INVARIANT IMBEDDING AND NONLINEAR FILTERING THEORY,

Abstract

Suppose that a system is undergoing a process which we believe can be described by the differential equation dx/dt= g(x, t). On the time interval (0, T) we observe the function x, in a noisy manner, and denote this experimental function by the symbol y. We wish to determine the state of the system at time t = T which is such that J is minimized, where J = the integral with respect to dt, from 0 to T, of (x(t) - y(t)) to the second power. Many problems of orbit determination and adaptive control are of this type. A solution is suggested in both the scalar and vector cases, which makes use of certain ideas from the theory of invariant imbedding, and some numerical examples are provided. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1964
Accession Number
AD0608944

Entities

People

  • Harriet H. Kagiwada
  • R. Sridhar
  • Richard E. Bellman
  • Robert E. Kalaba

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Filtration
  • Integrals
  • Intervals
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Control Systems Engineering.
  • Linear Algebra

Technology Areas

  • Space