Square‐Root Cubature‐Quadrature <scp>K</scp>alman Filter

Bhaumik, Shovan

doi:10.1002/asjc.704

Cited by 31 publications

(23 citation statements)

References 13 publications

(24 reference statements)

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“…Others have tried to select the sample size adaptively over time [23,14,4,22,12]. Kullback-Leibler distance (KLD) sampling [4,22] is the other efficient method that is utilized here as well for adaptive adjustment of the sample size in CQPF.…”

Section: Nomenclaturementioning

confidence: 99%

“…CQKF has been presented as a novel algorithm where the multivariate moment integral is computed numerically using the third-order cubature rule and multiple Gauss-Laguerre quadrature points [2]. As a more generalized form of the cubature Kalman filter (CKF) [1], the CQKF has two implementation variants: standard CQKF and the square root CQKF (SR-CQKF) [3]. Unlike ordinary CQKF, the SR-CQKF propagates and updates square root of the error covariance and ensures positive semi-definiteness of the state covariance matrix.…”

Section: Nomenclaturementioning

confidence: 99%

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Adaptive square-root cubature–quadrature Kalman particle filter via KLD-sampling for orbit determination

Kiani

Pourtakdoust

2015

Aerospace Science and Technology

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Section: Nomenclaturementioning

confidence: 99%

Section: Nomenclaturementioning

confidence: 99%

Adaptive square-root cubature–quadrature Kalman particle filter via KLD-sampling for orbit determination

Kiani

Pourtakdoust

2015

Aerospace Science and Technology

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“…The conventional CQKF suffers significant numerical errors in matrix inversion for higher probability of delay (p) and hence its square-root version [16] is used for implementation. From the plots, it could be concluded that the performance of CQKF-RD is significantly better than the ordinary CQKF, in the presence of a delay.…”

Section: A Problemmentioning

confidence: 99%

A Modified Bayesian Filter for Randomly Delayed Measurements

Singh

Date

Bhaumik

2017

IEEE Trans. Automat. Contr.

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Abstract-The traditional Bayesian approximation framework for filtering in discrete time systems assumes that the measurement is available at every time instant. But in practice, the measurements could be randomly delayed. In the literature, the problem has been examined and solution is provided by restricting the maximum number of delay to one or two time steps. This paper develops an approach to deal with the filtering problems with an arbitrary number of delays in measurement. Pursuing this objective, traditional Bayesian approximation to nonlinear filtering problem is modified by reformulating the expressions of mean and covariances which appear during the measurement update. We use the cubature quadrature rule to evaluate the multivariate integral expressions for the mean vector and the covariance matrix which appear in the developed filtering algorithm. We compare the new algorithm which accounts for delay with the existing CQKF heuristics on two different examples and demonstrate how accounting for a random delay improves the filtering performance.Index Terms-Nonlinear filtering, Bayesian framework of filtering, Random delay in measurements, Cubature quadrature Kalman filter.

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“…The simulation results show that SSRCKF can achieve more accurate results compared with CKF for high-dimensional system. Bhaumik [15,16] adopts -order generalized Gauss-Laguerre quadrature rule to calculate the radial integral and puts forward the cubature quadrature Kalman filter (CQKF). It is pointed out that CQKF is the generalized form of CKF; that is, CKF is the simplified form of CQKF with the first-order Gauss-Laguerre quadrature rule.…”

Section: Introductionmentioning

confidence: 99%

Simplex Cubature Kalman‐Consensus Filter for Distributed Space Target Tracking

Yang

Ding

et al. 2018

Wireless Communications and Mobile Computing

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A simplex cubature Kalman-consensus filter, which is suitable for distributed space target tracking using multiple radars, is proposed to improve the target tracking accuracy. The detailed orbital dynamics model and radar measurement model are given as the system filtering models. The intractable nonlinear Gaussian weighted integral in the filter is decomposed into the spherical integral and radial integral, which are calculated using the spherical simplex rule and the second-order Gauss-Laguerre quadrature rule, respectively. In this way, a new simplex cubature rule is derived. By means of the statistical linear regression method, the posterior mean, covariance, and the transmitted messages in the extended Kalman-consensus filter are approximated using the deduced simplex cubature rule, which results in the proposed simplex cubature Kalman-consensus filter. No data fusion center exists in the filter, and each radar only needs to exchange the information with its neighbors to reach a consensus estimate. The simulation results show that the proposed filter can achieve more accurate results compared with the cubature Kalman-consensus filter.

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Square‐Root Cubature‐Quadrature Kalman Filter

Cited by 31 publications

References 13 publications

Adaptive square-root cubature–quadrature Kalman particle filter via KLD-sampling for orbit determination

Adaptive square-root cubature–quadrature Kalman particle filter via KLD-sampling for orbit determination

A Modified Bayesian Filter for Randomly Delayed Measurements

Simplex Cubature Kalman‐Consensus Filter for Distributed Space Target Tracking

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