# An Efficient Single-Anchor Localization Method Using Ultra-Wide Bandwidth Systems
## 3 Single-Anchor Localization Method
### Localization Protocol  
We first introduce the localization protocol of the SAL method. As shown in Figure 1, the anchor first broadcasts an Init message to agents and initiates the measurement process. In the payload of the Init message, the anchor writes the fixed time delay \(t_{0}^{I}\) of the Init and Sync messages. At the same time, the anchor assigns a fixed delay \(\delta_{i},i\in\mathcal{N}_{\mathrm{a}}\) to agent \(i\) according to their device ID and writes them into the payload. Then the agents can extract their respective delay based on their ID after receiving the message. Note that \(\delta_{i}\) means an extra delay and this delay is different for each agent. The purpose of introducing \(\delta_{i}\) is to distinguish different messages from different agents and since the width of each UWB pulse is within 10 nanoseconds, then two MPCs with the arrival time more than 10 nanoseconds can be discriminated from the CIR. Note that as the difference between the distances from multiple agents to the anchor increases, the interval also needs to be increased, otherwise there may be overlap. Common ultra-wideband chips can achieve ranging over 100 m. After mathematical conversion, the \(\delta_{i}\) needs to be greater than about 600 nanoseconds. However, the length of the CIR register is 1016 ns, and the allowable agent capacity will be less than three, which is a huge limitation for the proposed protocol. However, the angle measurement error will increase as the distance between the agent and the anchor increases. Therefore, in order to ensure high accuracy, the distance between the agent and the anchor should not be too long. In the case where the coverage range of the anchor is 20 m, in order to ensure that the messages of all agents do not overlap, the number of agents is less than about 7. In practical, we can dynamically allocate delays so that the CIR can be better utilized. Thus, we set the agent interval \(\delta_{i}\) around tens of nanoseconds or even more than one hundred nanoseconds. Then, the anchor will send a Sync message after a predetermined time. The agent \(i\) will send its Resp message after a fixed delay \(\Delta r\) and a delay \(\delta_{i}\) since it received the Sync message. In the Resp message, the agent \(i\) writes the clock drift and the delay \(t_{i}^{II}\triangleq\Delta r+\delta_{i}\) into its payload. Finally, after the anchor receiving all the Resp messages, the measurement process completes. The localization protocol of the SAL method is based on the work in [47]. As shown in Figure 2, compared with the conventional ranging protocol (Figure 2a) that requires at least \(2N+1\) UWB signals for a \(N\)-agent system, the protocol in Figure 2b can determine all the TOAs within the minimum frames, i.e., \(N+2\) UWB signals. Moreover, since the agents initial the measuring process in the conventional protocol (Figure 2a), the unengaged agent transmission order will incur message conflict at the anchor side. While for the protocol in Figure 2b, such conflicts can be avoided by broadcasting the response order in the first two messages. In addition, if we reverse the structure in Figure 2a (i.e., the anchor broadcast the Init message, the agents return the Resp messages, and the anchor broadcast the Final message), it can also reduce the number of signals to \(N+2\) and avoid conflicts. In this method, the distance measurement is obtained at the agent side, so it is an agent-based architecture. However, since the anchor is equipped with an antenna array, the angle measurement needs to be sent to the agent to achieve measurement fusion. Therefore, our proposed algorithm is not suitable for agent-based measurement. In our method, the  
Figure 1: An illustration of the proposed SAL method. For brevity, we take the two-agent scenario as an example, which can be extended to multi-agent cases. (**a**) The relationship between the anchor and the agents. (**b**) The message exchange process. Figure 2: Comparison of two extended two-way ranging methods.