Skip to main content
SpringerLink
Log in

On-line estimation of smooth signals with partial observation

  • Methods of Signal Processing
  • Published:
Problems of Information Transmission Aims and scope Submit manuscript

Abstract

The paper concerns the estimation of a smooth signal S(t) and its derivatives in the presence of a noise depending on a small parameter ε based on a partial observation. A nonlinear Kalman-type filter is proposed to perform on-line estimation. For the signal S in a given class of smooth functions, the convergence rate for the estimation risks, as ε → 0, is obtained. It is proved that such rates are optimal in a minimax sense. In contrast to the complete observation case, the rates are reduced, due to incomplete information.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ibragimov, I.A. and Khas’minskii, R.Z., Asimptoticheskaya teoriya otsenivaniya, Moscow: Nauka, 1979. Translated under the title Statistical Estimation. Asymptotic Theory, New York: Springer, 1981.

    MATH  Google Scholar 

  2. Chow, P.L., Khasminskii, R., and Liptser, R., Tracking of Signal and Its Derivatives in the Gaussian White Noise, Stochastic Process. Appl., 1997, vol. 69, no. 2, pp. 259–273.

    Article  MathSciNet  Google Scholar 

  3. Khasminskii, R., Nonlinear Filtering of Smooth Signals, Stoch. Dyn., 2005, vol. 5, no. 1, pp. 27–35.

    Article  MathSciNet  Google Scholar 

  4. Bensoussan, A., Stochastic Control of Partially Observable Systems, Cambridge: Cambridge Univ. Press, 1992.

    MATH  Google Scholar 

  5. Bensoussan, A. and Blankenship, G.L., Nonlinear Filtering with Homogenization, Stochastics, 1986, vol. 17, no. 1–2, pp. 67–90.

    MathSciNet  Google Scholar 

  6. Picard, J., Nonlinear Filtering of One-Dimensional Diffusions in the Case of a High Signal-to-Noise Ratio, SIAM J. Appl. Math., 1986, vol. 46, no. 6, pp. 1098–1125.

    Article  MathSciNet  Google Scholar 

  7. Ibragimov, I.A. and Khas’minskii, R.Z., On the Estimation of a Signal, Its Derivatives and the Maximum Point for Gaussian Observations, Teor. Veroyatnost. i Primenen., 1980, vol. 25, no. 4, pp. 718–733 [Theory Probab. Appl. (Engl. Transl.), 1980, vol. 25, no. 4, pp. 703–720].

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wayne State University, Detroit, USA

    P. L. Chow & R. Z. Khasminskii

  2. Institute for Information Transmission Problems, RAS, Moscow, Russia

    R. Z. Khasminskii

Authors
  1. P. L. Chow
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Z. Khasminskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © P.L. Chow, R.Z. Khasminskii, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 4, pp. 77–86.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chow, P.L., Khasminskii, R.Z. On-line estimation of smooth signals with partial observation. Probl Inf Transm 42, 330–339 (2006). https://doi.org/10.1134/S0032946006040053

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946006040053

Keywords

Search

Navigation