ON THE PARTIAL DIFFERENTIAL EQUATION FOR THE CONDITIONAL PROBABILITY DISTRIBUTION FOR NONLINEAR DYNAMIC SYSTEMS WITH NOISY MEASUREMENTS,

Abstract

The partial integro-differential equation is derived for the conditional probability density distribution of the output of a nonlinear system excited by nonadditive white Gaussian noise, with nonlinear measurements corrupted by white Gaussian noise. This equation reduces to the well-known Kolmogoroff forward equation when there are no measurements. The usefulness of the differential equation is demonstrated by deriving from it, for linear systems, the Wiener-Kalman filter. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 02, 1963
Accession Number
AD0434872

Entities

People

  • R. L. Kashyap

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Gaussian Noise
  • Kalman Filters
  • Linear Systems
  • Measurement
  • Noise
  • Nonlinear Systems
  • Partial Differential Equations
  • Probability
  • Probability Distributions

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.