A STUDY OF DIGITAL FILTER-OBSERVER SYSTEMS USING THE SECOND METHOD OF LYAPUNOV.
NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF
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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
- Numerical Mathematics