This paper presents an algorithm that uses a Mul-tiplicative Extended Kalman Filter to estimate the deterministic errors of a gyroscope in spacecraft applications. These errors include bias, scale factors, and misalignment errors. To develop and test the algorithm, the angular movement of a spacecraft during various maneuvers is modeled. Two sensor readings, one from a gyroscope and the other from a star tracker, are obtained based on the angular movement model, with possible errors added. Then, a base estimation algorithm is developed, which estimates quaternions and angular velocities. This algorithm is tuned and tested to ensure its accuracy. Once the accuracy of the base filter is verified, it is expanded to estimate errors. Finally, a fully developed algorithm is tested with different cases. Results show that the algorithm is accurate for all simulations.