In practical engineering, the frequency splitting of Hemispherical Resonator Gyro (HRG) caused by uneven mass distribution seriously affects the precision of HRG. So, the inherent frequency is an important parameter of micro-Hemispherical Resonator Gyro (m-HRG). In the processing of hemispherical resonator, there are some morphological errors and internal defects in the hemispherical resonator, which affect the inherent frequency and the working mode of m-HRG, and reduce the precision and performance of m-HRG. In order to improve the precision and performance of m-HRG, the partial differential equation of the hemispherical resonator is solved, and the three-dimensional model using ANSYS software accurately reflected the actual shape is established in this paper. Then, the mode of hemispherical resonator in ideal state and uneven mass distribution state are simulated and analyzed. The frequency splitting mechanism of the hemispherical resonator is determined by calculation and demonstration, and the frequency splitting of the hemispherical resonator is suppressed by partial mass elimination. The results show that the absolute balance of energy can ensure the high-quality factor and the minimum frequency splitting of the hemispherical resonator. Therefore, during the processing of hemispherical resonator, the balance of mass should be achieved as much as possible to avoid various surface damage, internal defects and uneven mass distribution to guarantee the high-quality factor Q and minimum frequency splitting of hemispherical resonator.

The centralized Kalman filter is always applied in the velocity and attitude matching of Transfer Alignment (TA). But the centralized Kalman has many disadvantages, such as large amount of calculation, poor real‐time performance, and low reliability. In the paper, the federal Kalman filter (FKF) based on neural networks is used in the velocity and attitude matching of TA, the Kalman filter is adjusted by the neural networks in the two subfilters, the federal filter is used to fuse the information of the two subfilters, and the global suboptimal state estimation is obtained. The result of simulation shows that the federal Kalman filter based on neural networks is better in estimating the initial attitude misalignment angle of inertial navigation system (INS) when the system dynamic model and noise statistics characteristics of inertial navigation system are unclear, and the estimation error is smaller and the accuracy is higher.

Aiming at the problem of the combined navigation system of on-board GNSS (global navigation satellite system)/SINS (strapdown inertial navigation system), the accuracy of the combined navigation system decreases due to the dispersion of the SINS over time and under the condition of No GNSS signals. An improved LSTM (long short-term memory) neural network in No GNSS signal conditions is proposed to assist the combination of navigation data and the positioning algorithm. When the GNSS signal is normal input, the current on-board combination of the navigation module’s output sensor data information is used for training to improve the LSTM algorithm and to establish the incremental output of the GNSS position of the mapping of the different weights. In No GNSS signal conditions, using the improved LSTM algorithm can improve the combination of navigation and positioning algorithms. Under No GNSS signal conditions, the improved LSTM training model is used to predict the dynamics of SINS information component data. Under No GNSS signal conditions, the combined navigation filtering design is completed, and the error correction of SINS navigation and positioning information is carried out to obtain a more accurate combination of navigation and positioning system accuracy. It can be seen through the actual test experiment using a sports car in the two trajectories under the conditions of No GNSS signals that the proposed algorithm can be compared with the LSTM algorithm. In testing road sections, the proposed algorithm, when compared with the LSTM algorithm to obtain the northward position that the mean square errors were improved by 55.63% and 76.64%, and the eastward position mean square errors were improved by 43.42% and 54.67%. In a straight-line trajectory, improving the effect’s navigation and positioning accuracy and reliability is significant.

Because the accuracy of the existing airborne navigation is lacking in the polar region, it is difficult to ensure the safety and reliability of the aircraft when it is flying over the polar region. The integrated navigation system based on the inertial navigation technology uses multi-information fusion to assist collaborative navigation and obtain an indirect grid navigation algorithm that combines the azimuth navigation algorithm and the grid navigation algorithm to solve the existing problems. This paper analyzes the principle of the inertial navigation system in the polar region, the semiphysical simulation experiments are carried out by using the navigation theory and the background engineering, and the accuracies of the integrated navigation system of the indirect grid frame in the polar region and the integrated navigation system in the middle and low latitudes are consistent, which verifies the feasibility and effectiveness of the SINS/CNS/GPS integrated navigation system in the polar region. In addition, the paper provides the theoretical basis and the application of engineering to achieve the SINS/CNS/GPS integrated navigation system in the polar region.

Hemispherical Resonator Gyro (HRG) is a new type gyro with high precision, high reliability, shock resistance, no need of preheating, short start time, and long life. It is a kind of vibrating gyro with standing wave rotating along the sensitive base of annular precession, has a unique application prospect in the field of high precision inertial sensors, and is widely used in unmanned aerial vehicle control in complex environments. Based on the theory of the structure characteristics of the hemispherical resonator, the mathematical model of energy of the resonator is established to research the rule of resonant frequency when the hemispherical resonator is rotated around the central axis. In this paper, the influence of precession factor, which are the top angle, the bottom angle, and wall unevenness of the hemispherical resonator, are analyzed. A series of hemispherical resonator models are constructed by ANSYS software to prove the results of theoretical research. The simulation results show that precession factor of the hemispherical resonator is more sensitive of the top angle than the bottom angle, and the error of angular velocity which is caused by the change of the top angle is larger than that which is caused by the change of the bottom angle.

As the inertial navigation system cannot meet the precision requirements of global navigation in the special geographical environment of the Polar Regions, this paper presents Strapdown Inertial Navigation System (SINS)/Celestial Navigation System (CNS) integrated navigation system of airborne based on Grid Reference Frame (GRF) and the simulation is carried out. The result of simulation shows that the SINS/CNS integrated navigation system is superior to the single subsystem in precision and performance, which not only effectively inhibits the error caused by gyro drift but also corrects the navigation parameters of system without delay. Comparing the simulation in the middle and low latitudes and in the Polar Regions, the precision of SINS/CNS integrated navigation system is the same in the middle and low latitudes and in the Polar Regions.