Closed-form analytical representations of the rigid body orientation quaternion, angular velocity vector and the external moment vector satisfying kinematic equations and equations of motion are derived. In order to analyze errors of orientation algorithms for strapdown inertial navigation systems, reference models for specific rigid body rotation cases are formulated. Based on solutions, analytical expressions for ideal signals of angular velocity sensors in the form of quasi-coordinates are derived. For several sets of parameters, numerical implementations of the reference models are performed and trajectories in the configuration space of orientation parameters are presented. Numerical analysis of the drift error for the third-order orientation algorithm is performed. The results show that the value of the accumulated drift error using the derived two-frequency models exceeds the value of the accumulated drift error in the conventional case of a regular precession.

推导了满足运动学方程和运动方程的刚体取向四元数，角速度矢量和外力矩矢量的闭式解析表示。为了分析捷联惯性导航系统的定向算法误差，制定了特定刚体旋转情况的参考模型。基于解决方案，以准坐标形式导出了角速度传感器的理想信号的解析表达式。对于几组参数，执行参考模型的数值实现，并给出方向参数配置空间中的轨迹。对三阶定向算法的漂移误差进行了数值分析。