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A Novel Doppler Frequency Dynamic Model with Its Applications

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Abstract

We propose a novel dynamic model of Doppler frequency and phase, called as a polynomial prediction model (PPM), where a constant acceleration or deceleration motion law described by a polynomial is assumed, then a new self-validating optimal filtering algorithm, based on the proposed model and the unscented Kalman filter (UKF), is developed for the frequency and phase estimates of the Doppler signal in a variable acceleration and/or deceleration motion scenario. The analytical results show that the proposed algorithm can effectively track Doppler frequency and phase whatever the maneuvering motion between the transceivers is. The analytical results are verified by the simulations and the experimental results of a real live GPS receiver, which show that the proposed algorithm is superior to most of those reported in the literature when the received signal power is over a guaranteed value in the case of GPS.

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References

  1. Proakis J. G. (1995) Digital communications[M] (3rd ed.). McGrawHill, New York

    Google Scholar 

  2. Kaplan E. D., Hegatry C. J. (2006) Understanding GPS principles and applications (2nd ed.). Artech House, Norwood, MA

    Google Scholar 

  3. Bao-Yen Tsui J. (2005) Fundamentals of global positioning system receivers-a software approach (2nd ed.). Wiley, Hoboken, New Jersey

    Google Scholar 

  4. Borre K., Akos D.M., Bertelsen N. (2006) A software-defined GPS and Galileo receiver. Birkhauser, Boston

    Google Scholar 

  5. Vilnrotter V. A., Hinedi S., Kumar R. (1989) Frequency estimation techniques for high dynamic rrajectories. IEEE Transactions on Aerospace and Electronic Systems 25: 559–577

    Article  Google Scholar 

  6. Kay S. M. (1993) Fundamentals of statistical signal processing volume I: estimation theory. Prentice Hall, New Jersey

    Google Scholar 

  7. Julier, S. J., & Uhlmann, J. K. (1997). A new extension of the Kalman filter to nonlinear systems, the 11th international symposium on aerospace/defence sensing, simulation and controls. Orlando, Florida, Vol. Multi Sensor Fusion, Tracking and Resource Management II.

  8. van der Merwe, R., Doucet, A., & de Freitas, N. (August 2000). The unscented particle filter. Oregon Graduate Institute.

  9. Julier S. J., Uhlman J. K. (2004) Unscented filtering and nonlinear estimation. Proceedings of the IEEE 92: 401–422

    Article  Google Scholar 

  10. Arulampalam M.S., Maskell S., Gordon N. (2002) A tutorial on particle filters for online nonlinear non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing 50: 174–188

    Article  Google Scholar 

  11. Li X. R., Jilkov V. P. (2003) Survey of maneuvering target tracking. Part I: dynamic models. IEEE Transactions on Aerospace and Electronic Systems 39: 1333–1364

    Article  Google Scholar 

  12. Bar-Shalom Y., Li X. R., Kirubarajan T. (2001) Estimation with applications to tracking and navigation: theory, algorithm, and software. Wiley, New York

    Book  Google Scholar 

  13. Heinonen P., Neuvo Y. (1998) FIR-median hybrid filters with predictive FIR substructures[J]. IEEE Transactions on Acousitics, Speech and Signal Processing 36: 892–899

    Article  Google Scholar 

  14. Valiviita S., Ovaska S. J., Vainio O. (1999) Polynomial predictive filtering in control instrumentation: a review. IEEE Transactions on Industrial Electronics 46: 876–888

    Article  Google Scholar 

  15. HartiKainen, J., Sarkka, S. (2008). Optimal filtering with Kalman filters and smoothers—a Manual for Matlab toolbox EKU/UKF.

  16. Wu Y., Hu D., Wu M., Hu X. (2005) Unscented Kalmen filtering for additive noise case: augmented versus nonaugmented. IEEE Signal Processing Letters 12: 357–360

    Article  MathSciNet  Google Scholar 

  17. Weisstein, E. W. Weierstrass approximation theorem. From MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/WeierstrassApproximationTheorem.html.

  18. Melrra R. K. (1970) On the identification of variance and adaptive Kalman filtering. IEEE Transactions on Automatic Control 15: 175–184

    Article  Google Scholar 

  19. Parzen E. (1961) An approach to time series analysis. The Annals of Mathematical Statistics 32: 951–989

    Article  MathSciNet  MATH  Google Scholar 

  20. Fitzgerald R. J. (1971) Divergence of the Kalman filter. IEEE Transactions on Automation Control 16: 736–747

    Article  Google Scholar 

  21. Best R. E. (1999) Phase-locked loop design, simulation and application (4th ed.). McGraw-Hill, Columbus, OH

    Google Scholar 

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Correspondence to Jian Jun Yin.

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Zhao, J., Yin, J.J., Zhang, J.Q. et al. A Novel Doppler Frequency Dynamic Model with Its Applications. Wireless Pers Commun 66, 275–289 (2012). https://doi.org/10.1007/s11277-011-0338-z

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