## 2 Materials and Methods
### Geographic Polarization Suppression Model
#### 2.2.2 Orientation Information Solution Method  
The inherent fluctuation of the sea surface significantly impacts the stable imaging of maritime monitoring platforms, complicating the effective suppression of sea surface glare. To address this challenge, this study employs an orientation information solution method to mitigate the effects of sea surface fluctuations. During the implementation process, MEMS inertial sensors are utilized to capture the gyroscope's angular velocity, and in conjunction with the orientation information solution method, precise orientation data is extracted. Within the orientation angle solution framework, Euler angles, direction cosine, and quaternion methods are extensively employed. However, the quaternion method is favored in this paper due to its low computational complexity, absence of singularities, capacity for comprehensive orientation measurement, and superior measurement accuracy [22]. Let quaternion \(\overset{\rightarrow}{Q}=q_{0}+q_{1}\overset{\rightarrow}{i}+q_{2} \overset{\rightarrow}{j}+q_{3}\overset{\rightarrow}{k}\) be defined, where \(q_{0},q_{1},q_{2},q_{3}\) is a real number, and \(\overset{\rightarrow}{i},\overset{\rightarrow}{j},\overset{\rightarrow}{k}\) represents mutually orthogonal unit vectors. The quaternion \(q_{0},q_{1},q_{2},q_{3}\) solution expression is shown in Equation (13). \[\left\{ \begin{array}{l}q_{0}=q_{0}+\frac{1}{2}\Delta t\big{(}-\omega_{x}q_{ 1}-\omega_{y}q_{2}-\omega_{z}q_{3}\big{)}\\ q_{1}=q_{1}+\frac{1}{2}\Delta t\big{(}\omega_{x}q_{0}-\omega_{y}q_{3}+\omega_ {z}q_{2}\big{)}\\ q_{2}=q_{2}+\frac{1}{2}\Delta t\big{(}\omega_{x}q_{3}+\omega_{y}q_{0}-\omega_ {z}q_{1}\big{)}\\ q_{3}=q_{3}+\frac{1}{2}\Delta t\big{(}-\omega_{x}q_{2}+\omega_{y}q_{1}+\omega _{z}q_{0}\big{)}\end{array} \right. \tag{13}\]Here, the initial values of \(q_{0},q_{1},q_{2},q_{3}\) are 1, 0, 0, and 0, respectively, and \(\omega_{x},\omega_{y},\omega_{z}\) represent the angular velocity values from the MEMS inertial sensor gyroscope. The coordinate transformation matrix from the object coordinate system to the geographical coordinate system is denoted as \(C_{b}^{E}\), expressed by the quaternion as follows:  
\[C_{b}^{E}= \begin{bmatrix}q_{0}^{2}+q_{1}^{2}-q_{2}^{2}-q_{3}^{2}&2(q_{1}q_{2}- q_{0}q_{3})&2(q_{0}q_{2}-q_{1}q_{3})\\ 2(q_{0}q_{3}+q_{1}q_{2})&q_{0}^{2}-q_{1}^{2}+q_{2}^{2}-q_{3}^{2}&2(q_{2}q_{3}- q_{0}q_{1})\\ 2(q_{1}q_{3}-q_{0}q_{2})&2(qq_{0}q_{1}+q_{2}q_{3})&q_{0}^{2}-q_{1}^{2}-q_{2}^{ 2}+q_{3}^{2}\end{bmatrix}  \tag{14}\]  
Place the MEMS inertial sensor horizontally with the sensor's internal center as the origin, horizontally to the right as the \(x\)-axis, vertically upward as the \(z\)-axis, and directly forward as the \(y\)-axis, establishing a spatial Cartesian coordinate system. This coordinate system also aligns with the geographical and the initial object coordinate systems, as illustrated in Figure 3.  
Define the rotation around the \(z\)-axis as the object's heading angle \(\psi\), with the transformation matrix denoted as \(r_{z}\); the rotation around the \(y\)-axis as the object's pitch angle \(\gamma\), with the transformation matrix as \(r_{y}\); and the rotation around the \(x\)-axis as the object's roll angle \(\theta\), with the transformation matrix as \(r_{x}\). The transformation matrices \(r_{x}\), \(r_{y}\), and \(r_{z}\) are shown in Equation (15). \[\left\{ \begin{array}{l}r_{x}=\left[\begin{array}{ccc}1&0&0\\ 0&\cos\theta&\sin\theta\\ 0&-\sin\theta&\cos\theta\\ \end{array}\right]\\ r_{y}=\left[\begin{array}{ccc}\cos\gamma&0&-\sin\gamma\\ 0&1&0\\ \sin\gamma&0&\cos\gamma\\ \end{array}\right]\\ r_{z}=\left[\begin{array}{ccc}\cos\psi&\sin\psi&0\\ -\sin\psi&\cos\psi&0\\ 0&0&1\end{array}\right]\end{array} \right. \tag{15}\]  
The object's orientation transformation is equivalent to the composite rotation of the object around the x, y, and z axes. The composite orientation matrix is \(C_{E}^{b}\), with the rotation  
Figure 3: Coordinate system reference diagram. sequence in this paper being \(Z\to Y\to X\).