The Filtering Problem

1995 ◽  
pp. 75-102
Author(s):  
Bernt Øksendal
Keyword(s):  
Filtering Problem

scholarly journals Unbiased estimation of the solution to Zakai’s equation

2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra
Keyword(s):  
Continuous Time ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Linear Filtering ◽  
Multilevel Monte Carlo ◽  
Zakai Equation ◽  
Unbiased Estimators ◽  
First Order ◽  
Multilevel Monte Carlo Method ◽  
Filtering Problem

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

Explicit solution to the unstable stationary filtering problem

1986 ◽  
Vol 31 (2) ◽  
pp. 185-189 ◽  
Author(s):  
U. Shaked ◽  
E. Soroka
Keyword(s):  
Explicit Solution ◽  
Filtering Problem

scholarly journals Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 117
Author(s):  
Xuyou Li ◽  
Yanda Guo ◽  
Qingwen Meng
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Space Model ◽  
Performance Evaluations ◽  
Gaussian State ◽  
Variational Bayesian ◽  
Space Model ◽  
Bandwidth Parameter ◽  
Non Gaussian ◽  
Filtering Problem

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.

scholarly journals Solution of a time-varying Wiener filtering problem

1967 ◽  
Vol 3 (12) ◽  
pp. 562 ◽  
Author(s):  
B.D.O. Anderson ◽  
J.B. Moore
Keyword(s):  
Wiener Filtering ◽  
Time Varying ◽  
Filtering Problem
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