Grid-based Gaussian Nonlinear Estimation
This chapter presents class of approximate Bayesian estimation algorithms under the Gaussian assumption. It can significantly improve the accuracy of the linearization based nonlinear filters such as extended Kalman filter (EKF) schemes. The sparse-grid quadrature (SGQ) is based on the Smolyak’s rule for multivariate extension of the univariate quadrature rule and integration operators. The anisotropic sparse-grid quadrature can be used to further improve the computation efficiency of the SGQ. The SGQ is isotropic in the sense that all dimensions are assumed to be equally important and it uses an isotropic sparse-grid, which may result in more points than necessary. Various numerical integration rules can be applied to generate deterministic sampling points to approximate the Gaussian-weighted integrals. The Gauss-Hermite Quadrature is a numerical rule to approximate the Gaussian integral. The grid-based Gaussian approximation filter is a competitive alternative of the EKF, which uses the linearization technique and the classical Kalman filter.