Sparse-grid quadrature nonlinear filtering

Jia, Bin; Xin, Ming; Cheng, Yang

doi:10.1016/j.automatica.2011.08.057

Cited by 243 publications

(210 citation statements)

References 24 publications

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“…The estimation of the augmented states can be done in two steps [13], namely (i) measurement noise estimation (ii) state estimation.…”

Section: Assumptionsmentioning

confidence: 99%

“…The curse of dimensionality problem associated with product rule could be circumvented by considerably reducing the number of support points using Smolyak formula [26]; also see [13] for its use in filtering. Using this rule, the product rule is replaced by a linear combination of tensor product.…”

Section: Smolyak 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%

“…So the support point requirement for GHF-1RD increases exponentially with the dimension of the system, hence suffers from the curse of dimensionality problem. The said problem is overcome in the SGHF-1RD which uses Smolyak rule, introduced in [13,26] to extend the single dimensional quadrature points to multidimensional space without affecting estimation accuracy achieved in GHF-1RD.…”

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 estimation of the augmented states can be done in two steps [13], namely (i) measurement noise estimation (ii) state estimation.…”

Section: Assumptionsmentioning

confidence: 99%

Section: Smolyak Rulementioning

confidence: 99%

Section: Introductionmentioning

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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Continuous discrete cubature quadrature Kalman filter

Swati¹

2021

Asian Journal of Control

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In this paper, cubature quadrature Kalman filter algorithm has been reformulated for nonlinear state space model of continuous-discrete nature. The developed method is named as continuous-discrete cubature quadrature Kalman filter (CD-CQKF). The formulated algorithm has been applied to track the trajectory of an aircraft. The process is described with coordinated turn model. From the simulation result, it has been observed that the developed CD-CQKF provides better estimation compared with continuous-discrete cubature Kalman filter.

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EM‐based adaptive divided difference filter for nonlinear system with multiplicative parameter

Wang

Song

Liang

2016

Intl J Robust & Nonlinear

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Summary This paper is concerned with application of expectation maximization (EM) algorithm for deriving an adaptive version of divided difference filter for joint state estimation and multiplicative parameter identification of nonlinear system with the colored measurement noise. Owing to the fact that there exist a mutual coupling and interaction of state and parameter on each other, it requires a joint or simultaneous estimation of both state and parameter by a mutual iteration, and justly, EM iterates Expectation (E‐)step and Maximization (M‐)step to meet such requirement. Firstly, E‐step involves state filtering and smoothing issues under knowing the previous parameter identification results, which is well solved by resorting to the Gaussian approximation with a trade‐off between accuracy and complexity. Further, such Gaussian approximation estimators are applied for evaluating the condition expectation of complete‐data likelihood function, nonlinearly characterized by the multiplicative parameter needed to be optimized. Secondly, M‐step deals with the maximization of the condition expectation by directly making its derivative as zero to obtain the current general parameter identification equation as the nonlinear integral. Thirdly, by iteratively operating E‐step and M‐step, an adaptive divided difference filter is proposed for joint state estimation and parameter identification by using the second‐order Stirling interpolation to compute the associated nonlinear integral. Finally, the robust performance of the EM‐based adaptive version of divided difference filter to the unknown or time‐varying multiplicative parameter, as compared with the standard augmentation method, is demonstrated by a maneuvering target tracking example. Copyright © 2016 John Wiley & Sons, Ltd.

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Sparse-grid quadrature nonlinear filtering

Cited by 243 publications

References 24 publications

Quadrature filters for one-step randomly delayed measurements

Quadrature filters for one-step randomly delayed measurements

Continuous discrete cubature quadrature Kalman filter

EM‐based adaptive divided difference filter for nonlinear system with multiplicative parameter

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