Gaussian filters for nonlinear filtering problems

  title={Gaussian filters for nonlinear filtering problems},
  author={Kazufumi Ito and Kaiqi Xiong},
  journal={IEEE Trans. Autom. Control.},
We develop and analyze real-time and accurate filters for nonlinear filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We also discuss the mixed Gaussian filters in which the conditional probability density is approximated by the sum of Gaussian distributions. A new update rule of weights for Gaussian sum filters is proposed. Our numerical tests… 
Gaussian filter for nonlinear filtering problems
  • K. Itõ
  • Mathematics
    Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
  • 2000
We develop and analyze real-time and accurate filters for nonlinear filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop
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  • S. Särkkä, Jouni Hartikainen
  • Mathematics, Computer Science
    2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)
  • 2013
This work proposes a variational Bayes and Gaussian non-linear filtering based algorithm for efficient computation of the approximate filtering posterior distributions that allows the use of efficient Gaussian integration methods such as unscented transform, cubature integration and Gauss-Hermite integration along with the classical Taylor series approximations.
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A Tutorial on Bayesian Estimation and Tracking Techniques Applicable to Nonlinear and Non-Gaussian Processes
An overview of techniques for nonlinear filtering for a wide variety of conditions on the nonlinearities and on the noise is presented and a general Bayesian approach to filtering is developed which is applicable to all linear or nonlinear stochastic systems.
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Approximations to optimal nonlinear filters
  • H. Kushner
  • Mathematics
    IEEE Transactions on Automatic Control
  • 1967
Let the signal and noise processes be given as solutions to nonlinear stochastic differential equations. The optimal filter for the problem, derived elsewhere, is usually infinite dimensional.
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