A Robust Indoor Positioning Method based on Bluetooth Low Energy with Separate Channel Information - MDPI

sensors
Article
A Robust Indoor Positioning Method based on
Bluetooth Low Energy with Separate
Channel Information
Baichuan Huang 1 , Jingbin Liu 1,2 , Wei Sun 3,4 and Fan Yang 1,5, *
 1 State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing,
 Wuhan University, Wuhan 430079, China
 2 Department of Remote Sensing and Photogrammetry and the Center of Excellence in Laser Scanning
 Research, Finnish Geospatial Research Institute, 02430 Masala, Finland
 3 Key Laboratory of Precise Engineering and Industry Surveying, National Administration of Surveying,
 Mapping and Geoinformation, Wuhan University, Wuhan 430079, China
 4 Wuhan Geomatics Institute, Wuhan 430079, China
 5 State Key Laboratory of Geodesy and Earth’s Geodynamics, Chinese Academy of Sciences,
 Wuhan 430079, China
 * Correspondence: yangfanpost@whu.edu.cn
 



 Received: 22 June 2019; Accepted: 7 August 2019; Published: 9 August 2019 


 Abstract: Among the current indoor positioning technologies, Bluetooth low energy (BLE) has gained
 increasing attention. In particular, the traditional distance estimation derived from aggregate RSS
 and signal-attenuation models is generally unstable because of the complicated interference in indoor
 environments. To improve the adaptability and robustness of the BLE positioning system, we propose
 making full use of the three separate channels of BLE instead of their combination, which has generally
 been used before. In the first step, three signal-attenuation models are separately established for each
 BLE advertising channel in the offline phase, and a more stable distance in the online phase can be
 acquired by assembling measurements from all three channels with the distance decision strategy.
 Subsequently, a weighted trilateration method with uncertainties related to the distances derived
 in the first step is proposed to determine the user’s optimal position. The test results demonstrate
 that our proposed algorithm for determining the distance error achieves a value of less than 2.2 m at
 90%, while for the positioning error, it achieves a value of less than 2.4 m at 90%. Compared with
 the traditional methods, the positioning error of our method is reduced by 33% to 38% for different
 smartphones and scenarios.

 Keywords: indoor positioning; Bluetooth low energy (BLE); separate channels; separate signal-attenuation
 models; distance decision strategy; weighted trilateration

1. Introduction
 Positioning, navigation, timing, remote sensing and communication (PNTRC) systems will
change our life greatly in the future [1]. In the PNTRC system, the most fundamental and important
technologies are seamless positioning and ubiquitous navigation. In fact, outdoor positioning the
technology is relatively mature, owing to satellite positioning systems like Global Navigation Satellite
System (GNSS). However, currently, there is no single indoor positioning technology that is able to
balance cost, accuracy, performance, robustness, complexity, and limitations [2–4]. The general indoor
positioning technologies include infrared positioning [3,5], ultrasound positioning [3,6], radio frequency
positioning [4], magnetic positioning [7], microelectromechanical systems positioning [8,9], vision-based
positioning [10] and audible sound positioning [11,12]. In particular, radio positioning technologies,

Sensors 2019, 19, 3487; doi:10.3390/s19163487 www.mdpi.com/journal/sensors

Sensors 2019, 19, 3487 2 of 19
Sensors 2019, 19 FOR PEER REVIEW 2

technologies,
such such as radio
 as radio frequency frequency
 identification identification
 (RFID), wireless LAN (RFID),
 (WLAN), wireless
 ZigBee,LAN (WLAN),
 Bluetooth lowZigBee,
 energy
Bluetooth
(BLE) low energy (BLE)
 and ultrawideband (UWB),and have
 ultrawideband
 drawn much (UWB), have
 attention drawnofmuch
 because attention
 the issuance of because of the
 many wireless
issuance of many wireless radio standards [2,3]. Among these wireless
radio standards [2,3]. Among these wireless systems, the most commonly used ones for indoor systems, the most commonly
used ones for
positioning areindoor
 WiFi andpositioning
 Bluetooth are WiFi and Bluetooth [13].
 [13].
 WiFi has
 WiFi has over
 over 5050 sub-bands on the 2.4 GHz band, and each of them has a bandwidth of 20 MHz. MHz.
Most of the past past pioneering
 pioneering work simply used the WiFi received signal strength indication (RSSI),
which reflects
which reflects the the aggregate
 aggregate value value of of all
 all channel
 channel information
 information [14].
 [14]. The reason why they did not take
advantage
advantage of the sub-band information
 information is that the WiFi Access
 WiFi Access PointPoint (AP) used to collect information
such as RSSI, but RSSI was originally designed for communication so that the sub-band sub-band information
 information
remains private
remains private for for users.
 users. TheThe useuse ofof RSSI
 RSSI inin previous
 previous works
 works [4,13,15–17]
 [4,13,15–17] has has suffered from many
 suffered from many
problems, such as body blockage, the temporal environmental change
problems, such as body blockage, the temporal environmental change effect, etc. Unlike the RSSI, effect, etc. Unlike the RSSI, the
recent
the studies
 recent studies leveraging
 leveraging channel
 channelstatestate
 information
 information (CSI) fromfrom
 (CSI) all sub-bands
 all sub-bands havehave
 revealed thatthat
 revealed CSI
has has
CSI more fine-grained
 more information
 fine-grained information thanthanRSSI;RSSI;
 hence, CSI is
 hence, CSImore robust
 is more against
 robust bodybody
 against blockage and
 blockage
the temporal
and the temporal environmental
 environmental change
 change effect, and
 effect, andtherefore,
 therefore,a abetter
 betterpositioning
 positioningperformance
 performance can be
 can be
expected [16,18,19].
expected [16,18,19].
 The conceptofofsub-bands
 The concept sub-bands cancan
 alsoalso be employed
 be employed in BLEinpositioning.
 BLE positioning.Similarly,Similarly,
 BLE has BLE has 40
 40 channels
channels
on the 2.4on GHzthe 2.4
 band,GHzand band,
 eachand each channel
 channel has a bandwidth
 has a bandwidth of 2 MHz of 2 [14].
 MHz In [14]. In addition,
 addition, the BLEthe BLE
 has
has become
become the focus
 the focus of current
 of current indoor indoor positioning
 positioning technologies
 technologies because because
 it takesitadvantage
 takes advantage of low
 of low power
power consumption
consumption and easy anddeployment
 easy deployment [20]. A[20]. A comparison
 comparison of theoffrequency
 the frequencybandsbands between
 between WiFiWiFi
 and
and is
BLE BLE is illustrated
 illustrated in Figurein 1a.Figure 1a. Channels
 Channels 37, 38 and37, 39 38 and are
 of BLE 39 advertising
 of BLE arechannels,advertising channels,
 broadcasting
broadcasting
messages messages
 in loops, and thein loops,
 other 36 andchannels
 the other are36 channelsforare
 designed designed for in
 communication communication
 connection [21]. in
connection [21]. Meanwhile, the aggregate received signal strength
Meanwhile, the aggregate received signal strength (RSS) is sampled in the loop of three advertising(RSS) is sampled in the loop of
three advertising
channels [14], see channels
 Figure 1b,c. [14],Insee Figure
 fact, 1b,c. In channels
 the different fact, the different
 will produce channels will produceRSS
 the distinguished the
distinguished RSS measures because of the frequency band the
measures because of the frequency band the channel occupies. Therefore, an aggregate RSS loses channel occupies. Therefore, an
aggregate RSS loses the fine-grained information and will diminish
the fine-grained information and will diminish the details of the RSS measure from each channel. the details of the RSS measure
from
To thiseach
 end,channel.
 we propose To this
 taking end, we propose
 advantage taking
 of the threeadvantage of the three
 separate channels of theseparate channels
 BLE, similar to theof CSI
 the
BLE, similar to the CSI approach that has been successfully
approach that has been successfully applied for WiFi positioning systems. applied for WiFi positioning systems.

 Figure 1. (a) The three advertising channels of BLE and the three most common WiFi sub-bands.
 Figure 1. (a) The three advertising channels of BLE and the three most common WiFi sub-bands.
 Channels 37, 38 and 39 are the advertising channels of BLE. The workflow of (b) aggregated RSS and
 Channels 37, 38 and 39 are the advertising channels of BLE. The workflow of (b) aggregated RSS and
 (c) Separate RSS (i.e., Channel 37).
 (c) Separate RSS (i.e., Channel 37).
 To date, BLE-based indoor positioning technologies can be classified into a geometric mapping
 To date,
approach andBLE-based indoor
 fingerprinting positioning
 approach, withtechnologies can bethe
 the former being classified
 primary into a geometric
 focus mapping
 of this study [16].
approach and fingerprinting approach, with the former being the primary focus of this study [16]. In
In this case, methods such as triangulation, trilateration, and multilateration are generally used to locate
this case, methods such as triangulation, trilateration, and multilateration are generally used to locate
the target [22]. The aim of these methods is to accurately measure the distance between the target and

Sensors 2019, 19, 3487 3 of 19

the target [22]. The aim of these methods is to accurately measure the distance between the target and
APs by leveraging the time of arrival (TOA), time difference of arrival (TDOA), RSS, time of flight (TOF)
and received signal phase [4,16]. Regarding only the RSS approach, the distance can be calculated
by using the instant RSS measure and a radio-propagation model that was established in advance.
However, the distance estimation with the prebuilt radio propagation model in a complicated indoor
environment suffers from many problems, for instance, NLOS (not line of sight) [23], the multipath
effect and path loss [14], signal reflection [22], moving objects [4,24], a noise floor [25], and 802.11
interference [25], which are summarized as spatial variations. In detail, the so-called 802.11 interference
of BLE denotes the effect caused by WiFi because WiFi and BLE run on the same band (2.4 GHz);
see Figure 1a [14,21,25]. In addition, the narrow bandwidth of BLE advertising channels makes
individual RSS tend to fade fast, and the protocol of receiving an advertising package makes the
aggregate RSS tend to fluctuate [20]. Because of the interference depicted before, the traditional RSS
measurement (aggregate RSS from three channels) usually presents a larger uncertainty, which leads to
an incorrect distance estimate with the prebuilt single radio propagation model.
 In this paper, we aim to achieve a more robust and precise indoor positioning system.
The structure of the paper is as follows: Section 2 presents the previous work and the background
of the indoor positioning of BLE. In Section 3, the algorithms contain a stable RSS inquire,
the separate signal-attenuation models with the strategy of distance decision and weighted trilateration.
Separate channels and signal-attenuation models are designed to obtain a more stable RSS. In the
meantime, the distance decision and weighted trilateration strategies are used to increase the precision
and adaptability. Section 4 demonstrates the experimental setup and performance of the algorithms.
Finally, Section 5 presents the conclusions and future directions of research.

2. Related Work
 To obtain a more stable RSS, Kim [26] proposed an accurate indoor proximity zone detection
technique based on the time window and frequency of the RSS. Ozer [27] improved the performance
of BLE indoor positioning using the Kalman filter to make the RSS smoother. However, he could
not avoid the use of dirty data, resulting in a bad result. Furthermore, Ishida [28] first proposed BLE
separate channel fingerprinting using channel-specific features. Jovan [21] and Ramsey [14] used
three advertising channels to build fingerprinting maps in the process of removing fast fades with
an iPhone to investigate the value of separate channel information. Moreover, Giovanelli [29] used
the CC2650 tag and nRF52840 to estimate the distance covered by the signal corresponding to the
RSS. Nikoukar [25] measured the noise floor in different channels using nRF52480 SoC in different
environments to mitigate the noise and measured the separate RSS values. Although these authors
tried to simulate the real environment, they obtained only separate channel information with specific
devices. In this paper, we focus on the need for easy deployment. Beacons are arranged in separate
channels so that an off-the-shelf smartphone can work in our system.
 To improve the precision and adaptability, Subha [30] and Ali [25] proposed adding particular
terms to the original model to absorb the multipath error. Yu [31] put forward a new BLE propagation
model according to the location of the BLE beacons and fused the propagation model and multiple
sensors through the Kalman filter. Moreover, Canton Paterna [32] used frequency diversity, the Kalman
filter and a trilateration method to improve the precision of the BLE system. He compared the largest
RSS value, the mean RSS value and the maximum ratio combined with separate RSS (channel 37, 38 or
39) to choose the best RSS value. He also compared the log-distance path loss model with shadowing,
the International Telecommunication Union (ITU) model for indoor environments and the empirical
model to choose the best model for indoor location in the large analysis. However, Canton Paterna
did not improve the model to simulate the real environment. He chose only the best channel to
estimate the most accurate position without considering the changeable space and time variations
in indoor environments. Zhuang [33] combined the channel-separate polynomial regression model,
channel-separate fingerprinting, outlier detection and the extended Kalman filter. He experimented in

Sensors 2019, 19, 3487 4 of 19

densely and sparsely distributed BLE beacons in all three advertising channels to fit the best model and
to generate the fingerprinting without considering the bad channel results. However, these authors
 Sensors 2019,
ignored the19fact
 FORthat
 PEERindoor
 REVIEW environments are changeable and complicated. In contrast, we 4combine

the separated channels and the distance decision strategy to improve the adaptability. In particular,
 However, these authors ignored the fact that indoor environments are changeable and complicated.
separate signal-attenuation models provide the estimate distance for the distance decision strategy.
 In contrast, we combine the separated channels and the distance decision strategy to improve the
The distance decision
 adaptability. strategy
 In particular, is directly
 separate applied tomodels
 signal-attenuation every provide
 channelthe
 and evaluates
 estimate the comparison
 distance for the of
each. Moreover, weighted trilateration with the estimate distance derived from the distance
 distance decision strategy. The distance decision strategy is directly applied to every channel and decision
strategy
 evaluates performs well in obtaining
 the comparison the optimal
 of each. Moreover, position.
 weighted trilateration with the estimate distance
 derived from the distance decision strategy performs well in obtaining the optimal position.
3. Algorithm
 3. Algorithm
3.1. Separation of the BLE Channels for a More Stable Signal
 3.1. Separation of the BLE Channels for a More Stable Signal
 BLE broadcasts the messages in quick succession. In the protocol layer, CH 37 (channel 37), CH 38
(channelBLE38),
 broadcasts
 and CHthe 39messages
 (channelin39)
 quick succession.
 broadcast theIn the protocol
 same message layer, CH 37 (channel
 repeatedly to avoid 37), CH
 package loss.
 38 (channel 38), and CH 39 (channel 39) broadcast the same message repeatedly to avoid package
Regarding the listening rule, devices such as smartphones listen to broadcasted messages circulating in
 loss. Regarding the listening rule, devices such as smartphones listen to broadcasted messages
CH 37, CH 38 and CH 39. However, the final RSS obtained from BLE is indeed CH all (the aggregated
 circulating in CH 37, CH 38 and CH 39. However, the final RSS obtained from BLE is indeed CH all
RSS from all channels), which is summed from the three separate channels in loops. According to
 (the aggregated RSS from all channels), which is summed from the three separate channels in loops.
the rule
 Accordingof error
 to thepropagation, the aggregated
 rule of error propagation, RSS has aRSS
 the aggregated larger
 hasuncertainty than that
 a larger uncertainty thanofthat
 eachof channel.
Acquiring
 each channel. Acquiring a more stable RSS, deemed the foundation of positioning, requires separatechannels.
 a more stable RSS, deemed the foundation of positioning, requires separate
Fortunately, separate channel
 channels. Fortunately, can’t keep
 separate channel can’tinkeep
 badinand
 badstable character
 and stable allall
 character thethe
 time
 time[21].
 [21]. In this
 this design,
 design,
three three are
 beacons beacons are scheduled
 scheduled to run separately
 to run separately in CHin37,CH
 CH 37,38CH
 and38 CH
 and39,
 CHwhile
 39, while the other
 the other beacon is a
 beaconbeacon
normal is a normal
 thatbeacon that broadcasts
 broadcasts the aggregated
 the aggregated RSS as aRSS as a benchmark.
 benchmark. A simple
 A simple experiment
 experiment was carried
 was
out carried out
 between twobetween
 brands two brands phones
 of mobile of mobile tophones to demonstrate
 demonstrate the behaviors
 the behaviors of individual
 of individual RSS and the
 RSS and the aggregated RSS (see Figure 2).
aggregated RSS (see Figure 2).

 Figure2.
 Figure 2. Comparisons
 Comparisons between
 between separate
 separateRSSRSS
 values and the
 values andaggregate RSS when
 the aggregate RSSusing
 whenthe (a) Google
 using the (a) Google
 Pixel33LLand
 Pixel and (b)
 (b) Huawei
 HuaweiP20P20(for a distance
 (for of 2of
 a distance meters). The variance
 2 meters). of the separate
 The variance RSS values
 of the separate RSSand
 values and
 the aggregate RSS with increasing distance using the (c) Google Pixel 3 L and (d) Huawei
 the aggregate RSS with increasing distance using the (c) Google Pixel 3 L and (d) Huawei P20. P20.

Sensors 2019, 19, 3487 5 of 19
Sensors 2019, 19 FOR PEER REVIEW 5

 It can be seen
 It can be seenfromfromFigure
 Figure 2a2athat
 thatthetheRSS
 RSS ofof CH 37 37ranges
 rangesfrom
 from−31− 31
 dBm dBm to −dBm.
 to −27 27 dBm. In
 In addition,
addition,
 the RSSthe ranges
 RSS ranges
 fromfrom−31 −dBm 31 dBmto −28to −dBm
 28 dBm for CH
 for CH 38 and
 38 and fromfrom
 −29− dBm
 29 dBm to − dBm
 to −25 25 dBm forfor
 CH 39.
CH 39.
 TheThe variance
 variance of CHof CH all (1.6756)
 all (1.6756) is higher
 is higher thanthan
 one ofoneCHof37 CH 37 (0.9915),
 (0.9915), CH 38CH 38 (0.6654)
 (0.6654) and CH and39CH
 (0.7756).
39 (0.7756). The imply
 The results resultsthat
 implythethat
 RSS the
 variesRSSgreatly
 varies with
 greatlythewith the channel,
 channel, which iswhich is also supported
 also supported by Figure 2b.
by Figure 2b. Furthermore,
 Furthermore, it canthat
 it can be seen be seen that the aggregate
 the aggregate RSS ranges RSS ranges
 from −31 from
 dBm −to31 dBm
 −25 dBm.to −The
 25 dBm.
 aggregate
The aggregate
 RSS apparentlyRSS apparently
 has a largerhas a larger
 variance variance
 than that ofthan
 eachthat of each
 channel, channel,
 at almost allatdistances
 almost all distances
 (see Figure 2c,d).
(see Figure 2c,d). The
 The variance of CH variance of CH
 all (1.6465) all (1.6465)
 is higher thanisonehigher
 of CH than one of CH
 37 (0.3555), CH3738(0.3555),
 (0.4885)CH and38CH(0.4885)
 39 (0.5952).
and CH 39 (0.5952). The results are consistent with our previous assertation
 The results are consistent with our previous assertation that an individual RSS should be more that an individual RSSstable.
should be more with
 Therefore, stable.theTherefore,
 challengewith the challenge
 of temporal of temporal
 variations, variations,
 separate channelsseparate
 insteadchannels instead one
 of an aggregate
of anare
 aggregate
 adopted one arestudy
 in this adopted in thisastudy
 to acquire to acquire
 more stable a more stable and
 RSS measurement RSStomeasurement and to
 improve the positioning
improve the positioning performance because
 performance because of the stability of data source. of the stability of data source.

 3.2.Distance
3.2. The The Distance Decision
 Decision Strategy
 Strategy
 As separate
 As separate channels
 channels are used
 are used in study,
 in this this study, a distance
 a distance decision
 decision strategy
 strategy regarding
 regarding the distance
 the distance
 between
between the receivers
 the receivers (smartphones)
 (smartphones) and senders
 and senders (BLE(BLE beacons)
 beacons) shouldshould be developed
 be developed to fully
 to fully exploit
 exploit
 allchannel
all the the channel information.
 information. Here,Here,
 threethree
 stepssteps are taken
 are taken to achieve
 to achieve the objective;
 the objective; seeworkflow
 see the the workflow
shown shown in Figure
 in Figure 3. In 3.
 theInfirst
 the step,
 first step,
 threethree separate
 separate signal-attenuation
 signal-attenuation modelsmodels are trained
 are trained in theinoffline
 the offline
phase.phase. It’s necessary
 It’s necessary but but
 not not complex.
 complex. Second,
 Second, data
 data filtering
 filtering is is implementedtotoeliminate
 implemented eliminateabnormal
 abnormal RSS
RSS points (outliers)
 (outliers) and
 andinterpolate
 interpolatethe thefixed
 fixedpoint.
 point.Finally,
 Finally,a method
 a method is proposed for fusing
 is proposed the separate
 for fusing the
 distances
separate estimated
 distances for each
 estimated channel
 for each and outputting
 channel and outputting the final distance.
 the final distance.

 CH37 Model 37 Count=3 3-Channel
 Output
 Final
 Count of Distance
 Data
 CH38 Model 38 Valid Count=2 2-Channel
 Filtering
 Distance

 CH39 Model 39 Count=1 No output

 Figure
 Figure 3. Overview
 3. Overview of theof the proposed
 proposed algorithm
 algorithm for outputting
 for outputting the distance.
 the final final distance.

3.2.1.3.2.1. Separate
 Separate Signal-Attenuation
 Signal-Attenuation Models
 Models in theinOffline
 the Offline
 PhasePhase

 The The distance
 distance can becanestimated
 be estimated by measuring
 by measuring the instant
 the instant RSS RSS
 and and
 usingusing a prebuilt
 a prebuilt radioradio
 propagation
propagation model model that reveals
 that reveals the one-to-one
 the one-to-one corresponding
 corresponding relationship
 relationship between between distance
 distance and RSS. and
Actually, the log-distance path loss model was most frequently used in previous works because because
 RSS. Actually, the log-distance path loss model was most frequently used in previous works the
channel fading characteristic contains a log-normal distribution [23,32,33]. Therefore, our studystudy
 the channel fading characteristic contains a log-normal distribution [23,32,33]. Therefore, our
 chooses
chooses this model
 this model as well
 as well to train
 to train the signal-attention
 the signal-attention models,
 models, as shown
 as shown below:
 below:
 d
 !
  
 RSS
 = dre+
 = RSS f 10 loglog
 + 10α ++ Xσ (1) (1)
 dre f
wherewhere RSSis a dependent
 is a dependent variable, is an
 variable, d isindependent
 an independentvariable, 
 variable, is
 drethe reference distance,
 f is the reference distance,
and  is the RSS at the reference point. is the parameter representing the path-loss
 
 and RSS dre f is the RSS at the reference point. α is the parameter representing the path-loss exponent,
exponent, and 
 and Xσ followsfollows a Gaussian
 a Gaussian distribution,
 distribution, with
 with zero zero[33].
 mean mean [33].
 It is apparent that three
 It is apparent sets of
 that three signal-attenuation
 sets models
 of signal-attenuation are needed
 models because
 are needed the information
 because of of
 the information
threethree
 BLE BLEchannels is utilized in our design. Therefore, we establish three signal-attenuation
 channels is utilized in our design. Therefore, we establish three signal-attenuation models models
(denoted as 
 (denoted as, M38 
 M37 ,and and) M
 with) with
 39
 respect to CHto37,
 respect CHCH37,38CHand
 38 CH
 and39,CHrespectively, in theinoffline
 39, respectively, the offline
training phase.
 training However,
 phase. only only
 However, one model was trained
 one model for the
 was trained foraggregated RSS in
 the aggregated RSSthe
 inconventional
 the conventional
method.
 method.It is apparent that three
 It is apparent separate
 that three models
 separate can better
 models reveal
 can better the feature
 reveal of each
 the feature channel
 of each channel
information. This offline training phase normally includes two steps: (1) collection of the
 information. This offline training phase normally includes two steps: (1) collection of the RSS during RSS during
a given time time
 a given period at a fixed
 period position,
 at a fixed and use
 position, and of the
 use ofmean valuevalue
 the mean of the
 ofRSS measurements
 the RSS measurements as the
 as the
“observation” of this position; (2) the recording of a set of “observations” and the distances between
the receivers (smartphones) and senders (BLE beacons). In this way, a least-square method can be
utilized to find the optimal value of parameter in Equation (1) in the offline phase. Under the

Sensors 2019, 19, 3487 6 of 19

“observation” of this position; (2) the recording of a set of “observations” and the distances between the
receivers (smartphones) and senders (BLE beacons). In this way, a least-square method can be utilized
 Sensors
to find 2019, 19 FOR PEER
 the optimal value of parameter α in Equation (1) in the offline phase. Under the framework of6
 REVIEW

the least-square method, the three parameters can be obtained. α37 represents the path-loss exponent
 framework
 CH 37. CHof38the least-square
 CH 39 eachmethod, thea different
 three parameters
 parametercan
 as αbe obtained. represents the
in and may have 38 or α39 .
 path-loss exponent
 To test in CHsignal-attenuation
 the separate 37. CH 38 and CHmodels,
 39 eachamay
 longhave a different
 corridor parameter
 is selected or .
 as ourasexperimental
 To test the separate signal-attenuation models, a long corridor is selected as our experimental
environment, with the Google Pixel 3 L being used. Sixteen positions are chosen, and the distance
 environment, with the Google Pixel 3 L being used. Sixteen positions are chosen, and the distance
between each pair of adjacent positions is 1.2 m. Collection of the RSS for 5 minutes at every fixed
 between each pair of adjacent positions is 1.2 m. Collection of the RSS for 5 minutes at every fixed
position to a distance of 19.2 m is carried out, and the mean value of the collection is regarded as
 position to a distance of 19.2 m is carried out, and the mean value of the collection is regarded as the
the raw RSS. The raw RSS values are recorded with the true distance at every fixed position. In the
 raw RSS. The raw RSS values are recorded with the true distance at every fixed position. In the offline
offline phase, the record is trained to fit the signal-attenuation models (see Figure 4). The dotted line
 phase, the record is trained to fit the signal-attenuation models (see Figure 4). The dotted line
represents the mean value of the collected RSS at every fixed position, and the symbol ’*’ represents the
 represents the mean value of the collected RSS at every fixed position, and the symbol '*' represents
signal-attenuation models. R2 , called the goodness of fit, is employed to evaluate the established model.
 the signal-attenuation models. , called the goodness of fit, is employed to evaluate the established
It is apparent from Figure 4 that the separate signal-attenuation models have a higher R2 values than
 model. It is apparent from Figure 4 that the separate signal-attenuation models have a higher 
those of the aggregate signal-attenuation models. In the offline phase, the separate signal-attenuation
 values than those of the aggregate signal-attenuation models. In the offline phase, the separate signal-
models represent the relatively optimal models.
 attenuation models represent the relatively optimal models.

 Figure4.4. The
 Figure The signal-attenuation
 signal-attenuation models for the Google Pixel 3 L: the the fitting
 fitting model
 model for
 for (a)
 (a) CH
 CH all:
 all:
 R =
 2 0.5570;(b)
 =0.5570; (b)CH
 CH37: 2 = 0.7733;
 37: R =0.7733; (c)(c)
 CH CH R
 38:38: 2 = 0.7494;
 =0.7494; andand (d) CH
 (d) CH R = 0.7313.
 2
 39: 39:=0.7313.

 InInthe
 theonline
 onlinephase,
 phase,thethedistance
 distanceshould
 shouldthen
 thenbe beestimated
 estimatedfrom
 fromeach
 eachsignal-attenuation
 signal-attenuationmodelmodel
(M , M and M ). To verify the separate models in practice, another test in the
 ( , and ). To verify the separate models in practice, another test in the same long corridor
 37 38 39 same long corridor
using
 usingthe theGoogle
 GooglePixel 3 L3 is
 Pixel L carried out.out.
 is carried In this phase,
 In this the RSS
 phase, is collected
 the RSS for 10for
 is collected s at10every
 s at fixed
 everypoint,
 fixed
as in the
 point, as offline phase.phase.
 in the offline EveryEvery
 received RSS isRSS
 received input into into
 is input the separate signal-attenuation
 the separate signal-attenuation models
 modelsto
obtain an estimate distance. By recording the true distance and the estimated distance
 to obtain an estimate distance. By recording the true distance and the estimated distance inferred inferred from
the models,
 from we canwe
 the models, output
 can the CDFthe
 output (cumulative distribution
 CDF (cumulative function)function)
 distribution map of the maperrors, as shown
 of the errors, in
 as
Table
 shown 1. in Table 1.

 Table 1. Distance errors in CH 37, CH 38 and CH 39.
 Table 1. Distance errors in CH 37, CH 38 and CH 39.
 30% of30%
 Timeofin Error
 Time in Error60% of60%
 TimeofinTime
 Errorin Error90% of 90%
 TimeofinTime
 Errorin Error
 Channel ID
 Channel ID (m) (m) (m)
 (m) (m) (m)
 CH
 CH3737 2.0 2.0 3.5 3.5 5.2 5.2
 CH
 CH3838 1.6 2.6 4.6
 1.6 2.6 4.6
 CH 39 1.1 1.9 4.0
 CH 39 1.1 1.9 4.0

 The
 The implication
 implication of
 of the
 the results
 results shown
 shown in
 in Table
 Table11isisthat
 thatall
 allthree
 threesignal-attenuation
 signal-attenuationmodels
 modelscancan
estimate
 estimate a distance from the smartphones to the beacons. The 90 percentile distance errors are are
 a distance from the smartphones to the beacons. The 90 percentile distance errors no
 no less
less than 4.0 m, which is not sufficient for precise indoor positioning. For this, a distance
 than 4.0 m, which is not sufficient for precise indoor positioning. For this, a distance decision decision
algorithm
 algorithmwith
 withdata
 datafiltering
 filteringisisproposed
 proposedtotoachieve
 achieveadaptable
 adaptableandandrobust
 robustindoor
 indoorpositioning.
 positioning.

 3.2.2. Data Filtering
 In this study, three beacons (each of them is coded in the level of firmware to broadcast only one
 channel) are combined as a station to achieve the broadcast of separate channel information. It is
 worth mentioning that some of the past works directly modified the hardware of a single beacon to
 achieve the broadcast of three channels of information at the same time. Unlike previous works, we
 bypass the technical difficulty of modifying the hardware and manage to obtain the three channels
 of information by simply combining three beacons as a station (each of them is coded in the level of

Sensors 2019, 19, 3487 7 of 19

3.2.2. Data Filtering
 In this study, three beacons (each of them is coded in the level of firmware to broadcast only one
channel) are combined as a station to achieve the broadcast of separate channel information. It is
worth mentioning that some of the past works directly modified the hardware of a single beacon
to achieve the broadcast of three channels of information at the same time. Unlike previous works,
we bypass the technical difficulty of modifying the hardware and manage to obtain the three channels
of information by simply combining three beacons as a station (each of them is coded in the level
of firmware to broadcast only one channel). Despite this convenience, our method may introduce
a new problem, that is, the packet loss of some channels during one round of a scanning. We have
assumed that the RSSs from the three channels are completely synchronized, which is contrary to reality.
Hence, we develop a “lost detection” method to tag the channel that is unavailable for one round of
a scanning. In addition, outliers that make great jumps should be detected and removed/smoothed
at this stage, which can be achieved by the median filter algorithm [34]. The details are expanded in
the following.
 During a given time period, the received package has a different number of detected beacons.
If one beacon is not detected, the RSS of this beacon in this round of scanning is an empty one, that is,
it is lost. The “lost” RSS is critical for the later distance decision, so we have to distinguish which
beacon is “lost”. To this end, we carry out loss detection as follows (see Equation (2)), which is actually
a process of tagging. When Ri is empty, Ti is equal to 0. In contrast, Ti is equal to 1 if Ri is not empty.
Loss detection provides the tags needed for median filtering:
 (
 0 Ri is empty
 Ti = (2)
 1 Ri is not empty

where Ti is the tag in time period i and Ri represents the received RSS in time period i.
 After loss detection, median filtering is carried out to address the data with tags
sequentially.
n Here, we take CH 37 o as an example to illustrate the process of median filtering.
 RSS37,1 , RSS37,2 , RSS37,3 , . . . , RSS37,i , which denotes the RSS sequence of CH 37 (different smartphones
have
n different sampling frequencies) o during the sampling period, has a matched tag sequence
 tag37,1 , tag37,2 , tag37,3 , . . . , tag37,i , found by Equation (2). A sliding window of WL1 in length is adopted
to sample the median value. For i = 1, 2 . . . , t − WL1 + 1, we have:

 Ri , Ri+1 , . . . Ri+WL1 +1
 (
 Ti = 1
 RFi = (3)
 None Ti = 0

where WL1 is the length of the sliding window, RFi is the selected RSS and Ri represents the RSS of CH
37 in time period i; when the total count is t, the max of i is t − WL1 + 1.
 In other words, the purpose of median filtering is to remove the outlier, which behaves as a
sudden jumping point. Mainly, Ti , the tag of the last point in the sliding window, is deemed the
decisive point. If the value of the decisive point is zero, the whole sliding window should be thrown
out. Correspondingly, some fixed points, the median values of the sliding window, should be inserted.
 To test the approach of median filtering and loss detection, in the same long corridor, RSS values
are collected at every fixed position for 10 s, as in the online phase. For example, the set of RSS
values for the Huawei P20 at a fixed position 3 m away before and after the methodology is shown
in Figure 5. When the value of WL1 is 5, the probability of the outlier being here is 15%. In fact,
the probability of outliers mainly depends on the environment, which we cannot improve. Figure 5a
shows the plot of raw data, while the reprocessed data are shown in Figure 5b. The number of outliers
in Figure 5a has been considerably reduced in Figure 5b. After median filtering, the sharp noise was
deleted fully. Meanwhile, the process of loss detection is shown in Figure 5b. The fixed point has been
inserted. On the whole, the process of data filtering makes the RSS values more gathered and smooth.

Sensors 2019, 19, 3487 8 of 19

 The combination of loss detection and median filtering can output a reprocessed and clean sequence of
Sensors
 RSSs2019,
 for19later
 FOR PEER
 use inREVIEW
 the distance
 decision strategy. 8

 Figure 5. The
 Figure scatter
 5. The plotplot
 scatter of (a)
 of raw data;
 (a) raw (b) (b)
 data; processed data.
 processed Here,
 data. WL
 Here, is15 is
 in5Equation (3). (3).
 in Equation

 3.2.3.
3.2.3. Distance
 Distance Decision
 Decision
 AfterAfter
 data data filtering,
 filtering, thethe three
 three setssets of RSS
 of RSS values
 values correspond
 correspond withwith a series
 a series of distances
 of distances in separate
 in separate
 channels.
channels. ForFor example,
 example, thethe ithpoint
 pointofofthethefiltered
 filteredRSSRSS inin CH
 CH 37 can output
 output aadistance
 distanceresult calledD37 ,
 resultcalled
 as, aswell
 wellasasD38 and and D39 . However,
 . However, it should
 it should be noted
 be notedthatthat
 one one
 can never expect
 can never to acquire
 expect D37 , D 38 and
 to acquire ,
 and
 D 39 every time, as some of these parameters might be lost, as depicted before. To synthesize
 every time, as some of these parameters might be lost, as depicted before. To synthesize the final
thedistance, the distance
 final distance, decision
 the distance algorithm
 decision is implemented
 algorithm is implemented to analyze and optimally
 to analyze and optimallycombine the three
 combine
the three estimated distances derived from the separate signal-attenuation models. With thethat
 estimated distances derived from the separate signal-attenuation models. With the hypothesis
 three beacons
hypothesis that threein three channels
 beacons can channels
 in three be used tocan output
 be usedthe to
 final distance,
 output our distance
 the final distance,decision strategy
 our distance
 is illustrated
decision strategyasisfollows according
 illustrated to the
 as follows number to
 according of the
 valid distances.
 number of valid distances.
 2-Channel
 2-Channel is used
 is used when whenthethe number
 number of valid
 of valid distances
 distances (valid
 (valid channel
 channel information)
 information) is two.
 is two. In this
 In this
 case,
case, thethe possible
 possible combinations
 combinations presumably D37 and
 arepresumably
 are and D38, D 37 and
 andD 39 , ,ororD 38 and and D39 . Two
 . Two steps
 areare
steps followed:
 followed: (1) detecting
 (1) detectingthe variance
 the variance of a single channelchannel
 of a single and (2) and
 detecting the difference
 (2) detecting between the
 the difference
 two channels.
between the two channels.
 ForFor instance,
 instance, Dand Q and D( ,
 P (Q, P = 38,
 =37, 37, 39)
 38, 39)
 are are valid
 valid here.here. In the
 In the firstfirst
 step,step,
 there there
 is a is a threshold
 threshold andand
a sliding window for variance detection. The variance detection requires that < ℎ 1 (where σ is
 a sliding window for variance detection. The variance detection requires that σ < Thr (where is the
thevariance
 varianceofofaasingle singlechannel
 channeland andThr ℎ 
 1 represents
 represents the the
 threshold
 thresholdof variance
 of variancein step one).one).
 in step OnlyOnlyif theiftwo
thespecific channels
 two specific channelsmeet meet
 the requirement
 the requirement of variance detection
 of variance does step
 detection doestwo,stepcalled difference
 two, called detection,
 difference
 commence. The process of difference detection in 2-Channel
detection, commence. The process of difference detection in 2-Channel can be described can be described mathematically as shown
 in Equation (4):
mathematically as shown in Equation (4):
 Pi+WL2 −1
 |DQ,i − DP,i |
 ∑ i=1 | , − , | < Thr2 (4)
 WL2 < ℎ (4)
 
 where WL2 is the length of the sliding window, Thr2 represents the threshold of variance in difference
where is the length of the sliding window, ℎ represents the threshold of variance in
 detection in time period i, DQ,i is the value of the distance in channel Q and DP,i is the value of the
difference detection in time period , , is the value of the distance in channel Q and , is the
 distance in channel P.
value ofAs theadistance
 consequence, in channel P.
 the ultimate output distance Di is the weighted average of DQ and DP :
 As a consequence, the ultimate output distance is the weighted average of and :
 Di = = m1 ∗∗ , + + m2 ∗∗ 
 
  DQ,i DP,i
 ,
 ⎧ σP
 
 
 
 
 ⎪ m 1 = σ σ (5)
  = Q
 σ
 + P
 m2 = σ ++Qσ 
 
 (5)
 
 
 
 ⎨ Q
 P
 ⎪ =
 ⎩ + 
where and are the weights for channel Q and channel P, respectively, is the variance of
channel Q, and is the variance of channel P. High variance in variance detection means more
interference and lower weight.
 3-Channel is used when the number of valid distances is three. In addition, 3-Channel is more
precise and persuasive than 2-Channel in practice because of the greater availability of

Sensors 2019, 19, 3487 9 of 19

where m1 and m2 are the weights for channel Q and channel P, respectively, σQ is the variance of channel
Q, and σP is the variance of channel P. High variance in variance detection means more interference
and lower weight.
 3-Channel is used when the number of valid distances is three. In addition, 3-Channel is more
precise and persuasive than 2-Channel in practice because of the greater availability of measurements.
Similarly, two steps are also followed: (1) detecting the variance of each of the three channels separately
and (2) detecting the difference between every two channels. The differences between any two of the
three distances (D37 , D38 , and D39 ) should be taken into account.
 In the first step, there is a threshold and a sliding window for variance detection. The variance
detection requires that σ < Thr1 , as demanded by 2-Channel (where σ is the variance of a single channel
and Thr1 represents the threshold of variance in step one). Only if all three separate channels fulfill
the requirement of variance detection is step two, called difference detection, commenced. The process
of difference detection in 3-Channel can be described mathematically as shown in Equation (6):
  Pi+WL3 −1
 |D37,i −D38,i |
 i=1
 < Thr3
 
 
 WL
 
 Pi+WL3 −1 3
 
 
 
 |D37,i −D39,i |
 
 < Thr3 (6)
  i=1
 
 
  WL3
 
  Pi+WL3 −1
  |D38,i −D39,i |
 i=1
 < Thr3
 
 
 WL3

where WL3 is the length of the sliding window, Thr3 represents the threshold of variance in difference
detection in time period i, D37,i is the value of the distance in CH 37, D38,i is the value of the distance in
CH 38 and D39,i is the value of the distance in CH 39.
 Accordingly, the ultimate output distance Di is the weighted average of distance 37, distance 38
and distance 39: 
 
  Di = m1 ∗ D37,i + m2 ∗ D38,i + m3 ∗ D39,i
 σ38 +σ39
 
 
  1 = 2∗(σ37 +σ38 +σ39 )
 m
 
 
 
  m2 =
  σ37 +σ38 (7)
 
  2∗(σ37 +σ38 +σ39 )
 σ37 +σ38
 
 
  m =
 
 3 2∗(σ37 +σ38 +σ39 )

where m1 , m2 and m3 are the weights for CH 37, CH 38 and CH 39, respectively, σ37 is the variance of
CH 37, σ38 is the variance of CH 38 and σ39 is the variance of CH 39.
 In conclusion, the quality of broadcasting signal is affected by many reasons like walking people,
fixed obstacle (desk, chair, cupboard . . . ) and state of transmitter/receiver, etc. Because of these
complicate factors in indoor environment, the quality of broadcasting is varying time to time, and there
should be thus no fixed relation between the quality and the real distance. However, a direct quality
evaluation is possible in our method, by step (1) detecting the variance of each channel separately and
step (2) detecting the difference between every two channels. In this way, our method only employs
the RSS of “good quality”, resulting in a better distance estimation in theory.
 The basic rationale behind our distance decision strategy is that: the interruptions caused
by unpredictable factor like walking people on the three channels are different. In another word,
the three channels will consistently reflect a same distance estimate if no interruption, however,
a large interruption will lead to a large discrepancy of distance estimates between the three channels.
By detecting how large is the discrepancy between channels, our distance decision strategy can tell
if this is a good or bad measure, and avoid to output result in bad quality. However, the traditional
method will adopt all channel outputs without any particular treatment with the error.
 In particular, a validation is set up to test our distance decision strategy, as Figure 6 illustrates.
The distance between the station and the smartphone (Google Pixel 3 L) is 5 m. The test is set up
as real as possible by (1) distributing some desks and cupboards as obstacles and (2) rotating the
smartphones. Although the real case is usually more complicated than our setup, we suggest that
the experimental results under our setup still make sense. In addition, three locations (A, B, C) are

Sensors 2019, 19, 3487 10 of 19

 tested in the experiment: case A in Figure 6 represents the status of inherent influence. The case of a
Sensorssmartphone backing
 2019, 19 FOR PEER away from the station is marked as case C (blocked). In this case, the line of
 REVIEW 10sight
 is blocked. The case in which a smartphone is positioned vertically with straight lines between the
 station
station and and smartphones
 smartphones is is consideredcase
 considered caseBB (not blocked).
 blocked).The
 Thethree cases
 three provide
 cases powerful
 provide evidence
 powerful
evidence that the direction of the smartphone makes a difference. Table 2 shows the results of thecases
 that the direction of the smartphone makes a difference. Table 2 shows the results of the different
 whencases
different is 3 m2 ℎ 
 Thr1 when in the 3 step
 is first in of
 thethe distance
 first step ofdecision strategy,
 the distance and Thr
 decision and ℎ 
 2 in Equation
 strategy, (4), Thr
 in 3 in
Equation (4), ℎ 
 Equation (6) are
 inboth 5 m. (6) are both 5 .
 Equation

 5m

 5 Case C Case A
 m
 Case B
 10 m

 FigureFigure Test setup:
 6. setup:
 6. Test thepoint
 the red red point
 is theisstation;
 the station; the bars
 the gray gray denote
 bars denote
 desksdesks and cupboards;
 and cupboards; and the
 and the
 different
 different positions
 positions of people
 of people represent
 represent different
 different cases.cases.

 Table 2. Results of the test for different cases.
 Table 2. Results of the test for different cases.

 Case Case A A B B CC
 Number of Tests
 Number of Tests 10 10 10 10 10
 10
 Number
 Number of Empty of Empty Outputs 1
 Outputs 1 6 6 10
 10

 In NLOS
 In fact, fact, NLOS
 is oneisofone
 theofmain
 the main factors
 factors that deteriorate
 that may may deteriorate distance
 distance estimation
 estimation fromfrom RF signals
 RF signals
 (WiFi/BLE),
(WiFi/BLE), and many
 and many papers papers in previous
 in previous dedicate
 dedicate to minimize
 to minimize the NLOS
 the NLOS effecteffect
 [35], [35],
 whilewhile
 nonenoneof of
themthem
 claims claims to completely
 to completely solve thesolve the NLOS
 NLOS problem problem
 as far asaswe farknow.
 as weUnlike
 know.the Unlike
 previous the previous
 work thatwork
try tothat try tothe
 calibrate calibrate the RSSeven
 RSS measures measures
 in NLOSeven in NLOS
 case, this studycase,prefers
 this study prefers
 to avoid resultto output
 avoid result
 (usually output
in bad(usually
 quality)ininbad
 NLOSquality) in NLOS
 case (or case (or
 other cases, notother
 limitedcases, not limited
 to NLOS) so as to to stabilize
 NLOS) so theaspositioning.
 to stabilize the
 positioning.
As Table As Table in
 2 demonstrates, 2 demonstrates, in this trial,
 this trial, no results no results
 are output when arethe
 output
 line when
 of sighttheisline of sight
 blocked iniscase
 blocked
 in caseof
C. Because C.the
 Because of the
 tails of the separate
 tails of the separate signal-attenuation
 signal-attenuation models, a small models, a small
 jitter jitter will
 will result in a result
 large in a
 large
change. change.
 When When
 the line the line
 of sight of sight is
 is blocked, theblocked,
 value ofthe thevalue of the RSSvery
 RSS becomes becomes
 small,very
 which small,
 will which
 cause will
 cause
a large a large
 error error
 in terms of in
 theterms of the
 distance. distance.
 Hence, Hence,
 the case will the
 not case
 meetwillthe not meet the of
 requirement requirement
 the distanceof the
 distance
decision. decision.
 In other words,In the
 other words, theofprobability
 probability no outputof inno
 caseoutput in caseInCcase
 C is 100%. is 100%.
 B, theIndirection
 case B, the ofdirection
 the
 of the smartphones
smartphones does not
 does not improve improve
 stability stabilitywith
 compared compared withA,
 that in case that in case
 being A, being
 marked as anmarked
 inherentas an
 inherent
influence. Thus,influence. Thus,of
 the number the number
 times of timesoccurs
 no output no output
 in case occurs
 B is in case Bthan
 higher is higher
 that in than
 casethat
 A. in
 Thecase A.
 The rationale
rationale behind our behind
 distanceour decision
 distancestrategy
 decisionisstrategy
 that a moreis that a more
 precise precisecan
 distance distance can be with
 be obtained obtained
morewith more consistent
 consistent channel information
 channel information among the amongthreetheadvertising
 three advertising
 channels.channels.
 In brief,In brief, the distance
 the distance
resultresult is convincing
 is convincing whenwhen the three
 the three channels
 channels outputoutput
 similarsimilar distances.
 distances.
 By combining
 By combining the the
 useuseof of separate
 separate channelinformation
 channel information and and the
 thedistance
 distancedecision
 decision strategy,
 strategy,wewe suggest
 thatthat
suggest the result should
 the result havehave
 should moremore adaptability and more
 adaptability and morerobustness to signal
 robustness interruption
 to signal caused by,
 interruption
causedforby,
 example, body blockage.
 for example, Our distance
 body blockage. decisiondecision
 Our distance strategystrategy
 based onbaseda relatively long sequence
 on a relatively long can
 achieve
sequence cangreater
 achievepositioning accuracy,accuracy,
 greater positioning which is the major
 which objective
 is the major of this study.
 objective of this study.

 3.3. Weighted
3.3. Weighted Trilateration
 Trilateration
 WithWith the distances
 the distances measured
 measured fromfrom several
 several stations,
 stations, a weighted
 a weighted trilateration
 trilateration method
 method is proposed
 is proposed
 to realize positioning. In our experimental setup, a location station is equipped
to realize positioning. In our experimental setup, a location station is equipped with three beacons,with three
and beacons, and each
 each beacon beacon issuch
 is arranged arranged
 that such
 it hasthat it has
 one one advertising
 advertising channel, channel, as described
 as described before.
 before.
Considering the occurrence of packet loss at our location station, a four-station setup is suggested,
which is also very popular among the state-of-the-art geometric positioning systems.
 Trilateration can succeed in locating the target when the measurements taken converge at a
single point. However, in a practical environment, there are some distance errors that lead to an area
of possible locations instead of a single location point. Derivation from the difference detection of

Sensors 2019, 19, 3487 11 of 19

 Considering the occurrence of packet loss at our location station, a four-station setup is suggested,
 which is also very popular among the state-of-the-art geometric positioning systems.
Sensors 2019,Trilateration
 19 FOR PEER REVIEW
 can succeed in locating the target when the measurements taken converge at a11 single
 point. However, in a practical environment, there are some distance errors that lead to an area of
eachpossible
 station in Section instead
 locations 3.2.2 is utilized to increase
 of a single confidence
 location point. regarding
 Derivation fromthe
 thereceivers (smartphones)
 difference detection of each
closer to the senders (stations) by moving the target point.
 station in Section 3.2.2 is utilized to increase confidence regarding the receivers (smartphones) closer to
 In the case of evaluated errors shown in Figure 7, the intersection of circles creates an area. The
 the senders (stations) by moving the target point.
maximumInlikelihood estimate, the least-square method or the triangle centroid localization algorithm
 the case of evaluated errors shown in Figure 7, the intersection of circles creates an area.
can solve this problem. Here, the triangle centroid localization algorithm is adopted. In step one, the
 The maximum likelihood estimate, the least-square method or the triangle centroid localization
center point of the intersecting area should be given:
 algorithm can solve this problem. Here, the triangle centroid localization algorithm is adopted. In step
 one, the center point P of the intersecting area 1 + 2 +be
 should 3given:
 + 4
 =
 4 (8)
 1 + 2 + P3 3
 x +P4+
 x 4
 
 P1 x+ P2x +
 
 
 
 =x = 4
 (8)
  y = P1 y +P2 y +4P3 y +P4 y
 
 
 4
 where 1 is the point of intersection between station 3 and station 4, 1 is the value of 1
 where P1 is the
along the X-axis, 1 of
 andpoint is intersection 1 alongstation
 the value of between 3 and station 4, P1x is the value of P1 along the
 the Y-axis.
 X-axis, and P1 y is the value of P1 along the Y-axis.

 Station 2
 r2
 Station 1
 r1 P1

 P2
 P4 r4
 P3 Station 4

 r3

 Station 3

 Figure 7. Four
 Figure 7. intersecting circlescircles
 Four intersecting with evaluated errors.
 with evaluated errors.

 In step
 In step two, two, the weight
 the weight derived
 derived fromfrom difference
 difference detection
 detection for every
 for every side side
 can be cancalculated
 be calculated as as
shownshown in Equation
 in Equation (9). Assume
 (9). Assume thatthat the levels
 the levels of difference
 of difference detection
 detection of of
 thethe four
 four areareΣ Σ, 1Σ, Σ,2 , Σ3
 stations
 stations
Σ andandΣΣ.4A. Alow
 lowlevel
 levelofofdifference
 differencedetection
 detectionmeans
 meansthat
 thatthe
 thereal
 realtarget’s
 target’slocation
 locationisismore
 morelikely
 likelynear
 near the
 station.InIn
the station. reality,
 reality, thethe occurrence
 occurrence of of intersecting
 intersecting circles
 circles withwith evaluated
 evaluated errors
 errors is anisevent
 an event
 withwith
 highhigh
 probability;
probability; thus,
 thus, thethedistance
 distance decision
 decisionstrategy
 strategyplays an important
 plays role in trilateration.
 an important Consequently,
 role in trilateration.
 we give thewe
Consequently, weight
 give the for weight
 every side as follows:
 for every side as follows:
 ΣΣ2++ΣΣ3 ++Σ4 Σ
 k=1 = 3∗(Σ +
 
 ⎧  ΣΣ2 ++
 Σ3 +
 3 ∗ (Σ + Σ Σ4+) Σ )
 
 1
 ⎪
 
 Σ1 + Σ3 + Σ4
 
 ⎪ k2 = 3∗(ΣΣ1 ++Σ2Σ+Σ+ Σ
 
 3 + Σ4 )
 
 ⎪  = Σ1 + Σ2 + Σ4 (9)
 
  k3 3=∗ 3∗(Σ(Σ ++ Σ
 Σ ++Σ
 Σ Σ +) Σ )
 + (9)
  1 2 3 4
  k=4 = ΣΣ1+ +ΣΣ2 ++Σ3 Σ
 
 ⎨ 
 
 
 3∗(Σ1 +Σ2 +Σ3 +Σ4 )
 ⎪ 3 ∗ (Σ + Σ + Σ + Σ )
 ⎪ Σ +Σ +Σ
 where k1 , k2 , k3 and k4 are the weights ⎪ for= P1, P2, P3 and P4, respectively. A low level of difference
 detection means a more precise and⎩larger3weight. ∗ (Σ + Σ + Σ + Σ to) the order of weights, we move the
 According
wherecenter , P to
 , point andthe four
 areintersection
 the weights points
 for in 1,turn.
 2,For 3example, k1 >k2 >k3 >k4 ,Awelow
 and 4,ifrespectively. move theof
 level center
 point P to P
difference detection on the way towards
 01 means a more precise P at d , then we move
 1 and1 larger weight. According point P to P12 order of weights, weP2 at
 01 to the on the way towards
moved2the
 , then we move
 center to Pthe
 pointpoint 12 to P23 intersection
 four on the way towardspoints inP3turn.at d3 ,For
 andexample, if > 
 then we move > P
 point P34 on
 > 23 ,towe
move the center point to on the way towards at , then we move point to on the
way towards at , then we move point to on the way towards at , and then we
move point to on the way towards at . is the final location point. In detail, the
length of the distance moved is shown in Equation (10):

Sensors 2019, 19, 3487 12 of 19
Sensors 2019, 19 FOR PEER REVIEW 12

 the way towards P4 at d4 . P34 is the final location point. In detail, the length of the distance moved is
 = | − | ∗ 
 shown in Equation (10): ⎧
  ⎪ = | − | ∗ 
  d1 = ||P − P1 || ∗ k1 (10)
 = | − | ∗ 
 
 ⎨
 
 
  d⎪2 = ||P01 − P2 || ∗ k2
 
 
 | − P−3 || ∗ |k3∗ (10)
 d⎩3 = = ||P12
 
 
 
 
 
  d4 = ||P23 − P4 || ∗ k4
 
4. Results
 4. Results
4.1. Experimental Setup
 4.1. Experimental Setup
 MAX Beacon, from a company called Bright Beacon (Chungking, China), iwas chosen as the test
beacon.MAX MAXBeacon,
 Beacon is from a company
 equipped with acalled Bright Beacon
 Nordic51822AA unit,(Chungking,
 which is a BLE China),
 systemiwason achosen
 chip. MAX as the
 test beacon.
Beacon weighsMAX Beacon
 65 g and has is equipped
 a lifetime of with
 2 to 3ayears
 Nordic51822AA
 with a broadcast unit, which
 powerisofa −BLE system
 30 dBm to 4ondBm,
 a chip.
 MAX Beacon
broadcast frequencyweighs 65 gtoand
 of 100 1000hasms,a and
 lifetime of 2 todistance
 broadcast 3 years with a broadcast
 of 3 to 100 m. With power of −30 dBm
 a broadcast power to 4
of dBm,
 0 dBm, broadcast frequency
 we can detect of 100 to 1000
 the advertising ms, and
 package to asbroadcast
 far as 20 distance of 3 to 100
 m. By adjusting the m. With a broadcast
 firmware, we can
 power
make MAX of 0Beacon
 dBm, we can detect
 advertise in onethechannel.
 advertising We package to as far station
 set up a location as 20 m.with By adjusting
 three MAX theBeacons.
 firmware,
Thewethree
 can make
 MAX MAX Beacons Beacon advertiseasinMAX
 are denoted one channel.
 beacon1,We MAX set up a location
 beacon2 and station with three
 MAX beacon3. MAX MAX
 Beacons.
beacon1 The three
 broadcasts theMAX
 messageBeacons
 in CH are
 37,denoted
 MAX beacon2 as MAX beacon1, the
 broadcasts MAX beacon2
 message in and
 CH 38 MAXandbeacon3.
 MAX
 MAX beacon1
beacon3 broadcasts broadcasts
 the message the message
 in CH 39. in CH 37, MAX beacon2 broadcasts the message in CH 38 and
 MAX beacon3
 Figure 8 showsbroadcasts the messagesetups.
 two experimental in CH In 39.Figure 8a, four stations are deployed in an office
room with Figure 8 shows
 a size of 5 m two experimental
 × 10 setups. In
 m. Some furniture Figure
 (like 8a, four stations
 cupboards, so as to are deployed
 simulate in anWiFi
 NLOS), officeAPs
 room
 with a size of 5 m × 10 m. Some furniture (like cupboards, so as
and devices embedded with Bluetooth (to simulate 802.11 interruption) are placed in a classroom. to simulate NLOS), WiFi APs and
 devices
Figure 8b isembedded
 a typical with
 officeBluetooth
 room, which (to simulate
 is similar 802.11 interruption)
 to Figure are placed
 8a but with however in a aclassroom. Figure 8b
 different layout.
 is aoffice
This typicalroom office
 is inroom,
 a sizewhich
 of 9 mis× similar
 12 m and to filled
 Figure 8a but
 with a big with however
 cupboard and a adifferent
 desk. Thelayout. This office
 experimental
 room
setup is is
 asin a size
 real of 9 m × with
 as possible, 12 m someand filled
 extrawith a big cupboard
 artificial interference andlike
 a desk.
 moving Thepeople
 experimental
 and WiFi setup
 Aps,is as
to real
 verifyas the
 possible, withof
 reliability some
 our extra artificial
 proposed interference
 methods. It’s truelike
 thatmoving peopleindoor
 the practical and WiFi Aps, to verify
 environment (likethe
 reliabilitymall)
a shopping of ourmayproposed
 includemethods. It’s true
 several rooms andthat the practical
 corridors. indoordue
 However, environment (like a shopping
 to the limitations of BLE
 mall) mayitself,
technology include
 fourseveral rooms and
 station-based BLEcorridors.
 trilateration However,
 methoddue cantoonly
 the realize
 limitations of BLE
 accurate technology
 positioning
 itself,
inside four station-based
 a room, otherwise the BLENLOStrilateration
 effect causedmethod can only
 by walls canrealize
 heavilyaccurate
 contaminatepositioning
 the RSS inside a room,
 measures
 otherwise
[32,36]. the NLOS effect caused by walls can heavily contaminate the RSS measures [32,36].

 9
 m

 5
 m

 10 m 12 m

 (a) (b)

 Figure
 Figure 8. The
 8. The testtest setup:
 setup: (a)(a) a classroom
 a classroom (scenario
 (scenario #1);
 #1); (b)ananoffice
 (b) officeroom
 room(scenario
 (scenario#2).
 #2).The
 Thered
 redpoint
 point is
 thelocation
 is the location station;
 station; the
 the gray
 gray bars
 bars denote
 denote desks
 desks and
 and cupboards.
 cupboards.

4.2.4.2. Performance
 Performance of the
 of the Algorithm
 Algorithm
 4.2.1. The Distance Decision Strategy
4.2.1. The Distance Decision Strategy
 Some of the messages broadcast in the separate channels could be lost. The loss is random and
 Some of the messages broadcast in the separate channels could be lost. The loss is random and
 unpredictable, particularly in a complex environment. The typical raw data of the distance decision
unpredictable, particularly in a complex environment. The typical raw data of the distance decision
 are illustrated in Figure 9a. Figure 9a demonstrates the typical distribution when we input the median
are illustrated in Figure 9a. Figure 9a demonstrates the typical distribution when we input the median
 value of the sliding window into the traditional log-distance path loss model to obtain a distance;
value of the sliding window into the traditional log-distance path loss model to obtain a distance; see
Equation (1). The X-axis represents time. From 0 s to 20 s, there are only two valid channels (CH 37