## 5 Experiments and Discussion
### Computational Performance Analysis  
To evaluate the computational performance of the proposed method, all numerical operations were implemented and tested on a DSP using single-precision floating-point arithmetic. The main computation for determining the LOS pointing angles consists of scanning angle calculation, attitude transformation, and final angle solving camera angles \(\phi c\) and \(\theta c\). Based on the average of multiple test runs, the total execution time per update cycle is approximately 271 microseconds, consisting of 38.4 us, 102.0 us, and 130.0 us for each step, respectively. In addition, the image motion compensation is implemented through a position-based model that calculates angular displacement as a function of roll angle variation. The computation time for this step is approximately 66.8 microseconds per cycle, as measured on the same DSP platform. The execution time distribution for each computational step is summarized in Figure 23. This lightweight numerical structure supports real-time execution alongside other control tasks. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Proposed Method** & **Traditional Method** \\ \hline System structure & Two-axis frame & Three-axis frame \\ Compensation type & Mirror-based compensation & Three-axis frame compensation \\ Compensation accuracy & 2.4 mm/s & 2.6 mm/s \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of image motion compensation methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time (s)** & **Point (a)** & **Point (b)** & **Point (c)** & **Point (d)** \\ \hline
0 & (304.304, 1950.614) & (1721.270, 2544.267) & (66.847, 450.027) & (1347.972, 542.396) \\
0.005 & (304.614, 1950.379) & (1721.722, 2544.668) & (66.684, 450.012) & (1347.956, 542.487) \\
0.010 & (304.924, 1950.144) & (1722.174, 2545.068) & (66.521, 449.997) & (1347.940, 542.578) \\
0.015 & (305.234, 1949.909) & (1722.627, 2545.469) & (66.357, 449.983) & (1347.924, 542.669) \\
0.020 & (305.544, 1949.674) & (1723.080, 2545.869) & (66.194, 449.968) & (1347.908, 542.760) \\
0.025 & (305.854, 1949.439) & (1723.534, 2546.270) & (66.031, 449.953) & (1347.892, 542.851) \\
0.030 & (306.163, 1949.204) & (1723.988, 2546.671) & (65.867, 449.939) & (1347.875, 542.942) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Time-varying coordinates of ground projection boundary points during compensation. Figure 23: Execution time distribution. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Point (a)** & **Point (b)** & **Point (c)** & **Point (d)** \\ \hline RMS distance deviation (m) & 0.3899 & 0.6047 & 0.1639 & 0.0923 \\ RMS angular deviation (mrad) & 0.1305 & 0.0963 & 0.0798 & 0.0371 \\ \hline Image motion on focal plane (\(\upmu\)m) & 12.0 & 8.9 & 7.4 & 3.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: RMS deviations of ground projection boundary point displacements every 5 ms. Considering a typical control frequency of 1 kHz, which corresponds to a 1 ms processing window, the total computational load of the proposed method occupies less than 30% of the available cycle time. This indicates that the method is computationally efficient and suitable for real-time embedded deployment in airborne imaging systems. The numerical precision of the computed camera angles \(\phi c\) and \(\theta c\) was also examined through a simulation test with a scanning angular velocity of 0.3 rad/s over a duration of 0-2 s. As shown in Figure 24a, the computed values (red discrete points) match the high-precision reference curve (blue line) at every 0.2 s interval. Figure 24b presents the relative error between each computed value and the reference. The root-mean-square error is 4.25 \(\times\) 10\({}^{-8}\) rad, equivalent to 0.04 \(\upmu\)rad, which satisfies the accuracy requirements for most airborne stabilization and imaging tasks. In this test, all variables and operations were implemented using float-precision arithmetic.