A STUDY OF DIGITAL FILTER-OBSERVER SYSTEMS USING THE SECOND METHOD OF LYAPUNOV.

Abstract

The basic filter-observer equations of Kalman for optimal and suboptimal filters are studied using the concepts of Lyapunov functions and stability theory. The Second Method of Lyapunov is used to form a basis for comparison of the convergence rates of such filters. Lyapunov functions are also used to derive constraining relations for the elements of the filter gain matrix leading to design criteria for suboptimal filters. A derivation of the optimal filter gain based upon the Lyapunov function of a random variable is given. This derivation shows that the optimal filter converges most rapidly. A design of a suboptimal filter for one class of signal models is given based solely upon stability constraints. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1969
Accession Number
AD0701668

Entities

People

  • Edward Clair Rozelle

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Convergence
  • Design Criteria
  • Differential Equations
  • Digital Filters
  • Equations
  • Filters
  • Lyapunov Functions
  • Mathematical Analysis
  • Mathematics
  • Observers
  • Random Variables
  • Real Variables

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Systems Analysis and Design