1887
Volume 51, Issue 1
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

ABSTRACT

The iterated extended Kalman filter (IEKF) is a tool within the theory of optimal estimation used for nonlinear problems. The IEKF minimises variance in the estimation error in terms of a probabilistic approach. Despite the special terminology, the Kalman filter algorithm minimises the objective function, representing the normalised squared difference between the measured and calculated vectors for the parameters of a selected model. It works like the weighted least squares method – a conventional method for airborne electromagnetic data inversion. In this article, I describe the essence of the Kalman approach to solving inverse problems. I show how one-dimensional inversion with lateral constraints can be performed in terms of the Kalman filter. The described algorithm takes account of the measurement noise, which is specified as the dispersion of signals in the corresponding measurement channels at high altitude. A specific covariance matrix representation allows use of the corresponding Kalman filter calculation methods. They provide numerical stability of the algorithm. The Kalman approach makes it possible to combine modern techniques used in airborne survey data processing. Some examples of Kalman filter use in frequency-domain airborne data processing are given.

Loading

Article metrics loading...

/content/journals/10.1080/08123985.2019.1593790
2020-01-02
2026-01-17
Loading full text...

Full text loading...

References

  1. Chang-Chun, Y., R. Xiu-Yan, L. Yun-He, Q. Yan-Fu, Q. Chang-Kai, and C. Jing 2015 Review on airborne electromagnetic inverse theory and applications. Geophysics80, no. 4: W17–31. doi: 10.1190/geo2014‑0544.1
    https://doi.org/10.1190/geo2014-0544.1 [Google Scholar]
  2. Fraser, D.C. 1987 Layered-earth resistivity mapping. In Developments and applications of modern airborne electromagnetic surveys, ed. D.V. Fitterman, 33–41. Golden, Colo., USA: US Geological Survey Bulletin.
    [Google Scholar]
  3. Golovan, A.A., and N.A. Parusnikov 1998 A relationship between the stochastic estimability measure and singular matrix expansions. Automation and Remote Control59, no. 2: 190–93.
    [Google Scholar]
  4. Guillemoteau, J., P. Sailhac, and M. Béhaegel 2011 Regularization strategy for the layered inversion of airborne transient electromagnetic data: Application to in-loop data acquired over the basin of Franceville (Gabon). Geophysical Prospecting59: 1132–43. doi: 10.1111/j.1365‑2478.2011.00990.x
    https://doi.org/10.1111/j.1365-2478.2011.00990.x [Google Scholar]
  5. Hadamard, J. 1932Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques. Paris, France: Hermann.
  6. Havlik, J., and O. Straka 2015 Performance evaluation of iterated extended Kalman filter with variable step-length. Journal of Physics: Conference Series659: 12–22.
    [Google Scholar]
  7. Jupp, D.L.B., and K. Vozoff 1975 Stable iterative methods for the inversion of geophysical data. Geophysical Journal of the Royal Astronomical Society42: 957–76. doi: 10.1111/j.1365‑246X.1975.tb06461.x
    https://doi.org/10.1111/j.1365-246X.1975.tb06461.x [Google Scholar]
  8. Kalman, R. 1960 A new approach to linear filtering and prediction problems. ASME Journal of Basic Engineering82: 35–45. doi: 10.1115/1.3662552
    https://doi.org/10.1115/1.3662552 [Google Scholar]
  9. Karshakov, E., and J. Moilanen 2018 Combined interpretation both time domain and frequency domain data. Papers of the 7th International Workshop on Airborne Electromagnetics AEM-2018, 1–3. Kolding, Denmark.
    [Google Scholar]
  10. Karshakov, E.V., and M.V. Kharichkin 2008 A stochastic estimation problem at aeromagnetometer deviation compensation. Automation and Remote Control69, no. 7: 1162–70. doi: 10.1134/S0005117908070072
    https://doi.org/10.1134/S0005117908070072 [Google Scholar]
  11. Keppenne, C.L., and M. Rienecker 2003 Assimilation of temperature into an isopycnal ocean general circulation model using a parallel Ensemble Kalman filter. Journal of Marine Systems40–41: 363–80. doi: 10.1016/S0924‑7963(03)00025‑3
    https://doi.org/10.1016/S0924-7963(03)00025-3 [Google Scholar]
  12. Legault, J.M. 2015 Airborne electromagnetic systems – State of the art and future directions. CSEG Recorder40 no. 6: 38–49.
    [Google Scholar]
  13. Palacky, G.J. 1987 Resistivity characteristics of geologic targets. In Electromagnetic Methods in Applied Geophysics - Theory, ed. N. M. Nabighian, 53–129. Tulsa, Oklahoma, USA: Society of Exploration Geophysics.
    [Google Scholar]
  14. Simon, D. 2006Optimal state estimation. Kalman, H∞ and nonlinear approaches. Hoboken, NJ: John Wiley & Sons, Inc.
  15. Volkovitsky, A., and E. Karshakov 2013 Airborne EM systems variety: what is the difference? Mpumalanga, South Africa. Papers of the 13th SAGA Biennial @ 6th International AEM Conference AEM-2013, 1–4.
    [Google Scholar]
  16. Vovenko, T., E. Moilanen, A. Volkovitsky and E. Karshakov 2013 New abilities of quadrature EM systems: Mpumalanga, South Africa. Papers of the 13th SAGA Biennial @ 6th International AEM Conference AEM-2013, 1–4.
    [Google Scholar]
  17. Zhdanov, M.S. 2009Geophysical electromagnetic theory and methods. Amsterdam, Netherlands and Oxford, UK: Elsevier.
/content/journals/10.1080/08123985.2019.1593790
Loading
/content/journals/10.1080/08123985.2019.1593790
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): airborne electromagnetics; frequency domain; Inversion; Kalman filter; time domain

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error