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