Gaussian filters for nonlinear filtering problems

@article{Ito2000GaussianFF,
  title={Gaussian filters for nonlinear filtering problems},
  author={Kazufumi Ito and Kaiqi Xiong},
  journal={IEEE Trans. Autom. Control.},
  year={2000},
  volume={45},
  pages={910-927}
}
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… Expand
Gaussian filter for nonlinear filtering problems
  • K. Itõ
  • Mathematics
  • Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
  • 2000
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References

SHOWING 1-10 OF 39 REFERENCES
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.Expand
A new approach for filtering nonlinear systems
TLDR
A new recursive linear estimator for filtering systems with nonlinear process and observation models which can be transformed directly by the system equations to give predictions of the transformed mean and covariance is described. Expand
Nonlinear Bayesian estimation using Gaussian sum approximations
Knowledge of the probability density function of the state conditioned on all available measurement data provides the most complete possible description of the state, and from this density any of theExpand
Recursive bayesian estimation using gaussian sums
The Bayesian recursion relations which describe the behavior of the a posteriori probability density function of the state of a time-discrete stochastic system conditioned on available measurementExpand
A General Method for Approximating Nonlinear Transformations of Probability Distributions
In this paper we describe a new approach for generalised nonlinear ltering. We show that the technique is more accurate, more stable, and far easier to implement than an extended Kalman lter. SeveralExpand
Suboptimal state estimation for continuous-time nonlinear systems from discrete noisy measurements
This paper presents the derivation of the dynamical equations of a second-order filter which estimates the states of a non-linear plant on the basis of discrete noisy measurements. The filterExpand
Stochastic differential equations for the non linear filtering problem
The general nonlinear filtering or estimation problem may be described as follows. xty (0<t<T)y called the signal or system process is a stochastic process direct observation is not possible. TheExpand
Approximation of the Zakai Equation for Nonlinear Filtering
In this paper we consider numerical approximations of solutions to the Zakai equation. Time discretization based on the implicit Milshtein and Euler methods and Galerkin approximation in the spatialExpand
On approximate approximations using Gaussian kernels
This paper discusses quasi-interpolation and interpolation with Gaussians. Estimates are obtained showing a high-order approximation up to some saturation error negligible in numerical applications.Expand
Convergence of implicit discretization schemes for linear differential equations with application to filtering
Abstract : The motivation for the present work arises from a well-known problem in nonlinear filtering. If one wants to solve it recursively "online" on a digital computer, the best one can do is toExpand
...
1
2
3
4
...