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Localization and navigation not only serve to provide positioning and route guidance information for users, but also are important inputs for vehicle control. This paper investigates the possibility of using odometry to estimate the position and orientation of a vehicle with a wheel individual steering system in omnidirectional parking maneuvers. Vehicle models and sensors have been identified for this application. Several odometry versions are designed using a modular approach, which was developed in this paper to help users to design state estimators. Different odometry versions have been implemented and validated both in the simulation environment and in real driving tests. The evaluated results show that the versions using more models and using state variables in models provide both more accurate and more robust estimation.