Nonlinear filtering and time varying Schrodinger equation

Based on our previous work we have successfully reduced the nonlinear filtering problem for Yau filtering system to the time-varying Schrodinger equation. In order to solve the nonlinear filtering problem, one needs to solve the time-varying Schrodinger equation with an arbitrary initial condition....

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Bibliographic Details
Published in:IEEE transactions on aerospace and electronic systems 2004-01, Vol.40 (1), p.284-292
Main Authors: Shing-Tung Yau, Yau, S.S.-T.
Format: Article
Language:English
Subjects:
Aircraft components
Algebra
Differential equations
Electronic systems
Filtering
Filtering theory
Filtration
Initial conditions
Mathematics
Nonlinear equations
Nonlinearity
Partial differential equations
Polynomials
Power series
Quantum mechanics
Schrodinger equation
Schroedinger equation
Time varying systems
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Summary:Based on our previous work we have successfully reduced the nonlinear filtering problem for Yau filtering system to the time-varying Schrodinger equation. In order to solve the nonlinear filtering problem, one needs to solve the time-varying Schrodinger equation with an arbitrary initial condition. We then solve the time-varying Schrodinger equation by constructing the fundamental solution explicitly via a system of nonlinear ODES in case the potential is quadratic in state variables. This system of nonlinear ODES is solved explicitly by the power series method.
ISSN:0018-9251
1557-9603
DOI:10.1109/TAES.2004.1292160