**Acknowledgements**

*Gyroscopes - Principles and Applications*

drift with time, needing to be maintained frequently.

rate of 3.5% during the forecast period 2018–2026 [5].

imbalances inherent in the construction of the rotor, mechanical gyroscopes are typically noisier than other forms of gyroscopes, and their performances prone to

With the progress of science and technology, new kinds of gyroscopes based on new principles continuously came forth in our eyeshot and found their applications in our daily lives. Optical gyroscopes are the most successful ones, including ring laser gyroscopes and fiber-optic gyroscopes [4]. These devices send two beams of light around a circular path in opposite directions. If the path spins, a "fringe interference" pattern (alternate bands of light and dark) was detected that depended on the precise rate of rotation. They first appeared in the 1960s, following the invention of the laser and the development of fiber optics. Optical gyroscopes have the advantages of excellent measurement accuracy and having no moving parts and thus, no friction. The first ring laser gyroscope (RLG) was built in 1963 by Mecek and Davis. Owing to their high level of accuracy, cheap cost, high reliability, and easy maintenance, RLGs are perfect for integration in Inertial Navigation Systems. Today, RLGs have largely replaced their mechanical gyroscope predecessors in autopilot systems in aircrafts and guided missiles through missions where GPS is not safe to use. The global ring laser gyroscopes market is anticipated to reach a market value of US\$ 948.3 million by 2026, growing at a compound annual growth

Fiber-optic gyroscope (FOG) is another successful optical gyroscope [4]. It was first proposed and studied in 1970s and was initially considered to be devoted to medium-level applications. In 1978, McDonald Company developed the first practical FOGs, and in 1980, Bergh et al. devised the first all-fiber optic gyroscope. Since then, FOGs have experienced a period of rapid development, the angular velocity measurement accuracy has been improved to 0.001°/h, reaching the strategic level of performance and surpassing the ring laser gyroscope in terms of deviation noise and long-term stability. In addition to no moving and wearing parts, FOGs also have the advantages of small size, light weight, large dynamic range, and flexible design, which mean the performance of a fiber-optic gyroscope can be adjusted by altering the length and diameter of its coil. FOGs are now gradually evolving in the direction of low cost, high reliability, and long service life. FOGs are broadly used in inertial navigation systems in guided missiles, aircrafts, and vehicles for attitude measurement and navigation. The global market of FOGs is expected to worth US\$ 948.3 million by 2022, growing at a compound annual growth rate of 3.61% during the

MEMS gyroscope is the most successful commercial modal for angular velocity sensors [7]. MEMS gyroscopes are based on micro electrical mechanical systems (MEMS) technology and are very suitable to mass production. Benefiting from the advancements in MEMS technology, MEMS gyroscopes own their most prominent advantages: cheap, small, and light. The common type of MEMS gyroscope is made of silicon, with a massive object suspended in the air by an anchor or some springs. When a gyroscope is in operation, the suspended structure keeps vibrating. As the gyroscope experiences a rotation relative to its reference, a force called Coriolis force will act on the suspended structure and causes it to move in a direction perpendicular to its vibrating direction. This movement is proportional to the rotation speed and converts into electrical signals that can be amplified and read by a microcontroller, the angular velocity is then ascertained. Once the accuracy of MEMS gyroscopes was much lower than that of their competitors, such as optical gyroscopes and mechanical gyroscopes. So, their applications were restricted to low-end. In the last 10–15 years, the precision of MEMS gyroscope improves drastically and achieves the tactical grade level (0.1°/h). On the benefits of the small size, low costs, and light weight and due to its improved precision and environmental

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period 2016–2022 [6].

This work was/supported by the Taishan Scholars Program of Shandong Province No. tsqn201909108.
