# Independent Random Recurrent Neural Networks for Infrared Spatial Point Targets Classification
## 2 Infrared Radiation Sequence Model
### Infrared Radiation Sequence Simulation  
The infrared radiation model and the attitude motion model of the spatial point target are analyzed, and the main factor affecting the target radiation sequence (projection area) are discussed in Sections 2.1 and 2.2. Based on the above model, a visual simulation experiment is performed on the infrared radiation sequence of the spatial point target in this section.  
Our simulation is based on the elliptical ballistic theory to calculate the flight path of a spatial target. Assuming that the spatial target is only affected by the gravity of the Earth, according to the law of universal gravitation and [PERSON]'s second law, the differential equation of the basic motion of the space object is  
\[\mathbf{r}^{\prime\prime}=-\frac{\mu}{r^{2}}\frac{\mathbf{r}}{r}, \tag{8}\]  
where \(\mu=3.986005\times 10^{14}\) m\({}^{3}\)/s\({}^{2}\) is the gravity constant of the Earth.  
According to theoretical mechanics, the space target flight trajectory is located in the ballistic plane determined by its velocity vector and the Earth's gravitational vector. According to the law of conservation of momentum and the law of universal gravitation, the equation of elliptical ballistic motion of the target can be derived as  
\[r=\frac{P}{1+e\cos f}, \tag{9}\]  
where \(e\) is the eccentricity of the elliptical trajectory, and \(P\) is the half-diameter.  
We assume that the scanning frequency of the infrared sensor is 50 Hz, the aperture of the lens is 0.25 m, and the detection wavebands is 8-10 \(\upmu\)m [26]. Assume that the starting point of the free flight segment is (135\({}^{\circ}\) E, 52\({}^{\circ}\) N, 151 km) and the highest point of the flight path is 457.3 km from the ground. The unit vector of LOS is set as n' = [0.59, 0.34, 0.73].  
The simulation uses spatial point target data of four different shape types, including cone, cone-cylinder, ball-base cone, and curved pieces. The shape, physical property, micro-motion parameters, and sensor property parameters of various spatial targets are shown in Table 1[4; 13; 22].  
Considering the thermal noise, non-uniformity of the infrared sensor, etc., Gaussian additive white noise is used to describe the data deviation caused by these factors in the infrared radiation simulation to improve the authenticity of the data [22]. The gray scale sequences generated by these target shapes are shown in Figure 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Type1** & **Type2** & **Type3** & **Type4** \\ \hline
3 Dmodels & & & & \\ Size parameters & \(\mathrm{r=0.3\pm 0.05\,m}\) & \(\mathrm{r=0.3\pm 0.05\,m}\) & \(\mathrm{r=0.3\pm 0.05\,m}\) & \(\mathrm{r=0.3\pm 0.05\,m}\) & \(\mathrm{h=0.5\pm 0.20\,m}\) \\  & \(\mathrm{h=1.0\pm 0.25\,m}\) & \(\mathrm{h_{2}=0.6\pm 0.10\,m}\) & \(\mathrm{w_{t}=1.0\pm 0.25\,m}\) & \(\mathrm{\varphi=0.6\pm 0.1\pi}\) \\ Micro-motion & & & & \\  & \(\mathrm{\Theta=0.2\pi}\) & \(\mathrm{\theta=0.2\pi}\) & & \\ Micro-motion & & \(\mathrm{\omega_{s}=5.0\pi\,rad/s}\) & \(\mathrm{\omega_{s}=5.0\pi\,rad/s}\) & \(\mathrm{\theta=0.3\pi}\) & \(\mathrm{\theta=0.3\pi}\) \\  & \(\mathrm{\alpha_{c}=0.0\pi}\) & \(\mathrm{\alpha_{c}=0.0\pi}\) & \(\mathrm{\alpha_{t}=0.0\pi}\) & \(\mathrm{\alpha_{t}=0.0\pi}\) \\  & \(\mathrm{\beta_{c}=0.35\pi}\) & \(\mathrm{\beta_{c}=0.35\pi}\) & \(\mathrm{\beta_{t}=0.3\pi}\) & \(\mathrm{\beta_{t}=0.2\pi}\) \\  & \(\mathrm{\omega_{c}=1.0\pi\,rad/s}\) & \(\mathrm{\omega_{c}=1.0\pi\,rad/s}\) & \(\mathrm{\omega_{t}=1.0\pi\,rad/s}\) & \(\mathrm{\omega_{t}=1.0\pi\,rad/s}\) \\ Coating material & \(\mathrm{\alpha_{V}/\varepsilon\,IR}\) & 0.85/0.7 & 0.25/0.50 & 0.25/0.50 & 0.52/0.20 \\ Target weight (g) & 200 & 120 & 85 & 45 \\ Initial temperature (K) & 320 & 320 & 320 & 680 \\ Radiation Intensity & & & & \\ Sequence & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters for four classes of spatial targets.  
Figure 2: Infrared radiation intensity sequence of four shapes of spatial targets.