• Corpus ID: 17725612

Sigma-point kalman filters for probabilistic inference in dynamic state-space models

@inproceedings{vanderMerwe2004SigmapointKF,
  title={Sigma-point kalman filters for probabilistic inference in dynamic state-space models},
  author={Rudolph van der Merwe and Eric A. Wan},
  year={2004}
}
Probabilistic inference is the problem of estimating the hidden variables (states or parameters) of a system in an optimal and consistent fashion as a set of noisy or incomplete observations of the system becomes available online. The optimal solution to this problem is given by the recursive Bayesian estimation algorithm which recursively updates the posterior density of the system state as new observations arrive. This posterior density constitutes the complete solution to the probabilistic… 
Recursive Bayesian inference on stochastic differential equations
TLDR
The main contributions of this thesis are to show how the recently developed discrete-time unscented Kalman filter, particle filter, and the corresponding smoothers can be applied in the continuous-discrete setting.
Kalman Filter, Particle Filter and Other Bayesian Filters
TLDR
This chapter deals with optimal state estimation for dynamic systems, and extends the study to a variety of optimal estimation methods, inspired in the Kalman filter archetype and the Bayesian point of view.
Nonlinear Bayesian estimation: from Kalman filtering to a broader horizon
TLDR
A systematic introduction to the Bayesian state estimation framework is offered and various Kalman filtering U+0028 KF U-0029 techniques are reviewed, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KFFor nonlinear systems.
A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding
TLDR
It is argued there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein—von Mises theorem applies.
The Discriminative Kalman Filter for Bayesian Filtering with Nonlinear and Nongaussian Observation Models
TLDR
The DKF has computational complexity similar to the Kalman filter, allowing it in some cases to perform much faster than particle filters with similar precision, while better accounting for nonlinear and nongaussian observation models than Kalman-based extensions.
An improved constraint filtering technique for inferring hidden states and parameters of a biological model
TLDR
The constrained square-root unscented Kalman filter (CSUKF) was developed and was successfully used to estimate parameters of a glycolysis model in yeast and a gene regulatory network and is shown to be both accurate and computationally efficient.
Bayesian estimation for target tracking: part II, the Gaussian sigma‐point Kalman filters
This is the second part of a three part article examining methods for Bayesian estimation and tracking. In the first part we presented the general theory of Bayesian estimation where we showed that
Multiple Quadrature Kalman Filtering
TLDR
It is proved that partitioning schemes can effectively be used to reduce the curse of dimensionality in the Quadrature Kalman filter (QKF), and is studied a complexity reduction technique based on the partitioning of the state-space, referred to as the Multiple QKF.
On the evaluation of uncertainties for state estimation with the Kalman filter
TLDR
The relationship between the covariance matrix produced by the Kalman filter and a GUM-compliant uncertainty analysis and the results of a Bayesian analysis are considered and it is shown that all three approaches are compatible.
...
...

References

SHOWING 1-10 OF 208 REFERENCES
Learning Nonlinear Dynamical Systems Using an EM Algorithm
TLDR
A generalization of the EM algorithm for parameter estimation in nonlinear dynamical systems if Gaussian radial basis function (RBF) approximators are used to model the nonlinearities, the integrals become tractable and the maximization step can be solved via systems of linear equations.
Gaussian mixture sigma-point particle filters for sequential probabilistic inference in dynamic state-space models
  • Rudolph van der Merwe, E. Wan
  • Computer Science
    2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).
  • 2003
TLDR
A novel recursive Bayesian estimation algorithm that combines an importance sampling based measurement update step with a bank of sigma-point Kalman filters for the time-update and proposal distribution generation is presented.
The square-root unscented Kalman filter for state and parameter-estimation
  • Rudolph van der Merwe, E. Wan
  • Mathematics
    2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221)
  • 2001
TLDR
The square-root unscented Kalman filter (SR-UKF) is introduced which is also O(L/sup 3/) for general state estimation and O( L/sup 2/) for parameter estimation and has the added benefit of numerical stability and guaranteed positive semi-definiteness of the state covariances.
Nonlinear estimation and modeling of noisy time series by dual kalman filtering methods
TLDR
The dual Kalman filtering method is developed as a method for minimizing a variety of dual estimation cost functions, and is shown to be an effective general method for estimating the signal, model parameters, and noise variances in both on-line and off-line environments.
Novel approach to nonlinear/non-Gaussian Bayesian state estimation
TLDR
An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters, represented as a set of random samples, which are updated and propagated by the algorithm.
Spatial-temporal nonlinear filtering based on hierarchical statistical models
TLDR
This paper is a review of spatial-temporal nonlinear filtering, and it is illustrated in a Command and Control setting where the objects are highly mobile weapons, and the nonlinear function of object locations is a two-dimensional surface known as the danger-potential field.
The Extended Kalman Filter as a Parameter Estimator for Linear Systems
TLDR
The analysis gives insight into the convergence mechanisms and it is shown that with a modification of the algorithm, global convergence results can be obtained for a general case.
Nonlinear Bayesian estimation using Gaussian sum approximations
TLDR
In this paper an approximation that permits the explicit calculation of the a posteriori density from the Bayesian recursion relations is discussed and applied to the solution of the nonlinear filtering problem.
A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
TLDR
Both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters are reviewed.
Efficient derivative-free Kalman filters for online learning
TLDR
This paper introduces efficient square-root forms of the different filters that enables an implementation for parameter estimation (equivalent to the EKF), and has the added benefit of improved numerical stability and guaranteed positive semi-definiteness of the Kalman filter covariances.
...
...