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Title: Adaptive Sparse-grid Gauss-Hermite Filter
Authors: Date, P
Singh, A
Bhaumik, S
Radhakrishnan, R
Keywords: Nonlinear filtering;;Gauss–Hermite quadrature rule;;Product rule;Smolyak rule;;Complexity reduction;;Adaptive sparse-grid
Issue Date: 2018
Publisher: Elsevier
Citation: Journal of Computational and Applied Mathematics, 2018
Abstract: In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss–Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions equally, whereas the ASGHF assigns a fewer number of points along the dimensions with lower nonlinearity. It uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached. The performance of the proposed filter is illustrated with two nonlinear filtering problems. Simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparse-grid Gauss–Hermite filter (SGHF) and Gauss–Hermite filter (GHF) with a considerable reduction in computational load. Further, in the conventional GHF and SGHF, any increase in the accuracy level may result in an unacceptably high increase in the computational burden. However, in ASGHF, a little increase in estimation accuracy is possible with a limited increase in computational burden by varying the error tolerance level and the error weighting parameter. This enables the online estimator to operate near full efficiency with a predefined computational budget.
ISSN: 0377-0427
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