# 3D Void Handling Geographic P2P-RPL for Indoor Multi-Hop IR-UWB Networks
## 2 Related Works
### IR-UWB Based 3D Multi-Hop Self Localization with Bounding-Box and Mobile Tracking Scheme  
To perform the greedy forwarding strategy, the location information of network nodes is required. We propose a fully-distributed 3D multi-hop self localization algorithm as shown in Figure 2. Every node participates in the 3D bounding-box algorithm, which describes the statistically possible residing region of nodes as the B-box state [2; 12; 13]. By exchanging UWB ranging messages containing the nodes' current B-box states and ranging measurements between two nodes, these nodes update their previous B-box states based on the ranging measurement result and the other node's B-box state. In the 3D mobile tracking scheme, mobile nodes also estimate their movement by constructing the multi-sensor integrated localization (MSL) extended Kalman filter (EKF) [14] and use it to update their B-box states. Using the inertial measurement unit (IMU) data, the mobile nodes' navigation states are predicted from the inertial navigation system (INS) mechanism [15]. The obtained navigation states are used to construct the EKF system model by applying the INS error model [16]. Then, magnetometer, mass-flow sensor, and barometer data are calibrated and utilized in the heading and velocity updates in the EKF [14]. After the navigation state estimates are updated, the B-box states of the mobile nodes are updated and provided to static nodes through the UWB ranging message exchange procedure. The presented IR-UWB-based 3D multi-hop self localization with bounding-box and the mobile tracking scheme provides significant improvement of the network's overall positioning accuracy. Figure 1: Routing strategies of P2P-RPL, PF-P2P-RPL and GVA-P2P-RPL. In (**a**), P2P-RPL floods P2P-DIO messages throughout the whole network. In (**b**), PF-P2P-RPL floods P2P-DIO messages only to the nodes in the restricted flooding zone, which is determined by the source and destination’s locations. In (**c**), GVA-P2P-RPL selects the closest neighbor node to the destination and forwards the P2P-DIO message to that neighbor node. The overall 3D B-box determination process is illustrated in Figure 3. Node C's B-box state vector \(\mathbf{b}_{C}\) is determined when receiving B-box information \(\mathbf{b}_{B}\) from another node \(B\) in the ranging message exchange as follows:  
\[ \begin{split}\mathbf{b}_{C}=[\max(x_{C}^{lwb},x_{B}^{lwb}-(d_{CB}+ e_{r}))&\min(x_{C}^{upb},x_{B}^{upb}+(d_{CB}+e_{r}))\\ \max(y_{C}^{lwb},y_{B}^{lwb}-(d_{CB}+e_{r}))&\min(y_ {C}^{upb},y_{B}^{upb}+(d_{CB}+e_{r}))\\ \max(z_{C}^{lwb},z_{B}^{lwb}-(d_{CB}+e_{r}))&\min(z_ {C}^{upb},z_{B}^{upb}+(d_{CB}+e_{r}))]^{T}\end{split}  \tag{1}\]  
where \(x_{C}^{lwb},y_{C}^{lwb}\), \(z_{C}^{lwb}\) are lower bounds of \(\mathbf{b}_{C}\) and \(x_{C}^{upb},y_{C}^{upb},z_{C}^{upb}\) are upper bounds of \(\mathbf{b}_{C}\), \(d_{CB}\) is the measured distance between \(C\) and \(B\), and \(e_{r}\) is the maximum ranging error value. \(e_{r}\) is set to 50 cm in this paper's simulations, referring to the Decawave DW1000 module ranging measurements [17]. Mobile nodes also update their B-box states based on the position estimation of the mobile tracking scheme in addition to the previous B-box state update. Using the IMU data, the INS mechanization [15] provides the mobile nodes' navigation-state prediction. Applying the INS error model [16], the EKF system model is constructed as in [14]. Calibrating  
Figure 3: 3D bounding-box determination process. Node \(B\) initializes its B-box state vector \(\mathbf{b}_{B}\) after exchanging ranging message with node \(A\). Node \(C\) initializes its B-box state vector \(\mathbf{b}_{C}\) after exchanging ranging message with node \(D\). Finally, \(\mathbf{b}_{C}\) is updated after exchanging ranging message with \(B\) and is depicted as the bold dashed lines. Figure 2: IR-UWB-based 3D multi-hop self-positioning with bounding-box and mobile tracking scheme.