Advertisement

Optimal State Estimation and its Application to Inertial Navigation System Control

  • W. Hofmann
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

The behaviour of most functions in practical situations can always — at least approximately — be described by a finite-dimensional system of differential equations. The theory of optimal state estimation deals with the minimum error-variance reconstruction of the functions from a limited information in a noisy environment. The solution approach, algorithm and stability properties for the linear Gaussian estimation problem are reviewed. A general and typical way for the design of a suboptimal estimation algorithm with special regard to system properties and realization requirements is shown for the technical problem of the error estimation of an aided inertial navigation system. According to the closedloop system requirement of high accuracy in a noisy environment the considerations about the estimator design are extended to the design of simple, (sub-) optimal controllers. A comparison to the optimal estimation accuracy shows the efficiency of proposed output feedback controller design procedure in this technical example.

Keywords

Inertial Navigation System Error Angle Optimal Filter Random Disturbance Output Feedback Controller 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. [1]
    COURANT, R., HILBERT, D.: “Methods of Mathematical Physics”, Vol. I, I I. Interscience Publishers, New York, 1962.Google Scholar
  2. [2]
    KWAKERNAAK, H. SIVAN, R.: “Linear Optimal Control Systems”. Wiley-Interscience, New York, 1972.Google Scholar
  3. [3]
    ANDERSON, B.D.O., MOORE, J.B.: “Linear Optimal Control”. Prentice-Hall, Englewood Cliffs, 1971.Google Scholar
  4. [4]
    JAZWINSKI, A.H.: “Stochastic Processes and Filtering Theory”. Academic Press, New York, 1970.Google Scholar
  5. [5]
    PAPOULIS, A.: “Probability, Random Variables, and Stochastic Processes”. McGraw Hill, New York, 1965.Google Scholar
  6. [6]
    GELB, A., e.a.: “Applied Optimal Estimation”. The M.I.T. Press, Cambridge, 1974.Google Scholar
  7. [7]
    GELB, A., e.a.: “Theory and Applications of Kalman Filtering”. AGARDograph 139, 1970.Google Scholar
  8. [8]
    ATHANS, M.: “The Matrix Minimum Principle”. J. on Information and Control, vol. 11, p. 592–606, 1968.CrossRefGoogle Scholar
  9. [9]
    HOFMANN, W., KORTOM, W.: “Reduced-Order State Estimators with Application in Rotational Dynamics”. “Gyrodynamics”, Springer-Verlag, Berlin, 1974.Google Scholar
  10. [10]
    BROCKETT, R.W.: “Finite Dimensional Linear Systems”. John Wiley & Sons, New York, 1970.Google Scholar
  11. [11]
    BROCKETT, R.W.: “A Short Course on Kalman Filtering and Application”. The Analytic Science Corporation, Reading Mass.Google Scholar
  12. [12]
    KUCERA, V.: “A Contribution to Matrix Quadratic Equations”. IEEE Trans, on Automatic Control, vol. AC- 17 (June 1972), pp. 344–347.CrossRefGoogle Scholar
  13. [13]
    VAUGHAN, D.R.: “A Negative Exponential Solution for the Matrix Riccati Equation”, IEEE Trans. Automatic Control, vol. A014, (Feb. 1969), pp. 72–75.CrossRefGoogle Scholar
  14. [14]
    MULLER, P.C.: “Special Problems of Gyro dynamics”. International Centre of Mechanical Sciences, Courses and Lectures No. 63, Springer-Ver-lag, Udine, 1970.Google Scholar
  15. [15]
    HOFMANN, W.: “Die Anwendung der Kalman-Bucy-Filtertheorie beim Entwurf von Riickkopplungsnetzwerken fur Dopplergestiitzte Tragheitsnavigationssysteme im Flug”. DFVLR-IB Nr. 552–75/18.Google Scholar
  16. [16]
    BRYSON, A.E., HO, Y.: “Applied Optimal Control”. Ginn and Company, London, 1969.Google Scholar
  17. [17]
    HOFMANN, W.: “Application of Inners to the Design of Optimal State Estimators Under Stability Constraints”. Proceedings of the Conference on Information Sciences and Systems, Baltimore, 1976.Google Scholar
  18. [18]
    HOFMANN, W.: “Optimal Stochastic Disturbance Compensation by Output Vector Feedback”, to appear as DLR-Forschungsbericht.Google Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • W. Hofmann
    • 1
  1. 1.Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt e.V. (DFVLR)OberpfaffenhofenWest Germany

Personalised recommendations