# Positioning by Multicell Fingerprinting in Urban NB-IoT Networks +
## 5 Performance Evaluation
### Additional Performance Enhancements
#### 5.4.2 Additional Preprocessing: Data Smoothing  
The linear interpolation introduced to compensate for the data loss in the Rome dataset replaced each missing sample with a linear combination of the nearest available samples, which is shown in Section 5.3 to have had a beneficial effect on positioning accuracy. We decided thus to investigate whether additional preprocessing based on linear combinations of available samples might further improve performance. A first step in this direction was to extend the analysis on the impact of data preprocessing on the Oslo dataset presented in Section 4.4 in two ways: first, the performance of the linear interpolation technique was studied as a function of the percentage of RF values removed before interpolation; second, the minimum average positioning error as defined in Section 4.1 was used as the performance indicator. The results are presented in Figure 13, showing that when the percentage of RF values was randomly removed from the data and replaced with a linear interpolation of the data collected in the neighboring data points is in the range \([5,45]\), the positioning accuracy stayed close (within 10%) to the one obtained when using the full original data. This result can be explained by observing that the RF data values are heavily influenced by the time-varying channel conditions due to fast fading; linear interpolation generates synthetic values as a weighted average of real values and as such provides a smoothed version of the data that partially compensates for the loss of information. Based on this observation, a proper smoothing algorithm was introduced based on the so-called 40\(\lambda\)-rule proposed in [48] to remove fast fading from mobile channel data by using a moving average window. After filtering, each RF value at each data point is replaced with an average of the original measurements collected at data points in a range of \(\pm 20\lambda\) (i.e., \(\pm\approx 7.5\) m @ 800 MHz) from the data point being considered. Two different approaches to introduce data smoothing were investigated. In the first approach, referred in the following as \"RP smoothing\", smoothing was applied only to data contained in reference points after the split of data points into RPs vs. TPs. This approach aims to model a realistic condition where smoothing can be applied to data collected during the offline phase but not during the online phase. In the second approach, referred in the following as \"total smoothing\", smoothing was applied to all data before splitting the data points; this approach was considered in order to assess the advantage of smoothing in a best case scenario where fast fading is also mitigated in the online phase. Figure 13: Minimum average positioning error as a function of the percentage of RF values removed and replaced with synthetic values obtained by linear interpolation of remaining values using the Oslo data for Operator 1 and the _weighted average_ strategy in combination with RSRQ. Results obtained using the two smoothing approaches are presented in Table 11 for both datasets, using the _Weighted Coverage_ strategy in combination with RSRP for Rome and RSRQ for Oslo; for the Rome data, smoothing was applied on the interpolated dataset. A comparison of results obtained using smoothing vs. the results using raw data reported in Table 10 highlights that smoothing leads to a performance improvements in most cases; the only exceptions are for Operators 10 and 88 in the Rome data when the RP smoothing approach was used. This can be explained by observing that the Rome dataset is already the result of a linear interpolation, thus reducing the advantage of performing additional processing by smoothing.