Modern gyroscopy is characterized by a great diversity of gyroscopes that have been and are being developed. Dominant positions belong to wave optic gyroscopes implementing the relativistic Sagnac effect, and micromechanical vibratory gyroscopes the operating principle of which is based on Coriolis effect. At the same time, high-precision rotor mechanical gyroscopes based on the principles of rotating solid body dynamics partially retain their position; also, the research of gyroscopes developed on the principles of nuclear physics and quantum optics is progressing successfully. Current state and the prospects of gyroscopes development are discussed in this paper.

Reduction of optical quantum sensors in size, including nuclear magnetic resonance (NMR) gyroscopes, implies primarily downsizing of the working gas cell. This paper considers the dependence of isotope shift in the balanced scheme based on NMR in xenon isotopes on the dimensions of the gas cell. With this aim in view, an experimental and theoretical studies of the factors affecting the relaxation rate of xenon isotopes have been carried out. The proposed numerical model allows predicting the magnitude of the isotope shift for cells of various sizes with variations in their basic parameters, namely, temperature and pressure of the gas mixture. Based on the results of the numerical simulation, recommendations are given for optimizing the basic parameters of the gas cell by changing its dimensions.

A new mathematical model is constructed for the motion of a single-crystal resonator of a wave solid-state gyroscope in the form of a thin elastic shell of revolution on a moving base, taking into account the influence of an electrostatic oscillation excitation system. When compiling the expression for the potential energy of elastic deformation of the resonator, a low anisotropy of the cubic crystal type was taken into account, depending on the resonator orientation relative to the crystallographic axes. A discrete model is used to describe the energy of the electrostatic field of control sensors. Using the Lagrange-Maxwell formalism, nonlinear differential equations are obtained that describe, in the single-mode approximation, the oscillations of the elastic shell of revolution on a moving base. The forced and free oscillations of the resonator are considered. It is shown that a bias caused by anisotropy of the elastic properties of the resonator can be compensated by the effect of electrostatic forces of the control sensors. Control signals are proposed to compensate these errors.

The paper studies the problem of reducing the errors of heading and pitch/roll angles for a strapdown inertial navigation system (SINS) based on fiber-optic gyroscopes (FOG) of navigation accuracy grade during a vessel maneuvering. The solution of the problem is analyzed mainly for autonomous mode of the system operation using the water speed log data. A specific feature of the studied solution is that the gyro drifts and accelerometer biases are estimated only during the vessel maneuvering, based on the log data. In this case, an attribute is formed for the vessel’s maneuver start. The results of simulation, test-bench and field tests of the SINS on FOGs of navigation accuracy grade during the vessel maneuvering are presented, with the data of the system’s measurement unit, GNSS-receiver and log having been processed in MATLAB (Simulink) software, taking into account the simulation of ocean currents and vessel drift.