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JournalISSN: 0021-9223

Journal of Basic Engineering 

American Society of Mechanical Engineers
About: Journal of Basic Engineering is an academic journal. The journal publishes majorly in the area(s): Closure (topology) & Stress (mechanics). It has an ISSN identifier of 0021-9223. Over the lifetime, 1490 publications have been published receiving 74170 citations.


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TL;DR: The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.
Abstract: A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this \"variance equation\" completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side. Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.

6,152 citations

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Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
1972131
197186
1970119
1969109
196885
1967114