Simple harmonic oscillator and the Benes filter – Exact fundamental solution

PDF

Authors
  1. Balaji, B.
Corporate Authors
Defence R&D Canada - Ottawa, Ottawa ONT (CAN)
Abstract
The solution to the universal continuous-discrete filtering problem requires the solution of the Fokker-Planck-Kolmogorov forward equation (FPKfe) for the state process for an arbitrary initial condition. The fundamental solution for the FPKfe is derived for a state model of arbitrary dimension with Benes drift and a positive-definite diffusion matrix proportional to the identity matrix, and requires only the computation of elementary transcendental functions and standard linear algebra techniques. In particular, there is no need to solve a partial (or ordinary) differential equation. The measurement process may be a discrete-time nonlinear stochastic process, and the time step size can be arbitrary. These results can also be applied to explicitly solve the continuous-continuous Yau filtering problem with Benes drift.

Il y a un résumé en français ici.

Report Number
DRDC-OTTAWA-TM-2008-352 — Technical Memorandum
Date of publication
01 Mar 2009
Number of Pages
62
DSTKIM No
CA032271
CANDIS No
531363
Format(s):
CD ROM

Permanent link

Document 1 of 1

Date modified: