Simplified Gauss Hermite Filter Based on Sparse Grid Gauss Hermite Quadrature

In order to improve estimation accuracy of nonliear system with linear measurement model, simplified gauss hermite filter based on sparse grid gauss hermite quadrature (SGHF) is proposed. Comparing to conventional Gauss-Hermite filter (GHF) based on tensor product gauss quadrature rule, simplified SGHF not only maintains GHF’s advantage of precission controllable, high estimation accuracy, but also relieves the curse of dimension problem by reduce the number of gaussian intrgration points to the number of sigma points that scaled unscented transform uses. Theoretical analysis and experimental results show that estimation base on new filter performs significantly beter than extended kalman filter (EKF), and slightly better than unscented kalman filter (UKF) on estimation accuracy and convergence speed, and computational burden is significantly reduced comparing with traditional GHKF.