#
Positioning by Multicell Fingerprinting in Urban NB-IoT Networks^{ †}

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## Abstract

**:**

## 1. Introduction

^{2}vs. hundreds of m

^{2}, typically), this trade-off might not be achievable: the need to keep the efforts for the acceptable measurement collection might result in unacceptably low accuracy (Challenge 1). Regarding the online phase, the WkNN algorithm is characterized by a computational complexity that grows quadratically with the number of RPs [4]; in considering the coverage area of an outdoor system, the number of RPs might be in the order of thousands or tens of thousands of points. Given the expected high density of devices characterizing the IoT scenarios and the corresponding number of positioning requests, the processing workload during the online phase might be difficult to sustain (Challenge 2). Finally, a challenge common to both phases is related to the density of eNBs/NPCIs available in a commercial deployment: current NB-IoT networks are in fact deployed so as o satisfy coverage requirements defined in terms of communication availability and may not provide enough signal sources to support the accurate positioning by fingerprinting (Challenge 3).

- It investigates the feasibility of RF fingerprinting in NB-IoT networks and assesses its accuracy in two urban scenarios by leveraging two large-scale measurement campaigns executed in the cities of Oslo, Norway, in 2019 [3] and Rome, Italy in 2021;
- It proposes several strategies for designing the WkNN-based online phase that combines network coverage and RF signal information;
- It assesses the performance of the above strategies by taking into account (a) the RF parameter adopted in the definition of fingerprint, (b) the amount of RPs collected in the offline phase, and (c) the number of cells considered in the fingerprinting system;
- It studies the impact on positioning accuracy of combining data from multiple operators and data preprocessing to remove fast fading and discusses the adoption of data combination and preprocessing as a means to achieving a favorable trade-off between offline phase efforts and positioning accuracy;
- It provides a detailed description of the data used in the performance evaluation and information on how to access the datasets through an open-source license.

## 2. Background and Related Work

## 3. Proposed Fingerprinting System

#### 3.1. The WkNN Algorithm

#### 3.2. Proposed Fingerprinting Strategies

#### 3.2.1. Net

#### 3.2.2. Enhanced Net

#### 3.2.3. Coverage

#### 3.2.4. Weighted Coverage

## 4. Dataset Description and Analysis

#### 4.1. Measurement Setup

#### 4.2. Data Description and Availability

- Time stamp, including date, time, and coordinated universal time (UTC);
- GPS data, including estimates of latitude, longitude, altitude, speed and heading, and the number of satellites used for the estimation;
- Network data, including the E-UTRA absolute radio frequency channel number (EARFCN), the corresponding carrier frequency, the NPCI, the mobile country code (MCC), the mobile network code (MNC), the tracking area code (TAC), the cell identity (CI), the eNodeB-ID, and the cell ID.
- Signal data, including the RSSI, SINR, RSRP, and RSRQ values measured for the reference signals transmitted by the eNodeB on each of the two antenna ports used in NB-IoT (Tx0 and Tx1), as well as the power, RSSI, and carrier-to-interference noise ratio (CINR) values measured on the narrowband secondary synchronization signal (NSSS).

#### 4.3. Datasets Analysis and Comparison

- The Oslo dataset includes data from 7 driving measurement runs for a total of 118,880 data entries collected in 5266 data points over an area of approximately $2\times 2$ ${\mathrm{km}}^{2}$. Two different network operators were identified. The runs are presented in Figure 2a;
- The Rome dataset includes data from 6 campaigns for a total of 31,599 data entries collected in 2670 data points over an area of $8\times 2.5$${\mathrm{km}}^{2}$. Three different network operators were identified. The runs are presented in Figure 2b.

#### 4.4. Preprocessing of the Rome Dataset

- Previous: Indicating with i the index of a missing sample ${x}_{i}$, the sample is replaced with the value of the previous available sample, ${x}_{i}={x}_{k}$, where $k<i$ is the index of the last sample available before ${x}_{i}$;
- Next: The missing sample ${x}_{i}$ is replaced with the value of the next available sample, ${x}_{i}={x}_{l}$, where $l>i$ is the index of the first sample available after ${x}_{i}$;
- Nearest: The missing sample ${x}_{i}$ is replaced with the value of the nearest available sample, ${x}_{i}={x}_{j}$, where j is determined as the index of the available sample such that $\left|i-j\right|$ is the minimum;
- Linear: The missing sample ${x}_{i}$ is replaced as$${x}_{i}=\frac{\left(i-k\right){x}_{l}+\left(l-i\right){x}_{k}}{l-k},$$
- Moving average: The missing sample ${x}_{i}$ is replaced using$${x}_{i}=\frac{1}{{w}_{a}}\sum _{j=-{m}_{1}}^{{m}_{2}}{x}_{i+j},$$
- Moving median: The missing sample ${x}_{i}$ is replaced with the median value computed over the set composed of the ${m}_{1}$ samples before ${x}_{i}$ and the ${m}_{2}$ samples after it for a total averaging window length ${w}_{m}={m}_{1}+{m}_{2}+1$ (missing values are skipped in the computation);
- PChip: The missing sample ${x}_{i}$ is replaced by performing a piecewise cubic interpolation that preserves the curve convexity [44];
- m-Akima: The missing sample ${x}_{i}$ is estimated using a modified version of the Akima algorithm [45,46], which is also based on a piecewise polynomial interpolation of degree three or less, in this case determining the slope in the interpolated point as the weighted average of the slopes of the neighboring points; the modification to the original algorithm is in the weights given to the slopes, selected so to reduce overshoot in the vicinity of points with a horizontal slope.

- Randomly select a set of $N=500$ unique NPCIs to be analyzed and perform the subsequent steps for each NPCI in the set;
- Artificially remove a fraction ${P}_{L}$ of RF values equal to the average data loss observed in the Rome data—the removal was carried out by extracting a uniform random variable for each data point including the NPCI under analysis and by removing the RF data if the random variable outcome value was larger than ${P}_{L}$;
- Interpolate the missing data using each technique;
- Evaluate and compare the performance of each technique according to two indicators—the mean square error (MSE) and the determination coefficient ${R}^{2}$.

## 5. Performance Evaluation

#### 5.1. Experiment Setup and Settings

#### 5.2. Results for the Oslo Dataset

#### 5.2.1. Impact of Strategies and RF Parameters

#### 5.2.2. Performance under Limited Information

- Spatial density. Given the positioning service area, the desired spatial density determines the number of data points to be collected and, in turn, the time and effort spent in data collection during the offline phase: reducing this number may thus improve the positioning system scalability, making it easier to setup and maintain.In order to assess the impact of a decrease in spatial density, additional experiments were performed, where, in each run, a fraction ${P}_{RP}<1$ of the points originally labeled as RPs were randomly selected and kept in the offline database. Figure 10 shows the minimum average positioning error as a function of ${P}_{RP}$ for all strategies using SINR for all but Net.The results in Figure 10 show that all strategies are affected by a decrease in spatial density but not all to a similar extent. The Coverage strategy, in particular, is heavily affected by the reduction of RPs, with the highest positioning error for low ${P}_{RP}$ values, which questions its robustness. The Single Cell approach shows a relatively low error for ${P}_{RP}=0.01$ on par with the Weighted Coverage strategy; this comes, however, at the price of a low percentage of TPs for which the position is estimated at all. As ${P}_{RP}$ decreases, in fact, there is an increasing probability that no RP has NPCIs in common with a TP, making position estimation impossible. Although this is true for all strategies, Single Cell is the most affected, with only 89% of the TPs with a position fix for ${P}_{RP}=0.01$ vs. 96% or higher for the other strategies.Note that the optimal k value leading to the minimum average positioning error will in general depend on ${P}_{RP}$; the optimal k as a function of ${P}_{RP}$ is presented in Figure 11, highlighting a trend, common to all strategies, to require a higher optimal k as the spatial density increases, suggesting that as more RPs become available, strategies benefit from including a larger number of nearest neighbors.
- Number of detected NPCIs. Devices might be able to only detect and/or report the strongest detected cells based on their radio and processing capabilities [7]. It is therefore relevant to assess the impact of a reduction in the number of detected NPCIs at each location. This only affects fingerprints collected by the target device and has no effect on the offline database built by the operator. Therefore, experiments were carried out that only preserved the ${N}_{NPCI}$ strongest/best NPCIs in points to be labeled as TPs; no change was made to data points labeled as RPs. Figure 12 shows the minimum average positioning error for all the proposed strategies as a function of ${N}_{NPCI}$ in the range $[1,\phantom{\rule{0.166667em}{0ex}}9]$.The results show that, for all strategies, the positioning error decreases as the number of NPCIs used for each TP increases; in all cases, the error is close (within <2%) to the one obtained using all NPCIs (see Table 3) if at least 7 best NPCIs are used. This suggests that a trade-off can be found between complexity (i.e., the amount of information to be collected and sent by the target device) and positioning accuracy. The results also show that as in the case of spatial density, the Coverage strategy is the one most affected by a reduction in the number of NPCIs, confirming its poor performance under conditions of scarcity of information.The optimal k determining the minimum average positioning error varies with ${N}_{NPCI}$, as already observed for variations of ${P}_{RP}$; no clear common trend to all strategies was, however, identified for this parameter. Interestingly, the positive impact of the number of NPCIs on positioning accuracy observed in this work was not detected in [9], where using a single NPCI led to the best performance.

#### 5.2.3. Comparison between Operators

#### 5.3. Results for the Rome Dataset

#### 5.4. Additional Performance Enhancements

#### 5.4.1. Increasing Information: Combining Data from Multiple Operators

#### 5.4.2. Additional Preprocessing: Data Smoothing

## 6. Conclusions

- Challenge 1—Trade-off between efforts in the offline phase and accuracy: the data used in this work were collected during driving runs, with no run repetitions and without introducing any form of repeated measurements at each point. This is arguably the most straightforward measurement setup in an outdoor scenario and requires an effort comparable to other outdoor data measurement campaigns associated, for example, to services like Google Street View [49] and is thus definitely feasible for a company (e.g., an operator) willing to build its own positioning service. In addition, the performance improvement obtained by introducing interpolation reported in Section 5.3 suggests that the effort can be further reduced by increasing the spatial density using synthetic fingerprints, thus reducing the number of actual fingerprints collected during the runs. The experimental data collected using the above setup led to an average positioning error of about 15 m when adopting the data combination and preprocessing techniques described in Section 5.4, which is comparable to the error obtained when using GNSS receivers.
- Challenge 2—Computational complexity and processing workload during the online phase: each of the two datasets used in this work led to the definition of a few thousand RPs, as detailed in Section 4.3. Considering, for example, the Oslo dataset, characterized by an average of 3600 RPs, the average time to serve a positioning request was 0.6 ms on a Dell Precision Tower 3640 workstation, equipped with an Intel Core i7-10700k processor and 32 GBs of RAM, allowing for about 1600 requests per second. Assuming the adoption of the same average distance between two RPs characterizing the datasets (about 3 m) on a regular grid without any gap, covering an area of 1 km
^{2}would require approximately 110,000 RPs, leading to about 0.8 s per request in the same setup, assuming an increase of the processing time quadratic with the number of RPs as indicated in Section 1. Extending the grid to an entire city might thus lead in theory to millions of RPs, with a potentially high processing load. However, several approaches can be adopted to address this issue: these include, among others, the introduction of a hierarchical approach based on clustering, as discussed for example in [27], the adoption of a machine learning algorithm in place of WkNN at the price of some loss of accuracy [7], or the introduction of dimension reduction algorithms such as the principal component analysis before running WkNN. Most importantly, it should be noted that although the total number of RPs may become very high for large urban coverage areas, it can be assumed that a device will use its active NB-IoT connection to transfer its fingerprint to the positioning server, automatically restricting the set of relevant RPs to those falling within the coverage area of the serving eNB. - Challenge 3—The number of NPCIs per point and impact on positioning accuracy: the results presented in Section 5 show that the density of eNBs and NPCIs in a commercial network deployment is sufficient to achieve a positioning accuracy comparable to the one provided by a GNSS system, in particular when broadcast signals transmitted by multiple operators are combined.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

3GPP | 3rd Generation Partnership Project |

AP | Access Point |

CI | Cell Identity |

CINR | Carrier-to-Interference Noise Ratio |

EARFCN | E-UTRA Absolute Radio Frequency Channel Number |

eNodeB | evolved Node B |

GNSS | Global Navigation Satellite System |

kNN | k Nearest Neighbors |

LPWAN | Low-Power Wide Area Network |

LTE | Long-Term Evolution |

MA | Moving Average |

MM | Moving Median |

MNC | Mobile Network Code |

NB-IoT | Narrowband Internet of Things |

NPCI | Narrowband Physical Cell Identifier |

NPRS | Narrowband Position Reference Signal |

NSSS | Narrowband Secondary Synchronization Signal |

OTDOA | Observed Time Difference Of Arrival |

PCI | Physical Cell Identifier |

PRS | Position Reference Signal |

RP | Reference Point |

RSRP | Reference Signal Received Power |

RSRQ | Reference Signal Received Quality |

RSSI | Received Signal Strength Indicator |

RSTD | Reference Signal Time Difference |

SINR | Signal to Interference plus Noise Ratio |

TAC | Tracking Area Code |

TOA | Time of Arrival |

TP | Test Point |

UE | User Equipment |

UTC | Coordinated Universal Time |

WkNN | Weighted k Nearest Neighbors |

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**Figure 1.**The setup adopted for the measurement campaign in Rome, Italy: R&S TSMA6 mobile network scanner (

**a**), GPS antenna (

**b**), Samsung S20 5G mobile phone (

**c**), RF antenna (

**d**), and tablet used to remotely access the ROMES software running in the embedded PC within the TSMA6 scanner (

**e**) (image drawn from [33]).

**Figure 2.**Measurement runs used for the Oslo campaign (

**a**) and Rome campaign (

**b**); each color represents a different run.

**Figure 3.**Examples of data points from the Oslo and Rome datasets; missing RF data in the Rome data are highlighted in red.

**Figure 4.**Statistics for the number of unique NPCIs per data point with valid RF data for the Oslo dataset (

**left**) vs. the Rome dataset (

**right**).

**Figure 5.**RSSI RF data collected for a sample NPCI as a function of time during a measurement run for the Oslo dataset (

**a**) vs. the Rome dataset (

**b**).

**Figure 6.**MSE obtained for the considered interpolation techniques (

**a**) and the zoom of the same data in the range $[0,\phantom{\rule{0.166667em}{0ex}}20]$ (

**b**), where MA stands for moving average and MM for moving median; these techniques were tested for different average window lengths, from 5 to 20.

**Figure 7.**${R}^{2}$ obtained for the considered interpolation techniques (

**a**) and zoom of the same data in the range $[0,\phantom{\rule{0.166667em}{0ex}}1]$ (

**b**), where MA stands for moving average and MM for moving median; these techniques were tested for different average window lengths, from 5 to 20.

**Figure 8.**Comparison of best and worst interpolators vs.the original data for a sample NPCI from the Oslo dataset.

**Figure 9.**Average positioning error as a function of k for the proposed strategies vs. Single Cell [7] using SINR in all strategies but Net.

**Figure 10.**Minimum average positioning error as a function of ${P}_{RP}$ for the proposed strategies vs. Single Cell [7] using SINR in all strategies but Net.

**Figure 11.**Optimal k as a function of ${P}_{RP}$ for the proposed strategies and the approach proposed in [7] using SINR in all strategies but Net.

**Figure 12.**Minimum average positioning error as a function of ${N}_{NPCI}$ for the proposed strategies using SINR in all strategies but Net; the Single Cell was not analyzed since, by definition, it operates with ${N}_{NPCI}=1$.

**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.

Category | Data Field | Unit/Format | Example |
---|---|---|---|

Time stamp | Date | dd.mm.yyyy | 23.07.2019 |

Time | hh:mm.s | 08:25.5 | |

UTC | seconds | 1,566,583,704 | |

GPS data | Latitude | degrees | 59.922214 |

Longitude | degrees | 10.733242 | |

Altitude | meters | 46.98 | |

Speed | m/s | 8.03 | |

Heading | degrees | 199.36 | |

Sat | - | 6 | |

Network data | EARFCN | - | 6352 |

Frequency | Hz | 811,192,500 | |

NPCI | - | 243 | |

MCC | - | 242 | |

MNC | - | 1 | |

TAC | - | 40,601 | |

CI | - | 19,803,492 | |

eNodeB-ID | - | 77,357 | |

cell ID | - | 100 | |

Signal data | RSSI-Tx0 | dBm | −28.4 |

RSSI-Tx1 | dBm | −28.4 | |

NSINR-Tx0 | dB | 20.84 | |

NSINR-Tx1 | dB | 26.25 | |

NRSRP-Tx0 | dBm | −40.07 | |

NRSRP-Tx1 | dBm | −34 | |

NRSRQ-Tx0 | dB | −11.65 | |

NRSRQ-Tx1 | dB | −5.59 | |

NSSS-Power | dBm | −25.3 | |

NSSS-RSSI | dBm | −25.3 | |

NSSS-CINR | dB | −25.3 |

**Table 2.**Information associated with the generic n-th data point. The notation NPCI

_{$k,n$}indicates the unique NPCI, corresponding to a unique triplet <NPCI, eNodeB-ID, MNC> associated with the k-th data entry out of the ${L}_{n}$ collected at the coordinates <$Latitud{e}_{n},Longitud{e}_{n}$>.

$\mathit{L}\mathit{a}\mathit{t}\mathit{i}\mathit{t}\mathit{u}\mathit{d}{\mathit{e}}_{\mathit{n}}$ | $\mathit{L}\mathit{o}\mathit{n}\mathit{g}\mathit{i}\mathit{t}\mathit{u}\mathit{d}{\mathit{e}}_{\mathit{n}}$ | NPCI_{$1,\mathit{n}$} | RSSI_{$1,\mathit{n}$} | SINR_{$1,\mathit{n}$} | RSRP_{$1,\mathit{n}$} | RSRQ_{$1,\mathit{n}$} |

NPCI_{$2,n$} | RSSI_{$2,n$} | SINR_{$2,n$} | RSRP_{$2,n$} | RSRQ_{$2,n$} | ||

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ||

NPCI_{${L}_{n},n$} | RSSI_{${L}_{n},n$} | SINR_{${L}_{n},n$} | RSRP_{${L}_{n},n$} | RSRQ_{${L}_{n},n$} |

**Table 3.**Minimum average positioning error and corresponding optimal k for the proposed strategies and the single cell approach in [7] using the Oslo dataset.

Strategy | RF Parameter | k | Error [m] |
---|---|---|---|

Net | N/A | 8 | 54.0 |

Enhanced Net | RSSI | 2 | 34 |

SINR | 2 | 28.1 | |

RSRP | 2 | 24.0 | |

RSRQ | 3 | 30.1 | |

Coverage | RSSI | 3 | 23.9 |

SINR | 2 | 20.6 | |

RSRP | 2 | 20.8 | |

RSRQ | 2 | 20.1 | |

Weighted Coverage | RSSI | 3 | 22.3 |

SINR | 3 | 19.9 | |

RSRP | 2 | 19.9 | |

RSRQ | 3 | 19.5 | |

Single Cell [7] | RSSI | 22 | 102.4 |

SINR | 19 | 66.2 | |

RSRP | 30 | 76.9 | |

RSRQ | 30 | 72.9 |

**Table 4.**Comparison between data used for the Operator 1 vs. Operator 2 networks in the Oslo dataset; a valid data point is defined as a data point where at least one unique NPCI was detected for the considered operator.

Parameter | Operator 1 | Operator 2 |
---|---|---|

Unique NPCIs | 160 | 139 |

Valid data points | 4848 | 4577 |

Valid data points (%) | 92.1 | 86.9 |

Average number of NPCIs per valid data point | 6.1 | 6.6 |

**Table 5.**Minimum average positioning error and corresponding optimal k for the proposed strategies and the approach in [7] using RSRQ as the RF parameter in Operator 1 vs. Operator 2 networks in the Oslo dataset.

Strategy | Operator 1 | Operator 2 | ||
---|---|---|---|---|

k | Error [m] | k | Error [m] | |

Net | 8 | 54.0 | 7 | 64.2 |

Enhanced Net | 2 | 30.4 | 2 | 33.7 |

Coverage | 2 | 20.1 | 2 | 19.8 |

Weighted Coverage | 3 | 19.5 | 2 | 19.0 |

Single Cell [7] | 30 | 72.9 | 24 | 81.9 |

**Table 6.**Comparison between the data used for the three networks detected in the Rome dataset; a valid data point is defined as a data point where at least one unique NPCI was detected for the considered operator.

Parameter | Operator 1 | Operator 10 | Operator 88 |
---|---|---|---|

Unique NPCIs | 69 | 81 | 87 |

Valid data points | 2670 | 2669 | 2670 |

Valid data points (%) | 100 | 99.9 | 100 |

Average number of NPCIs per valid data point | 4.9 | 5.2 | 4.9 |

**Table 7.**Minimum average positioning error and corresponding optimal k for the proposed strategies and the Single Cell approach in [7] using data collected for Operator 88 in the Rome dataset in its original and interpolated versions.

Strategy | RF Parameter | Original | Interpolated | ||
---|---|---|---|---|---|

k | Error [m] | k | Error [m] | ||

Net | N/A | 40 ${}^{\u2605}$ | 148.4 | 40 ${}^{\u2605}$ | 149.1 |

Enhanced Net | RSSI | 3 | 85.3 | 3 | 69.5 |

SINR | 2 | 63.4 | 2 | 39.9 | |

RSRP | 2 | 55.9 | 1 | 36.5 | |

RSRQ | 3 | 64.0 | 2 | 43.0 | |

Coverage | RSSI | 2 | 76.6 | 3 | 36.4 |

SINR | 2 | 74.0 | 2 | 29.3 | |

RSRP | 1 | 68.7 | 2 | 26.9 | |

RSRQ | 2 | 74.0 | 2 | 28.6 | |

Weighted Coverage | RSSI | 4 | 57.4 | 4 | 35.6 |

SINR | 3 | 49.7 | 2 | 29.4 | |

RSRP | 3 | 49.0 | 2 | 26.8 | |

RSRQ | 3 | 49.2 | 2 | 28.7 | |

Single Cell [7] | RSSI | 19 | 213.5 | 25 | 215.9 |

SINR | 9 | 135.3 | 13 | 117.5 | |

RSRP | 12 | 151.5 | 20 | 142.9 | |

RSRQ | 10 | 137.3 | 17 | 124.9 |

**Table 8.**Minimum average positioning error (E) and corresponding optimal k for the proposed strategies and the approach in [7] all using RSRP as RF parameter in the three networks detected in Rome using the original and interpolated datasets.

Strategy | Original | Interpolated | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Op. 1 | Op. 10 | Op. 88 | Op. 1 | Op. 10 | Op. 88 | |||||||

k | E [m] | k | E [m] | k | E [m] | k | E [m] | k | E [m] | k | E [m] | |

Net | 25 | 146.8 | 32 | 137.6 | 40 | 148.4 | 35 | 147.2 | 32 | 137.5 | 40 | 149.1 |

Enhanced Net | 1 | 82.8 | 2 | 62.1 | 2 | 55.9 | 2 | 47.5 | 2 | 33.2 | 1 | 36.5 |

Coverage | 4 | 80.1 | 2 | 70.9 | 1 | 68.7 | 2 | 34.8 | 2 | 26.7 | 2 | 26.9 |

Weighted Cov. | 3 | 69.3 | 2 | 58.1 | 3 | 49.0 | 2 | 35.0 | 2 | 26.8 | 2 | 26.8 |

Single Cell [7] | 32 | 163.3 | 20 | 153.4 | 9 | 135.3 | 40 | 155.6 | 25 | 149.6 | 13 | 117.5 |

**Table 9.**Comparison between the Oslo and Rome datasets using combined data from all operators detected in each dataset; a valid data point is defined as a data point where at least one unique NPCI was detected.

Parameter | Oslo | Rome |
---|---|---|

Unique NPCIs | 299 | 237 |

Valid data points | 5266 | 2670 |

Valid data points (%) | 100 | 100 |

Average number of NPCIs per valid data point | 11.3 | 15.0 |

**Table 10.**Minimum average positioning error in meters using each the single-operator and combined-operators data in the Oslo and Rome datasets for the weighted coverage strategy in combination with RSRQ (Oslo) and RSRP (Rome); results using both the original and interpolated datasets are presented for Rome.

Dataset | Minimum Average Positioning Error [m] | |||
---|---|---|---|---|

Rome (original) | Op. 1 | Op. 10 | Op. 88 | Combined |

69.3 | 58.1 | 49.0 | 46.2 | |

Rome (interpolated) | Op. 1 | Op. 10 | Op. 88 | Combined |

35.0 | 26.8 | 26.8 | 15.3 | |

Oslo | Op. 1 | Op. 2 | - | Combined |

19.5 | 19.0 | - | 16.1 |

**Table 11.**Minimum average positioning error in meters using the “RP smoothing” and “total smoothing” approaches for the single-operator and combined-operators data in the Oslo and Rome datasets for the weighted coverage strategy in combination with RSRQ (Oslo) and RSRP (Rome).

Dataset | Minimum Average Positioning Error [m] | |||
---|---|---|---|---|

Rome (RP Smoothing) | Op. 1 | Op. 10 | Op. 88 | Combined |

34.2 | 26.8 | 27.1 | 15.2 | |

Rome (Total Smoothing) | Op. 1 | Op. 10 | Op. 88 | Combined |

25.5 | 21.9 | 21.1 | 14.9 | |

Oslo (RP Smoothing) | Op. 1 | Op. 2 | - | Combined |

19.0 | 18.5 | - | 15.7 | |

Oslo (Total Smoothing) | Op. 1 | Op. 2 | - | Combined |

13.8 | 14.5 | - | 14.5 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

De Nardis, L.; Caso, G.; Alay, Ö.; Neri, M.; Brunstrom, A.; Di Benedetto, M.-G.
Positioning by Multicell Fingerprinting in Urban NB-IoT Networks. *Sensors* **2023**, *23*, 4266.
https://doi.org/10.3390/s23094266

**AMA Style**

De Nardis L, Caso G, Alay Ö, Neri M, Brunstrom A, Di Benedetto M-G.
Positioning by Multicell Fingerprinting in Urban NB-IoT Networks. *Sensors*. 2023; 23(9):4266.
https://doi.org/10.3390/s23094266

**Chicago/Turabian Style**

De Nardis, Luca, Giuseppe Caso, Özgü Alay, Marco Neri, Anna Brunstrom, and Maria-Gabriella Di Benedetto.
2023. "Positioning by Multicell Fingerprinting in Urban NB-IoT Networks" *Sensors* 23, no. 9: 4266.
https://doi.org/10.3390/s23094266