The Artemis program requires robotic and crewed lunar rovers for resource prospecting and exploitation, construction and maintenance of facilities, and human exploration. These rovers must support navigation for 10s of kilometers (km) from base camps. A lunar science rover mission concept ("Endurance-A") has been recommended by the new Decadal Survey as the highest priority medium-class mission of the Lunar Discovery and Exploration Program, and would be required to traverse approximately 2000 km in the South Pole-Aitkin (SPA) Basin, with individual drives of several kilometers between stops for downlink. These rover mission scenarios require functionality that provides onboard, autonomous, global position knowledge ("absolute localization"). However, planetary rovers have no onboard global localization capability to date; they have only used relative localization, by integrating combinations of wheel odometry, visual odometry, and inertial measurements during each drive to track position relative to the start of each drive. At the end of each drive, a "ground-in-the-loop" (GITL) interaction is used to get an absolute position update from human operators in a more global reference frame. As a result, autonomous rover drives are limited in distance so that accumulated relative navigation error does not risk the possibility of the rover driving into a "keep-out zone"; in practice, drive limits of a few hundred meters are to be expected. In this work, we summarize recent developments from the LunarNav project, where we have developed algorithms and software to enable lunar rovers to estimate their global position and heading on the Moon with a goal performance of position error less than 5 meters (m) and heading error less than 3 degrees, 3 sigma, in sunlit areas. This new capability will eliminate the need for GITL interactions with human operators for lunar rover global position estimation, which will substantially increase operational productivity of lunar rovers and will reduce operations costs. This will be achieved autonomously onboard by detecting craters in the vicinity of the rover and matching them to a database of known craters mapped from orbit. The overall technical framework consists of three main elements: 1) crater detection, 2) crater matching, and 3) state estimation. In previous work, we developed crater detection algorithms for three different sensing modalities. This paper builds on that work, and focuses on the crater matching and state estimation aspects of the problem. In particular, we developed two algorithms for crater-based localization, and demonstrated them on datasets of both real and simulated lunar data, in representative environments. Our results suggest that rover localization with an error less than 5 m is highly probable during daytime operations.