## 1 Introduction  
With the development of modern high-speed strike weapons, traditional one-to-one interception will face more difficulties against high-speed maneuvering targets. Multivehicle cooperative interception has received a great deal of attention. Compared with a single interceptor, cooperative simultaneous engagement can increase the interception coverage area and improve the interception probability. As one of the key technologies of cooperative engagement, the multivehicle cooperative interception guidance law has been a research hotspot in recent years. In previous studies, the cooperative-guidance law has mainly been divided into two parts: biased proportional navigation guidance [1; 2; 3], and multidirection-guidance [4; 5]. However, some aspects of the guidance performance have yet to be improved, such as the maneuvering-target-capture ability and adaptive-control ability. Therefore, the multivehicle-cooperative-interception problem is of great significance. The biased proportional-based guidance law originates from the individual homing guidance [6; 7], in which the guidance law is designed individually, and the simultaneous engagement is reached by setting the same desired impact time for each interceptor in advance. [PERSON] et al. [6] designed an impact time control guidance (ITCG) law by biased proportional navigation guidance. Moreover, the biased term was designed as a time-error feedback form in the ITCG. As the earliest cooperative guidance method, ITCG laid the foundation for the biased proportional-based guidance law. The core of the biased proportional-based guidance law lies in the accurate estimate of the time-to-go under pure proportional guidance. Based on this, there are two directions that have mainly been studied. One is the improvement of the time-to-go estimation method. [PERSON] et al. [8] adjusted the time-to-go estimation form in 2016, which extended ITCG to nonlinear models,without the limitation of small-angle assumptions. Because of its simple form and high precision, the time-to-go estimation form in [8] is widely used. [PERSON] et al. [9] estimated the time-to-go of a hypersonic vehicle with a new numerical method. Another direction is two-stage guidance. In the two-stage cooperative-guidance law, the second stage is generally designed as the form of the time-feedback-control proportional-guidance law, and the first stage is designed to provide the proper initial condition for the second-stage control. Common design approaches for the first stage include consistency control [10, 11, 12], trajectory shaping [13], and other advanced control methods [14, 15]. It is worth mentioning that most time-to-go estimation forms are established on the basis of the constant-velocity hypothesis [8, 16, 17]. Moreover, most of the research on varying the velocity-time-estimation method is proposed based on uniform varying velocity [18, 19]. These assumptions about the flight velocity reduce the applicable scope of the guidance law in real situations. To solve the problem mentioned above, the multidirection-guidance method has been proposed in recent years. Similar to the traditional angle-constrained guidance law in line-of-sight (LOS) coordinate systems, a control in the normal direction of the LOS is designed to confirm the convergence of the LOS rate. Besides the control command in the normal direction of the LOS, the multidirection-guidance method adds the guidance law in the LOS direction to control the flight time. Therefore, the multidirection-guidance method can realize both the time constraint and the angle constraint. Consistency control is generally applied to guidance in the LOS direction. By exchanging information among vehicles via a communication network, the time-to-go of each vehicle can reach a consensus with a consensus protocol. [PERSON] et al. [20] introduced the fixed-time control technique into the multidirection-guidance method to improve the convergence rate of the system. [PERSON] et al.