# Correction Strategy of Online Midcourse Guidance for High-Speed Gliding Target Interceptor
## 2 Model Description
### Motion Model of the Interceptor in Midcourse Guidance  
An interceptor with multi-stage vectored thrust engines is investigated in this paper. The whole process of interceptor flight can be divided into the boost stage, midcourse guidance and terminal guidance. The boost engine works in the boost section, and the vectored thrust engine works to provide a maneuvering capability during midcourse and terminal guidance. The difference between the midcourse and terminal is whether the target seeker is on or off, and the target seeker only works in the terminal guidance. Therefore, the task of the midcourse guidance is to guide the interceptor to the vicinity of the target. The interceptor in the midcourse guidance and the terminal guidance are mainly driven by the engine system. The thrust direction is along the axis direction of the interceptor and passes through the interceptor centroid. By adjusting the attitude of the interceptor, the interceptor can maneuver in different directions. The attitude of the interceptor is determined by six attitude control engines distributed around the interceptor. The configuration of interceptor is shown in Figure 2. Due to the small distance covered by the interceptor compared to the Earth's circumference, and because the fuel consumption for most regular missiles is often assumed to be a constant value in calculations, the two following assumptions are made:  
The engine exhaust velocity and the normalized mass burn rate are constants;  
A nonrotating sphere model without J2 perturbation is used to describe the relationship between the state parameters and other variables. In the East-North-Up coordinate system, the motion model of the interceptor in midcourse guidance is  
Figure 2: Interceptor configuration. The attitude of the interceptor can be controlled by six attitude control engine combination switchers for three channels, of which engines No. 2 and No. 5 can be used for pitch channel control; (No. 1 + 6) and (No. 3 + 4) can be used for yaw channel control; and (No. 1 + 4) and (No. 3 + 6) can be used for roll channel control. \[ \begin{cases}\frac{dx}{dt}=V_{x}\\ \frac{dy}{dt}=V_{y}\\ \frac{dz}{dt}=V_{z}\\ m\frac{dV_{x}}{dt}=Pu_{on-off}\text{cos}\theta\text{cos}\psi-X\text{cos}\theta \text{cos}\psi_{V}\\ \phantom{\frac{dy}{dt}}+Y(\text{sin}\gamma_{V}\text{sin}\psi_{V}-\text{sin} \theta\text{cos}\gamma_{V}\text{cos}\psi_{V})\\ \phantom{\frac{dy}{dt}}+Z(\text{sin}\theta\text{sin}\gamma_{V}\text{cos}\psi_ {V}+\text{cos}\gamma_{V}\text{sin}\psi_{V})-mg_{x}\\ m\frac{dV_{y}}{dt}=Pu_{on-off}\text{sin}\theta-X\text{sin}\theta+Y\text{cos} \theta\text{cos}\gamma_{V}\\ \phantom{\frac{dy}{dt}}-Z\text{cos}\theta\text{sin}\gamma_{V}-mg_{y}\\ m\frac{dV_{z}}{dt}=-Pu_{on-off}\text{cos}\theta\text{sin}\psi+X\text{cos} \theta\text{sin}\psi_{V}\\ \phantom{\frac{dy}{dt}}+Y(\text{sin}\gamma_{V}\text{cos}\psi_{V}+\text{sin} \theta\text{cos}\gamma_{V}\text{sin}\psi_{V})\\ \phantom{\frac{dy}{dt}}+Z(\text{cos}\gamma_{V}\text{cos}\psi_{V}-\text{sin} \theta\text{sin}\gamma_{V}\text{sin}\psi_{V})-mg_{z}\\ \frac{dm}{dt}=-m_{0}u_{on-off}\delta_{T}\end{cases}  \tag{1}\]  
where \(x,y,z\) represent the positional coordinates in the East-North-Up coordinate system; \(V_{x},V_{y},V_{z}\) denote the individual components of the velocity vector; \(m\) is the mass of the interceptor; \(m_{0}\) is the initial mass; \(P\) is the thrust of the engine; \(u_{on-off}\) represents the engine on-off instruction; \(\vartheta\) and \(\psi\) are the pitch angle and yaw angle; \(X,Y,Z\) are the resistance, lift, and lateral force; \(\gamma_{V},\psi_{V},\theta\) are the inclination angle, trajectory deviation angle, and trajectory inclination angle; \(g_{x},g_{y},g_{z}\) represent the components of the gravitational acceleration under the central gravity field in the East-North-Up coordinate system; and \(\delta_{T}\) is the fuel consumption per second of the engine. \[\rho(h)=\rho_{0}e^{-h/H} \tag{2}\]  
where the sea-level atmospheric density \(\rho_{0}=1.226\) kg/m\({}^{3}\), \(H=7254.24\) m is the reference height.