It is proposed and researched algorithm of accelerated alignment in motion of an integrated navigation system, which consists of a strapdown inertial navigation system (SINS) and a satellite navigation system (SNS). Such a standard SNS is considered, in which orientation angles are not determined, that is, heading, pitch, roll. The algorithm is suitable for use on objects where the velocity vector coincides with the longitudinal axis of the object, that is, the heading angle coincides with the path angle. These can be ground vehicles, other vehicles at zero drift (wear) angles. The paper examines the estimation of the error of the heading alignment, because the heading alignment (gyrocompassing) is usually the most difficult procedure of the initial alignment. When determining the heading error, the benchmark is the heading that can be determined from the satellite speed readings or from the readings of the hybrid navigation system, which is built on the SINS algorithm, in which the speed is not determined, but the speed from the SNS is used. The study was conducted by modeling. At the same time, the standard characteristics of SNS, gyroscopes and accelerometers are taken into account. For comparison, a simulation of the well-known integrated SINS was also carried out using a weakly coupled open integration scheme (compensation scheme) using the Kalman filter (FK). It is shown that the determination of the error can be performed in a few seconds, if the SNS is already working in normal mode. The accuracy of the determination increases with an increase in the speed of movement and the frequency of issuing input data. The proposed algorithm shows higher accuracy than the FK algorithm. In the given example, for a ground object in 30 s, the accuracy of the alignment is less than 5 arc.min.