## 5 Numerical Results  
Consider a large warehouse that uses automatic guided vehicles (AGVs) for cargoes. The AGVs are treated as independent UNs that will locate themselves. To avoid network overload and lower the energy consumption, the communication between UNs and ANs is one-way and sequential, so the one-way sequential TOAs are measurable. Therefore, simulation experiments shall be carried out in a scenario where \(N=2\). Ten anchor nodes are deployed at \(\mathbf{s}_{1}^{o}=[0,0]^{T}\) m, \(\mathbf{s}_{2}^{o}=[0,800]^{T}\) m, \(\mathbf{s}_{3}^{o}=[500,800]^{T}\) m, \(\mathbf{s}_{4}^{o}=[700,600]^{T}\) m, \(\mathbf{s}_{5}^{o}=[900,400]^{T}\) m, \(\mathbf{s}_{6}^{o}=[700,200]^{T}\) m, \(\mathbf{s}_{7}^{o}=[500,0]^{T}\) m, \(\mathbf{s}_{9}^{o}=[250,80]^{T}\) m, and \(\mathbf{s}_{10}^{o}=[250,0]^{T}\) m. The true position of the user node is denoted as \(\mathbf{p}^{o}=[400,400]^{T}\) m. The geometric deployment is shown in Figure 4. The velocity of a UN is randomly generated within the range of 0 to 50 m/s, and the moving direction is random as well. ANs transmit signals sequentially with a fixed time interval of 5 ms; thus, \(t_{i}=5(i-1)\times 10^{-3}\) s. For each simulation test, the initial clock offset and clock drift of the UN are selected from uniform distributions. Specifically, the initial clock offset \(\gamma\) follows a distribution of \(\mathcal{U}(-10^{-5},10^{-5})\) s, while the clock drift \(\iota\) follows a distribution of \(\mathcal{U}(-20,20)\) parts per million (ppm). The known clock offsets \(\gamma_{i}\), \(i=1,2,\ldots,M\) between ANs were also random in each test, obeying \(\mathcal{U}(-10^{-5},10^{-5})\) s. The covariance matrices of the measurement noise and anchor position errors were set as \(\mathbf{Q}_{z}=\sigma^{2}\mathbf{I}_{M}\) and \(\mathbf{Q}_{s}=\sigma_{s}^{2}\mathbf{I}_{2M}\). Comparisons were conducted among the proposed CFPS (39), RIS (65), MLE implemented using GN iteration [9], and [PERSON]'s CFJLAS [11]. Both the RIS and GN were initialized through the CFPS. The performance was evaluated using the RMSE and bias. Additionally, we utilized the CRLB as a benchmark for the performance evaluation. The ensemble runs for assessing the RMSE and bias was \(T=1000\), unless specified otherwise. The RMSE and bias are defined as  
\[RMSE(\mathbf{\mathrm{p}}) =\sqrt{\frac{1}{T}\sum_{t=1}^{T}\|\mathbf{\mathrm{p}}^{(t)}-\mathbf{ \mathrm{p}}^{o}\|^{2}} \tag{84}\] \[RMSE(\mathbf{\mathrm{v}}) =\sqrt{\frac{1}{T}\sum_{t=1}^{T}\|\mathbf{\mathrm{v}}^{(t)}-\mathbf{ \mathrm{v}}^{o}\|^{2}}\] (85) \[bias(\mathbf{\mathrm{p}}) =\sqrt{\frac{1}{T}\sum_{t=1}^{T}\|\mathbf{\mathrm{p}}^{(t)}-\mathbf{ \mathrm{p}}^{o}\|}\] (86) \[bias(\mathbf{\mathrm{v}}) =\sqrt{\frac{1}{T}\sum_{t=1}^{T}\|\mathbf{\mathrm{v}}^{(t)}-\mathbf{ \mathrm{v}}^{o}\|} \tag{87}\]where \(\mathbf{p}^{(t)}\) and \(\mathbf{v}^{(t)}\) are the estimation result at the t-th test. The maximum number of iterations for the RIS and GN is \(K\) = 100,000, and the iteration residual threshold was set as \(\epsilon\) = 0.1. We first evaluated the RMSE and bias performance under varying noise levels. The position error level of the ANs was fixed at \(\sigma_{\mathrm{s}}=0.5\) m. After testing the dumping factor \(\kappa\) from 0 to 5, the results allowed us to determine the optimal selection. We chose \(\kappa\) = 1 to yield the most favorable results, striking a balance between reducing divergence and maintaining convergence speed. The performance in terms of the RMSE and bias is illustrated in Figures 5-8. The compared solutions can achieve CRLB accuracy when the noise is small, except the CFPS. It is reasonable that the CFPS ignores the inner connection between the redundant variables. The RIS can keep the CRLB's level of accuracy when the noise reaches 30 dB, and slightly deviates from the CRLB if the noise increases further. The RMSE of the RIS is about 7 dB lower than that of CFJLAS when \(10\log_{10}(\sigma^{2})=35\) dB. The GN diverges from the CRLB when the noise level surpasses 25 dB, exhibiting a lower noise tolerance compared to the RIS.