2015 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 13-16 October 2015, Banff, Alberta, Canada
Indoor Localization using Smartphones in Multi Floor Environments Without Prior
Calibration or Added Infrastructure
Simon Burgess, Kalle Åström
Centre for Mathematical Sciences
Lund University, Sweden
{simonb, kalle}@maths.lth.se
Abstract—Indoor positioning for smart phone users has
received a lot of attention in recent years. While many solutions
have been developed, most rely on extra sensors, a need for predeployment of infrastructure or collecting ground truth data to
train on. In this paper we see what can be done using only
existing WiFi-infrastructure and Received Signal Strength from
these, not using any extra sensors or calibration of the signal
environment. We expand on previous work by using a multi floor
model taking into account dampening between floors, and
optimize a target function consisting of least squares residuals, to
find positions for WiFis and the smartphone measurement
locations. Experiments indicate that floor detection needs to be
semi-supervised or in need of additional sensors. The method was
tested inside two buildings, with tree stories each, with mean
errors of smartphone positions of 15.2 m and 13.5 m respectively.
I.
INTRODUCTION
Indoor positioning for users of smart devices such as
computers, tablets or phones has attracted a lot of attention in
the past few years. We present a method of simultaneously
mapping the signal environment and positioning one or
several users from offline data. The data used are Received
Signal Strength Index (RSSI) from nearby WiFi and Bluetooth
devices, a now ubiquitous part of many indoor environments,
where GPS is most commonly not available. The users do not
need to provide additional information where they are, but
only walk around in the considered environment, and the data
can thus be crowdsourced. When the mapping of the signal
environment has been done, real-time localization using a
trilateration-like approach can readily be done.
Previous approaches using RSSI most commonly use a
supervised learning approach, where a setup phase of users
manually providing location data, manually installing beacons
with known parameters and locations, using floor maps or
dead reckoning, cf. [1]. An approach similar to ours is [2],
but whereas they use hand-tailored, simulated, gps signals to
fixate the signal environment map, we use only the sparse gps
signals that can be found in or just outside the location. We
furthermore provide several such data sets. We also consider
multi floor environments, a highly relevant topic for indoor
localization considering the new FCC rules for mobile carriers
[3], which states that an accuracy of 50m horizontally and 3m
vertically in 67% of the cases is needed. Previous attempts to
do floor localization using WiFi-RSSI has used atmospheric
Björn Lindquist, Rasmus Ljungberg, Koustubh
Sharma
Combain Positioning Solutions, Sweden
{bjorn.linquist, rasmus.ljungberg, koustubh}@combain.com
sensor pressures, c.f. [4], not readily available on most
phones. Here we try to push the limits of what is possible
without additional sensors for simultaneous 3D mapping and
localization.
II.
THE METHOD
We model the obtained RSSI measurements,
between
transmitter i and receiver j, as following the path loss model,
with the additional term of adding a linear dampening
depending on the number of floors the signal passed through.
Here Pij is the model for the obtained RSSI value, Ci is the
measured power at 1 m from a transmitter, dij is the distance in
m between transmitter i and receiver j, i is the path loss
exponent, which is 2 for no attenuation in power, >2 for power
loss over distances, and <2 if the signal is enhanced by the
environment, n is the number of floors separating transmitter i
and receiver j, Cfloor is the floor dampening constant for
passing through one floor, and Xij is assumed to be i.i.d.
Gaussian noise with zero mean.
Let rj = [rx,j ry,j rz,j] and be the 3D position of a receiver j, or
the position at a certain time of a moving receiver device, and
si = [sx,i sy,i sz,i] be the 3D position of transmitter i. The distance
dij is then
We further have access to a set of GPS measurements in
the x-y plane, gj, for a subset Jgps of the receiver indices j. GPS
measurements are most commonly obtained at the entrance of
the buildings or close to windows. An accuracy in m, j, is
provided. A gps lock in the vertical direction is commonly
also obtained, but this has been found to unreliable to use for
vertical positioning.
Our goal is to build an objective function to optimize, to
simultaneously locate receiver positions, transmitter positions
and transmitter parameters. Transmitters are commonly WiFi
access points.
From the data, the time stamps of each receiver’s scan profile is also available, as well as the i.d. of the receiver. It is
reasonable to assume that receiver positions pertaining to the
2015 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 13-16 October 2015, Banff, Alberta, Canada
same device, close in time, should be close spatially. Let j=[j1
j2 j3] be a set of three receiver indices that comes from the
same receiver device, and has the three indices next to each
other in time, and less than ten seconds apart. Let Jcc be the set
of all such triplets j.
From the power model, gps measurements, and the set J of
triplets of measurement position indices close in time, we
form the following three sets of squared residuals
where gps and cc are scaling parameters >0, which is needed
when the residuals are combined to
This is our target function, to be optimized over receiver and
transmitter positons, and transmitter parameters seen in (1).
Due to the crude model of the signal environment, and that the
gps locks in the vertical directions are unreliable, the full 3D
problem of optimizing over all three coordinates continuously
will not yield accurate results. Thus, we limit rz,j and sz,i to be
on one of several discrete floors, with known floor distances.
Thus, we have a mix of continuous and discrete variables.
Holding the discrete ones constant, one can use the
Levenberg–Marquardt algorithm to find a local optimum of
(4). It remains to find a good initialization. For the continuous
variables, a genetic algorithm approach, together with
Combain indoor positioning as initialization, is applied.
For initializing receivers and senders to the correct floor, a
symmetric similarity matrix W is assembled, where the first
part of rows/columns represent a sender each, and the second
part of rows/columns each represent a receiver position. A
similarity measure between a sender and receiver is calculated
as a monotonously increasing function of power. For
similarities between receiver-receiver, their scan profiles are
compared, e.g what senders they can see, and how similar the
power measurement is when the same sender is seen. The
same method is used for sender-sender similarities in W. W
can now be clustered using normalized cut [5]. In general, W
needs to be over-segmented, and then merging small clusters
depending on the inter-cluster powers. This approach works
well to segment the floors in simulated data, but on real data,
some help is needed giving the correct floor for some subset
of receivers/transmitters. We thus assume that the receiver
positions are known which floor they are on from hereon, and
transmitter positions is inferred from that, putting a transmitter
on the floor where its receiver with the highest power
measurement is on. To optimize over all discrete locations is
too computationally heavy to do in feasible time.
III.
RESULTS
The method has been tried on three data sets, one shopping
mall with one floor, and two indoor environments, called Ehouse and Centre for Mathematical Sciences, Lund university
(M.C.). For brevity’s sake, only the multi-floor results are
presented here. A Sonim XP7 smartphone was used as a
receiver. Ground truth is available for the receiver positions,
taken while walking through the different floors.
E-house is a building mixed with office, class rooms and
laboratories, consisting of three floors. The path walked is
contained in a 120 x 85 m2 horizontal square. The data are
collected from 776 different measurement positions, and 589
different transmitters were detected. The data have 486
different gps locks with a mean accuracy of 22.4 and mean
error of 20.5m. The mean and median absolute error in
receiver positions was 15.2m and 13.9m respectively.
M.C.’s top three floors where the data is collected are
office spaces on the sides of a corridor. The path walked is
contained in a 100 x 15 m2 horizontal square, whereas the
building is approximately 105 x 30 m2. The data consist of
436 measurement positions and 175 detected WiFi access
points as transmitters. The data have 308 gps locks with a
mean accuracy of 24.8m and a mean error of 24.3m. The mean
and median absolute error in receiver positions is 13.5m and
13.1 m respectively.
IV.
CONCLUSIONS
The clustering of what floor receivers and transmitter AP’s are on needs to be semi-supervised, or need augmented sensors,
such as altimeters. When the floor of sender positions are
known, mean error in receiver positions are 15.2 m and 13.5
for E-House and M.C respectively. Thus, an indoor
localization scheme with said accuracy, without need of
deployment or calibration seems feasible.
REFERENCES
[1]
[2]
[3]
[4]
[5]
Shang, J., Hu, X., Gu, F., Wang, D. & Yu, S. 2015, "Improvement
schemes for indoor mobile location estimation: A survey", Mathematical
Problems in Engineering, vol. 2015.
Chintalapudi, K., Iyer, A.P. & Padmanabhan, V.N. 2010, "Indoor
localization without the pain", Proceedings of the Annual International
Conference on Mobile Computing and Networking, MOBICOM, pp.
173.
Fedral Communications Commision, 2015, Wireless E911 Location
Accuracy Requirements
Yu, Y., He, N., Li, Z., Ren, Y. & Wang, X. 2011, "Smartphone-based
3D in-building localization and navigation service", Proceedings of the
10th International Conference on Mobile and Ubiquitous Multimedia,
MUM'11, pp. 161
Shi, J., & Malik, J. (2000). Normalized cuts and image
segmentation. Pattern Analysis and Machine Intelligence, IEEE
Transactions
on, 22(8),
888-90.