## 3 Pre-Processing of Multi-Sensor Data from the Unmanned Ship
### Coordinate Transformation  
In order to perform data fusion filtering on GPS/BDS positioning data and ZigBee blind node location information, it is necessary to transform the WGS-84/NGCS2000 coordinate system [19] and unify it to the local plane coordinates of the unmanned-ship navigation test with the ZigBee multi-node networking coordinate system. For this reason, the existing geodetic coordinates (\(B,L\)) were used in this paper to transform them into plane coordinates through Gauss-Kruger projection, and translate and rotate them to make them unified with the local plane coordinates of the unmanned ship navigation. The specific steps are as follows:  
Step 1 convert WGS-84/NGCS2000 geodetic coordinates (\(B,L\)) to WGS-84/NGCS2000 Gaussian plane coordinates (\(x^{s},y^{s}\)):  
\[\begin{array}{c}x^{s}=X_{0}^{B}+\frac{1}{2}N_{p}\cdot t\cdot m_{0}^{2}+ \frac{1}{2A}(5-t^{2}+9\eta^{2}+4\eta^{4})N_{p}\cdot t\cdot m_{0}^{4}\\ +\frac{1}{720}(61-58t^{2}+t^{4})N_{p}\cdot t\cdot m_{0}^{6}\end{array} \tag{16}\]  
\[\begin{array}{c}y^{s}=N_{p}\cdot m_{0}+\frac{1}{6}(1-t^{2}+\eta^{2})N_{p} \cdot m_{0}^{3}\\ +\frac{1}{120}(5-18t^{2}+t^{4}+14\eta^{2}-58\eta^{2}\cdot t^{2})N_{p}\cdot m_{ 0}^{5}\end{array} \tag{17}\]  
where \(m_{0}=\frac{\Delta L}{\gamma}\cos(B)\), \(t=\tan(B)\), \(\eta^{2}=(e^{\prime})^{2}\cos^{2}B\) and \(\Delta L\) are the difference between the longitude (\(L\)) of the desired point and the longitude (\(L_{0}\)) of the central meridian, namely \(\Delta L=L-L_{0}\). \(\gamma\) is the positioning coefficient error, \(B\) is the latitude of the desired point, and its unit is radians, and \(e^{\prime}\) is the second eccentricity of the ellipsoid.  
\(N_{p}\) is the curvature radius of the primary vertical circle passing through this point, which can be described as  
\[N_{p}=\frac{a}{\sqrt{1-e^{2}\sin 2\phi}} \tag{18}\]  
where \(a\) is the long radius of the ellipsoid, \(e\) is the first eccentricity of the ellipsoid, and \(\varphi\) is the geodetic dimension.  
\(X_{0}^{B}\) is the arc length from the equator to the central meridian cut by a parallel circle passing through this point and can be described as  
\[X_{0}^{B}=C_{0}-\cos B(C_{1}\sin B+C_{2}\sin^{3}B+C_{3}\sin^{5}B+C_{4}\sin^{7 }B) \tag{19}\]  
where \(C_{0}\), \(C_{1}\), \(C_{2}\), \(C_{3}\) and \(C_{4}\) are ellipsoid parameters.  
Step 2 transform the Gaussian coordinates of the unmanned ship navigation collected by GPS/BDS into the local coordinate system of the unmanned ship test through translation and rotation.  
\[\left[\begin{array}{c}x^{\text{G, B}}\\ y^{\text{G, B}}\end{array}\right]=\left[\begin{array}{c}\Delta x\\ \Delta y\end{array}\right]+(1+m)\left[\begin{array}{c}\cos\theta^{\prime}\sin \theta^{\prime}\\ -\sin\theta^{\prime}\cos\theta^{\prime}\end{array}\right]\left[\begin{array}[] {c}x^{s}\\ y^{s}\end{array}\right] \tag{20}\]  
where \((x^{\text{G, B}},y^{\text{G, B}})\) are the GPS/BDS plane positioning coordinates of the unmanned ship, \(\Delta x\) and \(\Delta y\) are the translation amount of the coordinate system, \(m\) is the scale factor, and \(\theta^{\prime}\) is the rotation angle of the two coordinate systems.