## 8 MATLAB Simulation and Experimental Data Analysis
### MATLAB Simulation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{t}\) & **100s** & **200 s** & **300 s** & **400 s** \\ \hline Actual position & (425.62,309.33) & (468.55,324.95) & (518.72,343.21) & (569.95,361.86) \\ actual \(\mathbf{Q}\) & (423.40,307.87) & (465.77,327.89) & (522.56,339.75) & (565.80,370.07) \\ inaccurate \(\mathbf{Q}\) & (418.16,307.41) & (459.91,325.95) & (514.08,337.08) & (559.67,367.68) \\ estimated \(\mathbf{Q}\)(no bp) & (420.67,307.57) & (465.98,324.37) & (519.27,342.07) & (564.27,369.43) \\ estimated \(\mathbf{Q}\)(bp) & (420.66,307.53) & (466.01,324.01) & (519.80,342.23) & (564.70,370.83) \\ \hline \(\mathbf{t}\) & **500 s** & **600 s** & **700 s** & **800 s** \\ \hline Actual position & (619.21,379.78) & (667.99,397.54) & (716.69,415.27) & (774.61,436.35) \\ actual \(\mathbf{Q}\) & (617.92,379.42) & (664.96,395.76) & (712.44,416.51) & (772.05,436.80) \\ inaccurate \(\mathbf{Q}\) & (611.10,376.80) & (657.22,392.95) & (702.91,413.09) & (760.39,432.78) \\ estimated \(\mathbf{Q}\)(no bp) & (615.34,381.67) & (662.36,396.33) & (709.57,416.38) & (770.31,435.70) \\ estimated \(\mathbf{Q}\)(bp) & (615.66,383.80) & (663.20,398.27) & (710.53,418.05) & (771.45,437.38) \\ \hline \(\mathbf{t}\) & **900 s** & **1000 s** & **1100 s** & **1200 s** \\ \hline Actual position & (833.52,457.79) & (889.72,478.24) & (942.95,497.62) & (993.39,515.98) \\ actual \(\mathbf{Q}\) & (829.13,457.78) & (880.61,481.03) & (936.05,494.27) & (986.33,516.49) \\ inaccurate \(\mathbf{Q}\) & (815.99,453.40) & (868.64,476.87) & (924.83,490.16) & (975.98,512.76) \\ estimated \(\mathbf{Q}\)(no bp) & (827.45,458.12) & (877.66,483.40) & (934.00,492.94) & (984.60,516.06) \\ estimated \(\mathbf{Q}\)(bp) & (828.57,460.04) & (879.21,485.23) & (935.84,494.92) & (986.23,518.22) \\ \hline \(\mathbf{t}\) & **1300 s** & **1400 s** & **1470 s** & \\ \hline Actual position & (1042.4,533.81) & (1091.1,551.54) & (1125.2,563.94) & \\ actual \(\mathbf{Q}\) & (1037.5,533.98) & (1087.7,552.10) & (1118.7,562.71) & \\ inaccurate \(\mathbf{Q}\) & (1027.3,530.24) & (1077.9,548.28) & (1108.8,558.88) & \\ estimated \(\mathbf{Q}\)(no bp) & (1034.5,533.93) & (1085.35,57.18) & (1116.0,562.42) & \\ estimated \(\mathbf{Q}\)(bp) & (1036.1,536.12) & (1086.8,554.10) & (1117.7,564.81) & \\ \hline \(\mathbf{t}\) & **1300 s** & **1400 s** & **1470 s** & \\ \hline Actual position & (1042.4,533.81) & (1091.1,551.54) & (1125.2,563.94) & \\ actual \(\mathbf{Q}\) & (1037.5,533.98) & (1087.7,552.10) & (1118.7,562.71) & \\ inaccurate \(\mathbf{Q}\) & (1027.3,530.24) & (1077.9,548.28) & (1108.8,558.88) & \\ estimated \(\mathbf{Q}\)(no bp) & (1034.5,533.93) & (1085.35,57.18) & (1116.0,562.42) & \\ estimated \(\mathbf{Q}\)(bp) & (1036.1,536.12) & (1086.8,554.10) & (1117.7,564.81) & \\ \hline \(\mathbf{t}\) & **1300 s** & **1400 s** & **1470 s** & \\ \hline Actual position & (1042.4,533.81) & (1091.1,551.54) & (1125.2,563.94) & \\ actual \(\mathbf{Q}\) & (1037.5,533.98) & (1087.7,552.10) & (1118.7,562.71) & \\ inaccurate \(\mathbf{Q}\) & (1027.3,530.24) & (1077.9,548.28) & (1108.8,558.88) & \\ estimated \(\mathbf{Q}\)(no bp) & (1034.5,533.93) & (1085.35,57.18) & (1116.0,562.42) & \\ estimated \(\mathbf{Q}\)(bp) & (1036.1,536.12) & (1086.8,554.10) & (1117.7,564.81) & \\ \hline \(\mathbf{t}\) & **1300 s** & **1400 s** & **1470 s** & \\ \hline Actual position & (1042.4,533. We use another set of simulation experiments to further illustrate the performance of the algorithm. The initial speed of MRS is \(u_{f,0}=0.3\) m/s, the initial heading of MRS is \(\psi_{f,0}=20^{\circ}\) in \(O_{1}\) coordinate frame. The initial position of MRS is \(\left(x_{f,0},y_{f,0}\right)=(50,50)\). The task of MRS is to move with \(u_{f}=0.3\) m/s and travels in a straight path with \(\psi_{f}=45^{\circ}\). The initial speed of AUV is \(u_{v,0}=0\) m/s, the initial heading of MRS is \(\psi_{v,0}=0^{\circ}\) in \(O_{1}\) coordinate frame. The initial position of AUV is \((x_{v,0},y_{v,0})=(0,0)\). The task of AUV is to homing to the MRS with \(u_{v}=0.6\) m/s.