2.2.3. Ballistic Target

The ballistic missile model is simulated including phases of boost, free-flight, and reentry as described in [26]. The acceleration acting on the ballistic target in each phase is expressed as follows.

$$\begin{aligned} \text{Boost phase}: \mathbf{a} &= \mathbf{a}\_{thrust} + \mathbf{a}\_{drag} + \mathbf{a}\_{gravity} \\ \text{Free}-\text{flight phase}: \mathbf{a} &= \mathbf{a}\_{gravity} \\ \text{reentry phase}: \mathbf{a} &= \mathbf{a}\_{drag} + \mathbf{a}\_{gravity} \end{aligned} \tag{2}$$

where

$$\begin{aligned} \mathbf{a}\_{thrust} &= -\frac{\mathbf{T}}{m} \mathbf{u}\_T\\ \mathbf{a}\_{\mathcal{G}matrix} &= -\frac{\mu}{||\mathbf{x}||^3} \mathbf{x} \\ \mathbf{a}\_{drag} &= -\frac{\rho(h) ||\mathbf{v} \parallel||}{2\beta} \mathbf{v} \end{aligned} \tag{3}$$

Here, acceleration regarding Coriolis force can be added according to the coordinate system [26]. In Equation (3), **T** stands for the thrust magnitude, *m* stands for target mass, **u***<sup>T</sup>* stands for the unit vector which indicates thrust direction, *μ* stands for the Earth's gravitational constant, **x** stands for the vector from the Earth center to the target, *ρ* stands for the air density, *h* denotes target altitude, *β* stands for the ballistic coefficient, and **v** denotes the target velocity vector. Based on this, the trajectories of the ballistic targets in the Earth-Centered Earth-Fixed (ECEF) coordinate systems were generated, as can be seen in Figure 2.

**Figure 2.** Randomly generated sample trajectories of ballistic targets.
