## 1 Introduction
### DGNSS for the Moon  
Transitioning to a lunar GNSS scenario, being the focus scenario of the present contribution, ionospheric delays become less of a concern as most of the GNSS signals received at lunar altitudes did not propagate through the ionosphere [41; 42]. However, the relative dynamics between users orbiting the Moon become more complex as the typical stable lunar orbits are not circular as is the case for the terrestrial ones, given the presence of lunar mass concentrations [43]. Furthermore, the GNSS signals power levels received by a receiver in lunar orbit are weak causing the measurements to be noisier [41]. Hence, the measurements are affected by a large amount of uncorrelated errors and applying differential techniques could be less beneficial [42]. Also, in noisier environments and high dynamics systems, cycle slips are more frequent making the integer ambiguity resolution of the carrier phase measurements more challenging [44].  
As a contingency scenario, the present contribution aims to assess the feasibility of GNSS-based differential ranging techniques between two lunar orbiters using only pseudorange observables. The importance and originality of this study lies in that it explores, for the first time, the applicability of DGNSS ranging to users in lunar orbits. Most significantly, the experimental analysis was performed on a real spaceborne receiver, namely the very first ESA GNSS receiver that will fly all the way to the Moon in the context of the ESA's Lunar Pathfinder mission. This research aims to contribute to a deeper understanding of the potential and limitations of DGNSS in space.  
More specifically, this work shows that modeling assumptions used for linearization of the relationship between the inter-user vector and the pseudorange single and double differences taken for granted in terrestrial and LEO applications are violated in the case of lunar GNSS differential scenarios. Subsequently, it analyzes the possibility of updating the parallelism assumption while keeping the considered algorithm linear for low-complexity purposes and compares the common techniques with the updated ones. It shows that updating the modeling assumption significantly improved the performances with respect to the terrestrial standard algorithm by reducing the bias introduced by the increasing baseline. However, the performances seem to be bounded by the sum of the individual covariances on the measurements of each user involved in the process, as per the Absolute Positions Differencing (APD) presented in [23; 45].  
In practice, the results are obtained both theoretically through Monte Carlo simulations, by Matlab post-processing of data obtained from Systems Tool Kit (STK), and experimentally, in the Radio Navigation Laboratory of ESA, making use of GNSS observables generated by a GNSS receiver specifically designed for a Moon mission, through a Hardware-in-the-Loop (HWiL) set-up. The Moon receiver is called the NaviMoon and will be hosted by the Lunar Pathfinder space mission [46].  
The paper is structured as follows: Section 2 describes the fundamentals of the GNSS-based baseline estimation, describes the limitations of this assumption for a space scenario and proposes potential updates in the algorithm. Section 3 describes the space scenario considered for the present analysis, the architecture of the theoretical Monte Carlo simulations as well as the functional blocks of the test bench designed to test the presented techniques on the NaviMoon receiver. Finally, Section 4 presents the results achieved with this environment and Section 5 discusses the potential performances of inter-spacecraft GNSS ranging in space, showing that the various techniques presented seem to be lower bounded by taking the difference of the individual Single Point Position (SPP).