Conditionally Linear and Non-Gaussian Processes

  • R. R. Mohler
  • W. J. Kolodziej

Abstract

A new theory and corresponding methodology is evolving for certain classes of nonlinear non-Gaussian signal processing. This research considers particular statistical model structures such as conditionally linear or bilinear. Some non-Gaussian distributions, which arise in underwater acoustical signal processing, are included, as are others. The results are based on rigorous developments related to, but not limited to, bilinear and conditionally Gaussian processes. Parameter or state estimation (e.g., acoustic source location) are studied as well as preliminary results in information transmission and coding.

Keywords

Covariance Assure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.S. Liptser and A.N. Shiryayev, Statistics of Random Processes II - Applications, Springer-Verlag, New York, 1978.MATHGoogle Scholar
  2. 2.
    R.R. Mohler and W.J. Kolodziej, “Optimal Control of a Class of Nonlinear Stochastic Systems,” IEEE Trans. Auto. Cont., Vol. AC-26, pp. 1048–1053, 1981.MathSciNetCrossRefGoogle Scholar
  3. 3.
    T.U. Halawani, R.R. Mohler and W.J. Kolodziej, “A Two-Step Bilinear Filtering Approximation,” IEEE Trans. Acous., Sp. & Sig. Proc., Vol. ASSP-32, pp. 244–352, 1984.Google Scholar
  4. 4.
    R.R. Mohler, W.J. Kolodziej, H.D. Brunk and R.S. Engelbrecht, “On Nonlinear Filtering and Tracking,” in Signal Processing in the Ocean Environment, ( E.J. Wegman, Ed.), Marcel-Dekker, New York, 1984.Google Scholar
  5. 5.
    W.J. Kolodziej and R.R. Mohler, “Analysis of a New Nonlinear Filter and Tracking Methodology,” IEEE Trans. Infor. Theory, Vol. IT-29, 1984, to appear.Google Scholar
  6. 6.
    V. Benes and I. Karatzas, “Estimation and Control for Linear, Partially Observable Systems with Non-Gaussian Initial Distribution,” Stochastic Processes and Their Applications, Vol. 14, pp. 233–248, 1983.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    R.S. Liptser and A.N. Shiryayev, Statistics of Random Processes I - General Theory, Springer-Verlag, New York, 1977.MATHGoogle Scholar
  8. 8.
    M.H.A. Davis, “The Separation Principle in Stochastic Control via Girsanov Solutions,” SIAM J. Control, Vol. 14, pp. 176–188, 1976.MATHCrossRefGoogle Scholar
  9. 9.
    W.J. Kolodziej and R.R. Mohler, “State Estimation and Control of Conditionally Linear Systems,” to appear, SIAM J. Control & Optimization, Vol. 25, 1985.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • R. R. Mohler
    • 1
    • 2
  • W. J. Kolodziej
    • 1
  1. 1.Department of Electrical and Computer EngineeringOregon State UniversityCorvallisUSA
  2. 2.Naval Postgraduate SchoolMontereyUSA

Personalised recommendations