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The state estimation problem

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 8))

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References

  1. Angel, E. and Jain, A. Filtering of multidimensional diffusion processes, 6th Asilomar Conf. on Circuits and Systems, Nov. 1972.

    Google Scholar 

  2. Angel, E. and Jain, A. A dimensionality reducing model for distributed filtering, IEEE Trans. Automatic Control, AC 18 (1973), pp.59–62.

    Google Scholar 

  3. Atre, S.R. and Lamba, S.S. Optimal estimation in distributed processes using innovations approach, IEEE Trans. Automatic Control, AC 17 (1972), pp.710–712.

    Google Scholar 

  4. Atre, S.R. and Lamba, S.S. Derivation of an optimal estimator for distributed parameter systems via maximum principle, IEEE Trans. Automatic Control, AC 17 (1972), pp.388–390.

    Google Scholar 

  5. Atre, S.R. Kalman filtering for systems corrupted by boundary and interior disturbances, IEEE Trans. Automatic Control, AC 17 (1972), pp.712–713.

    Google Scholar 

  6. Bagchi, A. A Martingale approach to continuous time linear smoothers, SIAM J. Appl. Math., 28 (1975), pp.276–281.

    Google Scholar 

  7. Balakrishnan, A.V. Applied functional analysis, Springer Verlag, Berlin, 1976.

    Google Scholar 

  8. Bensoussan, A. Filtrage optimal des systemes lineaires, Dunod 1971.

    Google Scholar 

  9. Coddington, E.A. and Levinson, N. Theory of ordinary differential equations, McGraw Hill, 1955.

    Google Scholar 

  10. Curtain, R.F. Infinite dimensional filtering, SIAM J. Control, 13 (1975), pp.89–104.

    Google Scholar 

  11. Curtain, R.F. A survey of infinite dimensional filtering, SIAM Review, 17 (1975), pp.395–411.

    Google Scholar 

  12. Curtain, R.F. A Kalman-Bucy filtering theory for affine differential equations, Int. Symp. on Control Theory, Numerical Methods and Computer Systems Modelling, June 1974. (Springer Verlag, Lecture Notes in Economics and Math. Systems, 107, 1974.)

    Google Scholar 

  13. Curtain, R.F. Infinite dimensional estimation theory for linear systems, Control Theory Centre Report No.38, University of Warwick.

    Google Scholar 

  14. Curtain, R.F. Estimation theory for abstract evolution equations excited by general white noise processes, SIAM J. Control, 14 (1976), pp.1124–1150.

    Google Scholar 

  15. Davis, M.H.A. Linear estimation and stochastic control, Chapman and Hall, 1977.

    Google Scholar 

  16. Delfour, M.C. Numerical solution of the operator Riccati equation for the filtering of linear stochastic hereditary diff differential systems, Optimization Techniques, Proc. 7th IFIP Conference, Nice, 1975. Lecture Notes in Computer Science 41, Springer Verlag, 1976.

    Google Scholar 

  17. Dunford, N. and Schwartz, J. Linear operators Part I, Interscience, 1957.

    Google Scholar 

  18. Doleans-Dade, C. and Meyer, P.A. Integrales stochastiques par rapport aux Martingales locales, Seminaire de Probabilities IV, Lecture Notes in Mathematics 124

    Google Scholar 

  19. Falb, P. Infinite dimensional filtering, Information and Control, (1967), pp.102–137.

    Google Scholar 

  20. Hwang, M., Seinfeld, J.H. and Gavalas, G.R. Optimal least squares filtering and interpolation in distributed parameter systems, J. Math. Anal. Appl., 39 (1972), pp.49–74.

    Google Scholar 

  21. Kwong, R. and Willsky, A. Optimal filtering and filter stability of linear stochastic delay systems, IEEE Trans., AC 22 (1977), pp.196–201.

    Google Scholar 

  22. Kushner, H.J. Filtering for linear distributed parameter systems, SIAM J. Control, 8 (1970), pp.346–359.

    Google Scholar 

  23. Kwakernaak, H. Optimal filtering in linear systems with time delays, IEEE Trans. AC 12 (1967), pp.169–173.

    Google Scholar 

  24. Lamont, G.B. and Kumar, K.S.P. State estimation in distributed parameter systems via least squares and invariant embedding, J. Math. Anal. Appl., 38 (1972), pp.588–606.

    Google Scholar 

  25. Meditch, J.S. Least squares filtering and smoothing for linear parameter systems, Automatica (1971), pp.315–322.

    Google Scholar 

  26. Mitter, S.K. and Vinter, R.B. Filtering for linear stochastic hereditary differential systems, Int. Symp. on Control Theory, Numerical Methods and Computer Systems Modelling, 1974. (Lecture Notes in Economics and Math. Systems, 107, Springer Verlag, 1974.)

    Google Scholar 

  27. Omatu, S., Tomita, Y. and Soeda, T. Fixed-point smoothing in Hilbert space, to appear in J. Information and Control.

    Google Scholar 

  28. Parthasarathy, K.R. Probability measures on metric spaces, Academic Press, 1967.

    Google Scholar 

  29. Phillipson, C.A. and Mitter, S.K. State identification of a class of linear distributed systems, Proc. 4th IFAC Congress, Warsaw, 1969.

    Google Scholar 

  30. Sakawa, Y. Optimal filtering in linear distributed-parameter systems, Internat. J. Control, (1972), pp.115–127.

    Google Scholar 

  31. Thau, F.E. On optimal filtering for a class of linear distributed parameter systems, J. Basic Eng., (1969), pp.173–178.

    Google Scholar 

  32. Tzafestas, S.G. and Nightingale, J. Optimal filtering, smoothing and prediction in linear distributed parameter systems, Proc. IEE (1968), pp.1207–1212.

    Google Scholar 

  33. Tzafestas, S.G. and Nightingale, J. Concerning optimal filtering of linear distributed parameter systems, Ibid., (1968), pp.1737–1742.

    Google Scholar 

  34. Tzafestas, S.G. and Nightingale, J. Maximum likelihood approach to the optimal filtering of distributed parameter systems, Ibid., (1969), pp.1085–1093.

    Google Scholar 

  35. Tzafestas, S.G. On optimum distributed parameter filtering and fixed interval smoothing for coloured noise, IEEE Trans. Automatic Control, AC 17 (1972), pp.448–458.

    Google Scholar 

  36. Tzafestas, S.G. Bayesian approach to distributed parameter filtering and smoothing, Internat. J. Control, 15 (1972), pp.273–295.

    Google Scholar 

  37. Tzafestas, S.G. On the distributed parameter least squares state estimation theory, Internat. J. Systems Sci., 4 (1973), pp.833–858.

    Google Scholar 

  38. Vinter, R.B. Filter stability for stochastic evolution equations, SIAM J. Control, 15 (1977), pp.465–487.

    Google Scholar 

  39. Vinter, R.B. On the evolution of the state of linear differential delay equations in M2: Properties of the generator, Technical Report Electronic Systems Lab. MIT 1974.

    Google Scholar 

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Ruth F. Curtain Anthony J. Pritchard

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(1978). The state estimation problem. In: Curtain, R.F., Pritchard, A.J. (eds) Infinite Dimensional Linear Systems Theory. Lecture Notes in Control and Information Sciences, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006767

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  • DOI: https://doi.org/10.1007/BFb0006767

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