## 3 Literature Review and Related Work
### Positioning Implementing Time-Series of Spatially Distributed Fingerprints
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ref.** & **Year** &
\begin{tabular}{c} **Fingerprints** \\ **Used** \\ \end{tabular} & **NN Type** & **Fingerprint Collection Method** & **\# Side Inf.** \\  & & & & & **Dimensions** \\ \hline
[171] & 2019 & RSS & LSTM & Along a path & 1D \\ \hline
[172] & 2019 & RSS & LSTM & Along a path & 1D \\ \hline
[173] & 2019 & Geomagnetic & LSTM & Along a path & 1D \\ \hline
[174] & 2019 & Geomagnetic & RNN and LSTM & Along a path, in two areas: 94.0 m \(\times\) 26.0 m & 1D \\  & & & and 609.0 m \(\times\) 49.0 m & \\ \hline
[175] & 2019 & RSS &
\begin{tabular}{c} Six types of \\ RNNs \\ \end{tabular} & Along a path, in an area of 21.0 m \(\times\) 16.0 m & 1D \\ \hline
[176] & 2019 & RSS & LSTM & Along a path, in only two or three steps & 1D \\ \hline
[177] & 2020 & RSS & LSTM & Along path of an estimated length of 40.0 m & 1D \\ \hline
[178] & 2020 & SNR & RNN & Along a path, in an area of approx. 3.0 m \(\times\) 4.0 m & 1D \\ \hline
[179] & 2020 & RSS & LSTM & Along paths of different lengths & 1D \\ \hline
[180] & 2020 & Geomagnetic & RNN & Along a path & 1D \\ \hline
[181] & 2020 & RSS & RNN & Along a path & 1D \\ \hline
[113] & 2020 & RSS and other & LSTM & Along a path & 1D \\ \hline
[182] & 2021 & RSS & LSTM & Along a path of 5.0 m, in an area of 5.0 m \(\times\) 10.0 m & 1D \\ \hline
[183] & 2021 & RSS & LSTM & Along a path & 1D \\ \hline
[184] & 2021 & RSS & LSTM & Along four paths of 32.5 to 234.0 m & 1D \\ \hline
[185] & 2021 & RSS &
\begin{tabular}{c} 1D CNN and \\ RNN \\ \end{tabular} & Along a path & 1D \\ \hline
[186] & 2021 & RSS & 1D CNN & Along a trajectory of a random length & 1D \\ \hline
[187] & 2021 & Geomagnetic & LSTM & Along a path, positioning node every 0.5 m, & 1D \\  & & & sequences with lengths of 10.0, 15.0, and 20.0 m & \\ \hline
[188] & 2021 & CSI &
\begin{tabular}{c} 1D CNN and \\ LSTM \\ \end{tabular} & Along a path & 1D \\ \hline
[189] & 2021 & CSI & LSTM & Along a path, from simulation & 1D \\ \hline
[137] & 2021 & RSS & LSTM & Along a path & 1D \\ \hline
[153] & 2022 & RSS & \
\begin{tabular}{c} 2D CNN and \\ LSTM \\ \end{tabular} &
\begin{tabular}{c} Along a path \\ \end{tabular} & 1D \\ \hline
[190] & 2022 & RSS &
\begin{tabular}{c} 1D CNN and \\ LSTM \\ \end{tabular} & Trajectory generated from radio map & 1D \\ \hline
[191] & 2022 & RSS & CNN-based & Along a path & 1D \\ \hline
[192] & 2022 & Geomagnetic &
\begin{tabular}{c} 1D CNN and \\ LSTM \\ \end{tabular} & Along a path & 1D \\ \hline
[193] & 2023 & RSS and other & LSTM & Along a path, outdoors & 1D \\ \hline
[194] & 2023 & RSS & LSTM & Along a path & 1D \\ \hline
[195] & 2024 & RSS & LSTM & Individually collected and arranged in a sequence & 1D \\ \hline
[196] & 2024 & RSS &
\begin{tabular}{c} 1D CNN and \\ LSTM \\ \end{tabular} & Along a path & 1D \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._RNNs and LSTM NNs are suitable for identifying the long-term dependencies of the time-series. In the context of this work, the temporal structure stored by the RNNs and LSTM NNs can be used to map a relationship between spatially distributed fingerprints and the target position to be estimated. In this case, the time domain is related to the space domain through the collection of the fingerprints, which consists of taking consecutive samples using a positioning device that is moved along a path. For example, in [172] a sequence-to-sequence prediction model is presented. The model takes as its input side information from a sequence of fingerprints collected along a trajectory. As the output, it produces a sequence of position estimates associated with the input. Moving a single sensor or receiver along a path to gather fingerprints, without additional information on the local displacement, yields as its result a time-series of fingerprints with spatial relationships only between consecutive and adjacent samples.