## 2 System Model
### Dual-Slot Dynamic ISAL Network
In an asynchronous network, without considering multi-path propagation, the localization signal received by the \(j\)th active node from the \(i\)th active node can be expressed as  
\[u_{i,j}(t)=\alpha_{i,j}s_{i,j}(t-\tau_{i,j}-\Delta t_{i,j})+e_{i,j}(t), \tag{5}\]  
where \(\alpha_{i,j}\), \(\tau_{i,j}\), and \(\Delta t_{i,j}\) are, respectively, the channel gain, the clock offset between active node \(i\) and \(j\), and the delay of the LOS path from the \(i\)th active node to the \(j\)th active node, while \(s_{i,j}(t)\) and \(e_{i,j}(t)\), respectively, represent the transmitted localization signal and the measurement error on the link. In an asynchronous network, the sensing signal transmitted by the \(i\)th active node, received by the \(j\)th active node, and reflected by the target \(tar\) can be expressed as  
\[u_{i,tar,j}(t)=\alpha_{i,tar,j}s_{i,tar,j}(t-\tau_{i,j}-\Delta t_{i,tar,j})+e_{ i,tar,j}(t), \tag{6}\]where \(\alpha_{i,tar,j}\), \(\tau_{i,j}\), and \(\Delta t_{i,tar,j}\) are, respectively, the channel gain, the clock offset between active node \(i\) and \(j\), and the delay of the NLOS path from the \(i\)th active node via the target \(tar\) to the \(j\)th active node, while \(s_{i,tar,j}(t)\) and \(e_{i,tar,j}(t)\), respectively, represent the transmitted sensing signal and the measurement error on the link. RLM-OWR is a ranging method that uses OWR for ranging and calibrates the signal propagation delay with the signals on the reverse link. This method can accurately obtain the relative clock drift rates between different clocks in the asynchronous ISAL networks. The schematic diagram is shown in Figures 5 and 6:  
The specific realization of RLM-OWR is as follows:  
1. Taking the circumstance in slot 1 in Figure 5 as an example, set the clock of node 1 \(c_{1}(t)\) as the reference clock, record \(c_{\text{1a}}\) when \(c_{1}(t)=c_{\text{1a}}\), and broadcast signals with a \"Need Feedback\" time stamp, which is shown as Figure 6a, to the environment by node 1. 2. When the clock of node 2 \(c_{2}(t)=c_{\text{2a}}\), node 2 receives the LOS signal with a \"Need Feedback\" time stamp transmitted from node 1. After the reply time to \(c_{2}(t)=c_{\text{2a}}^{\prime}\), node 2 calculates and records the average of \(c_{\text{2a}}\) and \(c_{\text{2a}}^{\prime}\) as \(c_{\text{2a}}^{\prime\prime}\) and transmits the received signal data packet back to node 1 after unloading its head \"Need Feedback\" and adding another head \"Feedback Authentication\". The signal data packet transmitting to node 1 is shown in Figure 6b. 3. When the clock of node 1 \(c_{1}(t)=c_{\text{1a}}^{\prime}\), node 1 receives the LOS signal with a \"Feedback Authentication\" time stamp transmitted from node 2, and node 1 records its time \(c_{\text{1a}}^{\prime}\). As the time taken to process the signal data packet in (2) is generally on the microsecond scale, it can be approximately assumed that the positions of the moving nodes remain unchanged during this period. Therefore, we take \(c_{\text{1a}}^{\prime\prime}=\frac{c_{\text{1a}}+c_{\text{1a}}^{\prime}}{2}\), and there is \(c_{2}(c_{\text{1a}}^{\prime\prime})=c_{\text{2a}}^{\prime\prime}\). 4. We can obtain \(\tau(c_{\text{1a}}^{\prime\prime})=\tau_{\text{a}}=c_{\text{1a}}^{\prime\prime }-c_{\text{2a}}^{\prime\prime}\). Figure 5: RLM-OWR schematic diagram, where the red line represents the signal propagation between two active nodes. Figure 6: RLM-OWR signal packet. (**a**) Forward link packet. (**b**) Reverse link packet. Similarly, in slot 2, record \(c_{\rm 1b}\), \(c_{\rm 1b}^{\prime}\), and \(c_{\rm 2b}^{\prime\prime}\). We take \(c_{\rm 1b}^{\prime\prime}=\frac{c_{\rm 1b}+c_{\rm 1b}^{\prime}}{2}\), and we can obtain \(\tau(c_{\rm 1b}^{\prime\prime})=\tau_{\rm b}=c_{\rm 1b}^{\prime\prime}-c_{ \rm 2b}^{\prime\prime}\). 6.