Least-squares estimation: from Gauss to Kalman: The Gaussian concept of estimation by least squares, originally stimulated by astronomical studies, has provided the basis for a number of estimation theories and techniques during the ensuing 170 years—probably none as useful in terms of today's requirements as the Kalman filter

IEEE Spectrum

Volumn 7, Issue 7, 1970, Pages 63-68

  Sorenson, H W ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATIC CONTROL; ESTIMATION THEORY; INFORMATION THEORY; STATISTICAL METHODS;

EID: 0014814475     PISSN: 00189235     EISSN: None     Source Type: Journal    
DOI: 10.1109/MSPEC.1970.5213471     Document Type: Article

References (28)

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3. Bell, E. T., Men of Mathematics. New York: Simon and Schuster, 1961.
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10. Wiener, N., The Extrapolation, Interpolation and Smoothing of Stationary Time Series. New York: Wiley, 1949.
11. Sorenson, H. W., and Stubberud, A. R., “Linear estimation theory,” Chapter 1 in Theory and Application of Kalman Filtering; AGAR Dograph, no. 139, 1970.
12. Yaglom, A. M., An Introduction to the Theory of Stationary Random Functions, translated by R. A. Silverman. Englewood Cliffs, N.J.: Prentice-Hall, 1962.
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16. Bucy, R. S., and Joseph, P. D., Filtering for Stochastic Processes with Applications to Guidance. New York: Interscience, 1968.
17. Kalman, R. E., and Bucy, R. S., “New results in linear filtering and prediction theory,” J. Basic Eng., vol. 83D, pp. 95–108, 1961.
18. Swerling, P., “A proposed stagewise differential correction procedure for satellite tracking and prediction,” Rept. P-1292, RAND Corp. Santa Monica, Calif., Jan. 1958; also published in J. Astronaut. Sci., vol. 6, 1959.
19. Blum, M., “Recursion formulas for growing memory digital filters,” IRE Trans. Information Theory, vol. IT-4, pp. 24–30, Mar. 1958.
20. Robbins, H., and Munro, S., “A stochastic approximation method,” Ann. Math. Stat., vol. 22, pp. 400–407, 1951.
21. Kiefer, J., and Wolfowitz, J., “Stochastic estimation of the maximum of a regression function,” Ann. Math. Stat., vol. 23, pp. 462–466, 1952.
22. Swerling, P., “Comment on ‘A statistical optimizing navigation procedure for space flight,’” AIAA J., vol. 1, p. 1968, Aug. 1963.
23. Sorenson, H. W., “Comparison of Kalman, Bayesian and maximum likelihood estimation techniques,” Chapter 6 in Theory and Application of Kalman Filtering; AGAR Dograph, no. 139, 1970.
24. Schice, F. H., Standish, C. J., and Toda, N. F., “Divergence in the Kalman filter,” AIAA J., vol. 5, pp. 1114–1120, June 1967.
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26. Kailath, T., “An innovations approach to least-squares estimation—Part I: linear filtering in additive white noise,” IEEE Trans. Automatic Control, vol. AC-13, pp. 646–655, Dec. 1968.
27. Jazwinski, A. H., “Adaptive filtering,” Automatica, vol. 5, pp. 475–485, 1969.
28. Mehra, R. K., “On the identification of variances and adaptive filtering,” Preprints 1969 Joint Automatic Control Conf., pp. 494–505.