Title :
Nonlinear filtering and time varying Schrodinger equation
Author :
Shing-Tung Yau ; Yau, Stephen S T
Author_Institution :
Harvard Univ., Boston, MA, USA
fDate :
1/1/2004 12:00:00 AM
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;
Journal_Title :
Aerospace and Electronic Systems, IEEE Transactions on
DOI :
10.1109/TAES.2004.1292160
