Multiple sparse-grid Gauss–Hermite filtering

Radhakrishnan, R.; Singh, Abhinoy Kumar; Bhaumik, Shovan; Tomar, Nutan Kumar

doi:10.1016/j.apm.2015.11.035

Cited by 27 publications

(17 citation statements)

References 23 publications

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“…The sparse‐grid Gauss‐Hermite filter was introduced to curb the curse of dimensionality problem associated with GHF, due to the exponential increase in quadrature point requirement with respect to the order of system. SGHF maintains similar accuracy levels as compared to GHF, with a significant reduction in computational burden []. Moreover, SGHF was found to be a competitive solution to the type of underwater BOT problems mentioned in this study [].…”

Section: Continuous‐discrete Sparse‐grid Gauss‐hermite Filter (Cd‐sghf)mentioning

confidence: 89%

Continuous‐discrete filters for bearings‐only underwater target tracking problems

Radhakrishnan

Bhaumik

Tomar

2019

Asian Journal of Control

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In this work, we develop a continuous-discrete shifted Rayleigh filter (CD-SRF) and a continuous-discrete sparse-grid Gauss-Hermite filter (CD-SGHF) for a real-life passive underwater bearings-only target tracking problem. The stochastic difference equation describing the process model is derived from its continuous equivalent using Ito-Taylor expansion of order 1.5. The performance of the proposed filters is compared in terms of root mean square error (RMSE), track divergence and computational time. For a fair comparison, popular filters like the unscented Kalman filter (UKF), cubature Kalman filter (CKF) andGauss-Hermite filter (GHF) are implemented. The effect of initial uncertainty, measurement noise covariance and sampling time on filtering accuracy is also studied. Finally, RMSEs of all the filters are evaluated in comparison with the Cramer-Rao lower bound (CRLB). From simulation results, it was observed that CD filters performed with higher accuracy than their discrete equivalents, with CD-SRF proving to be the most accurate among all the filters.

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Section: Continuous‐discrete Sparse‐grid Gauss‐hermite Filter (Cd‐sghf)mentioning

confidence: 89%

Continuous‐discrete filters for bearings‐only underwater target tracking problems

Radhakrishnan

Bhaumik

Tomar

2019

Asian Journal of Control

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“…Recall Definition 2; the cubature points in (20) can be categorized as three sets { 0 , 1 , 2 }; that is,…”

Section: Full Tensor-product Based Gauss-hermte Integral Rulementioning

confidence: 99%

“…Simulations prove the effectiveness of Smolyak's rule based Gauss-Hermite filter. Reference [20] proposes the multiple sparse grid Gauss-Hermite filter based on sparse grid Gauss-Hermite filter and state-space partitioning. It is claimed that the computational burden is further reduced with respect to the Gauss-Hermite filter and the sparse grid Gauss-Hermite filter.…”

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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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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“…The literature witnesses several Gaussian filters developed by using different numerical approximation methods. Some popular Gaussian filters are unscented Kalman filter (UKF) [18], cubature Kalman filter (CKF) [16] and its extensions [19], [20], and Gauss-Hermite filter (GHF) [17] along with several extensions [21]- [23].…”

Section: Introductionmentioning

confidence: 99%

Szegő Quadrature Kalman Filter for Oscillatory Systems

Singh

2020

IEEE Access

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Filtering problems with oscillatory system dynamics commonly appear in real-life. However, the existing Gaussian filters, like the unscented Kalman filter (UKF), cubature Kalman filter CKF, Gauss-Hermite filter (GHF) and cubature quadrature Kalman filter (CQKF), are accurate for the nonlinear systems with a particular order of polynomials only. This manuscript introduces a new Gaussian filter, which is accurate for oscillatory systems with 2π-period of oscillation. The proposed method is named as Szegő Quadrature Kalman Filter (SQKF). The SQKF transforms the intractable integrals that appear during the filtering over a unit circle. The transformed integral is approximated using the univariate Szegő quadrature rule. The univariate quadrature rule is extended in a multivariate domain using the product rule. Simulation results reveal an improved estimation accuracy for the SQKF in an oscillatory environment. The computational burden of the SQKF is similar to the GHF and higher than the UKF, CKF and CQKF. INDEX TERMS Nonlinear filtering, Gaussian filtering, Oscillatory system, Intractable integral, Szegő quadrature rule.

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Multiple sparse-grid Gauss–Hermite filtering

Cited by 27 publications

References 23 publications

Continuous‐discrete filters for bearings‐only underwater target tracking problems

Continuous‐discrete filters for bearings‐only underwater target tracking problems

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

Szegő Quadrature Kalman Filter for Oscillatory Systems

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