The aim of this paper is to present a new INS/GPS sensor fusion scheme, based on State-Dependent Riccati Equation (SDRE) nonlinear filtering, for Unmanned Aerial Vehicle (UAV) localization problem. SDRE navigation filter is proposed as an alternative to Extended Kalman Filter (EKF), which has been largely used in the literature. Based on optimal control theory, SDRE filter solves issues linked with EKF filter such as linearization errors, which severely decrease UAV localization performances. Stability proof of SDRE nonlinear filter is also presented and validated on a 3-D UAV flight scenario. Results obtained by SDRE navigation filter were compared to EKF navigation filter results. This comparison shows better UAV localization performance using SDRE filter. The suitability of the SDRE navigation filter over an unscented Kalman navigation filter for highly nonlinear UAV flights is also demonstrated.Index Terms-Sensor data fusion, state-dependent Riccati equation (SDRE) nonlinear filter, SDRE stability, unmanned aerial vehicle (UAV) localization.

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Our aim is to solve a problem of optimal control with free final time using the Pontryagin's maximum principle. As an illustration, we consider a navigation problem which is solved analytically and numerically by the shooting method in the case without constraint. The two approaches are compared. In the second case, we solve numerically the same problem with constraint on the state. At the end, we prove the convergence of the method for the second case.