Skip to main content
SpringerLink
Log in

The gravity estimation with square-root unscented Kalman filter in the cold atom gravimeter

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

In the atomic gravimeter, the interference fringe is obtained by scanning the chirp rate of the Raman lasers to compensate for the gravity induced Doppler frequency shift and then the gravitational acceleration can be obtained by extracting the phase of the atomic interference fringe. The phase of the interference fringe is proportional to the chirp rate, therefore the accurate estimation of the chirp rate is the key issue to obtain accurate gravitational acceleration. In practice, the model for estimating the chirp rate is not perfect, and there is system state error. In this paper, we propose a square root unscented Kalman filter (SR-UKF) approach for estimating gravitational acceleration, which can take the system state error into account. The experiments on simulated and real data are performed to demonstrate the feasibility and effectiveness of the SR-UKF method, which can provide an alternative approach for the gravity estimation. In addition, it can be combined with the tidal model for gravity estimation, and can also be used for real-time gravity measurement.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. Marson, J. Faller, J. Phys. E: Sci. Instrum. 19, 22 (1986)

    Article  ADS  Google Scholar 

  2. G. Boedecker, Metrologia 39, 429 (2002)

    Article  ADS  Google Scholar 

  3. J. Flury, R. Rummel, Future Satellite Gravimetry and Earth Dynamics (Springer, New York, 2005)

  4. G. Genevès, P. Gournay, A. Gosset, M. Lecollinet, F. Villar, P. Pinot, P. Juncar, A. Clairon, A. Landragin, D. Holleville, F.P. Dos Santos, IEEE Trans. Instrum. Meas. 54, 850 (2005)

    Article  Google Scholar 

  5. M.A. Gerber, Astron. Aeron. 16, 18 (1978)

    Google Scholar 

  6. R.J. Blakely, R.C. Jachens, Geol. Soc. Am. Bull. 103, 795 (1991)

    Article  ADS  Google Scholar 

  7. M. Kasevich, S. Chu, Appl. Phys. B 54, 321 (1992)

    Article  ADS  Google Scholar 

  8. S. Merlet, Q. Bodart, N. Malossi, A. Landragin, F.P. Dos Santos, O. Gitlein, L. Timmen, Metrologia 47, L9 (2010)

    Article  Google Scholar 

  9. B. Wu, X.L. Wang, H.L. Wang, Z.Y. Wang, Q. Lin, et al., Navig. Control 14, 1 (2015)

    Google Scholar 

  10. J. Le Gouët, T. Mehlstäubler, J. Kim, S. Merlet, A. Clairon, A. Landragin, F.P. Dos Santos, Appl. Phys. B 92, 133 (2008)

    Article  ADS  Google Scholar 

  11. L. Zhou, Z.Y. Xiong, W. Yang, B. Tang, W.C. Peng, Y.B. Wang, P. Xu, J. Wang, M.S. Zhan, Chin. Phys. Lett. 28, 013701 (2011)

    Article  ADS  Google Scholar 

  12. S.M. Dickerson, J.M. Hogan, A. Sugarbaker, D.M. Johnson, M.A. Kasevich, Phys. Rev. Lett. 111, 083001 (2013)

    Article  ADS  Google Scholar 

  13. Y. Bidel, O. Carraz, R. Charriere, M. Cadoret, N. Zahzam, A. Bresson, Appl. Phys. Lett. 102, 144107 (2013)

    Article  ADS  Google Scholar 

  14. M. Hauth, C. Freier, V. Schkolnik, A. Senger, M. Schmidt, A. Peters, Appl. Phys. B 113, 49 (2013)

    Article  ADS  Google Scholar 

  15. Z.K. Hu, B.L. Sun, X.C. Duan, M.K. Zhou, L.L. Chen, S. Zhan, Q.Z. Zhang, J. Luo, Phys. Rev. A 88, 043610 (2013)

    Article  ADS  Google Scholar 

  16. T. Farah, C. Guerlin, A. Landragin, P. Bouyer, S. Gaffet, F.P. Dos Santos, S. Merlet, Gyroscopy Navig. 5, 266 (2014)

    Article  Google Scholar 

  17. G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, G. Tino, Nature 510, 518 (2014)

    Article  ADS  Google Scholar 

  18. B. Wu, Z.Y. Wang, B. Cheng, Q.Y. Wang, A.P. Xu, Q. Lin, Metrologia 51, 452 (2014)

    Article  ADS  Google Scholar 

  19. B. Wu, Z.Y. Wang, B. Cheng, Q.Y. Wang, A.P. Xu, Q. Lin, Geophys. Geochem. Explor. 39, 47 (2015)

    Google Scholar 

  20. Z.J. Fu, Q.Y. Wang, Z.Y. Wang, B. Wu, B. Cheng, Q. Lin, Chin. Opt. Lett. 17, 011204 (2019)

    Article  ADS  Google Scholar 

  21. B. Cheng, Z.Y. Wang, A.P. Xu, Q.Y. Wang, Q. Lin, Chin. Phys. B 24, 113704 (2015)

    Article  ADS  Google Scholar 

  22. S. Merlet, J. Gouët, Q. Bodart, A. Clairon, A. Landragin, F. Pereira dos Santos, P. Rouchon, Metrologia 46, 87 (2009)

    Article  ADS  Google Scholar 

  23. X.C. Duan, M.K. Zhou, D.K. Mao, H.B. Yao, X.B. Deng, J. Luo, Z.K. Hu, Phys. Rev. A 90, 023617 (2014)

    Article  ADS  Google Scholar 

  24. G.T. Foster, J.B. Fixler, J.M. Mcguirk, M.A. Kasevich, Opt. Lett. 27, 951 (2002)

    Article  ADS  Google Scholar 

  25. J.K. Stockton, X. Wu, M.A. Kasevich, Phys. Rev. A 76, 033613 (2007)

    Article  ADS  Google Scholar 

  26. G. Varoquaux, R. Nyman, R. Geiger, P. Cheinet, A. Landragin, P. Bouyer, New J. Phys. 11, 113010 (2009)

    Article  ADS  Google Scholar 

  27. S.W. Chiow, S. Herrmann, S. Chu, H. Müller, Phys. Rev. Lett. 103, 5 (2009)

    Article  Google Scholar 

  28. C.F. Gauss, Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium (Perthes et Besser, Hamburg, 1809)

  29. L. Zhao, Nonlinear System Filtering Theory (National Defence Industry Press, Beijing, 2012)

  30. W.C. Waterhouse, Arch. Hist. Exact Sci. 41, 41 (1990)

    MathSciNet  Google Scholar 

  31. R.E. Kalman, Trans. ASME J. Basic Eng. 82, 35 (1960)

    Article  Google Scholar 

  32. S.J. Julier, J.K. Uhlmann, Proc. IEEE 92, 401 (2004)

    Article  Google Scholar 

  33. R.S. Bucy, K.D. Senne, Automatica 7, 287 (1971)

    Article  Google Scholar 

  34. S.J. Julier, J.K. Uhlmann, H.F. Durrant-Whyte, in Proceedings of American Control Conference (IEEE, Washington, 1995), Vol. 3, p. 1628

  35. R. Van Der Merwe, E.A. Wan, in Proceedings of International Conference on Acoustics, Speech, and Signal processing (IEEE, UT, 2001), Vol. 6, p. 3461

  36. I. Arasaratnam, S. Haykin, IEEE Trans. Autom. Control 54 1254 (2009)

    Article  Google Scholar 

  37. R. Van Der Merwe, E.A. Wan, in in Proceedings of European Symposium on Artificial Neural Networks (Bruges, Citeseer, 2001), p. 205

  38. Z.H. Hu, X.H. Zhao, H.F. Liu, P.C. Shi, EURASIP J. Adv. Sig. Proc. 2009, 1 (2009)

    Google Scholar 

  39. P. Cheiney, L. Fouché, S. Templier, F. Napolitano, B. Battelier, P. Bouyer, B. Barrett, Phys. Rev. Appl. 10, 034030 (2018)

    Article  ADS  Google Scholar 

  40. B. Wu, B. Cheng, Z.J. Fu, D. Zhu, Y. Zhou, K.X. Weng, X.L. Wang, Q. Lin, Acta Phys. Sin. 67, 190302 (2018)

    Google Scholar 

  41. B. Cheng, Z.Y. Wang, B. Wu, A.P. Xu, Q.Y. Wang, Q. Lin, Eur. Phys. J. D 68, 343 (2014)

    Article  ADS  Google Scholar 

  42. S.J. Julier, J.K. Uhlmann, in Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls (SPIE, Florida, 1997), Vol. 3068, p. 182

  43. A.P. Sage, G.W. Husa, in Proceedings of Joint Automatic Control Conference (IEEE, Colorado, 1969), p. 760

  44. Z.L. Deng, J.G. Wang, Acta Autom. Sin. 13, 375 (1987)

    Google Scholar 

  45. L. Zhao, X.X. Wang, M. Sun, J.C. Ding, C. Yan, Acta Autom. Sin. 36, 1007 (2010)

    Article  Google Scholar 

  46. X. Ming, H.Z. Qiu, Aerosp. Shanghai 19, 21 (2012)

    Google Scholar 

  47. J.K. Uhlmann, Tech. Rep., University of Oxford, 1994

  48. Y. Zhang, Z.L. Wang, Z.H. Hu, J. Med. Imaging Health Inf. 5, 783 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Zhejiang University of Technology, Hangzhou, 310023, P.R. China

    Liuqing Zhang, Yin Zhou, Kanxing Weng, Bing Cheng, Bin Wu, Qiang Lin & Zhenghui Hu

Authors
  1. Liuqing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kanxing Weng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bing Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Qiang Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Zhenghui Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenghui Hu.

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, L., Zhou, Y., Weng, K. et al. The gravity estimation with square-root unscented Kalman filter in the cold atom gravimeter. Eur. Phys. J. D 74, 147 (2020). https://doi.org/10.1140/epjd/e2020-100446-6

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2020-100446-6

Keywords

Search

Navigation