Future science-driven missions to Mars will require advanced guidance and navigation algorithms that are able to adapt to more demanding mission requirements by landing at selected locale with pinpoint accuracy while autonomously flying fuel-efficient trajectories. Current practice for navigation as applied to the powered descent phase of a Mars landing estimates the lander's downrange and crossrange position using inertial measurements and the lander's elevation using radar altimetry. As a consequence, only the lander's altitude may be accurately estimated, and downrange and crossrange position estimation errors that accumulate between the cruise stage separation and landing results in downrange and crossrange position uncertainties on the order of several kilometers. In this paper we present a novel real-time navigation algorithm that uses radar altimetry, a digital terrain model, and a particle filter to estimate the lander's position to an accuracy of several meters. We demonstrate how the navigation algorithm can be coupled with ZEM/ZEV guidance to achieve pinpoint landings on two targets unreachable using current practice: The bottom of Zumba crater and a hilltop in Uzboi Valis.