Sparse-Grid Quadrature $H_infty $ Filter for Discrete-Time Systems with Uncertain Noise Statistics

In This paper H_∞ technique is combined with the recently developed sparse-grid quadrature (SGQ) filtering to improve the accuracy and robustness of the state estimation when the noise statistics is not known a priori. The proposed new SGQ H_∞ filter (SGQH_∞F) is compared with other H_∞ filters via two numerical examples. It is shown that the SGQH_∞F is more robust and accurate than the extended H_∞ filter, unscented H_∞ filter, and cubature H_∞ filter. In addition it maintains a close performance to the Gauss-Hermite quadrature (GHQ) H_∞ filter but is computationally much more efficient since it uses far fewer quadrature points.