A systematic analysis of the observability of a strap down inertial navigation system (SDINS) in ground alignment with Bar-Itzhack and Berman's error model is presented. It is shown that the unobservable states are separately contained in two de-coupled subspaces. The constraints on the selection of unobservable states are discussed. An estimation algorithm, which is derived fully from the horizontal velocity outputs for computing the misalignment angles, is provided. It reveals that the azimuth error can be entirely estimated from the estimates of leveling error and leveling error rate, without using gyro output signals explicitly. Moreover, estimate of the strap down inertial navigation systems errors are presented using appropriate Kalman filter design.