Quadrature filters for one-step randomly delayed measurements

Singh, Abhinoy Kumar; Bhaumik, Shovan; Date, Paresh

doi:10.1016/j.apm.2016.04.016

Cited by 21 publications

(10 citation statements)

References 32 publications

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“…We can see that (9), (10), (14), and (15) are similar to those corresponding formulae of standard Kalman filter. The only difference between local Gaussian filter and standard Kalman filter is the calculation ofx | −1 ,ẑ | −1 , P | −1 , P | −1 , and P | −1 .…”

Section: Local Gaussian Filtersupporting

confidence: 74%

“…The core problem of local Gaussian filters is in fact a high dimensional Gaussian weighted integration, which has been studied in numerical analysis; see [6][7][8][9] and the references therein. Lots of researches concentrate on the numerical approximation methods to solve the Gaussian weighted integral problem, and different approaches result in different local Gaussian filters, such as the cubature Kalman filter [10], the quadrature Kalman filter [11], and related variants [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking

Peng

Duan

Zhu

2017

Modelling and Simulation in Engineering

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A new sparse Gauss-Hermite cubature rule is designed to avoid dimension explosion caused by the traditional full tensor-product based Gauss-Hermite cubature rule. Although Smolyak’s quadrature rule can successfully generate sparse cubature points for high dimensional integral, it has a potential drawback that some cubature points generated by Smolyak’s rule have negative weights, which may result in instability for the computation. A relative-weight-ratio criterion based sparse Gauss-Hermite rule is presented in this paper, in which cubature points are kept symmetric in the input space and corresponding weights are guaranteed to be positive. The generation of the new sparse cubature points set is simple and meaningful for practice. The difference between our new sparse Gauss-Hermite cubature rule and other cubature rules is analysed. Simulation results show that, compared with Kalman filter with those types of full tensor-product based Gauss-Hermite rules, our new sparse Gauss-Hermite cubature rule based Kalman filter can lead to a substantially reduced number of cubature points, more stable computation capability, and maintaining the accuracy of integration at the same time.

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Section: Local Gaussian Filtersupporting

confidence: 74%

Section: Introductionmentioning

confidence: 99%

A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking

Peng

Duan

Zhu

2017

Modelling and Simulation in Engineering

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“…Hence, it is worthy to study the performance of the proposed method in the domain of randomly delayed measurements. The paper will basically focus on the work of Carazo et al [28] and Abhinoy et al [9] which propose an algorithm for dealing with delayed measurements by restricting the maximum extent of it to be one time step. One-step delayed measurement y k could be modeled in terms of expected non-delayed measurements (z k = γ(x k , k) + v k ), as follows:…”

Section: Tcqkf For a System With Delayed Measurementsmentioning

confidence: 99%

“…However, several limitations, including smoothness requirement of function, lack of convergence for highly non-linear systems are associated with the EKF. To circumvent the problems, several derivative-free methods such as the unscented Kalman filter (UKF) [3,4] and its variants [5,6], the Gauss-Hermite filter [7][8][9], the sparse grid Gauss-Hermite filter [10,11], the central difference filter [12], the cubature Kalman filter (CKF) [13] and its extensions [14,15], the high-degree cubature quadrature (CQ) Kalman filter [16,17] have been introduced. In all the above-mentioned filters, the prior and the posterior probability density functions (pdfs) are approximated as Gaussian and characterised by mean and covariance.…”

Section: Introductionmentioning

confidence: 99%

Transformed cubature quadrature Kalman filter

Singh

Bhaumik

2017

IET signal process.

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An orthogonal transformation is applied to the cubature quadrature (CQ) points which are used to approximate the intractable integrals appeared during the estimation of states of a non-linear system. With the help of a theorem, it is shown that the transformed points reduce the higher order moments (HOM) appeared while approximating the mean and covariance. As the HOM act as residue, the proposed method results in an improved filtering accuracy. Further, the proposition is extended in delayed measurement environment. The proposed method has been implemented for two different simulation problems. The simulation results reveal that at the same computational load, the filter with transformed CQ points provides higher accuracy compared with the filter with ordinary CQ points. The performance has been verified in the delayed measurement environment and an improved accuracy has been reported.

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“…In Reference [ 22 ] and Reference [ 23 ], improved versions of the EKF and the unscented Kalman filter (UKF) are proposed for one-time step and two-time step randomly delayed measurements. In Reference [ 24 ], quadrature filters have been modified to solve nonlinear filtering problem with one-step randomly delayed measurements. In Reference [ 25 ], the cubature Kalman filter (CKF) [ 26 ] is used to tackle one-step randomly delayed measurements for nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Particle Filter for Randomly Delayed Measurements with Unknown Latency Probability

Tiwari

Bhaumik

Date

et al. 2020

Sensors

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This paper focuses on developing a particle filter based solution for randomly delayed measurements with an unknown latency probability. A generalized measurement model that includes measurements randomly delayed by an arbitrary but fixed maximum number of time steps along with random packet drops is proposed. Owing to random delays and packet drops in receiving the measurements, the measurement noise sequence becomes correlated. A model for the modified noise is formulated and subsequently its probability density function (pdf) is derived. The recursion equation for the importance weights is developed using pdf of the modified measurement noise in the presence of random delays. Offline and online algorithms for identification of the unknown latency parameter using the maximum likelihood criterion are proposed. Further, this work explores the conditions that ensure the convergence of the proposed particle filter. Finally, three numerical examples, one with a non-stationary growth model and two others with target tracking, are simulated to show the effectiveness and the superiority of the proposed filter over the state-of-the-art.

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Quadrature filters for one-step randomly delayed measurements

Cited by 21 publications

References 32 publications

A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking

A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking

Transformed cubature quadrature Kalman filter

Particle Filter for Randomly Delayed Measurements with Unknown Latency Probability

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