The present paper considers a new measurement concept of modeling measuring instruments for gyro-free determination of the parameters of moving objects. The proposed approach eliminates the disadvantages of the existing measuring instruments since it is based, on one hand, on a considerably simplified mechanical module, and on the other hand, on the advanced achievements in the area of nanotechnologies, microprocessor and computer equipment. A specific measuring system intended for measuring the trim, heel, roll, and pitch of a ship has been developed in compliance with the basic principles of this concept. The high dynamic accuracy of this measuring system is ensured by an additional measurement channel operating in parallel with the main channel. The operating principle of the additional measurement channel is based on an appropriate correction algorithm using signals from linear MEMS accelerometers. The presented results from the tests carried out by means of stand equipment in the form of a hexapod of six degrees of freedom prove the effectiveness of the proposed measurement concept.