# Correction Strategy of Online Midcourse Guidance for High-Speed Gliding Target Interceptor
## 1 Introduction
Some experts also used the polynomial function [7], multiple shooting method [8], and particle swarm optimization method [9]. In [10], an online trajectory planning algorithm was proposed to meet the current and terminal constraints, and then a simple guidance law was used to track the reference path. Some experts have also used convex optimization to generate trajectories online by virtue of its high efficiency for low thrust re-entry trajectory planning, landing path planning, and orbital transfer [11; 12]. In [11], an online guidance framework based on convex programming  
Figure 1: Interceptor and target location diagram. The trajectory of the interceptor can be divided into the boost stage, midcourse guidance stage, and terminal guidance stage. The target trajectory is uncertain, resulting in the continuous updating of the PIP. The function of the midcourse guidance stage is to guide the interceptor to the vicinity of the final PIP, which facilitates the target acquisition by the seeker in the terminal guidance phase. was proposed, and a command correction method was designed to reduce the delay effect based on the sensitivity analysis of nonlinear programming. Reference [13] proposed an autonomous entry guidance algorithm based on the convex programming theory, which could plan a new trajectory online. To improve the efficiency of online solutions, some researchers also proposed combining different methods. For example, references [14; 15] referred to the combination of the model predictive control (MPC) method and convex optimization. Based on the model predictive static programming, reference [16] established a new convex programming framework to solve the optimization problem in a computationally efficient way. Reference [17] proposed an improved continuous convex algorithm based on pseudo-spectrum to solve the rocket landing problem, which has high accuracy and computational efficiency by combining the pseudo-spectrum discretization and convex optimization. Although these methods made efforts to improve the computational efficiency constantly, multiple optimizations were inevitably needed in the multiple-update process of the PIP, which would bring a significant burden to the airborne calculation and affect the computational efficiency. Other methods are unwilling to abandon the nominal trajectory, as they prefer generating a suboptimal trajectory or developing online guidance instructions based on the original nominal trajectory according to the change of terminal constraints, rather than re-searching the appropriate correction instructions in a large allowable domain to carry out online correction as in traditional research. If the modified terminal constraint or disturbed state is not far from the original constraint or disturbed state, the original nominal trajectory can be used to generate a new trajectory through the adjacent optimal control theory. In [18; 19; 20], the terminal position modification was allowed by taking the current state disturbance and the modified terminal constraint as the feedback input, and the control modification was generated by further distinguishing the first-order optimality conditions, all of them used the indirect Legendre Pseudospectral feedback method to design a robust state feedback guidance law to offset the initial trajectory perturbation. In [21], an online optimal midcourse trajectory correction algorithm was designed to make full use of the nominal trajectory information by solving the terminal second-order equation and integrating the disturbance dynamics equation back to the initial time, so the problem of the co-state disturbance being difficult to express was solved. A new online guidance method based on the predictive guidance algorithm and neural network theory was proposed in reference [22], which could guarantee the guidance accuracy in real-time guidance. Based on the neighboring optimal control theory, reference [23] proposed a general guidance method to obtain the integrated guidance and control instructions online.