###### Abstract
In order to reduce the total cost of the system, including the user segment, a method that uses passive ranging is ideal, especially for the multiple rover missions that will occur in the future. Contrary to these previous studies, our research uses multi-epoch double-differenced pseudorange observations (MDPO), which is a passive system using a static reference station, and it works while accounting for the instability of both the satellite and user clocks. The comparison of the proposed method with other conventional methods is summarized in Table 1.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **User (Rover) Segment Burden** & **Space (Satellite) Segment Burden** & **Ground Segment Burden** \\ \hline Visual Sensor-based Navigation & Visual Sensor-based navigation when the lunar surface is flat with no landmarks. & - & - \\ \multirow{4}{*}{Accelerometers and Star Tracker Navigation} & Sensor alignment precision becomes outrageous to achieve high position accuracy. & - & - \\ \cline{2-4}  & & & \\  
In this study, we target mobile applications such as lunar rovers as users, which requires observation periods to be small. Since a method using only Doppler observation needs several tens of minutes of observation to provide a high user position accuracy [12], pseudorange observation data must be used. Besides this, regarding biases of the satellite and user clocks, methodologies using TOA or TDOA (pseudorange or single-differenced pseudorange) are insufficient because they were not designed to cope with both the satellite and user clock biases at the same time. Instead, in this study, double-differenced pseudorange was used to remove the bias of both the satellite and user clocks from the estimation (note that the double-differenced pseudorange is explained further in the following section). Moreover, our proposed method does not use frequency observation and uses the double-differenced pseudorange only, which can contribute to making the pseudorange receiver hardware design as simple as possible. Furthermore, in order to reduce the number of satellites, we introduce multi-epoch observations that use pseudorange measurements from multiple epochs (Figure 1). This paper consists of the following sections. In Section 2, the algorithm of MDPO is formulated and the expected accuracy of user position is discussed. In Section 3, the theoretical behavior of MDPO is confirmed by numerical simulation, along with achievable user position accuracy. Section 4 provides our conclusions. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **User (Rover) Segment Burden** & **Space (Satellite) Segment Burden** & **Ground Segment Burden** \\ \hline Two-way Ranging based Navigation & Active ranging between the satellite and user is required. & Two satellites in view are required, with no need for a stable satellite clock. & No need for frequent satellite clock bias estimation by the ground segment. \\ Dual Satellite MDPO Navigation (This research) & Use a passive ranging receiver with a static reference station. & Two satellites in view are required, with no need for a stable satellite clock. & No need for frequent satellite clock bias estimation by the ground segment. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 1: Overview of the MDPO concept in comparison with a conventional pseudorange-based method.