Modern mobile objects have significantly higher velocities, they are significantly more overloaded and uncontrollable mechanical disturbances (shocks, vibrations). Therefore, the requirements for the accuracy of means and methods for measuring the above-defined mechanical values of the instrument navigation complex have become much higher. However, the imperfection of the element base, the absence of new modern sensitive elements, the lack of the use of a new improved shock protection system, the lack of modern algorithmic methods do not allow to significantly improve accuracy and improve tactical and technical characteristics. The object of research in this work is the process of measuring the angular velocity and acceleration of a gyrostabilized platform. Ensuring the accuracy of the arms stabilizer is the most important modern problem, the solution of which ensures the security of Ukraine. According to tactical characteristics, the new weapon stabilizer expands combat capabilities of armored vehicles due to more precise guidance and stabilization on the target, facilitates the crew’s ability to control the tower. Instrumental weapon stabilizer complexes are designed for stabilized guidance and tracking in the horizontal and vertical planes of surface, air and surface targets. The use of a modern element base has significantly improved the characteristics of the entire range of the weapon stabilizer. According to the technical characteristics of the arms stabilizer, it expands the combat capabilities of armored vehicles through more precise guidance and stabilization on the target, facilitates the crew’s ability to control the tower. And also does not require redirection to the same goal after the shot. In this paper, an algorithm is considered that is applied when adjusting the position of the implement relative to the target during rapid joint movement of the tower and the machine. The algorithm is calculated in the mathematical block of the stabilization system. The algorithm is based on a mathematical analysis of the theory of motion of gyroscopes and improved from previous ones by supplementing the equation of motion. The formula is derived in the analytical form for its further application in the mathematical blocks of the stabilization system and calculations are given, as a result of which a mathematical model is obtained. If this mathematical model is introduced into the algorithmic block of the stabilization system, this will improve the accuracy of stabilization. The conclusions analyze the results and give recommendations on the application of the method.