## 5 Link Budget Analysis for the Measurements of Non-Cooperative Targets  
The complete link schematic of this part is shown in Figure 6, which mainly includes the analysis of the load-to-noise ratio of the non-cooperative spacecraft tracking and measurement link in Earth-Moon space based on the CEI and BeiDou interplanetary link. The BeiDou-3 satellite transmits the inter-satellite link signal, which is reflected back by the Earth-Moon space target after irradiating it, and the signal is then received by the CEI array on the ground. Figure 6: Complete link schematic for the measurements of non-cooperative targets. The load-to-noise ratio of the non-cooperative spacecraft tracking and measurement link in Earth-Moon space based on the CEI and BeiDou interplanetary link can be expressed as follows:  
\[C/N_{0}=C-N_{0} \tag{30}\]  
where \(C\) is the received signal power in \(dB\) at the CEI receiving array; \(N_{0}\) is the thermal noise power in \(dB\); and the carrier-to-noise ratio \(C/N_{0}\) is in \(dB-HZ\). The received signal power \(C\) and the thermal noise power \(N_{0}\) satisfy the following relations, respectively:  
\[C=T_{\rm transmit}+G_{\rm transmit}(BD\to space)+G_{\rm receive (space\rightarrow\rm CEI)} \tag{31}\] \[-L_{reflect}-L_{BD\to CEI}-L_{receive}\]  
\[N_{0}=10\log_{10}[k_{B}(T_{antenna}+T_{amplifier})] \tag{32}\]  
where \(T_{\rm transmit}\) is the GNSS interstellar link signal transmit power in dBW; \(G_{\rm transmit}(BD\to space)\) and \(G_{\rm receive(space\rightarrow\rm CEI)}\) are the antenna gain of the GNSS interstellar link transmit and the CEI array receive toward the targets in dBi, respectively; \(L_{reflect}\) is the GNSS GNSS interstellar link signal reflection loss through the targets in \(dB\); \(L_{BD\to CEI}\) is the GNSS signal transmission loss in \(dB\) in Earth-Moon space; \(L_{receive}\) is the reception loss in \(dB\) at the CEI receiving array end; \(k_{B}\) is Boltzmann constant, \(k_{B}=1.3806452\times 10^{-23}\) J/K; and \(T_{antenna}\) and \(T_{amplifier}\) are the antenna and amplifier noise temperature in \(K\), respectively. \(L_{BD\to CEI}\) in (31) satisfies:  
\[L_{BD\to CEI}=20\log_{10}[\frac{4\pi f_{iBD}(d_{i(BD\to space)}+d_{i(space \to CEI)})}{c}] \tag{33}\]  
where \(f_{iBD}\) is the Beidou interplanetary link signal power, \(d_{i(BD\to space)}\) is the distance between the Beidou-3 satellite transmitting the Beidou interplanetary link signal and the non-cooperative spacecraft, and \(d_{i(space\to CEI)}\) is the distance between the non-cooperative spacecraft and the ground-based CEI receiver array. The antenna noise temperature \(T_{antenna}\) and the amplifier noise temperature \(T_{amplifier}\) in (32) satisfy the following relations, respectively:  
\[T_{antenna}=T_{antenna\_1}+T_{antenna\_2}\] \[=T_{physical\_antenna}\cdot(\frac{1}{\epsilon_{antenna}}-1) \tag{34}\] \[+T_{physical\_antenna}\cdot[\frac{25\Omega_{matrix}T_{ brightness\_earth}+\Omega_{mean}T_{brightness\_mean}+(4\pi-\Omega_{earth}-\Omega_{mean})\cdot T_{brightness\_ cosmic}}{4\pi}]\]  
\[T_{amplifier}=T_{physical\_amplifier}\cdot(10^{N_{figure}}-1) \tag{35}\]  
where \(T_{antenna\_1}\) is the ohmic loss caused by the antenna's own defects; \(T_{antenna\_2}\) is the thermal noise captured by the antenna from the surrounding environment; \(T_{physical\_antenna}\) is the physical temperature of the antenna; \(e_{antenna}\) is the antenna efficiency; \(\Omega_{earth}\) and \(\Omega_{moon}\) are the fixed angles subtracted by the Earth and the Moon, respectively, when the CEI receiving array is the viewing angle; \(T_{brightness\_earth}\), \(T_{brightness\_moon}\) and \(T_{brightness\_cosmic}\) are the brightness temperatures of the Earth, the Moon, and the cosmic background, respectively; \(T_{physical\_amplifier}\) is the physical temperature of the amplifier; and \(N_{figure}\) is the amplifier noise factor.