This paper presents an indoor localization approach that determines the absolute position of a mobile robot platform with centimeter precision by fusing RFID localization results based on cost-effective, standard passive UHF RFID technology with the robot's odometry data. The mobile robot platform is equipped with a multistatic UHF RFID interrogation system, and several RFID tags are arbitrarily placed within the localization environment, serving as landmarks. The RFID localization concept is based on phase evaluations. To overcome the problem of ambiguous position estimations due to the 2πphase ambiguity of the RFID signal phase and mitigate the linearization problem of the nonlinear system, a novel algorithm based on an iterative multihypothesis Kalman filter is introduced. A realistic simulation setup is developed to validate the proposed filter algorithm. By tracking a UHF RFID-equipped mobile robot platform in a real-world office environment, the proposed approach is also practically tested in terms of real-time capability, everyday suitability, and multipath resistance. Given that centimeter precision is only achieved in environments with weak multipath propagation, the RFID localization results are fused with odometry data provided by the robot. This effectively compensates for offset and drift in the odometry sensor, achieving a root-mean-square localization error of 2.7 cm.