The paper considers the problem of improving the accuracy of determining the horizontal projections of linear velocity and coordinates of a moving cruising object by an autonomous inertial navigation system built on the basis of domestic  recision navigation accelerometers. Typically, these errors of such a system grow linearly and quadratically with the time of its autonomous operation. The main reason for this growth is the integration of instrumental additive errors of its horizontal accelerometers. It is proposed to intentionally form a harmonic character of the instrumental additive errors of horizontal accelerometers within an autonomous inertial navigation system. This leads to the fact that the errors in determining the horizontal projections of linear velocity do not increase in time during integration, and the errors in determining the coordinates increase only linearly in time during the second integration. This approach helps to improve the accuracy of the system and the possibility of increasing its autonomous operation time while ensuring the required accuracy. It is proposed to form the harmonic nature of the additive errors of horizontal accelerometers by rotating these accelerometers around the vertical axis of the object. A mathematical model for determining the horizontal projections of the linear velocity and coordinates of a moving object in the case of such a rotation of accelerometers, as well as a mathematical model of the errors of this determination, is obtained.
       The effectiveness of the proposed method of improving the accuracy of determining the horizontal projections of the linear velocity and coordinates of a moving object, as well as the adequacy of all the mathematical models obtained in this paper, has been confirmed by experimental studies.