This paper presents a method for state estimation on a ballbot; i.e., a robot balancing on a single sphere. Within the framework of an extended Kalman filter and by utilizing a complete kinematic model of the robot, sensory information from different sources is combined and fused to obtain accurate estimates of the robot's attitude, velocity, and position. This information is to be used for state feedback control of the dynamically unstable system. Three incremental encoders (attached to the omniwheels that drive the ball of the robot) as well as three rate gyroscopes and accelerometers (attached to the robot's main body) are used as sensors. For the presented method, observability is proven analytically for all essential states in the system, and the algorithm is experimentally evaluated on the Ballbot Rezero.