Monomial cubature rules since “Stroud”: a compilation
Journal of Computational and Applied Mathematics
Cubature formulae of the seventh degree of accuracy for the hypersphere
Journal of Computational and Applied Mathematics
Monomial cubature rules since “Stroud”: a compilation—part 2
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
A stochastic algorithm for high-dimensional integrals over unbounded regions with Gaussian weight
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
An encyclopaedia of cubature formulas
Journal of Complexity
Fully symmetric interpolatory rules for multiple integrals over hyper-spherical surfaces
Journal of Computational and Applied Mathematics
Higher-Dimensional Integration with Gaussian Weight for Applications in Probabilistic Design
SIAM Journal on Scientific Computing
Monte Carlo Statistical Methods
Monte Carlo Statistical Methods
Sparse-grid quadrature nonlinear filtering
Automatica (Journal of IFAC)
A tutorial on particle filters for online nonlinear/non-GaussianBayesian tracking
IEEE Transactions on Signal Processing
Adaptive approximation of higher order posterior statistics
Journal of Computational Physics
Hi-index | 22.15 |
The cubature Kalman filter (CKF), which is based on the third degree spherical-radial cubature rule, is numerically more stable than the unscented Kalman filter (UKF) but less accurate than the Gauss-Hermite quadrature filter (GHQF). To improve the performance of the CKF, a new class of CKFs with arbitrary degrees of accuracy in computing the spherical and radial integrals is proposed. The third-degree CKF is a special case of the class. The high-degree CKFs of the class can achieve the accuracy and stability performances close to those of the GHQF but at lower computational cost. A numerical integration problem and a target tracking problem are utilized to demonstrate the necessity of using the high-degree cubature rules to improve the performance. The target tracking simulation shows that the fifth-degree CKF can achieve higher accuracy than the extended Kalman filter, the UKF, the third-degree CKF, and the particle filter, and is computationally much more efficient than the GHQF.