This paper provides an overview of the study of optical resonant cavity stability, focusing on the relevant principles, key technological advances, and applications of optical resonant cavities in a variety of high-precision measurement techniques and modern science and technology. Firstly, the vibration characteristics, thermal noise, and temperature characteristics of the reference cavity are presented. Subsequently, the report extensively discusses the advances in key technologies such as mechanical vibration isolation, thermal noise control, and resistance to temperature fluctuations. These advances not only contribute to the development of theory but also provide innovative solutions for practical applications. Typical applications of optical cavities in areas such as laser gyroscopes, high-precision measurements, and gravitational wave detection are also discussed. Future research directions are envisioned, emphasising the importance of novel material applications, advanced vibration isolation technologies, intelligent temperature control systems, multifunctional integrated optical resonator design, and deepening theoretical models and numerical simulations.

In this paper, a rapid alignment method for high-precision rotation inertial navigation system (RINS) within group affine is proposed based on the Lie group theory. The proposed method can effectively solve the ultimate contradiction of initial alignment: speed and accuracy. It meets the requirements of fast response and high accuracy of high-precision RINS. We abandon the conventional coarse alignment + fine alignment scheme and realize a linear Kalman filter alignment method with arbitrarily initial misalignment based on the Earth-centered Earth-fixed frame RINS mechanization and the Lie group theory. Subsequently, considering the error characteristics of RINS two-position alignment, new left-invariant error model and observation model satisfying the group affine property are constructed to improve the convergence speed and accuracy of alignment. It is verified that the method can complete the initial alignment of arbitrary large misalignment and reach the ultimate accuracy in a short time, and the land vehicle navigation test shows that the proposed alignment method can complete the initial alignment of arbitrary misalignment in 5 min under the swaying disturbance and achieve better pure inertial navigation accuracy compared with the traditional scheme.

Initial alignment plays a pivotal role in inertial navigation systems, as even small orientation errors introduced at startup can significantly degrade subsequent positioning and attitude estimates. In this context, we propose a novel inverse alignment method for rotational inertial navigation that leverages the group affine property and high-speed computing to accelerate and refine the alignment process. Adopting inverse navigation and Lie group theory, we derive a left-invariant error model in the geocentric geosynchronous coordinate framework and rapidly achieve alignment by integrating forward and inverse Kalman filtering. During 2.5-h in-vehicle tests, our approach reduced both the maximum error and CEP (Circular Error Probable 50%) by 60% compared to standard alignment methods, and it surpassed the performance of conventional group affine alignment by improving accuracy by 7.2% and 20%, respectively. These results highlight the method’s ability to deliver swift, precise alignment across diverse initial misalignment angles, offering significant benefits for modern high-precision inertial navigation applications.

Inertial navigation systems (INS) are able to continuously provide the attitude, velocity, and position of the vehicle with high accuracy, nevertheless, the accelerometer scale factor asymmetry and the temperature-related accelerometer errors can cause significant navigation errors. To solve this problem, in this paper, a novel system-level calibration method is proposed, which achieves simultaneous compensation of accelerometer asymmetric errors and second-order temperature-related errors. First, the error model including accelerometer asymmetry and temperature-related errors is constructed. Then, a 51-dimensional Kalman filter is applied to estimate all error factors of accelerometers including biases, scale factor errors, installation errors, scale factor asymmetry, first-order and second-order temperature-related error coefficients at the same time. The effectiveness of the calibration method is proved by both simulation and experiment. The pure inertial navigation experiment results illustrated that, compared with the traditional 30-dimensional calibration, our method can reduce the root mean squares of radial position error and radial velocity error by 50% and 39%, respectively, which indicates that the proposed method can be used to improve the navigation performance of ground or aerial vehicles.

Autonomous underwater vehicles (AUVs) have obtained extensive application in the exploitation of marine resources. Terrain-aided navigation (TAN), as an accurate and reliable autonomous navigation method, is commonly used for AUV navigation. However, its accuracy degrades significantly in self-similar terrain features or measurement uncertainties. To overcome these challenges, we propose a novel terrain-aided navigation framework integrating an Improved Marine Predators Algorithm with Depth-First Search optimization (DFS-IMPA-TAN). This framework maintains positioning precision in partially self-similar terrains through two synergistic mechanisms: (1) IMPA-driven optimization based on the hunger-inspired adaptive exploitation to determine optimal trajectory transformations, cascaded with Kalman filtering for navigation state correction; (2) a Robust Tree (RT) hypothesis manager that maintains potential trajectory candidates in graph-structured memory, employing Depth-First Search for ambiguity resolution in feature matching. Experimental validation through simulations and in-vehicle testing demonstrates the framework’s distinctive advantages: (1) consistent terrain association in partially self-similar topographies; (2) inherent error resilience against ambiguous feature measurements; and (3) long-term navigation stability. In all experimental groups, the root mean squared error of the framework remained around 60 m. Under adverse conditions, its navigation accuracy improved by over 30% compared to other traditional batch processing TAN methods. Comparative analysis confirms superior performance over conventional methods under challenging conditions, establishing DFS-IMPA-TAN as a robust navigation solution for AUVs in complex underwater environments.

In the whole-angle mode of a hemispherical resonator gyro (HRG), the external input rotation angle is obtained by detecting the standing-wave rotation angle through electrodes. Due to this operational principle and manufacturing constraints of HRGs, the gyro output in an HRG inertial navigation system exhibits angle-dependent errors that are highly sensitive to temperature variations. To address this issue, this paper proposes a system-level calibration scheme to characterize and compensate for these correlated errors. Angle-dependent bias models were established through multi-temperature point experiments. A Kalman filter was subsequently designed, and a calibration path satisfying observability requirements was developed. System-level calibration experiments were conducted to determine and compensate for the identified errors. Finally, navigation experiments demonstrated the effectiveness of the proposed method, showing that the navigation accuracy of the HRG inertial navigation system was improved by up to 94.35%.