Abstract
Single-frequency precise point positioning (SF-PPP) is a potential precise positioning technique due to the advantages of the high accuracy in positioning after convergence and the low cost in operation. However, there are still challenges limiting its applications at present, such as the long convergence time, the low reliability, and the poor satellite availability and continuity in kinematic applications. In recent years, the achievements in the dual-frequency PPP have confirmed that its performance can be significantly enhanced by employing the slant ionospheric delay and receiver differential code bias (DCB) constraint model, and the multi-constellation Global Navigation Satellite Systems (GNSS) data. Accordingly, we introduce the slant ionospheric delay and receiver DCB constraint model, and the multi-GNSS data in SF-PPP modular together. In order to further overcome the drawbacks of SF-PPP in terms of reliability, continuity, and accuracy in the signal easily blocking environments, the inertial measurements are also adopted in this paper. Finally, we form a new approach to tightly integrate the multi-GNSS single-frequency observations and inertial measurements together to ameliorate the performance of the ionospheric delay and receiver DCB-constrained SF-PPP. In such model, the inter-system bias between each two GNSS systems, the inter-frequency bias between each two GLONASS frequencies, the hardware errors of the inertial sensors, the slant ionospheric delays of each user-satellite pair, and the receiver DCB are estimated together with other parameters in a unique Kalman filter. To demonstrate its performance, the multi-GNSS and low-cost inertial data from a land-borne experiment are analyzed. The results indicate that visible positioning improvements in terms of accuracy, continuity, and reliability can be achieved in both open-sky and complex conditions while using the proposed model in this study compared to the conventional GPS SF-PPP.
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References
Azúa BM, DeMets C, Masterlark T (2002) Strong interseismic coupling, fault after slip, and viscoelastic flow before and after the Oct. 9, 1995 Colimac Jalisco earthquake: continuous GPS measurements from Colima, Mexico. Geophys Res Lett 29(8):122
Beran T, Kim D, Langley RB (2003) High-precision single-frequency GPS point positioning. In: Proceedings of the 16th international technical meeting of the satellite division of the institute of navigation, Portland, OR, USA, p 912
Beran T, Bisnath SB, Langley RB (2004) Evaluation of high-precision, single-frequency GPS point positioning models. In: ION GNSS, pp 1893–1901 (2004)
Bisnath S, Gao Y (2009) Current state of precise point positioning and future prospects and limitations. In: Observing our changing earth. Springer, Berlin, pp 615–623
Bock H, Hugentobler U, Beutler G (2003) Kinematic and dynamic determination of trajectories for low Earth satellites using GPS. In: First CHAMP mission results for gravity, magnetic and atmospheric studies. Springer, Berlin, pp 65–69
Böhm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett 33:L7304. doi:10.1029/2005GL025546
Brown RG, Hwang PYC (1992) Introduction to random signals and applied Kalman filtering. Willey, New York
Cai C, Liu Z, Luo X (2013) Single-frequency ionosphere-free precise point positioning using combined GPS and GLONASS observations. J Navig 66(03):417–434
Cox DB (1978) Integration of GPS with inertial navigation systems. Navigation 25(2):236–245
Crespillo OG, Heirich O, Lehner A (2014) Bayesian GNSS/IMU tight integration for precise railway navigation on track map. In: 2014 IEEE/ION position, location and navigation symposium-PLANS, pp 999–1007 (2014)
Du S (2010) Integration of precise point positioning and low cost MEMS IMU. Unpublished masters dissertation, University of Calgary, Calgary, Canada
Dach R, Hugentobler U, Fridez P, Meindl M (2007) Bernese GPS software version 5.0. Astronomical Institute, University of Bern, 640, 114
Farrell JA, Barth M (1999) The global positioning systems and inertial navigation. McGraw-Hill, New York
Gao Y, Shen X (2002) A new method for carrier-phase-based precise point positioning. Navigation 49(2):109–116
Gao Y, Zhang Y, Chen K (2006) Development of a real-time single-frequency precise point positioning system and test results. In: Proceedings of ION GNSS, pp 26–29
Gao Z, Zhang H, Ge M, Niu X, Shen W, Wickert J, Schuh H (2015) Tightly coupled integration of ionosphere-constrained precise point positioning and inertial navigation systems. Sensors 15(3):5783–5802
Gao Z, Shen W, Zhang H, Niu X, Ge M (2016) Real-time kinematic positioning of INS tightly aided multi-GNSS ionospheric constrained PPP. Sci Rep 6:30488. doi:10.1038/srep30488
Ge M, Gendt G, Rothacher MA, Shi C, Liu J (2008) Resolution of GPS carrier phase ambiguities in precise point positioning (PPP) with daily observations. J Geod 82(7):389–399
Gendt G, Dick G, Reigber CH, Tomassini M, Liu Y, Ramatschi M (2003) Demonstration of NRT GPS water vapor monitoring for numerical weather prediction in Germany. J Meteorol Soc Jpn 82(1B):360–370
Geng J, Meng X, Dodson AH, Ge M, Teferle FN (2010) Rapid re-convergences to ambiguity-fixed solutions in precise point positioning. J Geod 84(12):705–714
Geng J, Teferle FN, Meng X, Dodson AH (2011) Towards PPP–RTK: ambiguity resolution in real-time precise point positioning. Adv Space Res 47(10):1664–1673
Grejner-Brzezinska DA, Da R, Toth C (1998) GPS error modeling and OTF ambiguity resolution for high-accuracy GPS/INS integrated system. J Geod 72(11):626–638
Hernández-Pajares M, Juan JM, Sanz J, Orus R, Garcia-Rigo A, Feltens J, Krankowski A (2009) The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geod 83(3–4):263–275
Héroux P, Gao Y, Kouba J, Lahaye F, Mireault Y, Collins P, Chen K (2004) Products and applications for precise point positioning-moving towards real-time. In: Proceedings of the 17th international technical meeting of the satellite division of The Institute of Navigation (ION GNSS 2004), pp 1832–1843
Héroux P, Kouba J (1995) GPS precise point positioning with a difference. Natural Resources Canada, Geomatics Canada, Geodetic Survey Division
Kim J, Jee GI, Lee JG (1998) A complete GPS/INS integration technique using GPS carrier phase measurements. In: Position location and navigation symposium, IEEE, pp 526–533 (1998)
Kleusberg A, Teunissen PJG (1996) GPS for geodesy. Lecture notes in earth sciences. Springer, Berlin, p 60
Kouba J (2013) A guide to using international GNSS service (IGS) products. In: Ocean Surface Topography Science Team (OSTST) Meeting in Boulder, CO
Larson KM, Bodin P, Gomberg J (2003) Using 1-Hz GPS data to measure deformations caused by the Denali fault earthquake. Science 300(5624):1421–1424
Le AQ, Tiberius CCJM, Van der Marel H, Jakowski N (2009) Use of global and regional ionosphere maps for single-frequency precise point positioning. In: Observing our changing earth. Springer, Berlin, pp 759–769
Li B, Shen Y (2009) Global navigation satellite system ambiguity resolution with constraints from normal equations. J Surv Eng 136(2):63–71
Li X, Ge M, Zhang H, Wickert J (2013) A method for improving uncalibrated phase delay estimation and ambiguity-fixing in real-time precise point positioning. J Geod 87(5):405–416
Li X, Ge M, Dai X, Ren X, Fritsche M, Wickert J, Schuh H (2015) Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo. J Geod 89(6):607–635
Lou Y, Zheng F, Gu S, Wang C, Guo H, Feng Y (2015) Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models. GPS Solut. doi:10.1007/s10291-015-0495-8
Montenbruck O (2003) Kinematic GPS positioning of LEO satellites using ionosphere-free single frequency measurements. Aerosp Sci Technol 7(5):396–405
Montenbruck O, Steigenberger P, Khachikyan R, Weber G, Langley R, Mervart L, Hugentobler U (2014) IGS-MGEX: preparing the ground for multi-constellation GNSS science. Inside GNSS 9(1):42–49
Niu X, Goodall C, Nassar S, El-Sheimy N (2006) An efficient method for evaluating the performance of MEMS IMUs. In: Position location and navigation symposium, 2006 IEEE/ION. San Diego, CA, USA, pp 766–771
Odijk D, Teunissen PJ, Zhang B (2012) Single-frequency integer ambiguity resolution enabled GPS precise point positioning. J Surv Eng 138(4):193–202
Øvstedal O (2002) Absolute positioning with single-frequency GPS receivers. GPS Solut 5(4):33–44
Petovello MG (2004) Real-time integration of a tactical-grade IMU and GPS for high-accuracy positioning and navigation. National Library of Canada, Ottawa
Rabbou MA, El-Rabbany A (2015) Tightly coupled integration of GPS precise point positioning and MEMS-based inertial systems. GPS Solut 19(4):601–609
Roesler G, Martell H (2009) Tightly coupled processing of precise point position (PPP) and INS data. In: Proceedings of ION GPS/GNSS, Institute of Navigation, Savannah, GA, USA, pp 1898–1905
Schaer S, Gurtner W, Feltens J (1998) IONEX: the ionosphere map exchange format version 1. In: Proceedings of the IGS AC workshop, vol 9, no 11, Darmstadt, Germany
Shi C, Gu S, Lou Y, Ge M (2012) An improved approach to model ionospheric delays for single-frequency precise point positioning. Adv Space Res 49(12):1698–1708
Shin EH, El-Sheimy N (2003) Accuracy improvement of low cost INS/GPS for land applications. National Library of Canada, Ottawa
Shin EH (2006) Estimation techniques for low-cost inertial navigation. Library and Archives Canada, Ottawa
Siouris GM (1993) Aerospace avionics systems: a modern synthesis. Academic Press, New York
Steigenberger P, Rothacher M, Fritsche M, Rülke A, Dietrich R (2009) Quality of reprocessed GPS satellite orbits. J Geod 83(3–4):241–248
Teunissen PJG, Khodabandeh A (2015) Review and principles of PPP–RTK methods. J Geod 89(3):217–240
Tu R, Ge M, Zhang H, Huang G (2013a) The realization and convergence analysis of combined PPP based on raw observation. Adv Space Res 52(1):211–221
Tu R, Zhang H, Ge M, Huang G (2013b) A real-time ionospheric model based on GNSS precise point positioning. Adv Space Res 52(6):1125–1134
Witchayangkoon B (2000) Elements of GPS precise point positioning. Doctoral dissertation. University of New Brunswick
Xu P, Shi C, Fang R, Liu J, Niu X, Zhang Q, Yanagidani T (2013) High-rate precise point positioning (PPP) to measure seismic wave motions: an experimental comparison of GPS PPP with inertial measurement units. J Geod 87(4):361–372
Yang Y, Li J, Xu J, Tang J, Guo H, He H (2011) Contribution of the compass satellite navigation system to global PNT users. Chin Sci Bull 56(26):2813–2819
Yunck TP (1996) Orbit determination. In: Parkinson BW, Spilker JJ (eds) Global positioning system-theory and applications. AIAA, Washington
Yao Y, Zhang R, Song W, Shi C, Lou Y (2013) An improved approach to model regional ionosphere and accelerate convergence for precise point positioning. Adv Space Res 52(8):1406–1415
Zhang Y, Gao Y (2005) Performance analysis of a tightly coupled Kalman filter for the integration of un-differenced GPS and inertial data. In: Proceedings of the 2005 national technical meeting of The Institute of Navigation, pp 270–275
Zhang X, Li X (2012) Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing. GPS Solut 16(3):315–327
Zhang H, Gao Z, Ge M, Niu X, Huang L, Tu R, Li X (2013) On the convergence of ionospheric constrained precise point positioning (IC-PPP) based on undifferential uncombined raw GNSS observations. Sensors 13(11):15708–15725
Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res Solid Earth 102(B3):5005–5017
Acknowledgements
This work was supported partly by National 973 Project of China (Grant Nos. 2013CB733301 and 2013CB733305), National Natural Science Foundation of China (Grant Nos. 41128003, 41210006, 41429401, 41574007), DAAD (Grant No. 57173947), NASG Special Project Public Interest (Grant No. 201512001) and the national key research and development program of China (Grant No. 2016YFB0501804).
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Gao, Z., Ge, M., Shen, W. et al. Ionospheric and receiver DCB-constrained multi-GNSS single-frequency PPP integrated with MEMS inertial measurements. J Geod 91, 1351–1366 (2017). https://doi.org/10.1007/s00190-017-1029-7
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DOI: https://doi.org/10.1007/s00190-017-1029-7