## 3 Local Consensus-Based Bundle Algorithm Method Considering Sensor Switching
### Value Loss Factor  
The traditional HGV altitude prediction is the center of the longitudinal uncertainty region (LUR). \(Lr\) is the LUR range, which is described in the following form:  
\[Lr=\left\{ \begin{array}{l}[h-R_{n}*A_{2}*v,h+R_{n}*A_{2}*v],A_{1}=0\\ [h-R_{n}(A_{2}*v-g),h+R_{n}(A_{2}*v-g)],A_{1}=1\end{array} \right. \tag{17}\]  
where \(A_{1}\) and \(A_{2}\) are output values of joint prediction networks, and \(h\) and \(v\) are obtained by the trajectory prediction algorithm. The LUR width coefficient \(R_{n}\) and gravitational acceleration \(g\) are constant values. The LUR of the vehicle is calculated separately according to longitudinal maneuver intentions \(A_{1}\). Then, the widths of LUR coefficients are set independently according to different maneuver types. _Tr_ is the lateral uncertainty region (HUR) range, which is described in the following form:  
\[Tr_{o}^{\max}=\alpha_{o}+k_{o}|A_{4}|\cos\Bigl{(}P-\frac{\pi}{2}*A_{3}\Bigr{)} /(R_{e}+H) \tag{18}\]  
\[Tr_{o}^{\min}=\alpha_{o}-k_{o}|A_{4}|\cos\Bigl{(}P-\frac{\pi}{2}*A_{3}\Bigr{)} /(R_{e}+H) \tag{19}\]  
\[Tr_{a}^{\max}=\alpha_{a}+k_{a}|A_{4}|\sin\Bigl{(}P-\frac{\pi}{2}*A_{3}\Bigr{)} /(R_{e}+H) \tag{20}\]  
\[Tr_{a}^{\min}=\alpha_{a}-k_{a}|A_{4}|\sin\Bigl{(}P-\frac{\pi}{2}*A_{3}\Bigr{)} /(R_{e}+H) \tag{21}\]  
where \(\alpha_{o}\) and \(\alpha_{a}\) are the predicted values of the vehicle's latitude and longitude in the conventional trajectory prediction algorithm; \(P\) and \(H\) are the predicted values of the bank angle and the altitude; and \(k_{o}\) and \(k_{a}\) are the latitude and longitude HUR width coefficients. As described in the literature, the LCBBA is an iterative two-phase algorithm. These two phases are a bundle building phase and a task consensus phase. In the bundle building phase, each vehicle greedily generates an ordered list of assignments. In the task consensus phase, conflicting duties are identified and resolved through local communication between neighboring satellites. The uncertainty loss factor and sensor rotation decision are improved for the bundle building phase, and the task consensus phase still uses the method of the LCBBA, which is not repeated in this paper. The line of sight angle \(\alpha_{s}\) of the satellite to the vehicle is defined as:  
\[\alpha_{s}=\alpha_{t}-\alpha_{e} \tag{22}\]  
where \(\alpha_{t}\) is the line of sight angle of the satellite to the vehicle, \(\alpha_{e}\) is the lower limit of the proximity observation angle and the line of sight angle of the satellite to the tangent of the Earth. The loss coefficients \(L_{l}^{u}\) are described as follows:\[L_{l}^{n}=\left\{ \begin{array}{ll}1-e^{-\frac{\alpha_{l}^{n}}{C_{l}n^{n}}}&,0 \leq\alpha_{s}^{n}-\alpha_{e}^{n}\leq\alpha_{j}\\ 0&,\alpha_{s}^{n}-\alpha_{e}^{n}<0\\ 1&,\alpha_{s}^{n}-\alpha_{e}^{n}>\alpha_{j}\end{array} \right. \tag{23}\]  
The angular range \(\alpha_{j}\) of the Earth's limbic interference and the scaling factor \(C_{l}\) are constants. The infrared sensor has a maximum detection distance constraint. The line of sight distance \(D_{s}\) between the satellite and the vehicle has a detection accuracy degradation problem when approaching the sensor detection distance maximum \(D_{l}\). The distance loss coefficient \(L_{t}^{n}\) is described as follows:  
\[L_{t}^{n}=\left\{ \begin{array}{ll}1&,D_{s}^{n}<D_{a}\\ 1-e^{-\frac{D\pi-D\pi}{C_{l}(D_{l}-D_{s}^{n})}}&,D_{s}^{n}\leq D_{s}^{n}\leq D _{l}\\ 0&,D_{s}^{n}>D_{l}\end{array} \right. \tag{24}\]  
where \(D_{a}\) is the distance when tracking accuracy starts to decline. The constant \(C_{t}\) is the decline scaling factor. The observation angle loss coefficient \(L_{t}^{n}\) and the distance loss coefficient \(L_{t}^{n}\) are simultaneously used on the value function to obtain the cumulative tracking score in the following form:  
\[C_{n,k}=L_{l}^{n}*L_{t}^{n}*C_{n,k}^{R} \tag{25}\]  
where \(C_{n,k}^{R}\) is the theoretical value of the value function.