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.

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.