# An Integrity Monitoring Method for Navigation Satellites Based on Multi-Source Observation Links
## 3 Design of Integrity Monitoring System with Multi-Source Observation Links
### Monitoring Processing  
The proposed integrity monitoring system can conduct multi-dimensional monitoring according to the observation conditions of the target satellite. The monitoring processing is shown in Figure 6.  
1. Collecting observation data of the target satellite through satellite-to-ground, inter-satellite, and satellite-based observation links. 2. Constructing a minimum satellite-based observation unit whose \(C_{\min}\) is no less than M. The main control station gains the returned navigation messages through the  
Figure 6: Processing of integrity monitoring system. minimum satellite-based observation unit. If more than half of returned navigation messages are inconsistent, the target satellite may be abnormal. 3. Constructing the orbit determination unit whose SPDOP is minimum and determining the orbit of the target satellite with the chosen observation links. If residuals of orbit determination exceed the threshold, the target satellite may be abnormal. 4. Estimating the integrity of the target satellite according to valid observation links. 1. When valid satellite-to-ground observation links are more than one, data in the signal field and message field should be synchronously collected by satellite-to-ground and satellite-based observation links. The data in the signal field mainly contains the state of the satellite clock, hopping indicators of frequency and phase in signal, and signal delay. Data in the message field mainly contain the messages mentioned in Table 1. Through fusion processing of multi-source observation data, the main control station can evaluate whether there are any anomalies in the target satellite and generate related integrity messages. 2. When there are no valid satellite-to-ground observation links, inter-satellite ranging data and autonomous navigation messages should be gained through inter-satellite links. The state of the target satellite can be judged by five kinds of information: SIF, residuals of observation data in orbit, residuals of observation in a clock, the difference value of orbit determination errors (\(\mathit{URE}_{\text{Orb},\mathit{t}_{i}}-\mathit{URE}_{\text{Orb},\mathit{t }_{i-1}}\)), and the difference value of absolute clock errors (\(\text{Clk}_{\text{abs}\_{i}}-\text{Clk}_{\text{abs}\_{i,\mathit{t}_{i-1}}}\)). If SIF, residuals of observation data, and/or difference value exceed the limitation, the target satellite may be abnormal. Residuals can be calculated using inter-satellite ranging data. Considering the time division bidirectional measurement system of inter-satellite links, two-way ranging data should be normalized at the same time. The observation data can be described as follows. \[ \begin{array}{l}\rho_{BA}(T_{0})=\rho^{\prime}_{BA}(T_{1})+\Delta\rho_{BA}\\ =\left|\overrightarrow{r}_{A}(T_{0})-\overrightarrow{r}_{B}(T_{0})\right|+c \cdot(clk_{A}(T_{0})-clk_{B}(T_{0}))+c\cdot(\tau_{A}^{\mathit{Recv}}+\tau_{B} ^{\mathit{Send}})+\Delta\delta_{BA}+\varepsilon\\ \\ \rho_{AB}(T_{0})=\rho^{\prime}_{AB}(T_{2})+\Delta\rho_{AB}\\ =\left|\overrightarrow{r}_{A}(T_{0})-\overrightarrow{r}_{B}(T_{0})\right|+c \cdot(clk_{B}(T_{0})-clk_{A}(T_{0}))+c\cdot(\tau_{B}^{\mathit{Recv}}+\tau_{A} ^{\mathit{Send}})+\Delta\delta_{AB}+\varepsilon\end{array}  \tag{8}\]  
where \(\rho_{BA}\) and \(\rho_{BA}\) represent ranging data, subscripts \(A\) and \(B\) represent satellite \(A\) and satellite \(B\), \(\overrightarrow{r}\) represents the three-dimensional position vector, \(clk\) is the clock error, \(\tau^{\mathit{Send}}\) and \(\tau^{\mathit{Recv}}\) represent respectively the sending delay and receiving delay, \(c\) is the speed of light, \(\varepsilon\) represents noise and other unmodeled errors, and \(\Delta\delta\) represents modeled errors such as the phase center correction of the satellite antenna and correction of the relativistic effect. By summing and differentiating the two-way ranging data, orbit and clock parameters can be decoupled. Residuals of observation data in orbit can be gained using Formula (8) plus Formula (9).