Skip to main content
SpringerLink
Log in

Kalman Filtering: Whence, What and Whither?

  • Chapter
Mathematical System Theory

Abstract

Undoubtedly, one of the major contributions of R.E. Kalman has been the Kalman filter, [1,2], the magnitude of the contribution being specifically recognized in the award of the Kyoto Prize.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.E. Kalman, “A new approach to linear filtering and prediction problems”, J Basic Eng, Trans ASME, Series D, Vol 82, March 1960, pp 35–45

    Article  Google Scholar 

  2. R.E. Kalman and R.S. Bucy, “New results in linear filtering and prediction theory”, J Basic Eng, Trans ASME, Series D, Vol 83, March 1961, pp 95–108

    Article  MathSciNet  Google Scholar 

  3. N. Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series, MIT Press, Cambridge, Mass, 1949

    MATH  Google Scholar 

  4. H.W. Bode and C.E. Shannon, “A simplifies derivation of linear least square smoothing and prediction theory”, Proc IRE, Vol 38, April 1950, pp 417–425

    Article  MathSciNet  Google Scholar 

  5. B.D.O. Anderson and J.B. Moore, Optimal Filtering, Prentice Hall, Inc, Englewood Cliffs, NJ, 1979

    MATH  Google Scholar 

  6. V. Kucera, “The discrete Riccati equation of optimal control”, Kybernetika, Vol 8, 1972, pp 430–447

    MathSciNet  MATH  Google Scholar 

  7. R.E. Kalman, “Contributions to the theory of optimal control”, Bol Soc Matem Mex, 1960, pp 102–119

    Google Scholar 

  8. B.D.O. Anderson and J.B. Moore, “Detectability and stabilizability of discrete-time linear systems”, SIAM J on Control & Optimization, Vol 19, 1981, pp 20–32

    Article  MathSciNet  MATH  Google Scholar 

  9. P. Swerling, “A proposed stagewise differential correction procedure for satellite tracking and prediction”, J Astronaut, Sci, Vol 6, 1959, pp 46–59

    Google Scholar 

  10. P. Faurre, M. Clerget, and F. Germain, “Opérateurs rationnels positifs”, Dunod, Paris, 1979

    MATH  Google Scholar 

  11. B.D.O. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis, Prentice Hall, Inc, Englewood Cliffs, N.J., 1973

    Google Scholar 

  12. T. Kailath, “A view of three decades of linear filtering theory”, IEEE Trans Info Theory, Vol IT-20, March 1974, pp 146–181

    Google Scholar 

  13. B.D.O. Anderson, J.B. Moore, and S.G. Loo, “Spectral factorization of time-varying covariance functions”, IEEE Trans Info Theory, Vol IT-15, September 1969, pp 550–557

    Google Scholar 

  14. L.E. Zachrisson, “On optimal smoothing of continuous-time Kalman processes”, Information Sciences, Vol 1, 0969, pp 143–172

    Google Scholar 

  15. W.W. Willman, “On the linear smoothing problem”, IEEE Tranns Auto Control, Vol AC-14, February 1969, pp 116–117

    Google Scholar 

  16. J.B. Moore, “Discrete-time fixed-lag smoothing algorithms”, Automatica, Vol 19, March 1973, pp 163–174

    Article  Google Scholar 

  17. S. Chirarattanon and B.D.O. Anderson, “Stable fixed-lag smoothing of continuous-time processes”, IEEE Trans Info Theory, Vol IT-20, January 1974, pp 25–36

    Google Scholar 

  18. D.C. Fraser and J.E. Potter, “The optimum linear smoother as a combination of two optimum linear filters”, IEEE Trans Auto Control, Vol AC-14, August 1969, pp 387–390

    Google Scholar 

  19. J.E. Wall, A.S. Willsky, and N.R. Sandell, “The fixed-interval smoother or for continuous-time processes”, Proc 19th IEEE Conference on Decision and Control, 1980, pp 385–389

    Google Scholar 

  20. H.E. Rauch, “Solutions to the linear smoothing problem”, IEEE Trans Auto Control, Vol AC-8, October 1963, pp 371–372

    Article  Google Scholar 

  21. E. Wong, Stochastic Processes in Information and Dynamical Systems, McGraw Hill Book Co., New York, 1971

    MATH  Google Scholar 

  22. R.J. Elliott, Stochastic Calculus and Applications, Springer Verlag, New York, 1982

    MATH  Google Scholar 

  23. D.L. Snyder, The State-Variable Approach to Continuous Estimation, MIT Press, Cambridge, Mass., 1969

    MATH  Google Scholar 

  24. B.D.O. Anderson and J.B. Moore, Optimal Control: Linear-Quadratic Methods, Prentice Hall, Englewood Cliffs, NJ, 1989

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Systems Engineering, Research School of Physical Sciences and Engineering, The Australian National University, GPO Box 4, ACT, 2601, Canberra, Australia

    B. D. O. Anderson & J. B. Moore

Authors
  1. B. D. O. Anderson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. B. Moore
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Rice University, 77251, Houston, Texas, USA

    Athanasios C. Antoulas

  2. Mathematical System Theory, E.T.H. Zürich, CH-8092, Zürich, Switzerland

    Athanasios C. Antoulas

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Anderson, B.D.O., Moore, J.B. (1991). Kalman Filtering: Whence, What and Whither?. In: Antoulas, A.C. (eds) Mathematical System Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08546-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-08546-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-08548-6

  • Online ISBN: 978-3-662-08546-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation