On Some Alternatives to Kalman Filtering

  • Burkhard Schaffrin
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 114)

Abstract

In a Dynamic Linear Model, the weighted least-squares approach is known to yield the Kalman filter equations. On the other hand, it is also known that any least-squares solution might adversely be affected by undetected model errors. After having previously derived “robust Kalman filters” — which are resistant against multiple scale errors — as one possible remedy, we now develop the so-called “look-ahead filters” which use some of the future observations for the update and can therefore operate only in almost real-time. It will be shown that this new class of filters turns out to be everywhere superior over Kalman filtering (in the Mean Square Error sense), and that some of the modified Kalman filters — including Salychev’s “wave algorithm” — belong to this class indeed.

Keywords

Covariance Remote Sensing Prep 

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References

  1. Arent, N., G. Hückelheim and K.R. Koch (1992): Method for obtaining geoid undulations from satellite altimetry data by a quasi-geostrophic model of the sea surface topography, Manus. Geodaet. 17 (1992), 174–185.Google Scholar
  2. Friedland, Bernard (1969): Treatment of bias in recursive filtering, IEEE Trans, on Autom. Control AC-14 (1969), 359–367.Google Scholar
  3. Nyblom, J. (1986): Testing for deterministic linear trend in time series, J. Amer. Statist. Ass. 81 (1986), 545–549.CrossRefGoogle Scholar
  4. Salychev, O. and A. Bykovsky (1991): Wave method in processing navigation information in survey systems, Proc. of the IAG Symp. on Kinematic Systems in Geodesy, Surveying and Remote Sensing, Springer: New York, etc. 1991, pp. 238–251.Google Scholar
  5. Salychev, O. and B. Schaffrin (1992): New filter approaches for GPS/INS integration, Proc. of the 6th Intl. Geodetic Symp. on Satellite Positioning, Columbus, Ohio, March 1992, Vol. II, pp. 670–680.Google Scholar
  6. Schaffrin, B. (1991): Generating robustified Kalman filters for the integration of GPS and INS, Inst, of Geodesy, University of Stuttgart, Tech. Report No. 15, Sept. 1991.Google Scholar
  7. Schaffrin, B. (1994): Quality control for sequential GPS satellite data, Paper prep, for COMPSTAT ′94 (11th Symp. on Computat. Statistics), Vienna, Austria, Aug. 1994.Google Scholar
  8. Schröder, D., Nguyen Chi Thong, S. Wiegner, E. Grafarend and B. Schaffrin (1988): A comparative study of geodetic inertial systems, Manus. Geodaet. 13 (1988), 224–248.Google Scholar
  9. Toutenburg, H. and B. Schaffrin (1988): Biased mixed estimation and related problems, Internal Report, SFB 228 “High Precision Navigation”, University of Stuttgart, Dec. 1988.Google Scholar
  10. Toutenburg, H. and B. Schaffrin (1989): Investigations concerning the MSE-superiority of several estimates of filter type with applications to the dynamic linear model, Internal Report, SFB 228 “High Precision Navigation”, University of Stuttgart, April 1989.Google Scholar
  11. Wang Zewen, B. Schaffrin and O. Salychev (1995): A test strategy for the wave algorithm, Mobile Mapping Symp., Columbus, Ohio, May 1995.Google Scholar
  12. West M. and P.J. Harrison (1986): Monitoring and adaptation in Bayesian forecasting models, J. Amer. Statist. Assoc. 81 (1986), 741–750.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Burkhard Schaffrin
    • 1
  1. 1.Dept. of Geodetic Science and SurveyingThe Ohio State UniversityColumbusUSA

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