Filtering via Markov chains approximation

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 65)


Markov Chain Markov Process Stochastic Differential Equation Conditional Probability Density Standard Wiener Process 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

3.9 References

  1. 3.1
    R. Stratonovich, On the theory of optimal nonlinear filtration of random functions, Theory of Probability and its Applications, 4, pp 223–225, 1959.Google Scholar
  2. 3.2
    H.J. Kushner, On the dynamical equations of conditional probability density functions with applications to optimal stochastic control theory, J. Math. Anal. App., 8, pp 332–344, 1964.Google Scholar
  3. 3.3
    H.J. Kushner, On the differential equations satisfied by conditional probability densities of Markov processes, with applications, J. SIAM Control, 2, pp 106–119, 1964.Google Scholar
  4. 3.4
    W.M. Wonham, Some applications of stochastic differential equations to optimal nonlinear filtering, J. SIAM Control, 2, pp 347–369, 1965.Google Scholar
  5. 3.5
    R.S. Bucy, Nonlinear filtering theory, IEEE Trans. on Automatic Control, 10, p 198, 1965.Google Scholar
  6. 3.6
    R.S. Bucy and P.D. Joseph, Filtering for Stochastic Processes with Applications to Guidance, Interscience, New York, 1968.Google Scholar
  7. 3.7
    M. Zakai, On the optimal filtering of diffusion processes, Z. Wahr. Verw. Geb., 11, pp 230–243, 1969.Google Scholar
  8. 3.8
    A.H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, New York, 1970.Google Scholar
  9. 3.9
    P.A. Frost and T.K. Kailath, An innovations approach to least-square estimation — Part III: Nonlinear estimation in white Gaussian noise, IEEE Trans. Automat. Contr., 16, pp 217–226, 1971.Google Scholar
  10. 3.10
    T.P. McGarty, Stochastic Systems and State Estimation, John Wiley & Sons, New York, 1974.Google Scholar
  11. 3.11
    M. Fujisaki, G. Kallianpur and H. Kunita, Stochastic differential equations for the non linear filtering problem, Osaka J. Math., 9, pp 19–40, 1972.Google Scholar
  12. 3.12
    G. Kallianpur, Stochastic Filtering Theory, Springer-Verlag, New York, 1980.Google Scholar
  13. 3.13
    J.H. Van Schuppen, Stochastic filtering theory: A discussion of concepts, methods and results, in Stochastic Control Theory and Stochastic Differential Systems, M. Kohlmann and W. Vogel, eds., pp 209–226, Springer-Verlag, New York, 1979.Google Scholar
  14. 3.14
    H.J. Kushner, Probability Methods for Approximations in Stochastic Control and for Elliptic Equations, Academic Press, New York, 1977.Google Scholar
  15. 3.15
    G.B. Di Masi and W.J. Runggaldier, Continuous-time approximations for the nonlinear filtering problem, App. Math. Optim., 7, pp 233–245, 1981.Google Scholar
  16. 3.16
    G. Kallianpur and C. Striebel, Estimation of stochastic systems: arbitrary system process with additive white noise observation errors, Ann.Math.Stat., 39, pp 785–801, 1968.Google Scholar
  17. 3.17
    R.S. Liptser and A.N. Shiryayev, Statistics of Random Processes, Springer-Verlag, New York, Vol.I, 1977; Vol.II, 1978.Google Scholar
  18. 3.18
    B.Z. Kaplan, Rotation of a waveform generator, Electronics Letters 15, pp 158–159,1979.Google Scholar
  19. 3.19
    G.B. Di Masi and W.J. Runggaldier, An approximation to optimal non-linear filtering with discontinuous observation, in M. Hazewinkel and J.C. Willems (eds.) Stochastic Systems: The Mathematics of Filtering and Identification with Applications, pp 583–590, D. Reidel Publishing Company, Dordracht, 1981.Google Scholar
  20. 3.20
    G.B. Di Masi and W.J. Runggaldier, On robust approximations in non-linear filtering, in M. Kohlmann and N. Christopeit (eds.) Stochastic Differential Systems, pp 179–186, Lecture Notes in Control and Information Sciences, 43, Berlin, 1982.Google Scholar
  21. 3.21
    G.B. Di Masi and W.J. Runggaldier, Non-linear filtering with discontinuous observations and applications to life sciences, Bulletin of Mathematical Biology, 45, pp 571–577, 1983.Google Scholar

Copyright information

© Springer-Verlag 1985

Personalised recommendations