In this paper, we propose a way to model the resilience of the Iterative Closest Point (ICP) algorithm in the presence of corrupted measurements. In the context of autonomous vehicles, certifying the safety of the localization process poses a significant challenge. As robots evolve in a complex world, various types of noise can impact the measurements. Conventionally, this noise has been assumed to be distributed according to a zero-mean Gaussian distribution. However, this assumption does not hold in numerous scenarios, including adverse weather conditions, occlusions caused by dynamic obstacles, or long-term changes in the map. In these cases, the measurements are instead affected by large and deterministic faults. This paper introduces a closed-form formula approximating the pose error resulting from an ICP algorithm when subjected to the most detrimental adverse measurements. Using this formula, we develop a metric to certify and pinpoint specific regions within the environment where the robot is more vulnerable to localization failures in the presence of faults in the measurements.
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