Improved Surface Positioning with Measurement Differences in Joint Doppler and Ranging

Abstract

Measurement differencing with GPS is an important method to reduce shared error between a user and a nearby reference station. It may also be crucial for position, navigation, and timing of lunar surface users. In conjunction with a relative positioning method, users on the surface of the Moon can utilize measurement differencing to achieve high accuracy, real-time positioning. This report analyzes improvements in surface positioning performance with single and double differenced measurements implemented with Joint Doppler and Ranging (JDR). JDR is a relative Doppler and range-based positioning method that can localize a surface user with a minimal navigation infrastructure. Previous analyses show JDR is effective at positioning lunar surface users near a reference station with as few as a single satellite. This analysis introduces updated implementations of JDR with the use of single and double differencing for both code-based range and Doppler measurements. These implementations include three total differencing methods with JDR along with comparisons of their positioning performance. Along with the known benefits provided by differencing code-based range measurements, differencing Doppler measurements enables cancellation effects of transmitted and local frequency offsets. This report performs a navigation simulation to calculate position estimation performance for a lunar surface user. This simulation assumes two Lunar Relay Satellites (LRS) in 12-hour frozen orbits as navigation nodes with a pre-existing reference station located on the south pole of the Moon. Modelled simulation errors include satellite ephemeris and reference station errors as Gaussian variables and satellite and user frequency errors as Brownian noise processes. These bias and noise sources are carefully distinguished between navigation nodes to ensure that the user and reference station see the proper shared error. Results show significant improvements in navigation performance with double differenced JDR (DD-JDR) relative to standard JDR and single differenced JDR (SD-JDR). DD-JDR can also reduce the effects of user local oscillator errors, including frequency offsets and noise. The reduction of these shared errors not only leads to improved positioning accuracy, but also results in lower timing hardware and receiver hardware requirements for the user. This greatly decreases cost and increases compatibility of JDR for autonomous lunar surface users.