Multi-robot system attracted attention in various applications in order to replace the human operators. To achieve the intended goal, one of the main challenges of this system is to ensure the integrity of localization by adding a sensor fault diagnosis step to the localization task. In this paper, we present a framework able, in addition of localizing a group of robots, to detect and exclude the faulty sensors from the group with an optimized thresholding method. The estimator has the informational form of the Kalman Filter (KF) namely Information Filter (IF). A residual test based on the Kullback-Leibler divergence (KLD) between the predicted and the corrected distributions of the IF is developed. It is generated from two tests: the first acts on the means and the second deals with the covariance matrices. Thresholding using entropy based criterion and Receiver Operating Characteristics (ROC) curve are discussed. Finally, the validation of this framework is studied on real experimental data from a group of robots.