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Abstract

In this article, we propose an efficient approach to address mobile indoor localization using received signal strength from iBeacon combined with trusted-ranges model. In order to overcome the inconsistency of radio signal propagation, the trusted-ranges model supplies reliable ranges of received signal strength values from a certain number of nearest neighbor iBeacon nodes by classifying received signal strength values into various levels of range. By observing the signal propagation, the trusted-ranges model is built to provide important information for the training phase. Based on this, a partition scheme is applied to effectively determine the position of mobile devices. The experimental results show fast, robust, and accurate localization performance in the proposed method.

Keywords

Indoor localization received signal strength iBeacon trusted ranges

Introduction

Indoor localization has attracted a lot of research efforts in recent years. It aims to estimate the indoor position of a user (e.g. smartphone) to provide the service he or she needs. One typical method for obtaining location information is to use the global positioning system (GPS) service. This system provides a good accuracy and portable navigator for large-scale deployments but suffers from high cost and complex hardware. Moreover, GPS functions are not well performed in the indoor environment (e.g. buildings, tunnels). Thus, indoor localization technology would bring us huge benefit to improve the quality of Internet of things. For example, instead of spending enormous amount of time to find an item in a shopping center, a person can have an indoor map marked with his location on a mobile phone. With indoor positioning system, the shopping center can also deliver the location content and other location-based advertising. In this article, we consider an indoor localization scheme that employs Bluetooth low-power equipment (BLE) (e.g. iBeacon), received signal strength (RSS), and trilateration. A device detects the RSS signals from the iBeacon, calculates roughly the distance to iBeacon, and estimates its location if it is in the range of more than two iBeacons. Our task is first to find a good trusted-range model to describe the RSS–distance relationship during the training phase, then a trilateration technique is applied to determine the user position during the online phase. We have put more effort to provide an easy scheme for localization at the finest resolution area (under 1 m accuracy) which is good enough to distinguish kiosks or rooms in a building. In this case, the variations of RSS measurements are also taken into account to provide accurate position estimate.

The benefits of BLE in indoor localization have been shown in several works.^1–7 Jianyong et al.¹ proposed a theoretical RSS-based BLE positioning method, which is divided into the following steps: (1) establishing an accurate RSS model, (2) smoothing online RSS readings, (3) RSS-based trilateration positioning methods, and (4) adjusting the RSS model periodically. A practical localization scheme² used only the RSS measurements and multi-lateration method for a Bluetooth smartphone. The effects of furniture and human body were also addressed in the RSS model. The BlueSentinel system³ only adapted iBeacon to detect the number of users in a room, while their locations are estimated by a building management system. Chen et al.⁴ proposed the RSS-based localization scheme for BLE device. The authors deployed the iBeacon hardware developed by Estimote, Inc., which have large variations in measurements. In order to achieve good accuracy, the iBeacon nodes should be deployed in high density. By jointly using iBeacon and inertial sensors, the protocols^5,6 consisted of two modes: iBeacon localization mode and particle filter mode. Then, the position was estimated based on Wi-Fi fingerprinting approach. In order to achieve high accuracy, iBeacon nodes were only deployed to cover the areas that have poor Wi-Fi signals. Noh et al.⁷ proposed a system deploying dead reckoning for RSS-based localization, where Wi-Fi access points (APs) were used as reference points. However, these aforementioned inertial sensor-based protocols are not only complex but also have many drawbacks. With a theoretical RSS model,¹ the results from an experimental study were not presented, while the system² deploys the Bluetooth 2.1 standard, which is old and low response. Errors from measuring and calculating procedure need to be addressed via practical experiments. Even if the distribution of errors is known, complexity and convergence issues may limit the performance of the algorithm^3,4 in practice. Also, it is inefficient for self-localization if we maintain such a management system or building fingerprinting database. Another challenge related to the computational capability of the mobile devices is that inertial sensor-based approaches^5,6 have comprehensive performance but they require higher hardware complexity and cost for the dual architecture. Wi-Fi can be used in a similar way as BLE beacons. Although its signals are stronger and can cover more distance than BLE, it requires an external power source, more setup cost, and pricey equipment. The accuracy of Wi-Fi solution⁷ highly depends on the number of APs, that is, increasing the number of APs will increase the deployment cost. Moreover, scanning Wi-Fi signals is slower than Bluetooth ones. In order to tackle these issues, we first experienced the relationship between the distance and the RSS signals measured from an iBeacon node. The signal experiment varies over time at the same location. This information is collected to build a trusted-range table, which is used to determine the position of a mobile device during the online phase. In this article, we aim to propose a real-time indoor positioning and tracking system based on iBeacon devices that can give accurate position estimate and can be implemented for self-localization on mobile devices, so that location-based services can be applied. In the context of this article, the mobile device refers to the handheld devices (i.e. smartphones) which have limited power, memory, and computational capability; thus, not only a light-weight localization algorithm but also the capability to have real-time operation as well as accurate performance is required. In addition, we presented different ways to improve those aforementioned conventional approaches, such as determination of region of interest, selection of the zone, and the use of estimation method. Then, we obtained the effective localization scheme by the following procedures:

Measure the RSS from the nearest neighbor iBeacon nodes;

Calculate and choose a zone that offers the best fit of the mobile position;

Use a localization algorithm based on the triangulation method to estimate the position. Our approach provides low complexity and rapid processing.

There are several reasons that we choose the iBeacons to improve the performance of localization system. First, they are inexpensive and small that makes them easy to deploy as standard on devices. Second, since they have long battery life and do not require external energy source, there is no need of system maintenance. Third, they have high adjustment capability and are very responsive for small chunks of information broadcasted without a pairing sequence. Through practical experiments, we proved that the scanning time can be reduced by 65% when using iBeacon compared to when using the Wi-Fi. In our previous work,⁸ we proposed an indoor localization scheme based on iBeacon and provided some simulation results. This scheme offers a simple and accurate localization solution with low complexity. Based on this work, we modified and extended the localization algorithm and included some new experimental results under real indoor environments.

The remainder of our article is organized as follows. Section “iBeacon propagation measurements” briefly introduces the iBeacon characteristics and a basic idea of the trusted-ranges model. The proposed localization algorithm and a practical setup scheme are presented in section “Localization algorithm.” Section “Experimental results” shows the experimental results and the corresponding evaluation on the algorithm performance. Finally, the conclusion is given in section “Conclusion.”

Notations: We used the following notations throughout the article. Mean and variance of a random variable X are denoted as $\bar{X}, σ_{X}^{2}$ , respectively. Thus, $σ_{X}$ is the square root of the variance, which is known as standard deviation. Card $(S)$ denotes the number of elements in the set S. The intersection operation of sets is denoted as ⋂. The notation ∃ means “there exists.” $x \in S$ means that x belongs to a set S.

iBeacon propagation measurements

Single iBeacon node measurements

An iBeacon node–equipped BLE works similar to a stand-alone radio base station, which allows Bluetooth devices to broadcast a small amount of data through the air within short distance.⁹ It is inexpensive, small in size, and has a long battery life. In general, its wireless signal is significantly affected by several ambient materials such as wall materials, metal, and human body from the measured environment. The accuracy estimated based on RSS measurements does vary depending on manufacturers but can be as good within 1.5 m.¹⁰ In this section, we consider the following environment for experiment setup. A lobby with the size of 8 m × 10 m has a floor made of solid granite rock. The roof is about 6-m high covered by slim flat metal sheets on which several small lights and speakers are attached. The walls are 10 m in length and are made of concrete and glass with aluminum frames. The space does not consist of furniture or people.

In this experiment, we use RedBean iBeacon¹¹ and set the advertising interval at 200 ms and transmit (TX) power at +4 dBm. An iBeacon node is placed at the corner of the room. The antenna of iBeacon is pointed straight upward. A smartphone is placed on the ground with the screen facing up, parallel with the iBeacon node. RSS readings from the iBeacon are recorded by the smartphone at various distances. Since the orientation of the antenna inside the iBeacon affects the RSS reading, the device is put at a specific orientation when collecting RSS reading at each point. In this work, RSS readings are collected at four directions represented by ${0 °, 90 °, 180 °, 270 °}$ as shown in Figure 1. Starting from 0.5 m from an iBeacon, the smartphone consecutively moves an additional 0.5 m for every 5 min along the 45° diagonal line of corner wall until reaching the room length as illustrated in Figure 2. Thus, we obtained a raw set of RSS time samples collected from iBeacon at different positions and orientations. The reflection effects are also addressed in the measurements. In particular, when we measured the RSS in a diagonal line at 45° from the wall, the reflection effects were strong that yields a larger range of RSS signals. This situation can be considered as worst case because the measured signal may include not only multi-path signals but also path loss signals. If such case is solved, the easier cases (e.g. iBeacon is placed in the center of the room without surrounding obstacles or near along the wall) can also be solved.

Figure 1.

Four orientations of iBeacon: (a) 0°, (b) 90°, (c) 180°, and (d) 270°.

Figure 2.

Single iBeacon node measurements with a smartphone.

Since the average RSS values are used by the positioning and tracking system to estimate the smartphone’s location, it is important to obtain a reliable average value. Figure 3 shows the average of RSS readings at several times of a day. Each measurement was taken almost 2 h to be done. At each reference point, we collected 300 RSS recordings during 5 min. The measurement was taken three times a day and was repeated for three Sundays. We choose these time schedules because they are business time slots, that is, localization-based services are needed. The RSS recordings at 9 a.m. can be classified into three levels: those from −65 to −56 dBm at 0.5 m from the iBeacon node, −76 to −66 dBm at 1 m, and −85 to −77 dBm at 1.5 m. Even then we measured at different times of the day (e.g. 2 p.m. and 6 p.m.), we also obtained similar results despite slight differences in ranges as shown in Figure 3(b) and (c). From this observation, the concept of trusted-ranges table which consists of three levels of RSS ranges is appropriate. We denoted the measurement step as u, which indicates the distance between the receiver and the transmitter. In our experiment, we generated linear u six points in the interval $[0.1, 0.7] m$ . Overall, $u = 0.5 m$ is enough to distinguish the RSS readings into different levels of ranges. Thus, we set $u = 0.5 m$ for further experiment. Note that this value does vary depending on circumstances, that is, iBeacons from different manufacturers may require different measurement steps to separate signals. The measurement step u will be examined first until the measurement signals have the forms similar to Figure 3.

Figure 3.

Average RSS from a single iBeacon node to a smartphone at several times of a day: (a) 9 a.m., (b) 2 p.m., and (c) 6 p.m.

Trusted-ranges model

After collecting the RSS time samples, we observed that the RSS readings versus distances from the same pattern at a certain time thus can be classified into three levels of ranges. We selected the reliable RSS values as trusted ranges given by equation (1). Moreover, an additional range level is also included in the table to address the case when mobile device receives the RSS values outside of the predefined range. This “out-of-ranges” level plays a prominent role in distinguishing spatial areas. Assuming there are N iBeacon nodes, let $B_{i}$ be the single measured RSS value of $i th$ iBeacon node and $b_{i}$ and $B_{it}$ be the set of RSS values of $b_{i}$ at measurement time t of a day. For t time samples along a day, the trusted ranges $T_{l}$ at level l are defined as follows

$T_{l} = ⋂_{t} {B_{it}}_{l} l = 1, \dots, 4$ (1)

where $t \in N$ and ${B_{it}}_{l}$ are the set of received RSS values in the $l th$ range level. In order to obtain RSS distributions over time, we collected their samples at a regular time interval. We may need more time samples for achieving the desired accuracy, hence greater costs. In this work, we collected data at working time for which many people would need localization-based services. The standard deviation of each $T_{l}$ is defined as follows

$σ_{l} = \sqrt{\frac{\sum_{t' = 1}^{n_{l}} {(B_{ilt'} - {\bar{B}}_{il})}^{2}}{n_{l} - 1}}$ (2)

Here, $n_{l}$ is the number of records collected at range level l over time t and ${\bar{B}}_{il}$ is the mean of all samples at range level l. The number of range levels l can be determined by the number of RSS signal ranges. Also, using different iBeacon nodes which have stronger signals, the level of signal ranges can be more clearly separated. Thus, in order to achieve a better estimation, we can increase l to predict the more accurate position information.

Due to time varying characteristics of the propagation wireless channel, RSS readings collected during training phase will be stored for the computation of position estimation. The actual RSS readings recorded at 9 a.m., 2 p.m., and 6 p.m. are given in Table 1. The RSS values are classified into four levels in terms of distance. We evaluated the trusted ranges of all recorded RSS values from an iBeacon node to a smartphone using equation (1). These trusted ranges show the RSS–distance relationship, so that the smartphone can estimate the distance from the iBeacon based on the RSS collected at that location. For example, if a smartphone receives a signal at −34 dBm from an iBeacon, the distance between them must be within 0.5 m, and if the RSS has a value in the range of (−63, −56), then the distance between them is limited from 0.5 to 1.0 m. The accuracy of the proposed localization scheme depends on finding a good trusted-range model that can best describe the behavior of the RSS values.

Table 1.

RSS ranges at various times and corresponding trusted ranges.

Range of RSS values (dBm)		Class of distance (m)
		0.5 (≤0.5)	1.0 (0.5–1.0)	1.5 (1.0–1.5)	$\geq 2.0$
Time	9 a.m.	$(- 65, - 56)$	$(- 76, - 66)$	$(- 85, - 77)$	$(- 94, - 86)$
	2 p.m.	$(- 63, - 55)$	$(- 71, - 66)$	$(- 84, - 79)$	$(- 96, - 85)$
	6 p.m.	$(- 68, - 55)$	$(- 78, - 67)$	$(- 84, - 75)$	$(- 92, - 85)$
Trusted ranges		$(- 63, - 56)$	$(- 71, - 66)$	$(- 84, - 79)$	$(- 92, - 86)$

RSS: received signal strength.

While the RSS signals at distance 0.5 to 1.5 m are distinguished, the rest are difficult to analyze. Some of them have RSS values near trusted ranges, although the distance is far more than 2 m. The chaos of out of ranges could affect the accuracy of our proposed algorithm. For that reason, we carefully analyzed the probability of out-of-ranges interference as shown in Table 2. After collecting the signals in several distances, we calculated the percentage of the out-of-ranges distance that has RSS values in the trusted-ranges table. For instance, there is 12.7% chance of generated the RSS values at distance 2.0 m similar to the trusted range in distance 1.5 m (−84, −79). For our particular iBeacon type, the distance from 2 to 4.5 m has the acceptable value of interference (e.g. lower than 30%). In the trusted range (−71, −66), there is only one case of interference at distance 4 m.

Table 2.

Interference probability of various out-of-ranges distances to trusted range.

Out-of-ranges probability (%)		Distance (m)
		2.0	2.5	3.0	3.5	4.0	4.5	5.0	5.5	6.0
Trusted range	(−84, −79)	12.7	1.1	4.66	16.3	24.3	20.1	58.1	51.4	75.3
Trusted range	(−71, −66)	0.0	0.0	0.0	0.0	0.001	0.0	0.0	0.0	0.0

Localization algorithm

Most RSS-based localization algorithms utilize triangulation or fingerprinting methods to compute the position estimate. However, when exploiting the triangulation method in a large-scale area, its accuracy is no longer guaranteed due to calculation error and path loss propagation.² On the other hand, the accuracy of the fingerprinting method depends highly on how good the radio map is, for example, radio map has finer resolution and thus allows for a better estimation. The building and maintaining of fingerprint database are time-consuming and costly. To overcome these issues, we utilized a RSS–location relationship in real situation and performed an improved triangulation method to obtain the smartphone position. Thus, it is able to reduce the labor efforts, time required for creating radio map, and estimation errors.

Area allocation

We consider a grid of N iBeacon nodes whose locations are denoted by $b_{i} (x_{bi}, y_{bi})$ , where $x_{bi}$ and $y_{bi}$ are the major and minor values of an iBeacon node representing $b_{i}' s$ coordinate, respectively. The values $x_{bi}$ and $y_{bi}$ can be adjusted by the user when iBeacon is broadcasting signals.⁹ We assumed that a certain cell is bounded by four closest iBeacon nodes, as illustrated in Figure 4, which describes a cell created by $b_{1}, b_{2}, b_{3}, and b_{4}$ iBeacons. Each iBeacon node creates a small area within a cell called a partition (I, II, III, and IV) where $b_{1} \in I, b_{2} \in II, b_{3} \in III, and b_{4} \in IV$ are in the positions shown in the figure. In another cell created by $b_{3}, b_{4}, b_{5}, and b_{6}$ , the corresponding partitions are $b_{3} \in I, b_{4} \in II, b_{5} \in III, and b_{6} \in IV$ . Let D be the distance step between two iBeacon nodes, which also represents the edge length of a cell. Each cell is divided into four partitions $(I, II, III, and IV)$ equally belonging to the four iBeacons located inside. Four iBeacon nodes create a square region defined by zone. The sizes of all zones are equal in length, which is quite close to human stride length, that is, how far a person walks with each step. On average, it is approximately 0.73 m for a man and 0.67 m for a woman.⁷ In fact, a walking stride cannot exceed the length of two continuous zones (e.g. about 1 m); thus, a partition of 0.5 m edge length is reasonable for localization use. A partition contains a total of $n_{z}$ zones followed by

$n_{z} = {(\frac{D}{2 \times u})}^{2}$ (3)

Figure 4.

Partition schemes of a cell, partitions, and zones with $D = 4$ .

Figure 4 shows an example of partition where $D = 4$ . A single cell which is sized 4 m × 4 m has four partitions. Each partition is divided into four zones. We denote the unknown position of smartphone as $P (x, y)$ and the center point of the ith zone as $z_{i} (x_{zi}, y_{zi})$ . For instance, $z_{1} (0.25, 0.25)$ represents the coordinate of center point of zone 1, which is bounded by a 0.5-m × 0.5-m square. In partition I, zones are labeled from left to right and from top to bottom. In partition II, zones are labeled from right to left and from top to bottom. Partition III has the label rule from bottom to top and from left to right. Finally, in partition IV, zones are labeled from bottom to top and from right to left.

Regarding Table 1, zones can be divided into five groups based on their closeness to the iBeacon node. From Figure 4, group 1 includes zone 1, which is the closest zone to the iBeacon node within 0.5 m. Similarly, group 2 includes the zones 2, 5, and 6, which are 1 m to the iBeacon. Zones 3, 7, 6, 9, and 10 are assigned to group 3, which are those zones of distance 1.5 m to iBeacon. Group 4 involves the zones 4, 8, 11, 13, and 14 that indicate distances of 2 m. The last group included zones 12, 15, and 16, which represents the RSS values out of the trusted ranges. Thus, we modified the method to determine the zone for locating the smartphone in the next section.

Proposed localization algorithm

Without loss generality, assume that iBeacon nodes are placed at the positions as illustrated in Figure 4, and the smartphone is near to iBeacon $b_{1}$ . In order to reduce the computation time and minimize the maximum estimation errors, the localization process also constrains the region of interest into smaller relevant area. The process follows a step-wise process: locating the partition, locating the group, and locating the zone. By this way, before estimating the smartphone location, we confined the area into a subset of relevant zones and a subset of iBeacon nodes, which can distinguish the RSS readings easily. In detail, the following flow chart describes the individual blocks as shown in Figure 5.

Figure 5.

The flow chart of the proposed localization algorithm.

First, the smartphone scans iBeacon signals and may not recognize all N nodes. In this scheme, the measurement vector is filtered to determine n iBeacon nodes that have the strongest RSS readings. Mathematically, we wrote the set of n received RSS signals $B = {B_{i}} (i = 1, \dots, n), n \leq N$ . Among them, a cell is formed by the four iBeacon nodes which are selected according to equation (4). Thus, the corresponding RSS signals are sorted in descending order in the new list, that is, $B 1 \geq B 2 \geq B 3 \geq B 4$

$B 1 = max {B}, Bi = max {B \ B (i - 1)}$ (4)

where $i = 2, \dots, n$ . The selected partition is the one containing the strongest RSS value $B 1$ . In other case, a smartphone is near to $b_{2}$ (e.g. $B_{2} \geq B_{4} \geq B_{2} \geq B_{1}$ ), the elements in set B would be $B 1 = B_{2}, B 2 = B_{4}, B 3 = B_{2}, B 4 = B_{1}$ . If the scanning step failed, which means $\exists Bi = Bj = 0$ , we performed the scanning step again. Let k be the maximum number of loops needed to achieve the desired accuracy; we repeated this step k times and found the mean value $\bar{B} i$ of nearest iBeacon nodes. Herein, each element in the set B is the mean value after k iterations $Bi (Bi = \bar{B} i)$ . In this article, we set $k = 5$ . Increasing k will lead to a slightly better result but will also take more time, about 1.3 s for each loop.

Second, a group G which may contain the smartphone is selected by mapping $B 1$ into the trusted-ranges table. The standard deviation $σ_{l}$ is also calculated accordingly using equation (2). If group 1 is selected $(G = 1)$ , the smartphone must belong to $zone 1$ and its position can be estimated. To distinguish those members in groups 4 and 5, we first considered the difference of RSS values between two closest neighbors of iBeacon nodes, for example, $B 2$ and $B 3$ . This value is denoted by $Δ$

$Δ = | B 3 | - | B 2 |$ (5)

Since the RSS readings collected at different distances are different, it can vary up to −56 dBm. This indicates that with the same distance, the trust-range model cannot be used by mobile devices. For example, when the smartphone is located at zone 6, the RSS values of $B 2$ and $B 3$ are not equal all the time. Thus, we used an additional threshold called $σ_{l}$ for angle separation. A value $Γ$ represents the difference among $B 1$ and $B 2$ , $B 3$ given by

$Γ = \frac{1}{g_{out}} (| B 1 - B 2 | + | B 1 - B 3 |)$ (6)

where $g_{out}$ is the number of groups that are out of trusted ranges in a partition (e.g. in Figure 4, $g_{out} = 2$ ). If $Γ \leq | Δ |$ , group 5 is selected; otherwise, group 4 is chosen.

Third, in order to select the zone, we used $Δ$ to decide which part the smartphone may belong to. In particular, the zone selection rule is followed by

(C1) $Δ = 0$ or $| | B 1 - B 2 | - | B 1 - B 3 | | \leq σ_{l}$ $\Rightarrow P (x, y) \in$ {zones 1, 6, 11, and 16}.

(C2) $Δ > 0 \Rightarrow P (x, y) \in {zones 2, 3, 4, 7, 8, and 12}$ .

(C3) $Δ < 0 \Rightarrow P (x, y) \in {zones 5, 9, 10, 13, 14, and 15}$ .

From a previous step, we already know the group which could distinguish the iBeacon easily. Next, the step of selecting the zone where the smartphone position may belong to is described as follows:

$P (x, y)$ in group 1 $(l = 1)$ : Zone 1 is selected.

$P (x, y)$ in group 2 $(l = 2)$ . If (C2) happens, zone 2 is selected; else if (C3), zone 5 is selected; else if (C1), $P (x, y) \in zone 6$ .

$P (x, y)$ in group 3 $(l = 3)$ . If (C2) happens and $Δ > σ_{l}$ , we select zone 3; else $Δ \leq σ_{l}$ , we select zone 7. If (C3) happens and $Δ > σ_{l}$ , we select zone 9; otherwise, zone 10 is chosen. If (C1) happens, zone 6 is selected.

$P (x, y)$ in group 4 $(l = 4)$ . Similar to equation (3), if (C2) and $Δ \leq σ_{l}$ , we select zone 8; else if select zone 4. If (C3) and $| Δ | > σ_{l}$ , we select zone 13; otherwise, select zone 14. When (C1) happens, zone 11 is chosen.

$P (x, y)$ in group 5 $(l = 4)$ . If $Γ \leq σ_{l}$ , the position $P (x, y)$ is assigned to zone 16; otherwise, we choose zone 12 if $Δ > 0$ , else zone 15.

Finally, the smartphone obtains the information on $(partition, group, zone)$ ; thus, its position can be calculated as follows

$P (x, y) = {\begin{matrix} (D x_{bi} + x_{zi}, D y_{bi} + y_{zi}) & b_{i} \in I \\ (D x_{bi} - x_{zi}, D y_{bi} + y_{zi}) & b_{i} \in II \\ (D x_{bi} + x_{zi}, D y_{bi} - y_{zi}) & b_{i} \in III \\ (D x_{bi} - x_{zi}, D y_{bi} - y_{zi}) & b_{i} \in IV \end{matrix}$ (7)

Note that the coordinate is used based on pixel screen coordinator in which the system uses the top-left corner as staring point.

Experimental results

Application description

In this section, to implement our proposed algorithm, we made a simple application based on Xcode and iPhone 5 as shown in Figure 6. The grid map on the main screen is a simplified map where the position estimation performs. The red point located at the screen corner represents the current estimated location of $P (x, y)$ . Note that this point has the same size with a zone and may change when the smartphone moves. Width and Height represent size of the experiment area, Sample Count is the number of loop k, and Unit Value provides the value of D. The user can select which localization algorithms that he or she wants to use (e.g. triangulation, trusted ranges). The value Nearest Nodes shows four nearest iBeacon nodes that the smartphone was found in the order of decreasing received RSS values. Estimated Position represents the estimated position after pushing the button of localization algorithm. One Time button performs single run of a random experiment, while Start Demo button performs several one-time runs to update the smartphone position in real time, especially in walking route experiment. When the red point is placed exactly at the zone where the smartphone is located, we can achieve the “ideal” accuracy. Otherwise, if it is placed at the neighbor zone where the smartphone is located, the location error is about u value (in this experiment, $u = 0.5 m$ ), meaning that we can get a “correct” estimation. In other cases (e.g. the red point is way too far the smartphone position), we statistically analyzed the samples and determined the errors, which is shown in the next section.

Figure 6.

A developed iPhone application for experiment.

Random position experiments

Before analyzing the localization performance of a random position, we tried several grid resolutions to find the optimal value D and then performed the localization methods on the mobile testing test. In this case, a smartphone is placed at random position. As we described in section “Single iBeacon node measurements,” we used the same environment to examine the accuracy of measurement results. The experiment was set during the university vacation to reduce the interference by unexpected pedestrians. All iBeacon nodes were deployed on the floor in grid positions as shown in Figure 7, which include the entire lobby area. Note that $D = 4$ means the distance between two neighbor nodes is 4 m.

Figure 7.

Deployment of iBeacon nodes with $D = 4$ .

The smartphone was randomly deployed at a position, thus placed on the floor in a random zone, which is estimated. Meanwhile, no pedestrian, furniture, or tester was around. Then, we collected the localization errors by calculating the Euclidean distance d between the real position $P_{r} (x_{r}, y_{r})$ and the estimated position $P (x, y)$ as follows

$d (P, P_{r}) = \sqrt{{(x_{r} - x)}^{2} + {(y_{r} - y)}^{2}}$ (8)

If $d (P, P_{r}) \leq u$ , the estimated position was considered to be correct and counted it as 1; otherwise 0. For each distance D, the smartphone position is a random choice and its estimated position is an average point after repeating q times. The corresponding average accuracy $A_{D}$ over the q runs is obtained as follows

$A_{D} = \frac{1}{q} \sum_{q} {d (P_{q}, P_{r}) : d (P_{q}, P_{r}) \leq u}$ (9)

Figure 8 depicts the localization accuracy (equation (9)) versus distance D when $q = 100$ . The figure shows that our approach achieves a good performance and thus attains the small errors when D = 1, 2, 3, and 4. We can conclude that the best localization accuracy is about 93.5% at $D = 1$ , while the accuracy at $D = 4$ is about 79% (i.e. the accuracy decreased by 14.5%). Meanwhile, a number of iBeacon nodes have been used which rapidly decreases from 117 $(D = 1)$ to 12 $(D = 4)$ , that is, 89% of resource is saved. Thus, we should have a reasonable number of iBeacon node according to the desired accuracy level. In other cases (e.g. $D = 5 or 6$ ), the accuracy percentage is quite low and thus the error estimation will be high. This may be due to the hardware limitation of iBeacon. The distance value D exceeds the trusted-range cover, then it is more difficult to distinguish the RSS range level. Moreover, according to Table 2, we conclude that the optimal solution is achieved at $D = 4$ because it provides a good trade-off between the number of iBeacon nodes used and accuracy and it also guarantees an acceptable interference probability.

Figure 8.

Accuracy for random positions according to various D values.

Real-time walking route experiments

Based on the previous result, we performed real-time localization experiments in which a user carries a smartphone and walks around the area of interest following a route. In order to provide accuracy position, the presence of effects along z-axis caused by the user-holding height h from the floor to the device is also addressed in this section. We observed that the distance changes from an iBeacon to the smartphone along the diagonal lines as shown in Figure 9.

Figure 9.

Mapping trusted ranges by combining user-holding height.

Let a be the distance from iBeacon to the smartphone and w be the distance from iBeacon node to the user’s foot. We improved the positioning system by choosing the correct relevant region during the coarse stage and adjusting the range according to user trajectory. First, the value of a can be obtained by mapping the received RSS reading on the smartphone to the trusted-ranges table. Second, we calculated w by applying the Pythagorean theorem (equation (10)). Thus, the localization problem can be treated as flat two-dimensional (2D) partition scheme to determine area allocation based on the value of w. In case the return value a is outside of the trusted ranges, the CoreLocation API¹² is applied to obtain a more accurate value a. Next, in case the estimated number w is contained in the trusted-ranges table, we will move to the next step. Otherwise, we keep scanning iBeacon signals again

$w = \sqrt{a^{2} - h^{2}}$ (10)

In fact, h can be either input by user or provided by an available altitude sensor equipped with smartphone. This section examines a setting scheme where a user was 1.75-m tall, used a smartphone at height around 1.2–1.3 m, and walked at a normal speed of 4.8 km/h. The smartphone was carried by the user following the route, as shown in Figure 10, from the left bottom to the right top. In this figure, the green dots are the actual trace, the blue dots are the triangulation-based positioning results, and the red dots are the results of the proposed tracking scheme. Notice that the user will obtain the real-time estimation position updates periodically from the device. We observed that in our scheme, the device is able to track the trajectory more accurate than the triangulation method, that is, the estimated route shown in Figure 10(c) was closer to the actual one. Moreover, for those cells near to the iBeacon nodes, we do have a good coverage of the iBeacon, which leads to good result. When the smartphone is located in a central area of cell, it makes the system hard to identify the correct ranges because its RSS measurements were outside of trusted-ranges table due to the user-holding height. We also observed that the error obtained from mobile user testing is slightly higher than the stationary case. It takes a little more computation time when walking for a long period, which may be caused by the walking speed of the user.

Figure 10.

Localization results in real-time experiments with $D = 3$ : (a) real position route, (b) triangulation-estimated position route, and (c) trusted-ranges-estimated position route.

Next, in order to evaluate the efficiency of our proposed approach, we analyzed the localization accuracy versus distance D as shown in Figure 11. At this time, $D = 5, 6$ were neglected due to very low accuracy as we discussed in the random position experiments. We would like to remind that when the application performs the triangulation algorithm, the position is determined by choosing the zone of which the estimated point is located. We studied the improvements of our proposed approach over existing ones based on the complexity, power consumption, and localizable capability. It is sufficient to compare our work to triangulation method² other than fingerprinting method.^3,4 While the prerequisite of the triangulation method uses a signal propagation model to convert RSS measurements to a transmitter–receiver and separate distance estimate, the fingerprinting method requires extensive offline phase values that have to be predetermined, separately for each particular indoor environment (i.e. location fingerprint database). Thus, in order to build a self-localization system, it motivates a considerable effort to compare our scheme to that by Wang et al.² in an energy-efficient way. The performance of the tracking system can be evaluated in terms of the position error, which is defined by equation (8)

$AR = \frac{1}{N_{t}} \sum_{i = 1}^{N_{t}} A_{D}^{(i)}$ (11)

where $N_{t} = 1270$ in our scheme and $N_{t} = 1180$ in the triangulation method. The results show that at D = 1, 2, 3, and 4, our proposed algorithm outperforms the traditional triangular algorithm with respective accuracy values $90 %, 85 %, 79 %, and 74 %$ compared to 76%, 75%, 71%, and 69%. Although the triangulation method exhibits a stable performance in various resolutions, its accuracy achieves at medium level. With an acceptable accuracy level (e.g. 79%), we observed that the optimal value D is 4 in the static random position experiment, while in this case, the optimal one is $D = 3$ . In another perspective, in terms of robustness, Figure 12 shows the histogram of positioning errors at $D = 3$ . We aimed to measure how frequent the proposed approach can achieve a good result for an upper bound of error $ε$

$F_{d} = Card {P_{r} : | | P - P_{r} | | \leq ε}$ (12)

As can be seen from the figure, the trusted-ranges method shows better results than the conventional triangulation one. For instance, it shows that more than 80% of results achieve the localization error lower than 0.5 m, while this value is about 67.7% in the second scheme. Hence, the attained position errors are significantly lower.

Figure 11.

Real-time walking accuracy rate with various D values.

Figure 12.

Histogram of positioning errors at $D = 3$ in real-time experiments.

Scanning time performance

Since Wi-Fi and BLE technologies are best suited for indoor localization due to their deployed infrastructures,¹³ in this section, we aim to conduct experiment to compare the performances between them. Throughout the above experiments, we first obtained a set of optimal parameters that produce the best performance of the proposed positioning system and then compared it to Wi-Fi in terms of running time. Note that a mobile may have limited processing power and memory. If the running time is too high, it would be a bad experience for user. We divided consumption during the localization procedure which consists of two parts: the time consumed during scanning iBeacon/Wi-Fi and the time consumed during estimating user position. We observed that there are no large differences in the estimates of user position (around 0.3 s) in two approaches. Thus, we only concerned the scanning time required on an iPhone 5 with iOS 9. To measure how long the scanning time of Bluetooth signal to take, we added the time portions of code using API functions. Invoking “TIC” starts the timer, and the next “TOC” reads the elapsed time. A demo of recorded log code is displayed in Figure 13. We consider measuring it running in a loop and then average to find the time for a single run. In this figure, the smartphone scans 30 iBeacon nodes and records the time when it is done. With different number of iBeacon nodes (5, 10, 20, and 30), the scanning process is performed at least 10 times for each. The final results are described in Table 3.

Figure 13.

Bluetooth scanning speed of 30 iBeacon nodes.

Table 3.

Average Wi-Fi and Bluetooth scanning speed for several number of Wi-Fi nodes and iBeacon nodes.

Scanning time (s)	Number of nodes
Scanning time (s)	$5$	$10$	$20$	$30$
Wi-Fi	$2.6$	$4.3$	$5.1$	$5.4$
Bluetooth	$0.91$	$0.98$	$1.02$	$1.3$
Time improved	$65 %$	$79.1 %$	$80 %$	$76 %$

Unfortunately, scanning time of Wi-Fi cannot be measured easily as Bluetooth did because iPhone API function refuses to access the Wi-Fi information that is outside the code. To complete this task, we launched the “Settings” icon on the iPhone 5 and turned on the Wi-Fi option. As illustrated in Figure 14, the scanning time in this case is the time that the smartphone has taken for realizing the available networks after the user turns on the Wi-Fi. We used a stopwatch timer to measure performance from In scanning (Figure 14(a)) to Done scanning (Figure 14(b)). Measure time is recorded with several number of Wi-Fi APs like iBeacon nodes. Time-consuming statistics for both approaches are described in Table 3. We observed that it requires less time to identify iBeacon signals than Wi-Fi ones, for example, the scanning time significantly reduces by at least 65%. Also, the simplicity and accuracy of iBeacon make it a good technology to be implemented on any mobile device.

Figure 14.

Wi-Fi scanning within five densities of Wi-Fi access points: (a) In scanning and (b) Done scanning.

Conclusion

To overcome the limitations of fingerprinting and triangulation methods, we proposed an alternative indoor localization scheme based on iBeacon technology, which is called the trusted-ranges method. In this scheme, a reasonable trust-ranges model is first built based on the RSS measurements between iBeacon node and a smartphone. Then, the smartphone location is accurately obtained by finding an appropriate zone to which it belongs. In terms of database construction, we built a trusted-range model to describe that the RSS propagation varies over time and distance instead of rebuilding the fingerprint database periodically. In terms of position estimation, inspired by the triangulation method, we improved the performance by restricting the relevant area. In terms of running time, our proposed scheme reduces the running time using simple algorithm and taking the advantage of highly responsive iBeacon nodes instead of the Wi-Fi nodes (scanning time for iBeacon is at least 0.91 s, while that for Wi-Fi is 2.6 s).² In terms of accuracy, we achieved a better result than other works.^1,2,7,8 Although trusted ranges have limited covering distances, the accuracy can be easily improved using higher density of iBeacon nodes whose price is not too much expensive. Moreover, using better iBeacon nodes from different manufacturers can also improve the cover range and accuracy. In summary, our scheme can perform better than the previous algorithms, especially in a short-range communication, while having a low complexity and fast speed. In the future work, we would like to extend this study with the presence of interference like obstacles and human.

Footnotes

Handling Editor: Zenghua Zhao

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This work was supported by the NRF of Korea grant funded by the Korea government (MSIT) (2016R1A2B2014497).

ORCID iD

Tuan D Vy

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