## 2 Measurement System Composition and Principles  
The laser tracking attitude measurement system is primarily led by laser tracking equipment, combined with cameras, an IMU, and cooperative targets to complete the task of dynamic attitude measurement. As is shown in Figure 1, this system aims to measure the attitude of cooperative targets relative to the laser tracking equipment. The system integrates the high precision of vision with the high frequency of IMU data comprehensively to ensure the dynamic performance of the combined attitude angle measurement. As shown in Figure 1, the positions of the laser tracking equipment and the camera are relatively fixed. The origin of the laser tracking equipment coordinate system (O\({}_{\text{L}}\)-X\({}_{\text{L}}\)Y\({}_{\text{L}}\)Z\({}_{\text{L}}\)) is located at the laser head of the laser tracking equipment, where the X\({}_{\text{L}}\)-axis is perpendicular to the horizontal code disk, and the Y\({}_{\text{L}}\)-axis is perpendicular to the vertical code disk. The origin of the camera coordinate system (O\({}_{\text{C}}\)-X\({}_{\text{C}}\)Y\({}_{\text{C}}\)Z\({}_{\text{C}}\)) is positioned at the optical center of the camera, with the X\({}_{\text{C}}\).axis, Y\({}_{\text{C}}\)-axis, and Z\({}_{\text{C}}\)-axis parallel to the three axes of the laser tracking equipment coordinate system. The cooperative target is fixed with the target to be measured, and the origin of the target coordinate system (O\({}_{\text{T}}\)-X\({}_{\text{T}}\)Y\({}_{\text{T}}\)Z\({}_{\text{T}}\)) is located at the center of the target sphere with the Z\({}_{\text{T}}\)-axis perpendicular to the plane pointing to the IMU, and the X\({}_{\text{T}}\)-axis and Y\({}_{\text{T}}\)-axis determined by the right-hand rule. The origin of the IMU coordinate system (O\({}_{\text{I}}\)-X\({}_{\text{Y}}\)Y\({}_{\text{I}}\)Z\({}_{\text{I}}\)) is located at the sensitive center of the IMU, with the X\({}_{\text{T}}\)-axis, Y\({}_{\text{I}}\).axis, and Z\({}_{\text{I}}\).axis parallel to the three axes of the target coordinate system. The distance between the center of the target sphere and the IMU is \(l\). The IMU is fixedly installed inside the cooperative target, and the rotational and translational relationship between its coordinate system and the target coordinate system is determined by system calibration. Taking the initial position of the laser tracking device coordinate system as the reference coordinate system, we define \({}_{\text{L}}^{\text{C}}\)\(\mathbf{R}\) as the rotation matrix between the camera coordinate system and the laser tracker coordinate system, \({}_{\text{T}}^{\text{C}}\)\(\mathbf{R}\) as the rotation matrix between the camera coordinate system and the cooperative target coordinate system, and \({}_{\text{T}}^{l}\)\(\mathbf{R}\) as the rotation matrix between the IMU coordinate system and the cooperative target coordinate system. After rotating around its own Z axis, X axis and Y axis, the cooperative target coordinate system coincides with the camera coordinate system. According to the definition of Euler angles, the rotation matrix representing the relationship between these two coordinate systems can be expressed as  
Figure 1: Composition of the laser tracking attitude dynamic measurement system. \[ \begin{split}\frac{C}{T}\mathbf{R}=R_{\phi}R_{\theta}R_{\varphi}= \left(\begin{array}{ccc}\cos\phi&0&\sin\phi\\ 0&1&0\\ -\sin\phi&0&\cos\phi\end{array}\right)\left(\begin{array}{ccc}1&0&0\\ 0&\cos\theta&-\sin\theta\\ 0&\sin\theta&\cos\theta\end{array}\right)\left(\begin{array}{ccc}\cos\varphi& -\sin\varphi&0\\ \sin\varphi&\cos\varphi&0\\ 0&0&1\end{array}\right)\\ =\left(\begin{array}{ccc}\cos\phi\cdot\cos\varphi+\sin\theta\cdot\sin \phi\cdot\sin\varphi&\cos\varphi\cdot\sin\theta\cdot\sin\phi-\cos\phi\cdot\sin \varphi&\cos\theta\cdot\sin\phi\\ \cos\theta\cdot\sin\varphi&\cos\theta\cdot\cos\varphi&-\sin\theta\\ \cos\phi\cdot\sin\theta\cdot\sin\varphi-\cos\sin\phi&\sin\phi\cdot\sin\varphi+ \cos\phi\cdot\cos\varphi\cdot\sin\theta&\cos\theta\cdot\cos\phi\end{array} \right)\\ \end{split}