Multiple sparse-grid Gauss–Hermite filtering

Highligts•A computationally efficient nonlinear filtering algorithm is proposed.•A combination of state-space partitioning and Smolyak rule is used.•The number of quadrature points are reduced, but accuracy still remains almost same.•The proposed method is illustrated using two examples and the resu...

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Bibliographic Details
Published in:Applied mathematical modelling 2016-04, Vol.40 (7-8), p.4441-4450
Main Authors: Radhakrishnan, Rahul, Singh, Abhinoy Kumar, Bhaumik, Shovan, Tomar, Nutan Kumar
Format: Article
Language:English
Subjects:
Accuracy
Bayesian estimation
Complexity reduction
Computation
Computer simulation
Filtering
Filtration
Gauss–Hermite quadrature
Mathematical analysis
Mathematical models
Nonlinear filtering
Partitioning
Sparse-grid
State-space partitioning
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Summary:Highligts•A computationally efficient nonlinear filtering algorithm is proposed.•A combination of state-space partitioning and Smolyak rule is used.•The number of quadrature points are reduced, but accuracy still remains almost same.•The proposed method is illustrated using two examples and the results, discussed. A new method for nonlinear estimation, based on sparse-grid Gauss–Hermite filter (SGHF) and state-space partitioning, termed as Multiple sparse-grid Gauss–Hermite filter (MSGHF) is proposed in this work. Gauss–Hermite filter is a widely acclaimed filtering technique for its high accuracy. But the computational load associated with it is so high, that it becomes difficult to apply it on-board for higher dimensional problems. SGHF showcased comparable performance with the GHF, with less computational burden. The proposed technique, MSGHF, further reduces the computational burden considerably, with the filter accuracy remaining almost the same. Simulation results illustrate the performance of the proposed filter with respect to GHF and SGHF.
ISSN:0307-904X
DOI:10.1016/j.apm.2015.11.035