Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.
Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition
IEEE Transactions on Aerospace and Electronic Systems ; 33 , 4 ; 1295-1308
1997-10-01
1868337 byte
Article (Journal)
Electronic Resource
English
V: Solution to Kolmogorov Equation Arising From Linear Filtering with Non-Gaussian Initial Condition
Online Contents | 1997
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Online Contents | 1998
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