# LCNS Positioning of a Lunar Surface Rover Using a DEM-Based Altitude Constraint
###### Abstract
In addition, serving one user at a time substantially limits the autonomy of assets on the lunar surface. To overcome this issue, several studies have considered dedicated lunar navigation systems [18; 20; 21] consisting of 1 or 2 satellites (potentially complemented by a pseudolite or reference station on the lunar surface) to augment the previously (e.g., visual odometry) mentioned technologies. As demonstrated in [18], using a joint Doppler and ranging approach, a relative (with respect to a reference station) positioning accuracy of 10-15 m can be obtained using 2 satellites and a surface beacon. An absolute accuracy of 100 m can be obtained globally after processing 2 h of observations. The LiASON (Linked Autonomous Interplanetary Satellite Orbit Navigation) concept exploits inter-satellite link range and range-rate data to compute relative and inertial absolute positioning, obtaining a navigation accuracy of 150 m (1-sigma) using the inter-satellite links alone. When adding 4 h of daily DSN (deep space network) observations, a navigation positioning accuracy on the order of 10 m can be achieved [21]. A dedicated LCNS, such as the one proposed within the ESA's Moonlight initiative, would provide several advantages over the previously mentioned technologies. First of all, its performance is not dependent on illumination conditions. This is important as rovers may need to traverse permanently shadowed regions on the lunar South Pole [22] as these may contain water ice [23]. Secondly, it would improve the autonomy of the rover as it passively uses the LCNS signals in one-way ranging mode (i.e., it will not actively use resources of the LCNS satellites for navigation purposes). Thirdly, the navigation accuracy is not governed by the size and shape of features that are used to register local and global maps. Finally, the positioning accuracy is only marginally impacted by the accuracy of available maps (e.g., DEMs and feature maps). This paper presents the results of a covariance analysis covering the navigation performances achievable by a lunar rover using the Moonlight navigation service as received by a Moonlight user together with inertial measurement units (IMU) and DEM information. This contribution considers a lunar traverse covering the South Pole. The considered algorithm is based on an extended Kalman filter (EKF) in which the altitude is constrained (with respect to the lunar ellipsoid) by the DEM available onboard the rover, allowing for complete autonomy from ground operations. This not only improves the accuracy of the rover position but also enables the rover to compute its position using only 3 satellites (contrary to the 4 satellites that are typically required for terrestrial global navigation satellite systems (GNSS) receivers), thereby improving the availability of the LCNS service. The uncertainty of the DEM is monitored considering the uncertainty of the DEM (due to interpolation and orbital errors) and the uncertainty of the rover position (which can result in a large altitude uncertainty near the edge of a crater). Thanks to detailed maps generated by the measurements performed by the LOLA (Lunar Orbiter Laser Altimeter) instrument [24] flying in the Lunar Reconnaissance Orbiter (LRO) [25], DEMs are available covering the South Pole at a resolution of 5 m per pixel and a geolocation uncertainty of 10-20 cm horizontally and 2-4 cm vertically [26]. This paper is structured as follows. Section 2 provides an overview of the lunar rover traverse used and its characteristics. Section 3 describes the LCNS constellation considered in this publication as well as the characteristics of the rover, including the satellite orbits, payload characteristics and rover receiver. Section 4 addresses the mathematical formulation of the covariance analysis. Section 5 reports the results of the simulations, and Section 6 provides the conclusive remarks.