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In this paper, we present a new approach to the problem of simultaneously localizing a group of mobile robots capable of sensing one another. Each of the robots collects sensor data regarding its own motion and shares this information with the rest of the team during the update cycles. A single estimator, in the form of a Kalman filter, processes the available positioning information from all the members of the team and produces a pose estimate for every one of them. The equations for this centralized estimator can be written in a decentralized form, therefore allowing this single Kalman filter to be decomposed into a number of smaller communicating filters. Each of these filters processes the sensor data collected by its host robot. Exchange of information between the individual filters is necessary only when two robots detect each other and measure their relative pose. The resulting decentralized estimation schema, which we call collective localization, constitutes a unique means for fusing measurements collected from a variety of sensors with minimal communication and processing requirements. The distributed localization algorithm is applied to a group of three robots and the improvement in localization accuracy is presented. Finally, a comparison to the equivalent decentralized information filter is provided.