Any sort of autonomous task is predicated on a system's ability to sense its surroundings, as a way to understand its current state before deciding what its next action should be in order to achieve a determined goal. For mobile robot navigation, an accurate model for terrain representation is crucial, since it dictates which areas the vehicle can traverse safely and which ones would result in a collision, or some other sort of unfavorable outcome. The main challenges in creating an accurate terrain model lie in the presence of measurement uncertainties, data incompleteness and handling details in unstructured areas, which becomes even more challenging in large-scale scenarios, which is the case for most current applications. Any sensor is inherently inaccurate, and these inaccuracies are compounded by uncertainty in vehicle localization, as new data is collected during navigation to produce a global representation of observed areas. Data point density rapidly decays as we move away from the sensor, creating low-resolution areas in which large portions of the environment within range remain unobserved. Terrain details (i.e. sharpness and sudden discontinuities) should be correctly captured for an accurate representation of observed data, however if the model is too complex it might overfit and produce poor estimates under testing conditions.
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