• DocumentCode
    1430356
  • Title

    Finite-dimensional filters with nonlinear drift X: explicit solution of DMZ equation

  • Author

    Yan, S.S.-T. ; Hu, Guo-Qing

  • Author_Institution
    Dept. of Math. Stat. & Comput. Sci., Illinois Univ., Chicago, IL, USA
  • Volume
    46
  • Issue
    1
  • fYear
    2001
  • fDate
    1/1/2001 12:00:00 AM
  • Firstpage
    142
  • Lastpage
    148
  • Abstract
    In this note, we consider the explicit solution of Duncan-Mortensen-Zakai (DMZ) equation for the finite-dimensional filtering system. We show that Yau´s (1990, 1994) filtering system (δfj/δxi)-(δfi /δxi)=cij=constant for all (i,j) can be solved explicitly with an arbitrary initial condition by solving a system of ordinary differential equations and a Kolmogorov-type equation. Let n be the dimension of state space. We show that we need only n sufficient statistics in order to solve the DMZ equation
  • Keywords
    differential equations; filtering theory; multidimensional systems; nonlinear filters; DMZ equation; Duncan-Mortensen-Zakai equation; Kolmogorov-type equation; explicit solution; finite-dimensional filtering system; finite-dimensional filters; multidimensional state space; nonlinear drift; ordinary differential equations; Algebra; Convergence; Differential equations; Filtering; Job shop scheduling; Nonlinear equations; Nonlinear filters; Queueing analysis; Statistics; Stochastic processes;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/9.898707
  • Filename
    898707
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1430356