## 4 Results
### Performance Comparison  
The following presents an analysis of the experimental results obtained from the different methods evaluated in the study. As shown in Table 2, several methods are compared, including the proposed method (8B-PGDM) and different orders of dead reckoning (DR) methods under various conditions. For the method 8B-PGDM, according to the parameter estimation (\(x_{f}^{*}=3998\), \(y_{f}^{*}=-39,999\), \(\theta_{f}^{*}=1.0471\) rad) obtained by the 8B-PGDM, the flight trajectory of the missile can be obtained by introducing the guidance law of the formula in Equation (24) to an inner continuous system simulation process as per Equation (4). \[ \begin{split}\dot{\theta}&=4\cdot\dot{q}+2(1.0471- q)\cdot\frac{\dot{r}}{r}\\ q(0)&=tan^{-1}\frac{-39,999-y(0)}{3998-x(0)}\\ r(0)&=\sqrt{3998^{2}+(-39,999)^{2}}\end{split}  \tag{24}\]  
As for the control group, the current state is estimated by extrapolation in the same way as the step size 1 ms of the continuous system simulation, and the motion state of the object is obtained through observation or communication only when the update condition is triggered (threshold \(\leq\) 10 m or \(T\) = 1 s). The Mean Squared Error (MSE) values of different methods provide crucial insights into their performance. As shown in Table 2, the proposed method, 8B-PGDM, achieves an MSE of 0.94459, which is remarkably lower than those of the other methods. In contrast, the first-order DR method shows varying MSE values depending on the update criteria. When the update criterion is a fixed period of 1 s, the MSE is 18.053. However, when the update is triggered by the condition, the MSE increases slightly to 19.913. The second-order DR method exhibits a significantly higher MSE of 53176 when the update criterion is a fixed period of 1 s, suggesting poor performance under this condition. Interestingly, when the update is based on the condition, the second-order DR method has the same MSE as the first-order DR method under the same condition, with a value of 19.913. This comparison  
Figure 7: The 8-Branch Pseudodgradient Descent Method. Only branch 7 in red line decorated with triangles that corresponding to the situation \({}^{*}\!s_{2},s_{1},s_{0}=---+^{+}\) asynchronous convergence to reach the termination threshold with \(\epsilon=1.094\) after 9 iterations. indicates that the 8B-PGDM method outperforms both the first and second-order DR methods in terms of minimizing the MSE, regardless of the update criteria. The large MSE of the second-order DR method under the fixed 1 s update criterion might imply that the second-order approximation is not effective under this setting. Meanwhile, the similar MSE of both first and second-order DR methods under this condition suggests that the order of approximation may not be the sole factor influencing the MSE, and other factors related to the update criteria could have a more significant impact. The number of samples required by each method also reveals important information about their computational cost, observation, and communication needs. As presented in Table 2, the 8B-PGDM method uses only three samples, which is considerably fewer than the sample times of the other methods. The first and second-order DR methods both require 146 samples when the update criterion is a fixed period of 1 s, indicating a higher computational cost associated with this update strategy. When the update is based on this condition (\(\epsilon>10\) m), both methods use 122 samples, showing that the error-based update criteria reduce the number of samples required compared to the fixed 1 s update criteria. The substantial difference in sample times between the 8B-PGDM method and the DR methods suggests that the 8B-PGDM method is more efficient in terms of computational cost, especially considering its relatively low MSE.