A recursive linear MMSE filter for dynamic systems with unknown state vector means

详细信息    查看全文

• 作者：Amir Khodabandeh (1)
  Peter J. G. Teunissen (1) (2)
  
• 关键词：Minimum mean squared error (MMSE) ; Best linear unbiased estimation (BLUE) ; Best linear unbiased prediction (BLUP) ; Kalman filter ; BLUE ; BLUP recursion ; 60G25 ; 60G35 ; 93E11
• 刊名：GEM - International Journal on Geomathematics
• 出版年：2014
• 出版时间：April 2014
• 年：2014
• 卷：5
• 期：1
• 页码：17-31
• 全文大小：285 KB
• 参考文献：1. Acharya, R., Roy, B., Sivaraman, M., Dasgupta, A.: Estimation of equatorial electrojet from total electron content at geomagnetic equator using Kalman filter. Adv. Space Res. 47(6), 938鈥?44 (2011) CrossRef
  2. Anderson, B.D.O., Moore, J.B.: Optimal Filtering, vol. 11. Prentice-hall Englewood Cliffs, New Jersey (1979)
  3. Bar-Shalom, Y., Li, X.: Estimation and Tracking-Principles, Techniques, and Software. Artech House Inc, Norwood (1993)
  4. Bertino, L., Evensen, G., Wackernagel, H.: Combining geostatistics and Kalman filtering for data assimilation in an estuarine system. Inverse Probl. 18(1), 1 (2002) CrossRef
  5. Brammer, K., Siffling, G.: Kalman-Bucy Filters. Artech Hous, Norwood (1989)
  6. Candy, J.: Signal Processing: Model Based Approach. McGraw-Hill Inc, New York (1986)
  7. Cao, Y., Chen, Y., Li, P.: Wet refractivity tomography with an improved Kalman-filter method. Adv. Atmos. Sci. 23, 693鈥?99 (2006) CrossRef
  8. Christensen R (2001) Advanced Linear Modeling: Multivariate, Time Series, and Spatial Data; Nonparametric Regression and Response Surface Maximization, 2nd edn. Springer, Heidelberg
  9. Ferraresi, M., Todini, E., Vignoli, R.: A solution to the inverse problem in groundwater hydrology based on Kalman filtering. J. Hydrol. 175(1), 567鈥?81 (1996) CrossRef
  10. Gelb, A.: Applied Optimal Estimation. MIT Press, Cambridge (1974)
  11. Gibbs, B.: Advanced Kalman Filtering, Least-squares and Modeling. A Practical Handbook. Wiley, New York (2011) CrossRef
  12. Goldberger, A.: Best linear unbiased prediction in the generalized linear regression model. J. Am. Stat. Assoc. 57(298), 369鈥?75 (1962) CrossRef
  13. Grafarend, E.W.: Geodetic applications of stochastic processes. Phys. Earth Planet. Inter. 12(2), 151鈥?79 (1976) CrossRef
  14. Grafarend, E.W., Rapp, R.H.: Advances in Geodesy: selected papers from reviews of Geophysics and Space Physics. American Geophysical Union 1, Washington DC (1984)
  15. Grewal, M.S., Andrews, A.P.: Kalman Filtering; Theory and Practice Using MATLAB, 3rd edn. Wiley, New York (2008) CrossRef
  16. Gross, R.S., Eubanks, T.M., Steppe, J.A., Freedman, A.P., Dickey, J.O., Runge, T.F.: A Kalman-filter-based approach to combining independent Earth-orientation series. J. Geod. 72(4), 215鈥?35 (1998) CrossRef
  17. Herring, T.A., Davis, J.L., Shapiro, I.I.: Geodesy by radio interferometry: the application of Kalman filtering to the analysis of very long baseline interferometry data. J. Geophys. Res (1978鈥?012) 95(B8), 12561鈥?2581 (1990) CrossRef
  18. Ince, C.D., Sahin, M.: Real-time deformation monitoring with GPS and Kalman Filter. Earth Planets Space 52(10), 837鈥?40 (2000)
  19. Jazwinski, A.: Stochastic Processes and Filtering Theory. Dover Publications, New York (1991)
  20. Kailath, T.: A view of three decades of linear filtering theory. IEEE Trans. Inf. Theory 20(2), 146鈥?81 (1974) CrossRef
  21. Kailath, T.: Lectures on Wiener and Kalman Filtering, p. 140. Springer, Heidelberg (1981) CrossRef
  22. Kailath, T., Sayed, A.H., Hassibi, B.: Linear Estimation. Prentice-Hall, New Jersey (2000)
  23. Kalman, R.E.: A new approach to linear filtering and prediction problems. J. Basic Eng. 82(1), 35鈥?5 (1960) CrossRef
  24. Marx, B.A., Potthast, R.W.E.: On instabilities in data assimilation algorithms. GEM-Int. J. Geomath. 3(2), 253鈥?78 (2012) CrossRef
  25. Maybeck, P.: Stochastic Models, Estimation, and Control, vol. 1, Academic Press, Massachusetts (1979)
  26. Sanso, F.: The minimum mean square estimation error principle in physical geodesy (stochastic and non-stochastic interpretation). Boll. Geod. Sci. Affi. 39(2), 112鈥?29 (1980)
  27. Sanso, F.: Statistical methods in physical geodesy. In: Sunkel, H. (ed.) Mathematical and Numerical Techniques in Physical Geodesy. Lecture Notes in Earth Sciences, vol. 7, pp. 49鈥?55. Springer, Berlin (1986) CrossRef
  28. Simon, D.: Optimal state estimation: Kalman, H (infinity) and Nonlinear Approaches. Wiley, Hoboken (2006) CrossRef
  29. Sorenson, H.W.: Kalman filtering techniques. In: Leondes, C.T., (ed.) Advances in Control Systems Theory and Applications, 3, 219鈥?92 (1966)
  30. Stark, H., Woods, J.: Probability, Random Processes, and Estimation Theory for Engineers. Prentice-Hall Englewood Cliffs, New Jersey (1986)
  31. Teunissen, P.J.G.: Best prediction in linear models with mixed integer/real unknowns: theory and application. J. Geod. 81(12), 759鈥?80 (2007) CrossRef
  32. Teunissen, P.J.G., Khodabandeh, A.: BLUE, BLUP and the Kalman filter: some new results. J. Geod. 87(5), 1鈥?3 (2013) CrossRef
  
• 作者单位：Amir Khodabandeh (1)
  Peter J. G. Teunissen (1) (2)
  
  1. Department of Spatial Sciences, GNSS Research Centre, Curtin University of Technology, Perth, Australia
  2. Department of Geoscience and Remote Sensing, Delft University of Technology, Delft, The Netherlands
  
• ISSN：1869-2680

文摘

In this contribution we extend Kalman-filter theory by introducing a new recursive linear minimum mean squared error (MMSE) filter for dynamic systems with unknown state-vector means. The recursive filter enables the joint MMSE prediction and estimation of the random state vectors and their unknown means, respectively. We show how the new filter reduces to the Kalman-filter in case the state-vector means are known and we discuss the fundamentally different roles played by the intitialization of the two filters.