In order to improve the measurement accuracy of borehole trajectory for inclinometer while drilling based on FOGs (FOGs-based IWD), Kalman filter is often used in combination measurement, so the misalignment angles of inclination, azimuth and tool face angle can be estimated. The estimation accuracy of attitude error is closely related to its observability, thus in order to improve the estimation accuracy, the observability in-drilling of attitude misalignment was analyzed by using piecewise linear constant system (PWCS) and singular value decomposition (SVD) under three drilling states of uniform speed, constant acceleration and uniform rotation. Then, the influences of inclination angle and rotation rate on the estimation accuracy of attitude misalignment were analyzed. Simulation results show that the azimuth misalignment angle is unobservable in uniform speed drilling. But the azimuth misalignment angle is observable in the uniform acceleration drilling and the observability is the strongest in the horizontal well. With the increase of inclination, the measurement accuracy of azimuth and inclination is improved. The observability and estimation accuracy of azimuth misalignment angle in rotary drilling are better than that in uniform and constant acceleration drilling. When the angular rate is increased from 0°/s to 5°/s, the estimation accuracy of attitude misalignment angle increases and tends to be stable. The rotation drilling movement proposed in paper can effectively improve the measurement accuracy of borehole trajectory.