On sequential Monte Carlo sampling methods for Bayesian filtering
Statistics and Computing
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches
Extended Symmetric Sampling Strategy for Unscented Kalman Filter
CASE '09 Proceedings of the 2009 IITA International Conference on Control, Automation and Systems Engineering (case 2009)
Accuracy Analysis of Unscented Transformation of Several Sampling Strategies
SNPD '09 Proceedings of the 2009 10th ACIS International Conference on Software Engineering, Artificial Intelligences, Networking and Parallel/Distributed Computing
Cubature kalman filtering for continuous-discrete systems: theory and simulations
IEEE Transactions on Signal Processing
A tutorial on particle filters for online nonlinear/non-GaussianBayesian tracking
IEEE Transactions on Signal Processing
New developments in state estimation for nonlinear systems
Automatica (Journal of IFAC)
High-degree cubature Kalman filter
Automatica (Journal of IFAC)
Gaussian filter for nonlinear systems with one-step randomly delayed measurements
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
In this paper, a novel nonlinear filter named Sparse-grid Quadrature Filter (SGQF) is proposed. The filter utilizes weighted sparse-grid quadrature points to approximate the multi-dimensional integrals in the nonlinear Bayesian estimation algorithm. The locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method. Then the univariate quadrature point sets are extended to form a multi-dimensional grid using the sparse-grid theory. Compared with the conventional point-based methods, the estimation accuracy level of the SGQF can be flexibly controlled and the number of sparse-grid quadrature points for the SGQF is a polynomial of the dimension of the system, which alleviates the curse of dimensionality for high dimensional problems. The Unscented Kalman Filter (UKF) is proven to be a subset of the SGQF at the level-2 accuracy. The performance of this filter is demonstrated by an orbit estimation problem. The simulation results show that the SGQF achieves higher accuracy than the Extended Kalman Filter (EKF), the UKF, and the Cubature Kalman Filter (CKF). In addition, the SGQF is computationally much more efficient than the multi-dimensional Gauss-Hermite Quadrature Filter (GHQF) with the same performance.