Self-localization and object tracking are key technologies for human-robot interactions. Most previous tracking algorithms focus on how to correctly estimate the position, velocity, and acceleration of a moving object based on the prior state and sensor information. What has been rarely studied so far is how a robot can successfully track the partially observable moving object with laser range finders if there is no preanalysis of object trajectories. In this case, traditional tracking algorithms may lead to the divergent estimation. Therefore, this paper presents a novel laser range finder based partially observable moving object tracking and self-localization algorithm for interactive robot applications. Dissimilar to the previous work, we adopt a stream field-based motion model and combine it with the Rao-Blackwellised particle filter (RBPF) to predict the object goal directly. This algorithm can keep predicting the object position by inferring the interactive force between the object goal and environmental features when the moving object is unobservable. Our experimental results show that the robot with the proposed algorithm can localize itself and track the frequently occluded object. Compared with the traditional Kalman filter and particle filter-based algorithms, the proposed one significantly improves the tracking accuracy.