Advertisement

Application of Unscented Kalman Filter in Nonlinear Geodetic Problems

  • D. Zhao
  • Z. Cai
  • C. Zhang
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 132)

Abstract

The Extended Kalman Filter (EKF) has been one of the most widely used methods for non-linear estimation. In recent several decades people have realized that there are a lot of constraints in applications of the EKF for its hard implementation and intractability. In this paper an alternative estimation method is proposed, which takes advantage of the Unscented Transform thus approximating the true mean and variance more accurately. The method can be applied to non-linear systems without the linearization process necessary for the EKF, and it does not demand a Gaussian distribution of noise and its ease of implementation and more accurate estimation features enable it to demonstrate its good performance. Numerical experiments on satellite orbit determination and deformation data analysis show that the method is more effective than EKF in nonlinear problems.

Keywords

EKF unscented transform satellite orbit simulation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Feng, K. (1978). Methods of Numerical Computation. Publishing House of National Defense Industry, Beijing.Google Scholar
  2. Distributions. Technical report, RRG, Dept. of Engineering Science, University of Oxford.Google Scholar
  3. Julier, S., Uhlmann J.K. (1997). A New Extension of the Kalman Filter to Nonlinear Systems. In Proc of AeroSense: The 11th International Symposium on Aerospace/Defence Sensing, Simulation and Controls.Google Scholar
  4. Julier, S., Uhlmann, J.K., Durrant-Whyte H. (1995). A new approach for filtering nonlinear systems. In Proceedings of the American Control Conference, pp. 1,628–1,632.Google Scholar
  5. Koch, K.P. (1990). Bayesian Inference with Geodetic Applications. Berlin Heidelberg: Springer-Verlag, pp. 92–98.Google Scholar
  6. Montenbruck, O., and Gill, E. (2000). Satellite orbits: Models, Methods and Applications. Springer Verlag New York Inc.Google Scholar
  7. Shi, Z.K. (2001). Computation Methods of Optimal Estimation. Beijing: Science Publishing House.Google Scholar
  8. Simon, H. (1996). Adaptive Filter Theory. Verlag: Prentice Hall, 3rd edition.Google Scholar
  9. Steven, M.K. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory (in Chinese). Publishing House of Electronics Industry: Beijing, pp. 301–382.Google Scholar
  10. Tor, Y.K. (2002). L1, L2, Kalman Filter and Time Series Analysis in deformation Analysis, FIG XXII International Congress, Washington, D.C. USA.Google Scholar
  11. Tor, Y.K. (2003). Application of kalman filter in real-time deformation monitoring using surveying robot, Surveying Magazine: civil engineering research, January, pp. 92–95.Google Scholar
  12. Wan E.A. and Nelson A.T. (2001). Kalman Filtering and Neural Networks, chap. Dual EKF Methods, Wiley Publishing, Eds. Simon Haykin.Google Scholar
  13. Xu, P.L. (1999). Biases and accuracy of, and an alternative to, discrete nonlinear filters. Journal of Geodesy, Vol. 73, pp. 35–46.CrossRefGoogle Scholar
  14. Xu, P.L. (2003). Nonlinear filtering of continuous systems: foundational problems and new results Journal of Geodesy, Vol. 77 pp. 247–256.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • D. Zhao
    • 1
    • 2
  • Z. Cai
    • 3
  • C. Zhang
    • 4
  1. 1.School of Geodesy and Geomatics, Wuhan UniversityHubei ProvinceP.R. China
  2. 2.Department of Geodesy and Navigation EngineeringZhengzhou Institute of Surveying and MappingHenan ProvinceP.R. China
  3. 3.Global Information Application and Development Center of BeijingBeijing 100094P.R. China
  4. 4.Department of Geodesy and Navigation EngineeringZhengzhou Institute of Surveying and MappingHenan ProvinceP.R. China

Personalised recommendations