A Comparison of Navigation Methods Enabled by a Deep Space Relay Architecture

A deep space relay architecture for communication and navigation was developed in two previous papers. The baseline architecture, consisting of a Mars leading and a Mars trailing relay, was designed to mitigate the Mars conjunction problem for optical communication while enabling deep space trilateration for inner solar system users. An expanded version of the architecture added a Mars halo relay which improved the architecture's data throughput and navigation potential. This paper further defines the navigation component of the architecture. Previous analysis assumed trilateration with idealized, instantaneous one- and two-way range measurements. Here, more realistic one- and two-way range measurement approaches are developed. A broadcast one-way range measurement mode is developed which offers benefits of user scalability and more timely positioning estimates. A point-to-point measurement mode, compatible with both one- and two-way range measurements, is developed as an alternative to the broadcast mode that levies less demanding time synchronization and antenna sizing requirements on the user. Pseudo-noise code-based ranging approaches compatible with each measurement mode are identified and a link analysis is performed to determine user service volumes and relay hardware requirements. The point-to-point measurement mode is found to be viable for even CubeSat-sized users throughout the inner solar system, while the broadcast measurement mode requires users with antenna diameters on the order of meters. The concept of a “deep space trilateration” algorithm is developed, in which the measurement models incorporate signal propagation time and the motion of users relative to the measurement providing nodes, both of which are non-negligible effects at deep space distances. Position estimation using the deep space trilateration method is simulated in a batch filter. This filter was found to converge even when presented with initial position errors of thousands of kilometers. The accuracy and timeliness of position estimates for a Mars cruise user are found to be on the order of 10 meters and 1 hour respectively, assuming 2-meter range measurement error.