\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Uplink** & \begin{tabular}{c} **LoS-** \\ **Blocked** \\ \end{tabular} & **Near-Field** & **Multi-User** & \begin{tabular}{c} **Direct** \\ **Approach 1** \\ \end{tabular} & \begin{tabular}{c} **Dynamic** \\ **Tracking 2** \\ \end{tabular} & \
\begin{tabular}{c} **Passive** \\ **RIS 3** \\ \end{tabular} &
\begin{tabular}{c} **CRLB** \\ **Utilized 4** \\ \end{tabular} \\ \hline [PERSON] et al. [20] & ✓ & ✗ & ✓ & ✗ & ✓ & ✗ & ✓ & ✓ \\ [PERSON] et al. [21] & ✗ & ✗ & ✗ & ✓ & ✗ & ✗ & ✓ & ✗ \\ [PERSON] et al. [22] & ✓ & ✓ & ✗ & ✗ & ✗ & ✗ & ✓ & ✗ \\ [PERSON] et al. [23] & ✗ & ✓ & ✗ & ✓ & ✗ & ✗ & ✓ & ✓ \\ [PERSON] et al. [24] & ✗ & ✓ & ✗ & ✗ & ✗ & ✗ & ✓ & ✗ \\ [PERSON] et al. [25] & ✗ & ✗ & ✓ & ✗ & ✓ & ✗ & ✓ & ✓ \\ [PERSON] et al. [31] & ✓ & ✓ & ✗ & ✗ & ✗ & ✗ & ✓ & ✗ \\ [PERSON] et al. [32] & ✗ & ✗ & ✗ & ✗ & ✗ & ✗ & ✓ & ✓ \\ [PERSON] et al. [36] & ✗ & ✓ & ✗ & ✗ & ✗ & ✓ & ✓ & ✓ \\ [PERSON] et al. [37] & ✗ & ✗ & ✓ & ✗ & ✓ & ✓ & ✓ & ✗ \\ [PERSON] et al. [41] & ✓ & ✓ & ✗ & ✓ & ✗ & ✗ & ✗ \\ [PERSON] et al. [42] & ✓ & ✓ & ✗ & ✓ & ✗ & ✓ & ✓ & ✓ \\ \hline \hline \end{tabular}  
* The direct approach denotes that the target position is estimated directly from the measured data, and the corresponding method is the two-stage method, which estimates the target position by estimating intermediate parameters. 2 Dynamic tracking denotes that the localizing is conducted in a dynamic scenario and the other corresponding method is snapshot localization without exploiting the temporal correlations of user locations. 3 RIS is the abbreviation of reconfigurable intelligent surface. 4 CRLB is the abbreviation of Cramer–Rao lower bound. The passive beamforming of RIS is designed by utilizing (Bayesian) CRLB, for instance, by minimizing (B) CRLB.  
\end{table} 
Table 1: Methods and types of the most relevant RIS-assisted positioning literature. The remainder of the study unfolds as follows. The tracking scenario, geometry, and signal model of the proposed system are described in Section 2. The basic navigation framework, including the transition model, observation model, and proposed tracking algorithm, is elaborated in Section 3. The BCRB of the proposed RIS-aided tracking scheme and the optimization of RISs' phase shift are presented in Section 4. A series of simulations are conducted, and the validity and accuracy of the proposed tracking system are demonstrated in Section 5. The conclusions are stated in Section 6. Additionally, notations and operators used in this work are enumerated in Table 2. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Symbol** & **Meaning** \\ \hline \(x\) & scalar \\ \(\mathbf{x}\) & vector \\ \(\mathbf{X}\) & matrix \\ \((\cdot)^{\mathrm{T}}\) & transpose \\ \((\cdot)^{*}\) & conjugate \\ \((\cdot)^{-1}\) & inverse \\ \(\
abla\) & partial derivative \\ \(tr(\mathbf{X})\) & trace of \(\mathbf{X}\) \\ \(\mathrm{diag}(\cdot)\) & diagonal matrix \\ \(\mathbb{E}[\cdot\cdot]\) & expectation \\ \(\mathbb{C}\) & complex domain \\ \(\mathbb{R}\) & real domain \\ \(A\times B\) & dimension of matrices \\ \(\mathfrak{R}(\cdot)\) & real part of complex value \\ \(\mathfrak{I}(\cdot)\) & imaginary part of complex value \\ \(||\cdot||\) & module of complex value \\ \(||\cdot||\) & \(l_{2}\)-norm \\ \(j=\sqrt{-1}\) & the imaginary unit \\ \(\mathcal{B},\mathcal{K},\mathcal{P},\mathcal{M}\) & set \\
**1** & identity matrix \\
**0** & zero matrix \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notations and operators. Figure 1: RIS-aided multi-user tracking scenario.