We simulated the glass-blowing process to model a shell resonator, which is a key component in MRIG (Micro Rate Integrating Gyroscope), using the finite elements method to solve a non-isothermal problem. We also calculated the mechanical characteristics of the modeled resonator, including effective mass, eigenfrequencies, angular gain, and energy loss, to predict the resonator's performance as a gyroscope. One key aspect we addressed is the bending of the resonator's rim toward the stem during glass-blowing process. This phenomenon occurs due to increased heat loss at the mold's edge and reduced heat flux at the side of the Gaussian heat source. To mitigate rim bending and the subsequent reduction in capacitance between the rim and 3D electrodes, which can degrade performance in micro glass-blown shell resonators for gyroscopes, we propose two potential mold solutions. The first is using a short-stem mold, which requires extensive polishing to eliminate the bent rim. The second solution is using a mold with a suitable chamfer at the edge, resulting in a straight rim. To quantitatively compare resonators created by these two types of molds, we calculated the noise factor for predicting its gyroscope performance. From these calculations, we find out that using the chamfered mold enables us to increase in the resonator's effective mass, eigenfrequency, angular gain, and quality factor, consequently reducing the noise factor compared to using the short-stem mold. This simulation process will assist us in getting insight into understanding a shell resonator as a gyroscope, designing a mold and determining experimental conditions.

This paper describes developing and analyzing an analytical model of Microelectromechanical Systems (MEMS) internal vibrating ring gyroscope. The internal ring structure consists of eight semicircular beams attached to the externally placed anchors. The paper analyses the vibrating ring gyroscope inplane displacement behavior and the resulting elliptical vibrational modes. The elliptical vibrational modes appear as pairs with the same resonance frequency due to the symmetric nature of the design. The analysis commences by conceptualizing the ring as a geometric structure with a circular shape, possessing specific dimensions such as thickness, height, and radius. We construct a linear model that characterizes the vibrational dynamics of the internal vibrating ring. The analysis encompasses comprehensive mathematical formulations for the radial and tangential displacements in local polar coordinates, considering the inextensional displacement of the ring structure. By utilizing the derived equations, we highlight the underlying relationships driving the vibrational characteristics of the MEMS vibrating ring gyroscope. These dynamic vibrational relationships are essential in enabling the vibrating ring gyroscope's future utilization in accurate navigation and motion sensing technologies.

Microelectromechanical System (MEMS) vibrating gyroscope design considerations are always intriguing due to their microscale mechanical, electrical, and material behavior. MEMS vibrating ring gyroscopes have become important inertial sensors in inertial measurement units (IMU) for navigation and sensing applications. The design of a MEMS vibrating ring gyroscope incorporates an oscillating ring structure as a proof mass, reflecting unique design challenges and possibilities. This paper presents a comprehensive design analysis of the MEMS vibrating ring gyroscope from the mechanical, electrical, and damping perspectives. The mechanical design of the MEMS vibrating ring gyroscope investigates the various frame designs of the vibrating ring structure, as well as the various beam structures, including curved, rectangular, and semicircular beam structures, which are analyzed using mathematical models and finite element analysis (FEA) simulations that provide an in-depth analysis of the stiffness and deflection of the vibrating structures. The electrical designs of the MEMS vibrating ring gyroscope were analyzed using various electrode configurations, electrostatic actuation, and capacitive detection mechanisms, respectively. The design analysis of various forms of damping, including viscous, structural, thermoelastic, and anchor damping, has been discussed. The variety of design structures investigated for MEMS vibrating ring gyroscopes' mechanical, electrical, and damping performance.

Tuning fork gyroscopes (TFGs) are promising for potential high-precision applications. This work proposes and experimentally demonstrates a novel high-Q dual mass tuning fork microelectro-mechanical system (MEMS) gyroscope utilizing three-dimensional (3D) packaging techniques. Except for two symmetrically-decoupled proof masses (PM) with synchronization structures, a symmetrically-decoupled lever structure is designed to force the antiparallel, antiphase drive-mode motion and basically eliminate the low-frequency spurious modes. The thermoelastic damping (TED) and anchor loss are greatly reduced by the linearly-coupled, momentum- and torque-balanced antiphase sense mode. Besides, a novel 3D packaging technique is used to realize high Q-factors. A composite substrate encapsulation cap, fabricated by through-silicon-via (TSV) and glass-in-silicon (GIS) reflow processes, is anodically bonded to the sensing structures at wafer scales. A self-developed control circuit is adopted to realize loop control and characterize gyro-scope performances. It is shown that a high-reliability electrical connection together with a high-air-impermeability package can be fulfilled with this 3D packaging technique. Furthermore, the Q-factors of the drive and sense modes reach up to 51947 and 49249, respectively. This TFG realizes a wide measurement range of ±1800° /s and a high resolution of 0.1° /s with a scale-factor nonlinearity 720 ppm after automatic mode-matching. Besides, the long-term zero-rate output (ZRO) drift can be effectively suppressed by temperature compensation, inducing a small angle random walk (ARW) of 0.923°/√h and a low bias instability (BI) of 9.270°/h.

For a fiber optic gyroscope, thermal deformation of the fiber coil can introduce additional ther-mal-induced phase errors, commonly referred to as thermal errors. Thermal error compensation techniques are effective means of addressing this issue. The principle behind these techniques involves real-time sensing of thermal errors and correcting them within the output signal. Since it is challenging to directly separate thermal errors from the output signal of the fiber optic gyro-scope, it is necessary to predict thermal errors based on temperature. To establish a mathematical model between temperature and thermal errors, this paper measured synchronized data of phase errors and angular velocity for the fiber coil under different temperature conditions and aimed to model it using data-driven methods. Due to the difficulty of conducting tests and the limited number of data samples, an algorithm called TD-model modeling is proposed to address the issue of overfitting, which can reduce the model's generalization ability. First, a theoretical analysis of the phase errors caused by thermal deformation of the fiber coil is performed. Subsequently, the critical parameters, such as the thermal expansion coefficient, are determined, and a theoretical model is established. Finally, the theoretical analysis model is incorporated as a regularization term and combined with the test data to jointly participate in the regression of model coefficients. Through experimental comparative analysis, it is shown that, relative to ordinary regression models, the TD-model effectively mitigates overfitting caused by the limited number of samples, leading to a 58% improvement in predictive accuracy.

The exceptional performance advantages of the fiber optic gyroscope (FOG) position it as a dominant player in middle and high-end inertial navigation systems. To prevent the loss of sensor precision caused by algorithm design and simplify the complex modeling strategy in traditional methods. We gradually demonstrate the significant role of Convolutional Neural Network (CNN) in the navigation system based on FOG, and utilize the particle swarm optimization algorithm (PSO) to expedite the convergence of the network. The experimental results demonstrate that the initial alignment method based on deep learning is more accurate than the traditional method. The attitude angle error is reduced by 81.25%, 92.54% and 36.53% respectively. The research provides support for the future application of deep learning in optical navigation systems.

Zero-rate output (ZRO) drift induces deteriorated micro-electromechanical system (MEMS) gy-roscope performances, severely limiting its practical applications. Hence, it is vital to explore an effective method toward ZRO drift reduction. In this work, we conduct an elaborate investigation on the impacts of the internal and packaging stresses on the ZRO drift at the thermal start-up stage, and propose a temperature-induced stress release method to reduce the duration and magnitude of ZRO drift. Self-developed high-Q dual mass tuning fork gyroscopes (TFGs) are adopted to study the correlations between temperature, frequency and ZRO drift. Furthermore, a rigorous finite element simulation model is built based on the actual device and packaging structure, revealing the temperature and stresses distribution inside TFGs. Meanwhile, the relationship between temperature and stresses are deeply explored. Moreover, we introduce a temperature-induced stress release process to generate thermal stresses and reduce the temperature-related device sensitivity. By this way, the ZRO drift duration is drastically reduced from ~2000 s to ~890 s, and the drift magnitude decreases from ~0.4 °/s to ~0.23 °/s. This stress release method achieves a small bias instability (BI) of 7.903 °/h and a low angle random walk (ARW) of 0.792 °/√h, and the long-term bias performance is significantly improved.

K-Rb-83Kr based atomic co-magnetometer for measuring moving MEGs is theoretically studied in this paper. Parameters such as the spin exchange rates, the spin dephasing rates and the polarization of the nuclear spins are studied to configure the co-magnetometer. Results show that the nuclear spin could generate around 700 nT magnetic field under which the nuclear spin could compensate wide range of magnetic fields. We also showed the hybrid optical pumping vapor cell fabrication process in this paper. Alkali metals were mixed in a glove box and then was connected to the alkali vapor cell fabrication system. The vapor cell fabrication process is illustrated in this paper.

It is shown that the termination of the channeling of the fundamental radiation mode in the waveguide can be observed upon heating of an optical integrated circuit based on proton exchange channel waveguides formed in a lithium niobate single crystal. This process is reversible, but restoration of waveguide performance takes tens of minutes. The effect of the waveguide disappearance is observed upon rapid heating (5 °C/min) from a low temperature (minus 40 °C). This effect can lead to a temporary failure of navigation systems using fiber optic gyroscopes with modulators based on a lithium niobate crystal