# Surface Correlation-Based Fingerprinting Method Using LTE Signal for Localization in Urban Canyon
## 3 Surface Correlation-based Fingerprinting Method
### Localization  
As mentioned before, the SC method selects the RP with the minimum SSD on the fixed reference trajectory as the current location. Figure 10b shows the result of localization according to the calculated similarity distance in Figures 9 and 10a. As shown in Figure 10b, it can be seen that a localization error occurs at the crossroad when the RP with the minimum similarity distance value is selected. A crossroad is a relatively open space; therefore, the RSS patterns between the reference trajectories are very similar. This increases ambiguity when compared with the measured _Surface_, resulting in a localization error. The proposed method gives a priority to the reference trajectory that matches a turn event from the PDR to reduce ambiguity at a crossroad, which means that the location is estimated from the reference trajectory that corresponds to a turn event from the PDR. However, various motions of the pedestrian can cause a false turn event reading of the PDR. To prevent this, the proposed method continuously calculates SSDs for all the generated reference trajectories until one of them is fixed. If the fixed reference trajectory is different from the turn event matched trajectory, localization is processed on the fixed reference trajectory. In this paper, we set a threshold to fix a reference trajectory as 1.16 to reduce the error of the PDR turn event at a crossroad.  
In addition to the left and right turn of a pedestrian, the event of turning back on a link should also be considered. The SC method generates a reference trajectory through a combination of links. Therefore, when the pedestrian is moving as shown in Figure 11a, the SC method computes the location using a reference trajectory comprising a combination of \(L1\), \(L2\), and candidate \(L3\) before the turn back event. It is possible to generate a reference trajectory by combining \(L1\), \(L2\), \(L2^{\prime}\) and \(L1^{\prime}\). But, in this case, it is impossible to perform an accurate comparison between _Surfaces_ because the reference trajectory contains RPs that the pedestrian did not actually pass. It is very difficult to determine an exact RP at the time of turn event; thus, it is also impossible to divide \(L2\) and \(L2^{\prime}\) to generate a reference trajectory.  
Figure 10: The problem of localization using the minimum SSD at a cross point: (**a**) SSD of each reference trajectory at a crossroad; (**b**) Localization error and compensation using Pedestrian Dead-Reckoning (PDR) turn event.  
For these reasons, the SC method performs an initialization process that resets both the measured _Surface_ and the current reference trajectory when a turn back event occurs as shown in Figure 11b. However, the resetting of the measured _Surface_ may cause ambiguity as in conventional fingerprinting methods as Figure 11c and d. The length of the _Surface_ is a very important factor in identifying the reliability of the location information through SC, along with the SSD. To mitigate the unstable performance due to the ambiguity after the turn event, the SC method fixes the reverse component of a current link as the reference trajectory and an RP as a start point when the turning event occurs. Then, it determines the location using length of the _Surface_ until its length (\(l_{l_{0}+\Delta t}^{+}\)) is greater than the length of the previous _Surface_ (\(l_{l_{0}}^{-}\)). Let \(t_{epoch}\) denote the fixed RP where the turn event has occurred and denote the total number of RPs on the reference trajectory. If \(l_{l_{0}+\Delta t}^{+}/l_{l_{0}}^{-}\geq 1\), the SC method determines the location as an RP\({}_{a^{*}}\) with the minimum SSD as presented below:  
\[a^{*}=\underset{1\leq a\leq t_{epoch}\leq m_{r}}{\text{arg min}}\rho_{[1,t_{ epoch}]} \tag{6}\]