## 2 System Model
### Dual-Slot Dynamic ISAL Network  
Figure 4 shows the system model of the dual-slot dynamic ISAL network. In this network, radars and targets are both considered movable, while only the positions of anchors remain the same in different time slots. The signal propagation in each time slot  
Figure 4: ISAL system model with spatiotemporal cooperation, where the solid red, blue, and black lines, respectively, represent the anchor transmission link, the radar transmission link, and the reflection link. The dashed black line and the dashed blue line are, respectively, the trajectories of the moving target and radars. The superscript \((n),n=1,2,\ldots,N\) represents the \(n\)th time slot. is the same as that of the single-slot static ISAL network. The major difference is that the radar mobility brings the possibility of introducing temporal cooperation between different time slots based on velocity information obtained from the intra-node measurements, such as Doppler measurements [14]. The temporal cooperation between different time slots can deliver the spatial localization information in the time dimension. The set of anchors, radars, and targets is respectively represented as \(\mathcal{N}_{\rm a}=\{1,2,\ldots,N_{\rm a}\}\), \(\mathcal{N}_{\rm r}=\{1,2,\ldots,N_{\rm r}\}\), and \(\mathcal{N}_{\rm t}=\{1,2,\ldots,N_{\rm t}\}\). Here, we only take into consideration that \(N_{\rm t}=1\). The node position is expressed as \(\mathbf{p}_{k}=[x_{k},y_{k}]^{\rm T}\), \(k\in\mathcal{N}_{\rm a}\cup\mathcal{N}_{\rm r}\cup\mathcal{N}_{\rm t}\). The distance between different nodes \(i\) and \(j\) is  
\[d_{ij}=\|\mathbf{p}_{i}-\mathbf{p}_{j}\|=\sqrt{(x_{i}-x_{j})^{2}+(y_{i}-y_{j}) ^{2}}, \tag{1}\]  
and the angle between different nodes \(i\) and \(j\) is  
\[\phi_{ij}=\arctan(\frac{y_{j}-y_{i}}{x_{j}-x_{i}}). \tag{2}\]  
There are two kinds of networks to be discussed, namely, the synchronous and the asynchronous ones. In this article, we mainly discuss the asynchronous networks in which there are only clock offsets between the anchors and different radars, but no clock offsets between anchors. We first consider the two kinds of networks in which one-way ranging (OWR) [27] is used for range estimation. Then, we provide a new ranging strategy called reverse-link-modified one-way ranging (RLM-OWR) to introduce temporal cooperation between the two time slots in the estimation of clock offsets. In synchronous 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  
\[r_{i,j}(t)=\alpha_{i,j}s_{i,j}(t-\Delta t_{i,j})+e_{i,j}(t), \tag{3}\]  
where \(\alpha_{i,j}\) and \(\Delta t_{i,j}\) are, respectively, the channel gain and the delay of the LOS path from the \(i\)th to the \(j\)th active node, and \(s_{i,j}(t)\) and \(e_{i,j}(t)\), respectively, represent the transmitted localization signal and the measurement error on the link. In a synchronous 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  
\[r_{i,tar,j}(t)=\alpha_{i,tar,j}s_{i,tar,j}(t-\Delta t_{i,tar,j})+e_{i,tar,j}(t), \tag{4}\]  
where \(\alpha_{i,tar,j}\) and \(\Delta t_{i,tar,j}\) are, respectively, the channel gain and the delay of the NLOS path from the \(i\)th active node via the target \(tar\) to the \(j\)th active node, and \(s_{i,tar,j}(t)\) and \(e_{i,tar,j}(t)\), respectively, represent the transmitted sensing signal and the measurement error on the link.