## 3 Target Tracking Method
### Maritime Target Tracking Method  
According to the estimated systematic error in Equation (28), the systematic error in Equations (1)-(6) is reduced to obtain the observation information of UAVs \(A\) and \(B\) to the cooperative platform and the sea target \(T\) at the moment \(k\), which are denoted as \(\mathbf{Z^{\prime}}_{AC}=\begin{bmatrix}r^{\prime}_{AC}&b^{\prime}_{AC}&c^{ \prime}_{AC}\end{bmatrix}^{T}\), \(\mathbf{Z^{\prime}}_{AT}=\begin{bmatrix}r^{\prime}_{AT}&b^{\prime}_{AT}&e^{ \prime}_{AT}\end{bmatrix}^{T}\), \(\mathbf{Z^{\prime}}_{BC}=\begin{bmatrix}r^{\prime}_{BC}&b^{\prime}_{BC}&e^{ \prime}_{BC}\end{bmatrix}^{T}\), \(\mathbf{Z^{\prime}}_{BT}=\begin{bmatrix}r^{\prime}_{BT}&b^{\prime}_{BT}&e^{ \prime}_{BT}\end{bmatrix}^{T}\). The attitude information of the platforms after inertial guidance compensation is \(\mathbf{\mu}_{A}=\begin{bmatrix}\Psi^{\prime}_{A}&\theta^{\prime}_{A}&\phi^{ \prime}_{A}\end{bmatrix}^{T}\) and \(\mathbf{\mu}_{B}=\begin{bmatrix}\Psi^{\prime}_{B}&\theta^{\prime}_{B}&\phi^{ \prime}_{B}\end{bmatrix}^{T}\), respectively. The above has completed the estimation of sensor observation errors and platform attitude errors, and then the data are aligned and compensated. Next, we move to the tracking of the target at sea.  
In order to fuse the observation information of the two UAVs, it is necessary to transform the observation information of both into a unified coordinate system, and the initial position of the cooperative platform \(\mathbf{X}_{Cin}^{d}\) is taken as the fusion center in this paper.  
Two different tracking methods are designed according to the motion state of the cooperative platform: one is the tracking method when the cooperative platform is stationary, and the other is the tracking method when the cooperative platform is in motion.  
When the cooperative platform is stationary, the fusion center is the position of the cooperative platform, and the geodetic coordinates of the cooperative platform are not required to transform observation information into a unified coordinate system at this time:  
\[\mathbf{X}_{CAT}=\mathbf{X}_{AT}-\mathbf{X}_{AC} \tag{33}\]  
\[\mathbf{X}_{CBT}=\mathbf{X}_{BT}-\mathbf{X}_{BC} \tag{34}\]  
However, considering the effect of wind, currents, and other factors, it is difficult to keep the cooperative platform absolutely stationary in the real scenario. Therefore, the motion of the cooperative platform must be considered.  
When the cooperative platform is in motion, the tracking and filtering fusion of the target directly using Equations (33) and (34) fails. It is necessary that the cooperative platform needs to send its own high-precision geodetic coordinate information in real time at the current moment \(\mathbf{X}_{Ci}^{d}\) to transform observation information into a unified coordinate system.  
Transform the target position into geodetic coordinates:  
\[\mathbf{X}_{CAT}^{d}=\mathbf{T}_{Ild}(\mathbf{X}_{CAT},\mathbf{X}_{Ci}^{d}) \tag{35}\]  
\[\mathbf{X}_{CBT}^{d}=\mathbf{T}_{Ild}(\mathbf{X}_{CBT},\mathbf{X}_{Ci}^{d}) \tag{36}\]  
where \(\mathbf{T}_{Ild}\) is the transformation of local geographic coordinates to geodetic coordinates.  
The target position is then transformed into a unified coordinate system based on the initial position information of the cooperative platform \(\mathbf{X}_{Cin}^{d}\):  
\[\mathbf{X}_{CATn}=\mathbf{T}_{dfl}(\mathbf{X}_{Cd^{\prime}}^{d},\mathbf{X}_{ Cin}^{d}) \tag{37}\]  
Figure 2: Spatial registration method.  
\[\mathbf{X}_{CBTn}=\mathbf{T}_{dtl}(\mathbf{X}_{CBT}^{d},\mathbf{X}_{Cin}^{d}) \tag{38}\]  
where \(\mathbf{T}_{dtl}\) is the transformation of geodetic coordinates into local geographic coordinates.  
Combined with Kalman filtering to complete the localization and tracking of the target, the specific flow chart is shown in Figure 3.