Knowing the location and the orientation of a wheelchair has its importance in a lot of health care surveillance applications. Though a lot of works have dedicated to this topic, none of them took the advantage of the 3D geometry nature of the wheelchair. This paper presents a novel way of determining the location and orientation of a wheelchair in the 3D world. We only need one perspective of the wheelchair and the calibration information to perform our algorithm. We improve a proposed mathematic method of ellipse-circle geometry by introducing it to a more generalized camera model and tested our algorithm in simulated and noisy real-data. The experiment shows good accuracy in both simulated and real data.