Nonlinear filtering and time varying Schrodinger equation

Author

Shing-Tung Yau ; Yau, Stephen S T

Author_Institution

Harvard Univ., Boston, MA, USA

Volume

40

Issue

1

fYear

2004

fDate

1/1/2004 12:00:00 AM

Firstpage

284

Lastpage

292

Abstract

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.

Keywords

Schrodinger equation; filtering theory; nonlinear differential equations; nonlinear filters; series (mathematics); time-varying filters; Kolmogorov equation; Yau filtering system; arbitrary initial condition; explicit algorithm; fundamental solution; nonlinear filtering problem; off-time computation; power series method; state variables; time varying Schrodinger equation; Algebra; Differential equations; Filtering theory; Mathematics; Nonlinear equations; Partial differential equations; Polynomials; Quantum mechanics; Schrodinger equation; Time varying systems;

fLanguage

English

Journal_Title

Aerospace and Electronic Systems, IEEE Transactions on

Publisher

ieee

ISSN

0018-9251

Type

jour

DOI

10.1109/TAES.2004.1292160

Filename

1292160