# Compensation Control Strategy for Orbital Pursuit-Evasion Problem with Imperfect Information
## 6 Results and Discussion
### Examples of Compensation Control Strategy  
To verify the effectiveness of the compensation control strategy proposed in this paper, we compare the orbital pursuit-evasion problem under three scenarios: no time delay, with compensation for time delay, and without compensation for time delay. Consider the following two examples: the first example is that the evader's information has no time delay, and the pursuer plays under the above three scenarios. The second example is that the pursuer's information has no time delay, and the evader plays under the above three scenarios. The covariance of the process noise is set as \(Q_{k}=\text{diag}\big{(}\big{[} \begin{array}{ccc}0.1&0.1&0.1&\end{array}  \big{]}\big{)}\), and the covariance of the measurement noise is set as \(R_{k}=\text{diag}\big{(}\big{[} \begin{array}{ccc}1.75\times 10^{-4}&1.75 \times 10^{-4}&1.75\times 10^{-4}\end{array} \big{]}\big{)}\). We present a Monte Carlo simulation for each case. Figure 5: (a) \(t_{go}\) and (b) \(\Delta t_{go}\) changing with time. Figure 6: The control variable of (a) the pursuer and (b) the evader changing with time. **Example 2**. : _The evader's information has no time delay, and the pursuer plays under three scenarios: no time delay, with compensation for time delay, and without compensation for time delay. The delay time is 1 s._  
1. _Terminal Time is Free_  
Figure 7 shows the estimation errors of the relative state. From Figure 7, it can be seen that the estimation errors in relative position are about the order of magnitude 1 \(\times\) 10\({}^{-5}\) m, and the estimation errors in relative velocity are about the order of magnitude 1 \(\times\) 10\({}^{-3}\) m/s. Figure 8 shows the average relative distance of 100 Monte Carlo runs between the players in three scenarios: the pursuer plays without time delay, without compensation for time delay, and with compensation for time delay. When the pursuer plays without time delay, the average interception time is 209.56 s. The average terminal distance between the two players is 0.9013 m, which is less than the safe distance. When the pursuer plays without compensation for time delay, the average relative distance between the two players reaches the minimum value of 19.1841 m at 206.89 s. After that, the relative distance increases. The reason is that after a period of acceleration, the velocity has reached a relatively large value. After the two players miss each other, it takes a while for the velocity to change. However, the distance between the players still increases, which  
Figure 7: The estimation errors of the relative state: (**a**) X, (**b**) Y, (**c**) Z, (**d**) V\({}_{\rm X}\), (**e**) V\({}_{\rm Y}\), and (**f**) V\({}_{\rm Z}\). means the pursuer cannot intercept the evader in a short time. When the pursuer plays with compensation for time delay, the average interception time is 211.69 s. The average terminal distance between the two spacecraft is 0.9763 m, which is less than the safe distance. By comparison, we can see that with compensation for time delay, the pursuer can significantly reduce the relative distance between the pursuer and the evader. Although the interception time is longer than that in the no time delay scenario, it still intercepts the evader successfully. Figure 9 shows the average \(t_{go}\) and \(\Delta t_{go}\) of 100 Monte Carlo runs between the players in three scenarios: the pursuer plays without time delay, without compensation for time delay, and with compensation for time delay. When the pursuer plays without time delay, \(t_{go}\) decreases linearly with time, \(\Delta t_{go}\) is a non-negative value during the confrontation. When the pursuer plays without compensation for time delay, the evader's time-to-go \(t_{go}^{E}\) suddenly increases at 177.76 s, which means the evader can avoid capture for a longer time. This phenomenon is caused by a change in the system state.