Fast fingerprints construction via GPR of high spatial-temporal resolution with sparse RSS sampling in indoor localization

Abstract

Effective indoor localization largely relies on the fingerprint database (model) of Received Signal Strength (RSS) in connection with Radio Frequency sources, such as the most widely used Bluetooth Low Energy (BLE) iBeacons. RSSs exhibit significant random variations in both the spatial and temporal domains. It is a notoriously onerous and challenging task to construct the fingerprint database for accurate localization, as the BLE RSSs must be captured via a full space scan from one point to another every few meters in a certain period of time. In order to tackle this problem, this study proposes an approach to fast fingerprints construction that only requires a sparse sampling of RSS of the space. First, a smartphone records the time series of RSS over a designated path, and a radio map for the path is then generated by a spatio-temporal mapping method using the Pedestrian Dead Reckoning algorithm. Second, the radio map of the entire space can be obtained via Gauss Process Regression (GPR), with outliers reduced to improve the reliability of the fingerprint database. Experiments have been performed in an underground carpark (38 m \(\times \) 14 m), and the experimental results indicate that the proposed approach can construct the fingerprint database 300% faster than the conventional approach does. The localization accuracy of both approaches is quite similar (80% error in 2.8 m). The proposed approach offers potential for the construction of a large-scale fingerprint database for a wide-area Location Based Service (LBS) of Smart City indoor and outdoor integration, where big RSS data processing is a must.

Full text

Noname manuscript No.
(will be inserted by the editor)
Fast Fingerprints Construction via GPR of High
Spatial-temporal Resolution with Sparse RSS
Sampling in Indoor Localization
Haojun Ai ·Kaifeng Tang ·Weiyi
Huang ·Sheng Zhang ·Taizhou Li
the date of receipt and acceptance should be inserted later
Abstract Effective indoor localization largely relies on the fingerprint database
(model) of Received Signal Strength (RSS) in connection with Radio Frequency
sources, such as the most widely used Bluetooth Low Energy (BLE) iBeacons.
RSSs exhibit significant random variations in both the spatial and temporal do-
mains. It is a notoriously onerous and challenging task to construct the fingerprint
database for accurate localization, as the BLE RSSs must be captured via a ful-
l space scan from one point to another every few meters in a certain period of
time. In order to tackle this problem, this study proposes an approach to fast
fingerprints construction that only requires a sparse sampling of RSS of the s-
pace. First, a smartphone records the time series of RSS over a designated path,
and a radio map for the path is then generated by a spatio-temporal mapping
method using the Pedestrian Dead Reckoning (PDR) algorithm. Second, the radio
map of the entire space can be obtained via Gauss Process Regression (GPR),
with outliers reduced to improve the reliability of the fingerprint database. Ex-
periments have been performed in an underground carpark (38m ×14m), and the
experimental results indicate that the proposed approach can construct the finger-
print database 300% faster than the conventional approach does. The localization
Haojun Ai
School of Cyber Science and Engineering, Wuhan University
Key Laboratory of Aerospace Information Security and Trusted Computing,Ministry of Edu-
cation, China
E-mail: aihj@whu.edu.cn
Kaifeng Tang
School of Cyber Science and Engineering, Wuhan University
Weiyi Huang
School of Computer Science, Wuhan University
E-mail: hwy2017@whu.edu.cn
Sheng Zhang
School of Cyber Science and Engineering, Wuhan University
E-mail: 2014301500353@whu.edu.cn
Taizhou Li
Northeastern University College of Professional Studies

2 Short form of author list
accuracy of both approaches is quite similar (80% error in 2.8m). The proposed
approach offers potential for the construction of a large-scale fingerprint database
for a wide-area Location Based Service (LBS) of Smart City indoor and outdoor
integration, where big RSS data processing is a must.
Keywords Fingerprint database ·Received Signal Strength ·Time Series ·
Gauss Process Regression ·Spatio-temporal Mapping ·Indoor Localization
1 Introduction
Indoor location is a supporting technology for extending Location Based Service
(LBS) from outdoor to indoor use, thus realizing the so-called Smart City con-
cept. Although there is not yet a formally accepted definition of Smart City, the
final aim is to make better use of the information supplied by electronic sensors,
increasing the quality of the services offered to the citizens while reducing the
operational costs. Due to the lack of indoor positioning infrastructure, such as
the Global Navigation Satellite System (GNSS) of outdoor localization, various
indoor localization solutions adaptable to smartphones have been proposed. They
can make full use of sensing and computing capabilities provided by smartphones
to achieve tracking and provide LBS without special infrastructure. One of the
major locating schemes is utilizing location-dependent radio frequency signal fea-
tures to estimate position by discriminative or generative models. As with other
supervised learning methods, it is divided into two phases, the offline and position
estimation phases. In the offline phase, a database called a fingerprint map (FM) is
constructed by recording received signal strength (RSS) at given positions as fin-
gerprints for a period of time in the target area. In the position estimation phase,
the smartphone scans radio signals in real time and compares the similarities with
the stored fingerprints to estimate current location. This algorithm achieves an
average accuracy of 1∼5 meters, depending on different implementation details of
the algorithm and test conditions [4, 19, 20, 26].
However, acquiring fingerprints is a heavy, time-consuming and inefficient pro-
cess when constructing an FM for a large area. For example, it takes 390 minutes
to construct an FM covering 500 square meters by collecting WiFi RSS at 338
points with known locations [10]. Therefore, seeking a convenient and efficient FM
construction method has important practical significance for the widespread use
of the indoor positioning system. There are many solutions for WiFi that involve
reducing the sampling time of each point [23] or walking along paths to collect
sensor and signal data in the offline phase [10–13]. Unfortunately, WiFi-based lo-
calization on the iPhone is no longer feasible after IOS 6.0, and Bluetooth-based
localization studies [19, 26, 27] focus more on improving localization accuracy and
system stability but pay little attention to the cost problem of FM construction.
Bluetooth Low Energy (BLE), a low power version of Bluetooth, was originally
used as a proximity sensor for Far and Near by Apple. Its transmission frequency
and the capture mode are different from WiFi [5]. Therefore, the fast construction
method for WiFi cannot be applied to BLE directly.
Our proposed fast FM construction method is based on the transceiver mech-
anism of BLE signals. Compared with the existing methods, the mapping from
the BLE time sequence to spatial locations is more refined than WiFi, as the BLE

Title Suppressed Due to Excessive Length 3
interface receives a packet and returns to the application at once. Additionally,
we train Gaussian Process Regression (GPR) model to form an FM outside the
walking path. Further, we design a detection rule for accidental BLE signals to
optimize the localization results. It was shown through an experiment conducted
by us that collection by walk mode is more efficient than the static collection, and
the removal of abnormal BLE packets improves fingerprint localization accuracy.
The main contributions of this paper are listed as follows:
1. We obtain displacement sequences from a sensor time sequence, and then we
put BLE packets on the path according to the time relationship between the
step events and them.
2. We design a detection rule for collected packets based on the probability of a
beacon being captured in a short period.
3. We train a GPR model for each beacon with the fingerprints on the walking
path to generate an FM outside the walking path.
This article is organized as follows: In Section 2, we review and summarize
related work. In Section 3, we present the overall structure of the system. In
Section 4, we detail each part of our proposed algorithm. We evaluate the validity
of the algorithm in a real scenario in Section 5 and conclude the paper in Section
6.
2 Related Work
In recent years, fingerprint localization has received considerable attention. Ra-
dio signals have been widely used for this purpose, mainly WiFi and Bluetooth.
The pioneering work of fingerprint localization RADAR was proposed in 2000 [1].
RADAR uses WiFi signal as a location fingerprint and designs a prototype method
of fingerprint localization. Since then, a large number of indoor localization sys-
tems have optimized algorithms and improved performance based on RADAR [4,
14,21, 24]. With the development of smartphone sensors, more abundant sensor in-
formation has been added to the fingerprint. However, the collection of fingerprints
is still the biggest bottleneck for practical application, regardless of the fingerprint
features.
Some main methods applied to the fast radio map construction are analyzed
in the following.
2.1 Dead-reckoning based on built-in sensor
The smartphone performs a scan and records the scanned RSS and Service Set
Identifier (SSID) of surrounding Access Points (APs) in every step [10–12]. Iner-
tial sensors and the map are merged to generate the coordinates of the sampling
points. Three collection methods are listed in [13], and experiments show that mov-
ing sampling (MS) and stepped MS (SMS) are comparable to static sampling (SS)
in terms of RSS value and positioning accuracy . For continuous position tracking
on three different smartphones, correction points with known locations are intro-
duced to estimate position and calibration step size, which has an accuracy rate of
more than 50% compared to using Pedestrian Dead Reckoning (PDR) [9]. In the

4 Short form of author list
case where the start point information is unknown, Ma L et al. match the PDR
trajectories from major possible paths, combining the image processing algorith-
m [16] to convert the relative PDR values into absolute values, and the average
positioning error is 3.47m. Although many PDR methods based on sensors for
WiFi exist, the signal transmission rule for APs is different from that of BLEs.
2.2 Propagation model for signal interpolation
Propagation models establish the relationship between RSS and distance. The
most common is the lognormal shadowing model [17]. The WiFi signals follow
the log-distance path loss model [7]. The Gaussian regression model also provides
flexible training of observations [10]. Kumar first attempted to adopt GPR and
establish the posterior mean and variance of each location, which can not only
predict RSS mean but also infer fluctuation [8]. Radial Basis Function (RBF) [24]
is an option to expand the sparse database, and in 78% of cases, the cumulative
error is less than 3m and the average error is 2.2m. For some areas that are not
accessible, Jinbo Zuo et al. adopt kriging interpolation, which depends on the
spatial autocorrelation of the Received Signal Strength Indication (RSSI) [27].
2.3 Crowdsource and SLAM
Some crowdsource methods [14, 18] build multi-modal RF signal maps easily.
Chengwen Luo et al. proposed PiLoc [14] without manual calibration, prior knowl-
edge, and hardware support. A clustering algorithm is used to separate the walking
path according to different indoor environments. Then, disjointed path segments
are matched, based on the similarity of the RSSI and the path. Finally, mul-
tiple walking paths are merged into a floor map. This proves the similarity of
signal changes of different models of mobile phones and overcomes the problem
of heterogeneity of crowdsourcing equipment. This approach achieved an average
positioning error of 1.5m. In 2018, they applied this idea to different indoor envi-
ronments on multiple floors, with an average error of 1.82m [15]. Yuan Zhuang
et al. propose two crowdsourcing-based WiFi positioning systems that requires no
floor plan or Global Positioning System (GPS) [25]. Zee [21] estimates location
with the help of an indoor map and particle filtering and then back propagates
to improve the historical accuracy. Although these methods need little specialist
involvement, there are some problems: data redundancy, inhomogeneous finger-
print density, unknown RSSI location tags, and heterogeneous mobile devices.
Meanwhile, diverse uncertainties regarding pedestrians result in difficulty in con-
structing appropriate algorithms and high-intensity calculations. After all, in the
positioning stage, users mostly hold mobile phones in their hands. Specialists are
more inclined to adopt a continuous collection method by collecting sensor data
and signal characteristics from the mobile phone.

Title Suppressed Due to Excessive Length 5
3 System Framework
Fig. 1 provides the overview of the smartphone-based BLE fingerprint map fast
construction method. The smartphone is used to measure sensing data from its
built-in sensors and signal data.
1. Data collection: The collector walks along a predetermined path, and the appli-
cation in the smartphone records sensor messages sr = (ax, ay, az, ori, t) and
signal data sl = (s, t′), where ax,ay,azare accelerations of the three direction
x,y,z,ori is the angle around the z-axis, a BLE packet scontains the Media
Access Control (MAC) address of overheard beacon and their corresponding
RSSs, and t,t′are timestamps of each message in sr,sl.
2. Simulation of the walking path: Sensor landmarks are selected based on relative
orientation reading, and we obtain the displacement and time sequences of
steps ⟨li, ti⟩.
3. Spatio-temporal mapping: We utilize the time relationship between packets
and each step to determine the packets’ positions by spatio-temporal mapping
and obtain the fingerprint database on the walking path.
4. GPR model training: The fingerprints on the walking path are used as a
training set to establish the GPR model for the BLE beacons and generate
a database in the entire target area F P . To ensure more precise predictions,
we use GPR algorithms twice from line to area.
5. Outlier detection of BLE packets: We design a detection rule based on the
probability of BLE packets being captured to avoid the case where accidental
packets deteriorate the localization results.
Fig. 1: System overview of fingerprint map creation.
4 Algorithm Description
4.1 Trajectory estimation
We need to set a walking path in advance so the collector can walk along the
path with the mobile phone collecting time sequences of sensor sr and signal sl.
PDR [6] is a common way to estimate movement routes, which relies on built-in
smartphone sensors.
Step detection. We take the step frequency and peak magnitude of people as a
threshold to eliminate false peak points after peak detection of acceleration.

6 Short form of author list
0 1 2 3 4 5 6 7 8 9 10
time[s]
-6
-4
-2
0
2
4
6
8
acceleration[m/s2]
a
mag
peak
Fig. 2: Example of step detection. The blue inverted triangles indicate all valid steps satisfying
set (2). There are 18 steps with timestamps detected.
Acceleration aiof each sample ican be calculated as:
ai=√a2
xi +a2
yi +a2
zi (1)
We obtain peak sequence ⟨magi, ti⟩after applying a low-pass filter to ai, in which
most original high-frequency noise is filtered. The minimum time per step spent
is δt, and the minimum acceleration magnitude of per step is a′. Then, the set of
valid steps among the peak sequence ⟨magi, ti⟩is:
{ti−ti−1> δ, magi> a′}(2)
We set δt= 1/3s,a′= 2m/s2.
AB
CD
Fig. 3: The walking path is calculated from inertial sensor data. It is basically consistent with
our predetermined path, where start and end points are both A.
We clip the accelerometer reading where the sampling frequency is 20Hz in
Fig. 2. We select a rectangular path in an underground car park (38m×14m), and
the following experiments are all based on the path (Fig. 3). The average accuracy
of step detection can achieve 99.80% after walking 10 rounds, as shown in Table
1.
Sensor landmark match. It is easy to list landmarks sensitive to sensors, such as
elevators, stairs, and corners. Matching landmarks can fix the current position
while overcoming the cumulative error of PDR. Fig. 4 shows how the landmarks

Title Suppressed Due to Excessive Length 7
Table 1: Accuracy of step detection
True value 145 146 147 145 147 148 147 147 148 149
Calculated value 145 146 147 147 147 148 147 147 148 150
Error rate(%) 0 0 0 1.38 0 0 0 0 0 0.67
Fig. 4: Landmark matching based on orientation.
reported by the orientation changes. If the difference between the end and start
of a step exceed a threshold, then we mark the event, for example, B, C, and D
corresponding to B, C, and D in Fig. 3, and assume the coordinates loc of these
known points.
Finally, steps are evenly placed on the road segment divided by sensor land-
marks, as indicated by the red points in Fig. 3. Note we assume step length as
SL =locB−locA
K, where Kdenotes steps between A and B, which is the number
of mag in the peak sequence, so the position of the jth step is
lj=locA+SL ×j(3)
Then, the displacement and time sequence of each step ⟨li, ti⟩is computed.
4.2 Spatiotemporal Mapping of BLE signals
It is crucial to infer the location tags for the unlabeled fingerprints collected by
walking. Besides, with the quick increases of data scales and dimensions in the
big data era, analysis of massive data with high density has recently become a
trend [2, 3, 22]. When scanning WiFi on Android, its driver returns the results
after scanning all the channels. If many APs are scanned, their RSSI, MAC, SSID
are returned at the same time, so the scan cycle is at least 200ms. Meanwhile, the
BLE interface immediately returns the result to the application after scanning one
BLE packet. Therefore, BLE packets can get a more refined location.
We get time series of BLE packets ⟨(s0, t′
0), ..., (sn, t′
n)⟩. Under the start mo-
ment and position of known step (ti, li), for packets captured at t′
i, we map the
time relationship between t′
iand the jth step to the spatial relationship propor-
tionally, for example, a step with a start time t1and end time t7, as shown in Fig.
5. Five packets are captured in one step, and the location of the packet captured
at t4is l1+(t4−t1)
(t7−t1×SL.

8 Short form of author list
Fig. 5: BLE signal location determination from temporal to spatial.
4.3 Fingerprint prediction
The gaussian regression model fits RSS to a Gaussian distribution [8, 10]. We get
BLE fingerprints with location tags on the walking path F={(x1, f1),(x2, f2), ..., (xn, fn)},
where fi=⟨fMac0
i, f Mac1
i, ...⟩and fMacj
idenotes the mean RSS value captured
from Macjat location i. The problem we have to solve is how to predict ffor
larger coverage by a Gaussian model on the basis of Fand additional position
input X.
Fig. 6: RSS prediction distribution in the target area. The solid blue circle indicates the location
of the iBeacon.
extract packets from the
same beacon
pick a number of points
in the prediction area
fingerprint database in the
prediction area
GPR model
their positions
Fig. 7: RSS value predicted by GPR in the designated area.
Assuming that RSSs from different beacons are independent, we train a Gaus-
sian process model for each beacon. We take two steps to predict the RSS of the
iBeacon in the target area: First, we extract BLE packets of one beacon from
Fand then pick n points on the walking path. More fingerprints are obtained
through the GPR model made by the collected packets, as shown in Fig. 7. In a
similar way, we get a fingerprint database FP outside the walking path through
the GPR model made by fp. Furthermore, GPR interpolation is too rough to fill

Title Suppressed Due to Excessive Length 9
in the radio strength in every untouched position with legal values. We set a limit
zone for prediction and regard the prediction value outside the zone as invalid. An
FM with a grid size of 0.28m ×0.31m covering the entire target area is formed
F P ={(X1, RSS1), ..., (XN, RS SN)}, where each of RSS1, RSS2, ... includes all
RSSs from visible beacons. Fig. 6 shows the predicted RSS distribution of one of
the beacons.
4.4 Detection of BLE advertisement packets outliers
In the car park, we set the advertising interval of all the beacons as 500ms. In
fact, Nexus 5 receives about 50 packets from some beacons in one second. We
receive fewer BLE packets when we are walking, so taking the mean value of RSS
as noise elimination is infeasible. Meanwhile, RSS and the probability that BLE
packets are captured attenuates as the distance from iBeacon to sampling position
increases [4, 20, 26].
If the probability of receiving packets from a beacon is low at a sampling
point and these packets are directly used to build an FM, they are still hard to
capture in the localization process. This may cause deterioration of the location
estimation results. Moreover, we find that the opportunity of smartphone scanning
the beacons far from the sampling point is small (Fig. 8). Therefore, we consider
removing packets with low captured probability.
Fig. 8: The number of packets captured from
different iBeacons during 5 seconds vs. the dis-
tance between the iBeacon and the sampling
point.
Fig. 9: The number of packets captured from
30 iBeacons during 5 seconds.
We proposed a simple and reasonable detection rule to discard accidental pack-
ets. The packets satisfying frej≥θfr e are reserved, where θfr e is the threshold
and frejis the number of packets from Macjwithin a short time T. Let θf r e = 3
and T= 5s. It can be seen that there are total 278 packets received from 30 bea-
cons, 23 packets received from each of 2 beacons, and one packet received from
each of 5 beacons (Fig. 9). Thus, 5 of 278 BLE packets are removed after the
detection rule, accounting for 1.80% of the total packets and having a negligible
impact on the original data. We prove that the fingerprint database after outlier
detection has better localization performance in the following.

10 Short form of author list
5 Field Experiments
5.1 Experimental Setup
We develop an app called ”SenBleScanner” on Nexus 5 to collect time sequences
of sensors sr = (ax, ay, az, ori, t) and signals sl = (s, t′). The tester held the Nexus
5 steadily and walked along a predetermined path for 7 rounds, indicated by a red
line, which took about 13 minutes for 7 rounds. Each set of data is collected from
walking in 1 round.
5.2 Performance evaluation
In the following, we compare the localization results of different FMs and describe
the performance of FM generated by our proposed algorithm.
The smartphone receives signals from several test points with truth locations.
Then, we calculate the mean RSS from different beacons after the accidental pack-
ets are removed. The research [23] points out that the stronger the RSS value, the
higher the beacon’s response rate. To reduce computation expense and improve
reliability, we select 10 beacons with the strongest RSSs from the test fingerprint
and calculate the Euclidean distances dist from FM.
We choose a simple algorithm KNN to evaluate the performance [5, 19]. That
is, the Kfingerprints in F P with the smallest dist from the test fingerprint are
selected, and the mean value of their coordinates is output as the result.
Xpr =ΣK
j=1Xj|argminΣK
j=1distj
K(4)
The cumulative distribution function (CDF) of localization error for four kinds
of databases are plotted in Fig. 10. The data-processing method contains the
outliers detection od, direct interpolation based on GPR a, and GPR interpolation
twice from the walking path to outside area la. We can see that the CDF curves are
close, but the combination of outlier detection and two-step prediction exhibited
better performance. In both environments, 80 percent of the combinations of od
and la have errors under 2.8m. The errors are higher for direct prediction of the
entire area without any detection a, with 80 percent under 3.3m. In Fig. 12, the
walking trajectory is estimated by matching with our proposed fingerprint map,
where the trajectory of the true path is shown in the red and that of the proposed
algorithm is shown in blue.
It is necessary to make a comparison between the proposed method and the
traditional approach and validate its effectiveness. A total of 33 sampling points
with 6-m intervals are selected in the target area, and each takes at least one
minute using the traditional fingerprint collection method. This takes 33×1=33
minutes, but our rapid collection method takes about 13 minutes, which is 300%
faster than the conventional approach. The proposed method combines the od,la
and traditional approaches using point by point collection, achieving an average
accuracy of 1.6217m. The comparison is shown in Fig. 11. Although this error is
larger than the average error when using the traditional fingerprint method, it is
comparable to that in many of the latest.

Title Suppressed Due to Excessive Length 11
0 1 2 3 4 5 6 7
x
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
F(x)
Empirical CDF
a
la
od+a
od+la
Fig. 10: CDF of position estimation errors of
FM built by two sets of packets.
0 2 4 6 8 10 12
x
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
F(x)
Empirical CDF
traditional method
proposed method
Fig. 11: Comparison between proposed method
and the traditional approach.
estimation path
true path
Fig. 12: Estimated trajectory using the proposed algorithm.
6 Conclusion
This paper proposes a fast fingerprint continuous collection method based on the
characteristics of BLE signals. We obtain the displacement sequence of steps from
the time sequence of the inertial sensor. Then, we map the relationship from tem-
poral to spatial and estimate the location of each packet on the walking path.
Finally, in order to establish a larger and more fined fingerprint map, two GPR
models for each beacon from line to area are trained to expand the sparse finger-
prints. In addition, we design a detection rule for BLE packets to optimize the
localization effect of the fingerprint map further. This work reduces the burden of
building a fingerprint map, avoids the high demands of crowdsourcing, and per-
forms well with an average accuracy 2.17m. The proposed approach believe the
proposed approach offers potential for the large-scale LBS of Smart City.
Acknowledgements This work is partially supported by The National Key Research and
Development Program of China (2016YFB0502201).
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