This thesis presents an algorithm for the estimation of the Euler angles in the satellite attitude determination problem. The whole algorithm consists of two parts. In the first phase, a new polygon matching algorithm is used to identify the observed star pattern by the sensor with the known star pattern stored in the star database. For faster and more accurate matching, we devise the star database by collecting only position invariant characteristics of stars. In the second phase, an extended Kalman filter is used to process a sequence of identified unit vector pairs to obtain the minimum variance estimate of the Euler angles which present the attitude of the satellite. Simulation results are presented to demonstrate the accuracy of the proposed algorithm.