  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.
