The paper proposes a human-following behavior of mobile robot and an intelligent space (ISpace) is used in order to achieve these goals. An ISpace is a 3-D environment in which many sensors and intelligent devices are distributed. Mobile robots exist in this space as physical agents providing humans with services. A mobile robot is controlled to track a walking human using distributed intelligent sensors as stably and precisely as possible. The moving objects is assumed to be a point-object and projected onto an image plane to form a geometrical constraint equation that provides position data of the object based on the kinematics of the intelligent space. Uncertainties in the position estimation caused by the point-object assumption are compensated using the Kalman filter. To generate the shortest time trajectory to track the walking human, the linear and angular velocities are estimated and utilized. The computer simulation and experimental results of estimating and trackinging of the walking human with the mobile robot are presented.