In this study, a two-stage approach for estimation of spacecraft's position and velocity by single station antenna tracking data is proposed. In the first stage, direct nonlinear antenna measurements are transformed to linear x-y-z coordinate measurements of spacecraft's position, and statistical characteristics of orbit determination errors are analyzed. Variances of orbit parameters' errors are chosen as the accuracy criteria. In the second stage, the outputs of the first stage are improved by the designed Unscented Kalman Filter (UKF) for estimation of the spacecraft's position and velocity on indirect linear x-y-z measurements. In simulations, position and velocity values of a geostationary satellite are found via proposed two-stage procedure.