On the observability of Mars entry navigation using radiometric measurements

• The beacon configuration had the major impact on the observability of an entry vehicle’s position and velocity.
• An improved observability and accuracy can be achieved by employing more beacons.
• The lower-bound of estimation errors in range-rate measurement case might be larger than that in range measurement case.
• Uncertainty in the initial states and atmospheric density both strongly affect the observability.

A thorough observability analysis of the Mars entry navigation using radiometric measurements from ground based beacons is performed. This analysis involves the evaluation of the Fisher information matrix which is derived from the maximum likelihood estimation. A series of navigation cases with multiple beacons are investigated, and both range and range-rate measurements are considered. The determinant of Fisher information matrix is used to quantify the observability of navigation system, while the trace of Fisher information matrix is used to determine the lower-bound of estimation errors. For one and two beacon cases, the navigation system is unobservable. However, the eigenvectors of Fisher information matrix give the observable and unobservable component. When three or more beacon measurements are employed, the states of entry vehicle become observable. Some valuable analytic conclusions on the relationship between the geometric configuration of beacons and observability are obtained consequently. Finally, simulation results from two navigation examples indicate that our effort is useful for understanding and assessing the observability of the Mars entry navigation using radiometric measurements.