Context. The article discusses the issues of increasing the accuracy of automatic control of a moving object using a mathematical model of a meter and a device observing measurement errors in the on-board controller of the control system. The object of the research is the processes of automatic control of a moving object with a mathematical model of a meter and a device observing measurement errors in the on-board controller of the control system. The subject of the research is a method and algorithms for increasing the accuracy of automatic control of a moving object with a mathematical model of a meter and a device observing measurement errors in the on-board controller of the control system.Objective. The aim of research is an improving the accuracy of automatic control of a moving object.Method. This aim is achieved through the use in the on-board controller of the control system of the mathematical meter model and the observing device built on its basis, the estimation of the useful component and the systematic error, depending on the motion parameters of the controlled object, using only the useful component for control, without systematic error.Results. A method and algorithms for increasing the control accuracy of a moving object through the use in the on-board controller of a mathematical meter model and an observer of systematic measurement errors, built on its basis, have been developed. The efficiency and effectiveness of the developed method and algorithms were confirmed by mathematical modeling in the MATLAB environment of the control processes of a moving object in a closed circuit with a control system.Conclusions. The results of mathematical modeling confirmed the operability and efficiency of the proposed method and algorithms and allow them to be used for practical purposes in the development of mathematical support for high – precision automatic control systems.