# Reliability Analysis of Hybrid Laser INS Under Multi-Mode Failure Conditions
## 1 Introduction  
The inertial navigation system (INS) is an autonomous navigation system that operates on the principles of Newtonian mechanics, measuring the acceleration of an aircraft in an inertial reference frame to calculate its velocity, displacement, attitude, and heading angle through integration [1; 2; 3]. During operation, INS offers several advantages such as not radiating energy externally, independence from external data, and immunity to electromagnetic interference, leading to its extensive use in aircraft and rockets. Advanced countries have consistently regarded INS as a critical technology, strongly supporting its development and optimization while maintaining strict control over related technology and products [4; 5; 6]. The concept of a hybrid INS was proposed by academician [PERSON] in 2015 [7], integrating a physically stabilized platform using digital servo control with a mathematically computed platform based on strapdown attitude calculations. Functionally, the hybrid INS not only isolates angular movements of the carrier, as a conventional INS does, but also achieves rotational capability, which enables inertial devices to rotate relative to the navigation frame, thereby enhancing error modulation [8]. Compared to a traditional platform-based INS [9] and \"self-contained\" INS [7], the hybrid laser INS introduces unique features in both principle and structure that impact its performance accuracy. This system presents numerous technical challenges such as the dual-frequency dithering characteristics of the laser gyroscope, which complicates stability control. Achieving optimal control performance requires an ideal design for the rotational mechanism and an understanding of its structural and mechanical transfer properties, providing a suitable operating environment for angular motion isolation under high-dynamic conditions. In the hybrid laser INS, the relative positioning between the inertial measurement unit (IMU), the rotational frame, and the base continuously changes, especially in high-overload and impact environments, affecting INS accuracy. This necessitates an in-depth analysis of the mechanical characteristics of the hybrid laser INS under high dynamics and overload conditions. Components such as the base, platform, and inner and outer frames are essential to the hybrid laser INS, where their static and dynamic properties critically affect the system's accuracy and stability [10]. Under mechanical conditions involving high overloads and severe impacts, structural elastic deformation can lead to deviations in the INS body coordinate system from the virtual coordinate system [11]. Therefore, structural elements such as the base, platform, and frames must exhibit high static and dynamic performance to ensure the accuracy and reliability of the hybrid INS [12]. During operation, the INS endures complex vibrational loads; when the frequency of these external vibrations is close to the natural frequency of structural elements, resonance can occur, severely impacting the accuracy and stability of the INS and even causing potential damage to the entire measurement system [13]. Additionally, the frames bear the weight of the platform and gyroscopes, causing deformation. Consequently, requirements for rigidity, strength, dimensions, and tolerances in components such as the base, platform, and frames are stringent. The stability of the reference coordinate system within the inertial measurement system is heavily influenced by factors such as structural deformation, angle sensor accuracy, motor control precision, and gyroscope accuracy. However, improving angle sensor accuracy, motor control precision, and gyroscope accuracy is often costly and complex. Hence, enhancingstructural rigidity and strength to reduce elastic deformation under high overload and impact conditions, thereby minimizing deviation of the INS body coordinate system from the virtual coordinate system, is the most direct approach. Scholars have conducted extensive research on improving structural rigidity in INSs.