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.
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References
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.
Friedland, Bernard (1969): Treatment of bias in recursive filtering, IEEE Trans, on Autom. Control AC-14 (1969), 359–367.
Nyblom, J. (1986): Testing for deterministic linear trend in time series, J. Amer. Statist. Ass. 81 (1986), 545–549.
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.
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.
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.
Schaffrin, B. (1994): Quality control for sequential GPS satellite data, Paper prep, for COMPSTAT ′94 (11th Symp. on Computat. Statistics), Vienna, Austria, Aug. 1994.
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.
Toutenburg, H. and B. Schaffrin (1988): Biased mixed estimation and related problems, Internal Report, SFB 228 “High Precision Navigation”, University of Stuttgart, Dec. 1988.
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.
Wang Zewen, B. Schaffrin and O. Salychev (1995): A test strategy for the wave algorithm, Mobile Mapping Symp., Columbus, Ohio, May 1995.
West M. and P.J. Harrison (1986): Monitoring and adaptation in Bayesian forecasting models, J. Amer. Statist. Assoc. 81 (1986), 741–750.
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© 1995 Springer-Verlag Berlin Heidelberg
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Schaffrin, B. (1995). On Some Alternatives to Kalman Filtering. In: Sansò, F. (eds) Geodetic Theory Today. International Association of Geodesy Symposia, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79824-5_32
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DOI: https://doi.org/10.1007/978-3-642-79824-5_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59421-5
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