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GPS Solutions

, Volume 21, Issue 2, pp 523–534 | Cite as

Improving prediction performance of GPS satellite clock bias based on wavelet neural network

  • Yupu Wang
  • Zhiping Lu
  • Yunying Qu
  • Linyang Li
  • Ning Wang
Original Article

Abstract

As one of the IGS ultra-rapid predicted (IGU-P) products, the orbit precision has been remarkably improved since late 2007. However, because satellite atomic clocks in space show complicated time–frequency characteristics and are easily influenced by many external factors such as temperature and environment, the IGU-P clock products have not shown sufficient high-quality prediction performance. An improved prediction model is proposed in order to enhance the prediction performance of satellite clock bias (SCB) by employing a wavelet neural network (WNN) model based on the data characteristic of SCB. Specifically, two SCB values of adjacent epoch subtract each other to get the corresponding single difference sequence of SCB, and then, the sequence is preprocessed through using the preprocessing method designed for the single difference sequence. The subsequent step is to model the WNN based on the preprocessed sequence. After the WNN model is determined, the next single difference values at the back of the modeling sequence are predicted. Lastly, the predicted single difference values are restored to the corresponding predicted SCB values. The simulation results have shown that the proposed prediction principle based on the single difference sequence of SCB can make the WNN model simple in architecture and the predicting precision higher than that of the general SCB prediction modeling. The designed preprocessing method specific to the single difference of SCB is able to further improve the prediction performance of the WNN model by reducing the effect from outliers. The proposed SCB prediction model outperforms the IGU-P solutions at least on a daily basis. Specifically, the average prediction precisions for 6, 12 and 24 h based on the proposed model have improved by about 13.53, 31.56 and 49.46 % compared with the IGU-P clock products, and the corresponding average prediction stabilities for 12 and 24 h have increased by about 13.89 and 27.22 %, while the average prediction stability of 6 h is nearly equal.

Keywords

Satellite clock bias Prediction model Data preprocessing Wavelet neural network IGU 

Notes

Acknowledgments

The authors thank the reviewers for their beneficial comments and suggestions. This study has been supported by National Natural Science Foundation of China (Grant Nos. 41274015 and U1431115), Chinese High-tech R&D (863) Program (Grant No. 2013AA122501), Open Research Foundation of State Key Laboratory of Geo-information Engineering (Grant No. SKLGIE2015-M-1-6).

References

  1. Aaron M, Kojiro I (2010) Inversion of a velocity model using artificial neural networks. Comput Geosci 36:1474–1483CrossRefGoogle Scholar
  2. Asimakopoulou G, Kontargyri V, Tsekouras G, Asimakopoulou F, Gonos I, Stathopulos I (2009) Artificial neural network optimization methodology for the estimation of the critical flashover voltage on insulators. IET Sci Meas Technol 3(1):90–104. doi: 10.1049/iet-smt:20080009 CrossRefGoogle Scholar
  3. Bock H, Dach R, Beutler G (2009) High-rate GPS clock corrections from CODE: support of 1 Hz applications. J Geodesy 83(11):1083–1094CrossRefGoogle Scholar
  4. Busca G, Wang Q (2003) Time prediction accuracy for a space clock. Metrologia 40:265–269CrossRefGoogle Scholar
  5. Davis J, Bhattarai S, Ziebart M (2012) Development of a Kalman filter based GPS satellite clock time-offset prediction algorithm. European Frequency and Time Forum (EFTF), pp 152–156Google Scholar
  6. Gao XZ, Ovaska S (2002) Genetic algorithm training of Elman neural network in motor fault detection. Neural Comput Appl 11(1):37–44CrossRefGoogle Scholar
  7. Garcia-Pedrajas N, Hervas-Martinez C, Munoz-Perez J (2003) A cooperative coevolutionary model for evolving artificial neural networks. IEEE Trans Neural Netw 14(3):575–596CrossRefGoogle Scholar
  8. Ge M, Chen JP, Douša J, Gendt G, Wickert J (2012) A computationally efficient approach for estimating high-rate satellite clock corrections in realtime. GPS Solutions 16(1):9–17CrossRefGoogle Scholar
  9. Hamed C, Nima A, Hamidreza Z (2015) Wind power forecast using wavelet neural network trained by improved clonal selection algorithm. Energy Convers Manag 89:588–598CrossRefGoogle Scholar
  10. Heo YJ, Cho J, Heo MB (2010) Improving prediction accuracy of GPS satellite clocks with periodic variation behaviour. Meas Sci Technol 21(7):073001CrossRefGoogle Scholar
  11. Hornick K, Stinchcombe M, White H (1989) Multilayer feed forward networks are universal approximators. Neural Netw 2(5):359–366CrossRefGoogle Scholar
  12. Huang GW, Zhang Q, Xu GC (2014) Real-time clock offset prediction with an improved model. GPS Solut 18(1):95–104CrossRefGoogle Scholar
  13. Indriyatmoko A, Kang T, Lee YJ (2008) Artificial neural networks for predicting DGPS carrier phase and pseudorange correction. GPS Solut 12(4):237–247CrossRefGoogle Scholar
  14. Kavzoglu T, Saka M (2005) Modelling local GPS/levelling geoid undulations using artificial neural networks. J Geodesy 78(9):520–527CrossRefGoogle Scholar
  15. Kerh T, Gunaratnam D, Chan Y (2010) Neural computing with genetic algorithm in evaluating potentially hazardous metropolitan areas result from earthquake. Neural Comput Appl 19(4):521–529CrossRefGoogle Scholar
  16. Kouba J, Springer T (2001) New IGS station and satellite clock combination. GPS Solut 4(4):31–36CrossRefGoogle Scholar
  17. Leick A, Rapoport L, Tatarnikov D (2015) GPS satellite surveying. Wiley, New JerseyCrossRefGoogle Scholar
  18. Li X (2009) Comparing the Kalman filter with a Monte Carlo-based artificial neural network in the INS/GPS vector gravimetric system. J Geodesy 83(9):797–804CrossRefGoogle Scholar
  19. Mosavi M, Shafiee F (2015) Narrow band interference suppression for GPS navigation using neural networks. GPS Solut. doi: 10.1007/s10291-015-0442-8 Google Scholar
  20. Panfilo G, Tavella P (2008) Atomic clock prediction based on stochastic differential equations. Metrologia 45:108–116CrossRefGoogle Scholar
  21. Ray J, Senior K (2003) IGS/BIPM Pilot Project: GPS carrier phase for time/frequency transfer and time scale formation. 4th international time scale algorithms symposium at BIPM, Sevres, France, 18–19 March 2002. Metrologia 40(3):270–288; Erratum 40(4): 205Google Scholar
  22. Riley W (2002) The calculation of time domain frequency stability. Hamilton Technical Services, BeaufortGoogle Scholar
  23. Riley W (2003) Techniques for frequency stability analysis. In: IEEE international frequency control symposium, Tampa, FL (vol 4)Google Scholar
  24. Riley W (2007) Handbook of frequency stability analysis. Hamilton Technical Services, BeaufortGoogle Scholar
  25. Schuh H, Ulrich M, Egger D, Müller J, Schwegmann W (2002) Prediction of earth orientation parameters by artificial neural networks. J Geodesy 76(5):247–258CrossRefGoogle Scholar
  26. Senior K, Ray J (2001) Accuracy and precision of carrier phase clock estimates. In: Proceedings of 33rd precise time and time interval applications and planning meeting, pp 199–217Google Scholar
  27. Senior K, Koppang P, Matsakis D, Ray J (2001) Developing an IGS time scale. In: Proceedings of 2001 IEEE international frequency control symposium, and PDA exhibition, pp 211–218Google Scholar
  28. Senior K, Koppang P, Ray J (2003) Developing an IGS time scale. IEEE Trans Ultrason Ferroelectr Freq Control 50(6):585–593CrossRefGoogle Scholar
  29. Senior K, Ray J, Beard R (2008) Characterization of periodic variations in the GPS satellite clocks. GPS Solut 12(3):211–225CrossRefGoogle Scholar
  30. Tabaraki R, Khayamian T, Ensafi A (2007) Solubility prediction of 21 azo dyes in supercritical carbon dioxide using wavelet neural network. Dyes Pigm 73:230–238CrossRefGoogle Scholar
  31. Vernotte F, Delporte J, Brunet M, Tournier T (2001) Uncertainties of drift coefficients and extrapolation errors: application to clock error prediction. Metrologia 38:325–342CrossRefGoogle Scholar
  32. Wang JG (2010) Research on Time Comparison based on GPS precise point positioning and atomic clock prediction. Dissertation, Graduate School of CAS, BeijingGoogle Scholar
  33. Wang JG, Hu YH, He ZM, Wu JF, Ma HJ, Wang K (2011) Prediction of clock errors of atomic clocks based on modified linear combination model. Chin Astron Astrophy 35(3):318–326CrossRefGoogle Scholar
  34. Wang YP, Lu ZP, Chen ZS, Cui Y (2013) Research the algorithm of wavelet neural network to predict satellite clock bias. Acta Geodaetica Cartogr Sin 42(3):323–330Google Scholar
  35. Xu G (2007) GPS: theory, algorithms and applications. Springer Science & Business Media, BerlinGoogle Scholar
  36. Yassami M, Ashtari P (2015) Using fuzzy genetic, Artificial Bee Colony (ABC) and simple genetic algorithm for the stiffness optimization of steel frames with semi-rigid connections. KSCE J Civil Eng 19(5):1366–1374CrossRefGoogle Scholar
  37. Zheng ZY, Lu XS, Chen YQ (2008) Improved grey model and application in real-time GPS satellite clock bias prediction. In: Proceedings of 4th international conference on natural computation, pp 419–423Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yupu Wang
    • 1
    • 2
  • Zhiping Lu
    • 1
  • Yunying Qu
    • 3
  • Linyang Li
    • 1
  • Ning Wang
    • 1
  1. 1.Institute of Surveying and MappingInformation Engineering UniversityZhengzhouChina
  2. 2.State Key Laboratory of Geo-information EngineeringXi’anChina
  3. 3.Institute of Arts and SciencesInformation Engineering UniversityZhengzhouChina

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