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.

This study analyses the GPS velocity estimation performances of three different estimation models, namely, the time-differenced carrier phase velocity estimation (TDCPVE), Doppler observation velocity estimation (DopplerVE), and precise point positioning velocity estimation (PPPVE). Static and vehicle kinematic experiments are conducted for validation. Under simulated kinematic conditions using static data, the accuracy of the DopplerVE is the worst, and the precision of the velocity by the PPPVE is the same as with the TDCPVE. Under kinematic conditions, the accuracies of the three methods are related to the motion state of the mobile carrier (such as its acceleration and turning). When the sampling interval is 1 s, the TDCPVE can obtain precise velocity using a singlefrequency stand-alone GPS receiver; the TDCPVE and DopplerVE can obtain accuracies of the same order of magnitude with broadcast and precise ephemerides, and can be used for real-time velocity measurement; the PPPVE can obtain not only an accurate position, but also an accurate velocity.

A new algorithm for geophysical map-aided navigation is proposed. It does not require any preliminary estimation of the field measured along the vehicle trajectory and, as consequence, does not need any stochastic field model. The algorithm uses a whole set of the available geophysical field measurements. The accuracy analysis procedure applied to estimate the effectiveness of the proposed algorithm is described. The features and advantages of this algorithm are illustrated by an example of marine gravity-aided navigation.

According to well-described literature concerning the work history of multipath mitigation in the global navigation satellite systems (GNSS), multipath is still the most dominant factor in a challenging environment. There are unperturbed harsh circumstances where GNSS signals cannot reach and smartphone navigation is not possible. The main objective of this research is to find an accurate solution for pedestrian smartphone navigation in a multipath environment. Experiments are done with micro-electro-mechanical system (MEMS) sensors mounted on a smartphone, and no extra hardware is needed. The latest Android smartphone is used to log the data files of GNSS and MEMS sensors. This scheme has been classified in the synopsis, and a rectangular route with three perpendicular turns has been selected for a pedestrian walk. The data is preprocessed using a low pass filter to remove high-frequency noise and smooth the signal. The description of accumulative error produced by the heading and step size estimation has been reduced by implementing the indices of mean cumulative heading error and cumulative step length error, respectively. In the end, the suboptimal extended Kalman filter algorithm is used to fuse the data of GNSS and pedestrian dead reckoning (PDR) for final results. In this paper, we try to give a technique to provide accurate pedestrian smartphone navigation. The fusion results show that the prospective method explores the possibility to use smartphone navigation in any case when GNSS or PDR information is not available. Substantial simulations are implemented and corroborate that the schemed method is sturdier to use in a harsh environments. The aim is to achieve high-level accuracy with an ultra-low-cost solution.

The article considers a problem of autonomous underwater vehicle (AUV) positioning with acoustic measurements of range and possibly radial velocity relative to a single beacon, velocity components and coordinate increments from an inertial navigation system, and the data from a water-speed log or a ground log. Interruptions are admitted in reception of acoustic measurements. Availability of a priori information on mutual position of AUV and the beacon is not assumed. In order to solve the problem, the author proposes a multiple model algorithm based on a bank of extended Kalman filters which independently estimate the initial horizontal range and errors of the used data under different hypotheses about a value of AUV initial azimuth relative to the beacon. Current coordinates of AUV are determined by the outputs of filters, taking into account the a posteriori probabilities of the corresponding hypotheses. The algorithm is rather simple for programming and does not require much computational power.