This paper describes the design of a Coordinates Tracking algorithm for EOTS and its error analysis. EOTS stabilizes the image sensors such as FLIR, CCD TV camera, LRF/LD, and so on, tracks targets automatically, and provides navigation capability for vehicles. The Coordinates Tracking algorithm calculates the azimuth and the elevation angle of EOTS using the inertial navigation system and the attitude sensors of the vehicle, so that LOS designates the target coordinates which is generated by a Radar or an operator. In the error analysis in this paper, the unexpected behaviors of EOTS that is due to the time delay and deadbeat of the digital signals of the vehicle equipments are anticipated and the countermeasures are suggested. This algorithm is verified and the error analysis is confirmed through simulations. The application of this algorithm to EOTS will improve the operational capability by reducing the time which is required to find the target and support especially the flight in a night time flight and the poor weather condition.