Gaussian filters for nonlinear filtering problems

Ito, Kazufumi; Xiong, Ke

doi:10.1109/9.855552

Cited by 1,259 publications

(857 citation statements)

References 12 publications

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“…The resulting set of sigma-points for the CDKF is once again a set of points deterministically drawn from the prior statistics of x. Studies (Ito & Xiong, 2000) have shown that in practice, just as UKF, the CDKF generates estimates that are clearly superior to those calculated by an EKF. Merwe & Wan, 2001) are numerically efficient square-root forms derived from UKF and CDKF respectively.…”

Section: The Central Difference Kalman Filtermentioning

confidence: 99%

“…The Central Difference Kalman Filter (CDKF) (Ito & Xiong, 2000) is another SPKF implementation, whose formulation was derived by replacing the analytically derived first and second order derivatives in the Taylor series expansion by numerically evaluated central divided differences. The resulting set of sigma-points for the CDKF is once again a set of points deterministically drawn from the prior statistics of x.…”

Section: The Central Difference Kalman Filtermentioning

confidence: 99%

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Applying REC Analysis to Ensembles of Sigma-Point Kalman Filters

Pina

Zaverucha

2006

Artificial Neural Networks – ICANN 2006

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The Sigma-Point Kalman Filters (SPKF) is a family of filters that achieve very good performance when applied to time series. Currently most researches involving time series forecasting use the Sigma-Point Kalman Filters, however they do not use an ensemble of them, which could achieve a better performance. The REC analysis is a powerful technique for visualization and comparison of regression models. The objective of this work is to advocate the use of REC curves in order to compare the SPKF and ensembles of them and select the best model to be used.

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Section: The Central Difference Kalman Filtermentioning

confidence: 99%

Section: The Central Difference Kalman Filtermentioning

confidence: 99%

Applying REC Analysis to Ensembles of Sigma-Point Kalman Filters

Pina

Zaverucha

2006

Artificial Neural Networks – ICANN 2006

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“…The sequence of measurement updates are displayed in figs. (5)(6). The GHF always uses Gaussian densities, whereas the GGHF (K = 10) can model the more realistic bimodal shape.…”

Section: Example: Ginzburg-landau Modelmentioning

confidence: 99%

“…Expectation values occuring in the time and measurement updates can be computed numerically by using Gauss-Hermite quadrature (GHF; cf. Ito and Xiong, 2000). Alternatively, such expectations are treated by truncated Taylor expansion, leading to the well known extended Kalman filter (EKF) or the second order nonlinear filter (SNF).…”

Section: Introductionmentioning

confidence: 99%

Generalized Gauss–Hermite filtering

Singer

2008

AStA

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“…This approach led to the unscented Kalman filter, UKF [8,9,10], linear regression Kalman filters LRKF [11,12,13], the shifted Rayleigh filter [14], and the filter in [15].…”

Section: Introductionmentioning

confidence: 99%

The Antiparticle Filter—An Adaptive Nonlinear Estimator

Folkesson

2016

Springer Tracts in Advanced Robotics

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We introduce the antiparticle filter, AF, a new type of recursive Bayesian estimator that is unlike either the extended Kalman Filter, EKF, unscented Kalman Filter, UKF or the particle filter PF. We show that for a classic problem of robot localization the AF can substantially outperform these other filters in some situations. The AF estimates the posterior distribution as an auxiliary variable Gaussian which gives an analytic formula using no random samples. It adaptively changes the complexity of the posterior distribution as the uncertainty changes. It is equivalent to the EKF when the uncertainty is low while being able to represent non-Gaussian distributions as the uncertainty increases. The computation time can be much faster than a particle filter for the same accuracy. We have simulated comparisons of two types of AF to the EKF, the iterative EKF, the UKF, an iterative UKF, and the PF demonstrating that AF can reduce the error to a consistent accurate value.

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Gaussian filters for nonlinear filtering problems

Cited by 1,259 publications

References 12 publications

Applying REC Analysis to Ensembles of Sigma-Point Kalman Filters

Applying REC Analysis to Ensembles of Sigma-Point Kalman Filters

Generalized Gauss–Hermite filtering

The Antiparticle Filter—An Adaptive Nonlinear Estimator

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