# Correction Strategy of Online Midcourse Guidance for High-Speed Gliding Target Interceptor
## 3 Design of Online Dynamic Correction Strategy for Interceptor
### Design of Online Correction Strategy for Multiple PIP Updates  
The main focus of this section is on the switch between engine start-up thresholds based on IIA and THPEA. During the process of the interceptor flight, unpredictability in PIP updates means that the speed gain \(\left|V_{g}\right|\) is not zero for a long time after each update. At this point, if the engine start threshold is set to the ideal condition \(\varepsilon=0\), then the frequently adjusting engine needs to stay operational throughout the midcourse guidance stage, resulting in excessive fuel consumption, which would diminish the intercepting capabilities at the final guidance stage. Therefore, it is imperative to set the starting threshold for the engine to prevent such waste. Since the PIP appears randomly, it is difficult to determine whether the PIP maneuver at the current instant is redundant. It can be seen that, in the initial stage, the variance of the target position prediction distribution and the THPEA is large. Over time, the tracking time for the target increases, the remaining time of trajectory prediction becomes shorter, and the accuracy of the target trajectory prediction increases. The THPEA gradually converges, which means that the closer it is to the end of midcourse guidance instant, the smaller the THPEA. At the stage of a large THPEA, the interceptor needs to respond to the update of PIP and correct the trajectory through the engine opening in time. As the interceptor flies, the THPEA will continue to converge, the update range of PIP will be reduced, and the maneuvering requirement for the interceptor will be weakened. At a given time, the interceptor could achieve the IIA coverage of THPEA, which means that even if the PIP still updates randomly, it is still within the IIA range of the interceptor and the interceptor no longer needs to perform additional maneuvers. The cover instant of the IIA to the THPEA is regarded as the stage switching point. By setting the start-up threshold in stages, the interceptor can complete the large deviation correction before the stage switching point, and avoid the frequent start-up in the later stage, which can reach the final PIP based on effective fuel saving. According to the analysis of the THPEA in Sections 3.1 and 3.2, the variance change rule of the target location prediction is obtained. The variance of the target position prediction at instant \(t\) is \(\sigma_{x}(t)\), \(\sigma_{y}(t)\), and \(\sigma_{z}(t)\). According to the 3\(\sigma\) criterion, the radius of the ellipsoid formed by the THPEA on three axes is  
\[ \begin{cases}R_{x}(t)<3\sigma_{x}(t)\\ R_{y}(t)<3\sigma_{y}(t)\\ R_{z}(t)<3\sigma_{z}(t)\end{cases}  \tag{32}\]  
since the distribution of target PIPs on the three-coordinate axes is independent for each one, \(R_{max}=\max\left(R_{x}(t),R_{y}(t),R_{z}(t)\right)\) has the greatest impact on the distribution of target PIPs. According to Equation (32), the range of the IIA satisfies \(M=\left\{\left. (x,y,z)\right|\left|x-x_{d}\right|=0,\right.\)\(\left.\left|y-y_{d}\right|\leq S_{max},\left|z-z_{d}\right|\leq S_{max}\right\}\), and \(S_{max}\) is the maximum lateral displacement. In the interception process, if \(R_{max}\geq S_{max}\), it indicates that the maximum IIA cannot cover the THPEA at the current instant, and that large-scale maneuvering correction is still needed; if \(R_{max}<S_{max}\), it means that, at maximum, the IIA can cover the THPEA. Even if there is a certain deviation in the midcourse guidance stage, the target can be successfully intercepted by the terminal guidance maneuver after the seeker starts. There is  
\[\varepsilon= \begin{cases}\varepsilon_{1},\ R_{max}\geq S_{max}\\ \varepsilon_{2},\ R_{max}<S_{max}\end{cases}  \tag{33}\]  
where \(\varepsilon_{1}\) is the engine start threshold in the first half stage and \(\varepsilon_{1}=0\) is taken to ensure the correction capability of the interceptor in this stage; \(\varepsilon_{2}\) is the starting threshold of the engine in the later stage.