# Performance Comparison of WiFi and UWB Fingerprinting Indoor Positioning Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

**RSS-Based WiFi Fingerprinting IPSs**—In the context of WiFi fingerprinting IPSs, different aspects have been investigated [5]. In this section, a general system model that is the basis of several proposed solutions is reported.

- Selection of k: Previous works have showed the impact of the value of k on the positioning accuracy. Existing schemes can be broadly divided into two families: a priori fixed k schemes and dynamic k schemes. In a priori fixed k schemes, k is predefined and does not depend on the positioning request; it has been empirically found that the average positioning error in these schemes is typically minimized by selecting k between 2 and 10 [16,17,18,19]. Dynamic k schemes typically rely on the introduction of a variable threshold in order to determine the value of k depending on the specific positioning request [19,23,24].
- Similarity metric: Different similarity metrics have been proposed [20]. A popular choice is the use of the inverse Minkowski distance with order $o\ge 1$ (orders typically used are $o=1$, i.e., the Manhattan distance, and $o=2$, i.e., the Euclidean distance). Denoting with ${\mathcal{D}}^{o}({\mathit{t}}_{m},{\mathit{s}}_{n})$ the Minkowski distance with order o, $\mathtt{sim}({\mathit{t}}_{m},{\mathit{s}}_{n})$ is then defined as follows:$$\mathtt{sim}({\mathit{t}}_{m},{\mathit{s}}_{n})={[{\mathcal{D}}^{o}({\mathit{t}}_{m},{\mathit{s}}_{n})]}^{-1}={\left[{\left(\sum _{l=1}^{L}{|{t}_{m,l}-{s}_{n,l}|}^{o}\right)}^{\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\frac{1}{o}}\right]}^{-1}$$

**CIR-Based UWB Fingerprinting IPSs**—While RSS is traditionally used as a signal feature in WiFi IPSs, several location-dependent CIR features are being considered for UWB IPSs.

## 3. Motivation and Contribution

- The two technologies are analyzed in the same scenario in combination with both a fixed kNN algorithm and a novel dynamic kNN algorithm, capable of taking advantage of both monodimensional and multidimensional fingerprints.

## 4. Fingerprinting Positioning Systems

#### 4.1. Notation

#### 4.2. Definition of Fingerprints

**WiFi IPS**—For the WiFi-based IPS, a single feature is adopted in defining the fingerprint associated to each RN or TN: the RSS measured at the corresponding position for the signals from the ${L}_{j}$ APs. As a result, the fingerprint ${\mathit{s}}_{n}$ for the nth RN consists of a vector of $1\times {L}_{j}$ RSS values; denoting as ${\mathtt{RSS}}^{n,l}$ the RSS for the pair formed by the nth RN and the lth AN, it follows that ${\mathit{s}}_{n}=({\mathtt{RSS}}^{n,1},\cdots ,{\mathtt{RSS}}^{n,{L}_{j}})$. Similarly, the fingerprint ${\mathit{t}}_{m}$ for the mth TN consists of a vector of $1\times {L}_{j}$ RSS values for signals received at the unknown position of the TN from the ${L}_{j}$ APs: ${\mathit{t}}_{m}=({\mathtt{RSS}}^{m,1},\cdots ,{\mathtt{RSS}}^{m,{L}_{j}})$.

**UWB IPS**—The proposed UWB fingerprint definition exploits two CIR location-dependent features, that is, energy and the RMS-DS. Denoting the CIR as $h(t)$, the energy, referred to in the following as $\mathcal{E}$, is evaluated by considering the maximum value of the convolution between $h(t)$ and its time-reversed version $h(-t)$:

#### 4.3. Algorithms

**Fixed**

**k**

**NN**—Following the traditional approach adopted in most fingerprinting systems, the algorithm adopts as the similarity metric the inverse Euclidean distance between two fingerprints, corresponding to the inverse of the Minkowski distance defined in Equation (2) with order $o=2$, in combination with a fixed k.

**Adaptive**

**k**

**NN**—The algorithm adapts the value of k on the basis of the fingerprint collected at the position of the TN by also taking advantage of multifeature fingerprints, when available. The algorithm is organized into $F+1$ steps and uses an iterative approach that eventually selects fingerprints for which all features meet a similarity condition defined on the basis of dynamic thresholds. In the following, the algorithm is described for the case of multifeature UWB fingerprints with $F=2$, while its application to monofeature WiFi fingerprints is presented at the end of the section.

- (a)
- For each generic nth RN, given ${\mathit{s}}_{n}^{1}$ and ${\mathit{t}}_{m}^{1}$, a vector ${\mathit{\alpha}}_{n,m}^{1}=({\alpha}_{n,m,1}^{1},\cdots ,{\alpha}_{n,m,{L}_{j}}^{1})$ is defined, where the generic lth component is defined as follows:$${\alpha}_{n,m,l}^{1}=\left\{\begin{array}{c}\hfill \frac{{\mathcal{E}}^{m,l}}{{\mathcal{E}}^{n,l}}\phantom{\rule{1.em}{0ex}}\mathrm{if}\phantom{\rule{0.166667em}{0ex}}{\mathcal{E}}^{m,l}>{\mathcal{E}}^{n,l}\\ \hfill \frac{{\mathcal{E}}^{n,l}}{{\mathcal{E}}^{m,l}}\phantom{\rule{1.em}{0ex}}\mathrm{if}\phantom{\rule{0.166667em}{0ex}}{\mathcal{E}}^{n,l}>{\mathcal{E}}^{m,l}\end{array}\right.$$
- (b)
- A set of thresholds ${\{\delta \}}^{1}=\{{\delta}_{min}^{1},\cdots ,{\delta}_{i}^{1},\cdots ,{\delta}_{max}^{1}\}$ is defined in order to assess whether ${\mathit{s}}_{n}^{1}$ and ${\mathit{t}}_{m}^{1}$ are similar, on the basis of ${\mathit{\alpha}}_{n,m}^{1}$. For the generic ith threshold ${\delta}_{i}^{1}$ selected from ${\{\delta \}}^{1}$, the lth components of ${\mathit{s}}_{n}^{1}$ and ${\mathit{t}}_{m}^{1}$ are considered similar if ${\alpha}_{n,m,l}^{1}\le {\delta}_{i}^{1}$. In turn, ${\mathit{s}}_{n}^{1}$ and ${\mathit{t}}_{m}^{1}$ are determined as similar if at least $\lceil {L}_{j}/2\rceil $ components have been considered similar. Thresholds are selected one by one, starting from the most restrictive, ${\delta}_{min}^{1}$, and the similarity of each RN to the TN is tested against it. When at least one RN is determined to be similar to the TN, the procedure is concluded.

The RNs passing the selection of steps 1a and 1b are considered similar to the TN in the energy domain, and they are transferred to step 2.- The same procedure defined in steps 1a and 1b for the energy domain is applied in the RMS-DS domain by defining the ${\mathit{\alpha}}_{n,m}^{2}$ vectors on the basis of ${\mathit{s}}_{n}^{2}$ and ${\mathit{t}}_{m}^{2}$ and by comparing their components with thresholds in a set ${\{\delta \}}^{2}=\{{\delta}_{min}^{2},\cdots ,{\delta}_{max}^{2}\}$, leading to further pruning of the set of RNs eventually transferred to step 3.
- Equation (1) is finally applied on the set of remaining RNs in order to estimate the position of the TN.

## 5. A Common Framework for Performance Comparison

## 6. Results and Discussions

#### 6.1. Fixed kNN

#### 6.2. Adaptive kNN

#### 6.3. UWB versus WiFi-Optimal Configuration

**Impact of ANs/RNs Densities**—Figure 7 and Figure 8 report the statistics and CDF of $\u03f5$ in the LD, MD and HD scenarios for WiFi-opt and UWB-combo, respectively. The results show that UWB-combo outperforms WiFi-opt in all density scenarios, always showing a lower median $\u03f5$ than WiFi; UWB-combo and WiFi-opt present some outliers in the MD and HD scenarios, respectively, ranging however on tight intervals close to the median error.

**Impact of ANs/RNs Topologies**—Previous results have been obtained by averaging the positioning errors of different ANs/RNs topologies. In order to highlight how the variability related to ANs/RNs topology affects the positioning accuracy and reliability, Figure 9 shows, for all density scenarios defined in Table 2, the variance of the average error $\overline{\u03f5}$ when (1) the ANs topologies change while the RNs topology is fixed, and (2) the RNs topologies change while the ANs topology is fixed. The results show that, for both systems, the variation of either the ANs or RNs topology has a similar impact on the positioning error. However, a significantly higher impact is observed for WiFi-opt, indicating that UWB-combo not only outperforms WiFi-opt in terms of accuracy, but its performance is also less affected by the variation of ANs/RNs placement, allowing a higher degree of freedom in system implementation.

**Impact of System Optimization**—The two systems were further compared in terms of robustness with respect to system optimization. On the one hand, the optimization may focus on the reduction of the dedicated infrastructure in terms of the number of ANs; on the other, it may focus on the reduction of required offline measurements in terms of the number of RNs. Two additional scenarios were thus defined, as reported in Table 3.

**Complexity Comparison**—The comparison between the complexity of WiFi-opt and UWB-combo should consider both offline and online phases for the two systems:

- Offline-phase complexity—The complexity of the measurement phase is comparable for the two systems: in the case of WiFi-opt, the RSS reading taken at each RN is commonly provided by off-the-shelf WiFi devices and does not require any particular advanced post-processing. Similarly, energy and RMS-DS readings, taken in the same number of RNs, can be easily obtained from data collected by off-the-shelf UWB devices, such as Decawave or Time Domain products, with simple post-processing techniques [35]. In terms of fingerprinting database storage, the UWB-combo needs twice the storage space compared to WiFi-opt, as two signal features are included in the fingerprint associated to a single RN. However, the results shown in Figure 10 indicate that UWB-combo can achieve the same positioning accuracy while using a lower RN density than WiFi-opt, in turn requiring less storage space.
- Online-phase complexity—The complexity of this phase depends on the adopted estimation algorithm.In the case of WiFi-opt, a traditional kNN algorithm is used; following the analysis presented in [36], the kNN complexity is determined by the computation of the Euclidean distances between TN and RNs RSS fingerprints ($\overline{N}\overline{L}$ multiplications) and the selection of the k nearest neighbors ($\overline{N}k$ comparisons). Overall, the asymptotic complexity can be expressed as $O(\overline{N}\overline{L})$ in terms of multiplications and $O(\overline{N})$ in terms of comparisons.In the case of UWB-combo, the complexity of the adaptive kNN algorithm operating on $F=2$ features can be estimated as follows. In step 1, $\overline{N}\overline{L}$ values of ${\alpha}^{1}$ are computed ($\overline{N}\overline{L}$ multiplications) and compared with the set of ${\{\delta \}}^{1}$ thresholds. In the worst case, this comparison is repeated over the entire set of thresholds, leading to the need for $\overline{N}\overline{L}\left|{\{\delta \}}^{1}\right|$ comparisons, where ${|\{\delta \}}^{1}|$ represents the cardinality of the set of energy thresholds. In step 2, if no RNs have been discarded during step 1 (worst-case analysis), $\overline{N}\overline{L}$ values of ${\alpha}^{2}$ are computed ($\overline{N}\overline{L}$ multiplications) and compared with the set of ${\{\delta \}}^{2}$ thresholds. If this comparison is repeated over the entire set of thresholds, $\overline{N}\overline{L}\left|{\{\delta \}}^{2}\right|$ comparisons are needed, where ${|\{\delta \}}^{2}|$ represents the cardinality of the set of RMS-DS thresholds. The asymptotic complexity can finally be expressed as $O(\overline{N}\overline{L})$ in terms of multiplications and $O(\overline{N}\overline{L})$ in terms of comparisons.UWB-combo is thus characterized by a slightly higher asymptotic complexity than WiFi-opt, but it is worth mentioning that the above analysis was carried out under an extreme worst-case scenario, in which, in particular, it is assumed that step 1 of the algorithm does not affect the following phase (no RNs are discarded using the energy parameter). However, experimental analysis has showed that such a scenario is quite unlikely: most of the RNs are in fact typically discarded in step 1, leading to a significantly reduced complexity for latter phases of the algorithm.

## 7. Conclusions and Future Work

## Author Contributions

## Conflicts of Interest

## Abbreviations

AN | Anchor node |

CIR | Channel impulse response |

DIET | Department of Information Engineering, Electronics and Telecommunications |

IPS | Indoor positioning system |

LoS | Line-of-sight |

MWMF | Multi-wall multi-floor |

NLoS | Non-line-of-sight |

RMS-DS | Root-mean-square delay spread |

RN | Reference node |

RSS | Received signal strength |

TDoA | Time difference of arrival |

TN | Target node |

ToA | Time of arrival |

UWB | Ultra-wideband |

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**Figure 2.**Example of anchor node/target node (AN/RN) Poisson point process (PPP) topology @ DIET Department; $\overline{L}=10$ and $\overline{N}=100$ (ANs: circles; RNs: squares).

**Figure 3.**Statistics of positioning error $\u03f5$ in low density (LD) scenario for WiFi, ultra-wideband (UWB)-energy and UWB root-mean-square delay spread (RMS-DS) with fixed k-nearest neighbor (kNN) algorithm ($k=\{1,2,3,4,5\}$).

**Figure 4.**Statistics of positioning error $\u03f5$ in medium density (MD) scenario for WiFi, ultra-wideband (UWB)-energy and UWB root-mean-square delay spread (RMS-DS) with fixed k-nearest neighbor (kNN) algorithm ($k=\{1,2,3,4,5\}$).

**Figure 5.**Statistics of positioning error $\u03f5$ in high density (HD) scenario for WiFi, ultra-wideband (UWB)-energy and UWB root-mean-square delay spread (RMS-DS) with fixed k-nearest neighbor (kNN) algorithm ($k=\{1,2,3,4,5\}$).

**Figure 6.**Statistics of positioning error $\u03f5$ in low, medium and high density (LD, MD and HD) scenarios for WiFi, ultra-wideband (UWB)-energy, UWB root-mean-square delay spread (RMS-DS) and UWB-combo with adaptive k-nearest neighbor (kNN) algorithm.

**Figure 7.**Statistics (

**a**) and cumulative distribution functions (CDFs) (

**b**) of the positioning error $\u03f5$ in low, medium and high density (LD, MD and HD) scenarios for the WiFi-opt system.

**Figure 8.**Statistics (

**a**) and cumulative density functions (CDFs) (

**b**) of the positioning error $\u03f5$ in low, medium and high density (LD, MD and HD) scenarios for the ultra-wideband (UWB)-combo system.

**Figure 9.**Variance of average positioning error $\overline{\u03f5}$ due to topology change in low, medium and high density (LD, MD and HD) scenarios for ultra-wideband (UWB)-combo vs WiFi-opt.

**Figure 10.**Average positioning error $\overline{\u03f5}$ in minimum infrastructure (mI) (

**a**) and minimum measurements (mM) (

**b**) scenarios for ultra-wideband (UWB)-combo vs WiFi-opt.

Parameter | WiFi/UWB |
---|---|

M | 50 |

$\overline{L}$ | $\{5,10,15\}$ |

$\overline{N}$ | $\{25,50,100\}$ |

k (fixed kNN) | $\{1,2,3,4,5\}$ |

${\{\delta \}}^{1,2}$ (adaptive kNN) | {1.1–1.5} |

Scenario | ($\overline{\mathit{L}}$,$\overline{\mathit{N}}$) |
---|---|

Low density (LD) | ($5,25$) |

Medium density (MD) | ($10,50$) |

High density (HD) | ($15,100$) |

Scenario | $\overline{\mathit{L}}$ | $\overline{\mathit{N}}$ |
---|---|---|

Minimum infrastructure (mI) | 5 | $\{25,50,100\}$ |

Minimum measurements (mM) | $\{5,10,15\}$ | 25 |

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## Share and Cite

**MDPI and ACS Style**

Caso, G.; Le, M.T.P.; De Nardis, L.; Di Benedetto, M.-G.
Performance Comparison of WiFi and UWB Fingerprinting Indoor Positioning Systems. *Technologies* **2018**, *6*, 14.
https://doi.org/10.3390/technologies6010014

**AMA Style**

Caso G, Le MTP, De Nardis L, Di Benedetto M-G.
Performance Comparison of WiFi and UWB Fingerprinting Indoor Positioning Systems. *Technologies*. 2018; 6(1):14.
https://doi.org/10.3390/technologies6010014

**Chicago/Turabian Style**

Caso, Giuseppe, Mai T. P. Le, Luca De Nardis, and Maria-Gabriella Di Benedetto.
2018. "Performance Comparison of WiFi and UWB Fingerprinting Indoor Positioning Systems" *Technologies* 6, no. 1: 14.
https://doi.org/10.3390/technologies6010014