh, H.
(2020) GPS+Galileo+BeiDou precise point positioning with triple-frequency ambiguity resolution. GPS Solutions, 24. https://doi.org/10.1007/s10291-020-00992-1
↵
1. Malys, S., &
2. Jensen, P. A.
(1990). Geodetic point positioning with GPS carrier beat phase data from the CAS UNO Experiment. Geophysical Research Letters, 17(5), 651–654, https://doi.org/10.1029/GL017i005p00651
↵
1. Montenbruck, O.,
2. Hugentobler, U.,
3. Dach, R.,
4. Steigenberger, P., &
5. Hauschild, A.
(2012). Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solutions, 16(3), 303–313. https://doi.org/10.1007/s10291-011-0232-x
↵
1. Montenbruck, O.,
2. Steigenberger, P.,
3. Prange, L.,
4. Deng, Z.,
5. Zhao, Q.,
6. Perosanz, F.,
7. Romero, I.,
8. Noll, C.,
9. Stürze, A.,
10. Weber, G.,
11. Schmid, R.,
12. MacLeod, K., &
13. Schaer, S.
(2017). The Multi-GNSS Experiment (MGEX) of the International GNSS service (IGS) – Achievements, prospects and challenges. Advances in Space Research, 59(7), 1671–1697. https://doi.org/10.1016/j.asr.2017.01.011
↵
1. Odijk, D.,
2. Zhang, B.,
3. Khodabandeh, A.,
4. Odolinski, R., &
5. Teunissen, P. J. G.
(2016). On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory. Journal of Geodesy, 90(1), 15–44. https://doi.org/10.1007/s00190-015-0854-9
↵
1. Petit, G.,
2. Kanj, A.,
3. Loyer, S.,
4. Delporte, J.,
5. Mercier, F., &
6. Perosanz, F.
(2015). 1 × 10−16 frequency transfer by GPS PPP with integer ambiguity resolution. Metrologia, 52(2), 301–309. https://doi.org/10.1088/0026-1394/52/2/301
↵
1. Ray, J. &
2. Senior, K.
(2003). IGS/BIPM pilot project: GPS carrier phase for time/frequency transfer and timescale formation. Metrologia, 40(3), S270–S288. https://doi.org/10.1088/0026-1394/40/3/307
↵
1. Ray, J.,
2. Gurtner, W. &
3. Coleman M. J.
(2017). RINEX extensions to handle clock information. https://files.igs.org/pub/data/format/rinex_clock304.txt
↵
1. Rovira-Garcia, A.,
2. Juan, J. M.,
3. Sanz, J.,
4. González-Casado, G., &
5. Bertran, E.
(2016). Fast precise point positioning: A system to provide corrections for single and multi-frequency navigation. NAVIGATION, 63(3), 231–247. https://doi.org/10.1002/navi.148
↵
1. Rovira-Garcia, A.,
2. Juan, J. M.,
3. Sanz, J.,
4. González-Casado, G.,
5. Ventura-Traveset, J.,
6. Cacciapuoti, L., &
7. Schoenemann, E.
(2021). Removing day-boundary discontinuities on GNSS clock estimates: methodology and results. GPS Solutions, 25(2). https://doi.org/10.1007/s10291-021-01085-3
↵
1. Sanz, J.,
2. Juan, J. M.,
3. Rovira-Garcia, A., &
4. González-Casado, G.
(2017). GPS differential code biases determination: methodology and analysis. GPS Solutions, 21(4), 1549–1561. https://doi.org/10.1007/s10291-017-0634-5
↵
1. Schöenemann, E.,
2. Becker, M., &
3. Springer, T.
(2011). A new approach for GNSS analysis in a multi-GNSS and multi-signal environment. Journal of Geodetic Science, 1(3), 204–214. https://doi.org/10.2478/v10156-010-0023-2
↵
1. Strasser, S.,
2. Mayer-Gürr, T., &
3. Zehentner, N.
(2019). Processing of GNSS constellations and ground station networks using the raw observation approach. Journal of Geodesy, 93(7), 1045–1057. https://doi.org/10.1007/s00190-018-1223-2
↵
1. Subirana, J. S.,
2. Zornoza, J. M. &
3. Hernández-Pajarez M.
(2013). GNSS Data Processing, Vol. I: Fundamentals and Algorithms. European Space Agency Communications. https://gssc.esa.int/navipedia/GNSS_Book/ESA_GNSS-Book_TM-23_Vol_I.pdf
↵
1. Zumberge, J. F.,
2. Heflin, M. B.,
3. Jefferson, D. C.,
4. Watkins, M. M., &
5. Webb, F. H.
(1997). Precise point positioning for the efficient and robust analysis of GPS data from large networks. Journal of Geophysical Research: Solid Earth, 102(B3), 5005–5017. https://doi.org/10.1029/96JB03860

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Keywords

[1] ↵
Allan, D. W.
(1966). Statistics of atomic frequency standards. Proceedings of the IEEE, 54(2), 221–230. https://doi.org/10.1109/PROC.1966.4634
CrossRef

[2] Allan, D. W.

[3] ↵
Beutler, G.,
Gurtner, W.,
Rothacher, M.,
Schildknecht, T., &
Bauersima, I.
(1986). Determination of GPS orbits using double difference carrier phase observations from regional networks. Bulletin Géodésique, 60(3), 205–220. https://doi.org/10.1007/BF02521052

[4] Beutler, G.,

[5] Gurtner, W.,

[6] Rothacher, M.,

[7] Schildknecht, T., &

[8] Bauersima, I.

[9] ↵
Beutler, G.,
Rothacher, M.,
Schaer, S.,
Springer, T.,
Kouba, J., &
Neilan, R.
(1999). The International GPS Service (IGS): An interdisciplinary service in support of Earth sciences. Advances in Space Research, 23(4), 631–653. https://doi.org/10.1016/S0273-1177(99)00160-X
CrossRef GeoRef Web of Science

[10] Beutler, G.,

[11] Rothacher, M.,

[12] Schaer, S.,

[13] Springer, T.,

[14] Kouba, J., &

[15] Neilan, R.

[16] ↵
Bock, H.,
Dach, R.,
Jäggi, A., &
Beutler, G.
(2009). High-rate GPS clock corrections from CODE: support of 1 Hz applications. Journal of Geodesy, 83(11), 1083–1094. https://doi.org/10.1007/s00190-009-0326-1

[17] Bock, H.,

[18] Dach, R.,

[19] Jäggi, A., &

[20] Beutler, G.

[21] ↵
Blewitt, G.
(1993). Advances in global positioning system technology for geodynamics investigations: 1978–1992. In D. E. Smith & D. L. Turcotte (Eds.), Contributions of space geodesy to geodynamics: Technology, Volume 25 (pp. 195–213).

[22] Blewitt, G.

[23] ↵
Collins, P.,
Bisnath, S.,
Lahaye, F., &
Hérroux, P.
(2010). Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing. NAVIGATION, 57(2), 123–135. https://www.doi.org/10.1002/j.2161-4296.2010.tb01772.x

[24] Collins, P.,

[25] Bisnath, S.,

[26] Lahaye, F., &

[27] Hérroux, P.

[28] ↵
Dach, R.,
Schildknecht, T.,
Hugentobler, U.,
Bernier, L.-G., &
Dudle, G.
(2006). Continuous geodetic time-transfer analysis methods. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 53(7), 1250–1259. https://doi.org/10.1109/tuffc.2006.1665073
PubMed

[29] Dach, R.,

[30] Schildknecht, T.,

[31] Hugentobler, U.,

[32] Bernier, L.-G., &

[33] Dudle, G.

[34] ↵
Delva, P.,
Puchades, N.,
Schönemann, E.,
Dilssner, F.,
Courde, C.,
Bertone, S.,
Gonzalez, F.,
Hees, A.,
Poncin-Lafitte, C.,
Meynadier, F.,
Prieto-Cerdeira, R.,
Sohet, B.,
Ventura-Traveset, J., &
Wolf, P.
(2018). Gravitational redshift test using eccentric galileo satellites, Physical Review Letters, 121(23). https://doi.org/10.1103/PhysRevLett.121.231101

[35] Delva, P.,

[36] Puchades, N.,

[37] Schönemann, E.,

[38] Dilssner, F.,

[39] Courde, C.,

[40] Bertone, S.,

[41] Gonzalez, F.,

[42] Hees, A.,

[43] Poncin-Lafitte, C.,

[44] Meynadier, F.,

[45] Prieto-Cerdeira, R.,

[46] Sohet, B.,

[47] Ventura-Traveset, J., &

[48] Wolf, P.

[49] ↵
European Union for the Space Programme Agency
(2017). Notice Advisory to Galileo Users (NAGU) 2017012. https://www.gsc-europa.eu/notice-advisory-to-galileo-users-nagu-2017012

[50] European Union for the Space Programme Agency

[51] ↵
Ge, M.,
Gendt, G.,
Rothacher, M.,
Shi, C. &
Liu, J.
(2008). Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. Journal of Geodesy, 82(7), 389–399. https://doi.org/10.1007/s00190-007-0187-4

[52] Ge, M.,

[53] Gendt, G.,

[54] Rothacher, M.,

[55] Shi, C. &

[56] Liu, J.

[57] ↵
Hatch, R.
(1982). The synergism of GPS code and carrier measurements. Proc. of the 3rd International Geodetic Symposium on Satellite Doppler Positioning, Las Cruces, NM, 1213–1231.

[58] Hatch, R.

[59] ↵
Herrmann, S.,
Finke, F.,
Lülf, M.,
Kichakova, O.,
Puetzfeld, D.,
Knickmann, D.,
List, M.,
Rievers, B.,
Giorgi, G.,
Günther, C.,
Dittus, H.,
Prieto-Cerdeira, R.,
Dilssner, F.,
Gonzalez, F.,
Schönemann, E.,
Ventura-Traveset, J., &
Lämmerzahl, C.
(2018). Test of the gravitational redshift with Galileo satellites in an eccentric orbit. Physical Review Letters, 121(23). https://doi.org/10.1103/PhysRevLett.121.231102

[60] Herrmann, S.,

[61] Finke, F.,

[62] Lülf, M.,

[63] Kichakova, O.,

[64] Puetzfeld, D.,

[65] Knickmann, D.,

[66] List, M.,

[67] Rievers, B.,

[68] Giorgi, G.,

[69] Günther, C.,

[70] Dittus, H.,

[71] Prieto-Cerdeira, R.,

[72] Dilssner, F.,

[73] Gonzalez, F.,

[74] Schönemann, E.,

[75] Ventura-Traveset, J., &

[76] Lämmerzahl, C.

[77] ↵
Johnston, G.,
Riddell, A., &
Hausler, G.
(2017). The International GNSS Service. In P. Teunissen & O. Montenbruck (Eds.), Springer handbook of global navigation satellite systems (pp. 967–982). Springer International Publishing. https://doi.org/10.1007/978-3-319-42928-1_33

[78] Johnston, G.,

[79] Riddell, A., &

[80] Hausler, G.

[81] ↵
Juan, J. M.,
Sanz, J.,
Rovira-Garcia, A.,
González-Casado, G.,
Ventura-Traveset, J.,
Cacciapuoti, L. &
Schoenemann, E.
(2020). A new approach to improve satellite clock estimates, removing the Inter-day jumps. Proc. of the 51st Annual Precise Time and Time Interval Systems and Applications Meeting, San Diego, CA, 279–301. https://doi.org/10.33012/2020.17306

[82] Juan, J. M.,

[83] Sanz, J.,

[84] Rovira-Garcia, A.,

[85] González-Casado, G.,

[86] Ventura-Traveset, J.,

[87] Cacciapuoti, L. &

[88] Schoenemann, E.

[89] ↵
Laurichesse, F. &
Mercier, D.
(2007) Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP. Proc. of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS 2007), Fort Worth, TX, 839–848. https://www.ion.org/publications/abstract.cfm?articleID=7584

[90] Laurichesse, F. &

[91] Mercier, D.

[92] ↵
Li, P.,
Jiang, X.,
Zhang, X.,
Ge, M., &
Schuh, H.
(2020) GPS+Galileo+BeiDou precise point positioning with triple-frequency ambiguity resolution. GPS Solutions, 24. https://doi.org/10.1007/s10291-020-00992-1

[93] Li, P.,

[94] Jiang, X.,

[95] Zhang, X.,

[96] Ge, M., &

[97] Schuh, H.

[98] ↵
Malys, S., &
Jensen, P. A.
(1990). Geodetic point positioning with GPS carrier beat phase data from the CAS UNO Experiment. Geophysical Research Letters, 17(5), 651–654, https://doi.org/10.1029/GL017i005p00651

[99] Malys, S., &

[100] Jensen, P. A.

[101] ↵
Montenbruck, O.,
Hugentobler, U.,
Dach, R.,
Steigenberger, P., &
Hauschild, A.
(2012). Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solutions, 16(3), 303–313. https://doi.org/10.1007/s10291-011-0232-x

[102] Montenbruck, O.,

[103] Hugentobler, U.,

[104] Dach, R.,

[105] Steigenberger, P., &

[106] Hauschild, A.

[107] ↵
Montenbruck, O.,
Steigenberger, P.,
Prange, L.,
Deng, Z.,
Zhao, Q.,
Perosanz, F.,
Romero, I.,
Noll, C.,
Stürze, A.,
Weber, G.,
Schmid, R.,
MacLeod, K., &
Schaer, S.
(2017). The Multi-GNSS Experiment (MGEX) of the International GNSS service (IGS) – Achievements, prospects and challenges. Advances in Space Research, 59(7), 1671–1697. https://doi.org/10.1016/j.asr.2017.01.011

[108] Montenbruck, O.,

[109] Steigenberger, P.,

[110] Prange, L.,

[111] Deng, Z.,

[112] Zhao, Q.,

[113] Perosanz, F.,

[114] Romero, I.,

[115] Noll, C.,

[116] Stürze, A.,

[117] Weber, G.,

[118] Schmid, R.,

[119] MacLeod, K., &

[120] Schaer, S.

[121] ↵
Odijk, D.,
Zhang, B.,
Khodabandeh, A.,
Odolinski, R., &
Teunissen, P. J. G.
(2016). On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory. Journal of Geodesy, 90(1), 15–44. https://doi.org/10.1007/s00190-015-0854-9

[122] Odijk, D.,

[123] Zhang, B.,

[124] Khodabandeh, A.,

[125] Odolinski, R., &

[126] Teunissen, P. J. G.

[127] ↵
Petit, G.,
Kanj, A.,
Loyer, S.,
Delporte, J.,
Mercier, F., &
Perosanz, F.
(2015). 1 × 10−16 frequency transfer by GPS PPP with integer ambiguity resolution. Metrologia, 52(2), 301–309. https://doi.org/10.1088/0026-1394/52/2/301

[128] Petit, G.,

[129] Kanj, A.,

[130] Loyer, S.,

[131] Delporte, J.,

[132] Mercier, F., &

[133] Perosanz, F.

[134] ↵
Ray, J. &
Senior, K.
(2003). IGS/BIPM pilot project: GPS carrier phase for time/frequency transfer and timescale formation. Metrologia, 40(3), S270–S288. https://doi.org/10.1088/0026-1394/40/3/307

[135] Ray, J. &

[136] Senior, K.

[137] ↵
Ray, J.,
Gurtner, W. &
Coleman M. J.
(2017). RINEX extensions to handle clock information. https://files.igs.org/pub/data/format/rinex_clock304.txt

[138] Ray, J.,

[139] Gurtner, W. &

[140] Coleman M. J.

[141] ↵
Rovira-Garcia, A.,
Juan, J. M.,
Sanz, J.,
González-Casado, G., &
Bertran, E.
(2016). Fast precise point positioning: A system to provide corrections for single and multi-frequency navigation. NAVIGATION, 63(3), 231–247. https://doi.org/10.1002/navi.148

[142] Rovira-Garcia, A.,

[143] Juan, J. M.,

[144] Sanz, J.,

[145] González-Casado, G., &

[146] Bertran, E.

[147] ↵
Rovira-Garcia, A.,
Juan, J. M.,
Sanz, J.,
González-Casado, G.,
Ventura-Traveset, J.,
Cacciapuoti, L., &
Schoenemann, E.
(2021). Removing day-boundary discontinuities on GNSS clock estimates: methodology and results. GPS Solutions, 25(2). https://doi.org/10.1007/s10291-021-01085-3

[148] Rovira-Garcia, A.,

[149] Juan, J. M.,

[150] Sanz, J.,

[151] González-Casado, G.,

[152] Ventura-Traveset, J.,

[153] Cacciapuoti, L., &

[154] Schoenemann, E.

[155] ↵
Sanz, J.,
Juan, J. M.,
Rovira-Garcia, A., &
González-Casado, G.
(2017). GPS differential code biases determination: methodology and analysis. GPS Solutions, 21(4), 1549–1561. https://doi.org/10.1007/s10291-017-0634-5

[156] Sanz, J.,

[157] Juan, J. M.,

[158] Rovira-Garcia, A., &

[159] González-Casado, G.

[160] ↵
Schöenemann, E.,
Becker, M., &
Springer, T.
(2011). A new approach for GNSS analysis in a multi-GNSS and multi-signal environment. Journal of Geodetic Science, 1(3), 204–214. https://doi.org/10.2478/v10156-010-0023-2

[161] Schöenemann, E.,

[162] Becker, M., &

[163] Springer, T.

[164] ↵
Strasser, S.,
Mayer-Gürr, T., &
Zehentner, N.
(2019). Processing of GNSS constellations and ground station networks using the raw observation approach. Journal of Geodesy, 93(7), 1045–1057. https://doi.org/10.1007/s00190-018-1223-2

[165] Strasser, S.,

[166] Mayer-Gürr, T., &

[167] Zehentner, N.

[168] ↵
Subirana, J. S.,
Zornoza, J. M. &
Hernández-Pajarez M.
(2013). GNSS Data Processing, Vol. I: Fundamentals and Algorithms. European Space Agency Communications. https://gssc.esa.int/navipedia/GNSS_Book/ESA_GNSS-Book_TM-23_Vol_I.pdf

[169] Subirana, J. S.,

[170] Zornoza, J. M. &

[171] Hernández-Pajarez M.

[172] ↵
Zumberge, J. F.,
Heflin, M. B.,
Jefferson, D. C.,
Watkins, M. M., &
Webb, F. H.
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A multi-frequency method to improve the long-term estimation of GNSS clock corrections and phase biases

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A multi-frequency method to improve the long-term estimation of GNSS clock corrections and phase biases

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