Robust H∞ filtering for GPS/INS relative navigation

A robust H∞ filtering was applied to a GPS/INS integrated system to improve the accuracy and reliability of relative navigation system and solve the relative navigation problem with cooperative targets. The relative navigation estimator is performed in two stages: First, the Taylor series expansion method is used to approximate the nonlinear model for the relative navigation system to the first order instead of solving the HJI inequality in the robust nonlinear H∞ filtering. And the high order terms of the nonlinear model are represented by an uncertain term to improve the accuracy of the relative navigation system. Then, the relative navigation estimator is designed based on the robust H∞ filtering. Compared with the relative navigation method based on the EKF or UKF, the proposed estimator doesn't need to know the exact information or the statistical properties of the noises in the relative navigation model, and the uncertainties in the system model can be also lowered. The numerical simulation demonstrates that the relative estimator performs excellently in the properties of the accuracy and the robustness against the uncertainties. The accuracy for the relative attitude angle estimation is 0.0072°, and the absolute maximum estimation error for the relative position is less than 0.1 m.