This paper describes a precision positioning technique that can be applied to vehicles or mobile robots in urban or leafy environments. Currently, the availability of satellite positioning is anticipated to improve because of the presence of various positioning satellites such as GPS of the U.S., GLONASS of Russia and GALILEO of Europe. However, because of the serious impact of multipath on their positioning accuracy in urban or leafy areas, such improvements in the availability of satellite positioning do not necessarily also facilitate high precision positioning. Our proposed technique mitigates GPS and GLONASS multipath by means of an omnidirectional infrared (IR) camera that can eliminate the need for invisible satellites by using IR images. With an IR camera, the sky appears distinctively dark. This facilitates the detection of the borderline between the sky and the surrounding buildings, which are captured in white, because of the difference in the atmospheric transmittance rates between visible light and IR rays. The proposed technique can automatically and robustly mitigate GPS and GLONASS multipath by excluding the invisible satellites. Positioning evaluation was carried out only with visible satellites that have less multipath errors and without using invisible satellites. The evaluation results confirm the effectiveness of the proposed technique and the feasibility of its highly accurate positioning.