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The problem of quantifying robot localization safety in the presence of undetected sensor faults is critical when preparing for future applications where robots may interact with humans in life-critical situations; however, the topic is only sparsely addressed in the robotics literature. In response, this work leverages prior work in aviation integrity monitoring to tackle the more challenging case of evaluating localization safety in Global Navigation Satellite System (GNSS)-denied environments. Localization integrity risk is the probability that a robot’s pose estimate lies outside pre-defined acceptable limits while no alarm is triggered. In this article, the integrity risk (i.e., localization safety) is rigorously upper bounded by accounting for both nominal sensor noise and other non-nominal sensor faults. An extended Kalman filter is employed to estimate the robot state, and a sequence of innovations is used for fault detection. The novelty of the work includes (1) the use of a time window to limit the number of monitored fault hypotheses while still guaranteeing safety with respect to previously occurring faults and (2) a new method to account for faults in the data association process.