A general approach is presented for the estimation of spacecraft attitude from rate gyroscope measurements of angular velocity and indirect inertial orientation measurements obtained from a pair of star sensors. The estimation algorithm is developed in such a way that the measured minus estimated angular velocity residuals are consistent with the apriori knowledge of the instrument error variance. The angular velocity history is modeled as a Fourier Series. whereas the attitude is modeled as the solution of the appropriate kinematic differential equations. The study presented addresses computer implementation issues and provides numerical results from several simulated attitude and velocity histories. The software is presented in FORTRAN code in an appendix. / Master of Science