The paper describes the current state of development of hemispherical resonator gyros (HRG). HRG is becoming the most perspective gyro for navigation systems of different applications. Its unique performance has made it a sensor of choice for the space industry. The gyro ensures high navigation accuracy while featuring smaller cost and size as compared to the ring laser and fiber-optic gyros. Multiple publications have been devoted to the HRG research and development. We provide a brief overview of publications describing the current state of the HRG technology and its further improvement and application.

A review of publications on the development of wave solid-state gyroscopes (SWG) with a metal resonator is presented; a typical design with piezoelectric elements used in the excitation and sensitivity modes is considered. The transfer functions of the angular rate sensor (ARS) based on the SWG (SWG-ARS) and the integrating gyroscope (SWG-IG) are obtained. The main technological features of the resonator manufacturing process are briefly described. The numerical values of unbalanced resonator edge vibrations are given. The SWG design is discussed, and the block diagram of the electronic module for the SWG-ARS operating in the compensation mode is given. The goals and features of tuning and calibration are described.
Temperature dependences of accuracy characteristics within specified ranges of angular rate and temperature variations are given.
Allan variances are analyzed, including those for different temperatures. The results of rotation, temperature, vibration and shock tests and the achieved accuracy of the SWGARS are discussed.

The paper discusses the modern state of optical resonator gyroscopes. The basic concept of this type of gyros is described. The main approaches to their design and the method for angular rate measurement are considered, with the main focus made on the pioneer and most popular approach based on the use of phase modulation spectroscopy and a tuned laser. An alternative approach based on low-coherent sources of light is also analyzed. The main sources of measurement errors and the methods to overcome them are considered. The best value of random drift has been so far achieved using fiber ring resonators: 2.0 deg/h with the ring diameter 60 mm and the integration time 1 s, and 1.23 deg/h in 5 s; with the diameter 120 mm, 0.37 deg/h has been achieved with the integration time 1 s and 0.06 deg/h with 370 s. The reasons that currently hinder the commercial development of optical resonator gyros are studied.

The paper presents a methodology of preparing and conducting airborne gravimetry survey using an inertial measuring unit (IMU) or strapdown inertial navigation system as an airborne gravimeter. We also discuss the key aspects of developing appropriate postprocessing algorithms and software and their application to processing raw gravimeter data. When solving the strapdown inertial airborne gravimetry problem, we use readings of the IMU sensors (accelerometers and gyroscopes) as primary information. The second no less important information is the raw (pseudorange, Doppler pseudorange rate, and carrier phase) measurements from the GNSS receivers onboard the aircraft and on the ground. The developed methodology, algorithms, and practical recommendations presented in the paper are based on the authors’ long-term experience in airborne gravimetry.

In strapdown airborne gravimetry, initial alignment of the gravimeter’s inertial measurement unit (IMU) is of great importance. It is performed to determine the gravimeter attitude angles from the IMU measurements at the aircraft standstill before the survey flight. Knowing the attitude helps to determine the gravimeter’s vertical accelerometer bias. After the flight the bias is determined again at the standstill and the bias linear drift can be removed from the vertical accelerometer measurements. However, measurements of the inertial sensors are disturbed by uncontrolled angular motions of the IMU due to external mechanical actions on the gravimeter body during the standstill. The paper proposes an algorithm for the gravimeter’s IMU initial and final alignment that includes determination of the IMU attitude angles and all three accelerometer biases at the standstill before and after the flight. We show that the accelerometers’ scale factor errors can also be determined by the algorithm. We also present numerical results for the algorithm performance under the angular motion of a state of the art strapdown gravimeter’s IMU. The accelerometer calibration results evaluated from comparison with another algorithm have been provided, and the position and velocity errors in the autonomous IMU dead-reckoning have been analyzed.

The paper discusses the development of a lunar navigation satellite system and a lunar orbital base, based on high near-circular orbits of an artificial Moon satellite and using Russian launch vehicles. Two tasks are studied within a complex problem of a lunar orbital system construction for the navigation support during future development of the Moon. The results of analysis of a spacecraft orbital evolution while moving in the real field of the Moon under the effect of gravitational perturbations are presented. It is shown that the high polar near-circular orbits around the Moon can retain their shape for a long time. Spacecraft launching to such orbits using a few launch scenarios is considered. Possible configuration of the lunar navigation satellite system is analyzed to illustrate the fundamental possibility of constructing such a navigation system and a lunar orbital base, based on high near-circular orbits around the Moon and using the launch vehicles of Soyuz family.

AUV positioning algorithms used in its homing and docking to underwater docking station are described. The homing and docking trajectory consists of several steps, where different positioning methods are applied using the standard equipment onboard modern heavyclass AUVs. Positioning errors at each step are estimated. The duration of positioning by the AUV onboard computer is assessed.

The paper studies the blur trajectory, i.e. the motion of a point light source projection along the image plane. It occurs when the digital camera and the observed scene move relative to each other during exposure. The blur trajectory is calculated by solving a set of differential equations of the point plane motion kinematics, written in terms of the measurements of velocity and specific force vectors. The formulated problem is called the special problem of inertial navigation in order to emphasize its differences from the problem of strapdown inertial navigation in the conventional sense. The set of equations of the special problem is obtained in the image plane coordinates. Model examples of blur trajectories calculation are presented for two limiting cases: a distant star and a close motionless target. In the first case, the possibility of increasing the probability of the star blurry image detection in noise is shown. Also, it is discussed how to eliminate the unpredictable systematic error in measuring the star’s coordinates.

The problem of stabilization of small oscillations of a gyroscopic system with many degrees of freedom and slowly varying parameters is considered and solved using Bellman’s principle of dynamic programming. The approximate procedures for the controller synthesis are based on the asymptotic solution of the Hamilton-Jacobi-Bellman equation by the averaging method. A quadratic optimality criterion is used, depending on the oscillation amplitudes of the system and control. The proposed method is applied to linear disturbances of the general type and those associated with a slow change in system parameters. The new approach allows the design of controllers in analytical form.