Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature

Arasaratnam, Ienkaran; Haykin, S.; Elliott, Robert J.

doi:10.1109/jproc.2007.894705

Cited by 511 publications

(370 citation statements)

References 43 publications

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“…The quadrature points are located at √ 2x i , where x i are the eigenvalues of J [11]. The weights W i is the square of the first element of the i th normalized vector.…”

Section: Single Dimensional Gauss-hermite Quadrature Rulementioning

confidence: 99%

“…This is a standard assumption in the literature on filters based on numerical integration such as GHF and SGHF, see, e.g. [11] and [13]. The proposed filters estimate the posterior mean and the covariance at each step recursively.…”

Section: Introductionmentioning

confidence: 99%

“…In order to achieve higher estimation accuracy with reasonable computational load, several nonlinear filters have been introduced. These include the extended Kalman filter (EKF) [6], the unscented Kalman filter (UKF) [7] and its variants [8], the cubature Kalman filter (CKF) [9,10], the Gauss-Hermite filter (GHF) [11,12], the sparse-grid Gauss-Hermite filter (SGHF) [13], the central difference filter (CDF) [14], the divided difference filter (DDF) [15] etc.…”

Section: Introductionmentioning

confidence: 99%

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Quadrature filters for one-step randomly delayed measurements

Singh

Bhaumik

Date

2016

Applied Mathematical Modelling

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In this paper, two existing quadrature filters, viz., the Gauss-Hermite filter (GHF) and the sparse-grid Gauss-Hermite filter (SGHF) are extended to solve nonlinear filtering problems with one step randomly delayed measurements. The developed filters are applied to solve a maneuvering target tracking problem with one step randomly delayed measurements.Simulation results demonstrate the enhanced accuracy of the proposed delayed filters compared to the delayed cubature Kalman filter and delayed unscented Kalman filter.

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“…The quadrature points are located at √ 2x i , where x i are the eigenvalues of J [11]. The weights W i is the square of the first element of the i th normalized vector.…”

Section: Single Dimensional Gauss-hermite Quadrature Rulementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quadrature filters for one-step randomly delayed measurements

Singh

Bhaumik

Date

2016

Applied Mathematical Modelling

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show abstract

“…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%

“…Or the Gaussian sum quadrature filter as presented in [13]. Exact batch methods and some of the graphical algorithms [26,27,28,29,30] can solve the exact system by successive approximation.…”

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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Modern Bayesian State–Space Processors

Candy

2008

Bayesian Signal Processing

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Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature

Cited by 511 publications

References 43 publications

Quadrature filters for one-step randomly delayed measurements

Quadrature filters for one-step randomly delayed measurements

The Antiparticle Filter—An Adaptive Nonlinear Estimator

Modern Bayesian State–Space Processors

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