Observability-based beacon configuration optimization for Mars entry navigation

In this paper, a novel observability analysis method of a nonlinear navigation system is proposed, and its application to the optimization of beacon configuration for Mars entry navigation is demonstrated. A Lie algebrabased approachto nonlinear observability is used to compute the observability matrix. The quadratic approximation to the Lie derivatives is then used to recursively calculate the observability matrix efficiently. Next, the inverse of the condition number of the observability matrix is chosen as a metric to evaluate the observability quality. To verify the accuracy and effectiveness of the proposed approach, Mars navigation scenarios with ranging measurements from multiple ground-based beacons are considered in simulation examples, and the optimal beacon configurations are obtained using a genetic algorithm. The extended Kalman filter is finally used to demonstrate the navigation performance.Itisconcluded that the proposed observability analysis methodis able tooptimize the beacon configuration of the Mars entry navigation system accurately and efficiently. For Mars entry navigation using ground-based beacons, the geometric configuration of the entry vehicle and beacons is a main contributor to the observability. A diminishing return of observability is obtained solely by adding beacon numbers.