Abstract <p>Calibration of a strapdown inertial navigation system (SINS) on a simple turntable is considered. SINS calibration is carried out in the autonomous mode, relying only on the SINS sensors. One of the well-known algorithms for calibration in this scenario is the algorithm based on the extended Kalman filter proposed by N.A. Parusnikov. The algorithm is accurate enough, so that under certain assumptions, it is close to optimal. Some difficulties in its application are due to linearization of the problem, which requires the knowledge of initial approximation of the parameters to be calibrated. As an alternative, an algorithm based on the Fourier transform and subsequent transition to data spectrum analysis is proposed, after which the calibration algorithm becomes purely algebraic and does not involve any convergence problems. The accuracy of the proposed algorithm, as well as its nonoptimality are discussed through the comparison with the theoretical Cramer Rao bound.</p>