A beacon configuration optimization method based on Fisher information for Mars atmospheric entry

The navigation capability of the proposed Mars network based entry navigation system is directly related to the beacon number and the relative configuration between the beacons and the entry vehicle. In this paper, a new beacon configuration optimization method is developed based on the Fisher information theory and this method is suitable for any number of visible beacons. The proposed method can be used for the navigation schemes based on range measurements provided by radio transceivers or other sensors for Mars entry. The observability of specific state is defined as its Fisher information based on the observation model. The overall navigation capability is improved by maximizing the minimum average Fisher information, even though the navigation system is not fully observed. In addition, when there is only one beacon capable of entry navigation and the observation information is relatively limited, the optimization method can be modulated to maximize the Fisher information of the specific state which may be preferred for the guidance and control system to improve its estimation accuracy. Finally, navigation scenarios consisted of 1–3 beacons are tested to validate the effectiveness of the developed optimization method. The extended Kalman filter (EKF) is employed to derive the state estimation error covariance. The results also show that the zero-Fisher information situation should be avoided, especially when the dynamic system is highly nonlinear and the states change dramatically.