The paper presents a new method for building measuring instruments and systems for gyro-free determination of the parameters of moving objects. To illustrate the qualities of this method, a system for measuring the roll, pitch, heel and trim of a ship has been developed on its basis. The main concept of the method is based, on one hand, on a simplified design of the base coordinate system in the main measurement channel so as to reduce the instrumental errors, and, on the other hand, on an additional measurement channel operating in parallel with the main one and whose hardware and software platform makes possible performing algorithms intended to eliminate the dynamic error in real time. In this way, as well as by using suitable adaptive algorithms in the measurement procedures, low-cost measuring systems operating with high accuracy under conditions of inertial effects and whose parameters (intensity and frequency of the maximum in the spectrum) change within a wide range can be implemented.