Sparse-Grid Quadrature H_∞ 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.