Fundamental Limits of Map Relative Localization during Spacecraft Entry, Descent, and Landing

Map relative localization is the process of estimating the location of a lander with respect to the terrain of a celestial body. Visual or topographic maps obtained from orbit are matched with camera or LiDAR data acquired onboard the lander using correlation-based techniques. For given orbital map and descent image resolutions, terrain information content, and measurement noise, there are fundamental limits on the accuracy to which the lander can be localized. Knowledge of these limits is useful in designing and judging the optimality of an estimator, or setting realistic accuracy requirements. This paper derives and validates mathematical expressions that predict these fundamental limits. The derivation, based on application of the Cramér-Rao lower bound, exposes a maximum-likelihood estimator which is confirmed to approach the derived accuracy limits. This work will be useful in the design of future map relative localization systems, as it can be used to inform requirements on desired localization accuracy, and to determine if a near-optimal estimator has been designed.