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sensors
Article
MapSentinel: Can the Knowledge of Space Use
Improve Indoor Tracking Further?
Ruoxi Jia 1,*, Ming Jin 1, Han Zou 2, Yigitcan Yesilata 3, Lihua Xie 2and Costas Spanos 1
1Department of Electrical Engineering and Computer Sciences, University of California, Berkeley,
CA 94720, USA; jinming@berkeley.edu (M.J.); spanos@berkeley.edu (C.S.)
2School of Electrical and Electronics Engineering, Nanyang Technological University,
Singapore 639798, Singapore; zouhan@ntu.edu.sg (H.Z.); elhxie@ntu.edu.sg (L.X.)
3Department of Electrical and Electronics Engineering, Middle East Technical University,
Ankara 06800, Turkey; yigitcan.yesilata@metu.edu.tr
*Correspondence: ruoxijia@berkeley.edu; Tel.: +1-510-693-7634
Academic Editor: Vittorio M. N. Passaro
Received: 25 January 2016; Accepted: 26 March 2016; Published: 2 April 2016
Abstract:
Estimating an occupant’s location is arguably the most fundamental sensing task in smart
buildings. The applications for fine-grained, responsive building operations require the location
sensing systems to provide location estimates in real time, also known as indoor tracking. Existing
indoor tracking systems require occupants to carry specialized devices or install programs on their
smartphone to collect inertial sensing data. In this paper, we propose MapSentinel, which performs
non-intrusive location sensing based on WiFi access points and ultrasonic sensors. MapSentinel
combines the noisy sensor readings with the floormap information to estimate locations. One key
observation supporting our work is that occupants exhibit distinctive motion characteristics at
different locations on the floormap, e.g., constrained motion along the corridor or in the cubicle
zones, and free movement in the open space. While extensive research has been performed on
using a floormap as a tool to obtain correct walking trajectories without wall-crossings, there have
been few attempts to incorporate the knowledge of space use available from the floormap into the
location estimation. This paper argues that the knowledge of space use as an additional information
source presents new opportunities for indoor tracking. The fusion of heterogeneous information is
theoretically formulated within the Factor Graph framework, and the Context-Augmented Particle
Filtering algorithm is developed to efficiently solve real-time walking trajectories. Our evaluation in a
large office space shows that the MapSentinel can achieve accuracy improvement of 31.3% compared
with the purely WiFi-based tracking system.
Keywords:
indoor tracking systems; non-intrusive; map-aided; WiFi; ultrasonic sensor networks;
particle filters
1. Introduction
The indoor location sensing technology has emerged as an inherent part of the “smart buildings”
as it provides great potential for building operation improvement and energy saving. For instance,
an on-demand ventilation or lighting control policy must know the usage of the building spaces,
which may involve when building occupants enter or exit the building, where they inhabit, what time
they occupy the spaces, the duration of occupancy, etc. Such applications require the location sensing
systems to provide real-time estimate of occupants’ locations, which is also termed “indoor tracking”,
in order to realize fine-grained, responsive building operations.
Most indoor tracking systems necessitate each occupant to carry or wear a powered device such
as an infrared [
1
], ultrasonic [
2
–
4
], or Radio Frequency transceiver [
5
–
7
]. Even if the transceiver
Sensors 2016,16, 472; doi:10.3390/s16040472 www.mdpi.com/journal/sensors
Sensors 2016,16, 472 2 of 19
is miniaturized into a convenient form, occupants are not willing or likely to carry it at all times.
Another subset of tracking systems alleviate the need for carrying specialized devices by using the
inertial sensors on smartphones to perform dead reckoning [
8
–
10
]. However, specialized programs are
required to be installed on smartphones to continuously collect inertial sensing data, and thereby the
associated energy issues or occupants’ engagement become the main impediment.
On the contrary, we enable non-intrusive indoor tracking by developing an information fusion
system that takes advantage of noisy measurements from various sensors, namely, WiFi access points
and ultrasonic sensors. WiFi access points are beneficial for wide spatial coverage while WiFi signals
transmitted in the indoor environments suffer from large variations [
11
]; ultrasonic sensors are able
to accurately locate the occupants in their detection zones which are nevertheless limited spatially.
Our vision is of occupants carrying some device with WiFi module, which can be smartphones,
tablets, wearable devices, etc., in the indoor space where ultrasonic sensors can provide opportunistic
calibration of the location estimation. The location sensing system is operating in a passive way, i.e.,
there is no need for specialized devices or programs for location inference.
In addition to the sensor measurements, another key input for our system is the floormap of the
indoor space of interest. Floormap information has been used to refine walking trajectory estimates
by eliminating wall-crossings or unfeasible locations [
12
–
14
]. There has also been efforts to use the
floormap to reduce the complexity of the tracking task by properly quantizing the indoor space [
15
–
18
].
In effect, we can also acquire some prior knowledge of occupants’ dynamic motion from the floormap.
The indoor space comprises several typical components, such as cubicles, offices, corridors, open areas,
etc., where occupants’ motion exhibit distinctive patterns. For example, when located at his/her office
or cubicle, the occupant is very likely to keep static; the occupant walking on a particular corridor
tends to continue the motion constrained along the corridor, while an occupant in an open space is
free to move in any direction. Such information of space use is useful to track occupants’ movement,
notwithstanding it is less considered in previous work. Gusenbauer et al. [
19
] exploited different types
of movements to improve the tracking model. This was done by introducing an activity recognition
algorithm based on accelerometer data to model pedestrians’ steps more reliably. Park [
20
] proposed
incorporating the floormap information by “path compatibility”, where occupants’ motion sequences
and motion-related information (e.g., duration and speed) are first estimated based on mobile sensing
data, and then localization is achieved via matching occupants’ motion sequences and the hypothetical
trajectories provided by the floormap. Kaiser et al. [
21
] proposed a motion model based on the floormap,
which weights the possible headings of the pedestrian as a function of the local environment. Our work
differs from [
19
] and [
20
] in that our work does not rely on the inertial measurements to recognize
the motion. Instead, the motion information is extracted from the floormap. We exploit the prior
knowledge that the floormap endows us about the occupants’ typical movement and activity, not
merely the possible headings at each point of the floormap as in [
21
]. It is, therefore, the objective of
this paper to propose MapSentinel, a non-intrusive location sensing system via information fusion,
which combines the various sensor measurements with the floormap information, not only as a sanity
check of estimating trajectories but as an input for occupants’ kinematic models.
Our main contributions are as follows:
•
We build a non-intrusive location sensing network consisting of modified WiFi access points and
ultrasonic calibration stations, which does not require the occupants to install any specialized
programs on their smartphones and prevents the energy and occupant engagement issues.
•
We propose an information fusion framework for indoor tracking, which theoretically formalizes
the fusion of the floormap information and the noisy sensor data using Factor Graph.
The Context-Augmented Particle Filtering algorithm is developed to efficiently solve the walking
trajectories in real time. The fusion framework can flexibly graft floormap information onto other
types of tracking systems, not limited to the WiFi tracking schemes that we will demonstrate in
this paper.
Sensors 2016,16, 472 3 of 19
•
We evaluate our system in a large typical office environment, and our tracking system can achieve
significant tracking accuracy improvement over the purely WiFi-based tracking systems.
The rest of this paper expands on each of these contributions. We conclude the paper and discuss
the future work in Section 6.
2. MapSentinel Architecture
Figure 1presents the overall architecture of MapSentinel. There are three key components in
MapSentinel: the non-intrusive sensing networks, the floormap processing engine, and the information
fusion algorithm. The non-intrusive sensing networks, as the name suggests, generate location-related
measurements without the need for computation on the smartphone end. Our sensing networks
consist of WiFi access points (APs) and ultrasonic calibration stations, which track locations by relating
the WiFi signal strength or the sound time-of-flight to the distance. The floormap processing engine
converts the pictorial floormap to the information that can be directly combined with the sensor
measurements in the fusion algorithm. The output of the floormap processing engine represents the
prior knowledge obtained from the map, and can be computed in the offline phase. We will present
the details of the main components of MapSentinel in this section.
WiFi$Access$Points$ Floormap$
Processing$Engine$$
Ultrasonic$Sensor$
Networks$
Contextual$Map$
Reachable$Set$
InformaBon$
Fusion$Algorithm$
Real-time Location Estimate
Central Sever
Ultrasonic Station
WiFi Router
Figure 1.
MapSentinel architecture—WiFi APs keep tracking occupants’ locations, and the estimation
is periodically refined using the ultrasonic stations deployed in the environment. Furthermore, the
sensor measurements and the floormap information are combined via the information fusion algorithm
to estimate location in real-time. The floormap processing engine helps transform the floormap to the
information accessible to the fusion algorithm.
2.1. WiFi Access Points
IEEE 802.11 (WiFi) is the most commonly used wireless networking technology with widely
available infrastructure in large numbers of commercial and residential buildings. Nearly every
existing commercial mobile device is WiFi enabled. The common method to utilize WiFi for indoor
location sensing is to enable the mobile device to collect WiFi Received Signal Strengths (RSS) of nearby
WiFi APs by installing an application on the mobile devices. Our system, on the contrary, leverages
Sensors 2016,16, 472 4 of 19
WiFi in a non-intrusive manner. Rather than modifying the hardware or software of occupants’ mobile
devices, we upgrade the software of the existing commercial WiFi APs to allow them to detect the RSS
of each mobile device, while providing basic internet service to occupants as well. The RSS and media
access control (MAC) address of each mobile device will be forwarded to the server and the occupant
can be identified through the unique MAC address of the mobile device.
2.2. Ultrasonic Calibration Stations
Ultrasonic sensors measure the distance to the obstacle in the front to accurately position the object
in its detecting range, which works by detecting the time of return, t, and the distance is given by:
d=vsound ×t
2(1)
where
vsound ≈
340 m/s is the velocity of sound in the air. The advantages include
centimeter-resolution distance measurements and limited span of detection angles, which make
it suitable for online calibration of indoor positioning systems. Figure 2demonstrates typical traces
of the ultrasonic sensor readings when the occupant moves across the detection zones. By properly
thresholding the distance measurements, the ultrasonic sensor can be used as an indicator of occupant
presence inside its detection zone.
50
100
22:01 22:02 22:03 22:04 22:05 22:06
Time
Distance (cm)
Ultrasonic Sensor Measurements
Sensor 1
Sensor 2
Sensor 3
The occupant
moves across the
detection zone
Figure 2.
The measurements of ultrasonic stations deployed in the space. When the occupant is within
the detection zone of the ultrasonic station, the sensor reading exhibits a smaller value.
The network consists of deployed ultrasonic stations and data collection center, which
communicate with XBee radio modules operating the IEEE 802.15.4 standard, more specifically, the
ZigBee protocols, as shown in Figure 3. The radios are low-power and can operate reliably in the
indoor space, where the network can be automatically established by the coordinator, in our case, the
data collection center. The data center controlled by Arduino enquires about the ultrasonic station for
measurements periodically, so that the measurement frequency is 1 Hz, and transfers the data to the
computer connected by serial ports. Each ultrasonic station is equipped with three ultrasonic sensors,
whose directions are offset by 15
◦
. As the measurement range spans 15
◦
for each ultrasound, this
covers an area of 45◦in the front of the station, which is sufficient for indoor area localization.
Sensors 2016,16, 472 5 of 19
E
C
Database
Ultrasonic station
! ultrasonic sensor module
! Arduino board as controller
! XBee for communication
Coordinator
! XBee for data collection
! Processor: PC
Request'@'1Hz'
Response'
Wall'
Figure 3.
Illustration of the configuration of the ultrasonic calibration station. The coordinator requests
measurements at 1 Hz frequency through the IEEE 802.15.4 protocol, and deposits collected data to the
local database. The ultrasonic station takes three independent measures from its sensor points to detect
occupant presence in the vicinity.
2.3. Floormap Processing Engine
The indoor space is well structured and typically organized into corridors, open areas, walls,
rooms, etc. Depending on the occupant’s present location, the motion is constrained by these external
factors. For instance, an occupant on a particular corridor has high probability continuing its motion
constrained along the corridor—or an occupant walking in the open area is free to move in any
direction. Likewise, an occupant in his/her cubicle area is more likely to stay static. Based on
different motion capabilities, we categorize the indoor space into several contexts, namely, open space,
constrained space and static space. In addition, the floormap processing engine is designed to convert
the original floormap into the contextual floormap that indicates the context of each point in the original
floormap. The details of each component of contextual floormap is provided in Table 1. We use the
word “canonical direction” to refer to the direction of constrained space along which the movement
has more freedom.
Table 1. Components of contextual floormap.
Context Symbols Motion Characteristics
Free Space FS Move freely, e.g., rooms
Constrained Space CS Move along canonical direction, e.g., corridors
Static Space SS Stay static, e.g., cubicles
In addition, the occupant motion is also constrained by speed restrictions. Another function of
the floormap processing engine is to compute the reachable set containing all the points visited with
admissible speed from a given starting point. In the indoor space, the geographical distance between
two positions in a floormap does not necessarily equal to the walking distance between them due to
the block of walls and other obstacles. Hence, the physical features of the indoor environments would
be ignored if the reachable set is confined within a fixed radius centered around the given starting
point. The floormap processing engine addresses this problem by converting the floormap to a graph
where all the non-barricade nodes connect to their neighboring non-barricade nodes and the barricade
nodes do not have connections to any other nodes. In this way, the reachable set of a given node can
be computed through finding the nodes within the maximum depth from the root node, which can be
efficiently solved by breadth-first search algorithm [22].
Sensors 2016,16, 472 6 of 19
3. Information Fusion Framework
In this section, we propose an information fusion framework that manages the heterogeneous
sensor measurements as well as the floormap and occupants’ context-related motion characteristics
to provide an online estimate of occupants’ location. There are two key components in the
fusion framework: Context-Dependent Kinematic Models (CDKM) and Probabilistic Sensor
Measurement Models (PSMM). CDKM is based on the observation that occupants’ movements exhibit
distinctive features in different parts of buildings as described in Section 2.3, and it captures this
context-dependency by defining different kinematic models for distinctive contexts. PSMM models
each sensor measurement as a probability distribution and multiple sensor data are combined via
Bayes’ rule to support the location inference.
3.1. Problem Formulation
Consider that the indoor space of interest is composed of
M
contexts, in each of which
occupants exhibit a particular sort of kinematic patterns. Denote the context at time
k
as
mk
where
mk∈ {FS,CS1,· · · ,CSR,SS}
. The subscript of
CS
represents the index of the certain direction of
constrained space and
R
is the total number of different directions. Let the state
xk= (zk
,
mk)
consist of
the position and velocity components of the occupant in the Cartesian coordinates
zk= (xk
,
yk
,
˙
xk
,
˙
yk)
, as well as the context
mk
. If the position is known, the context can be uniquely determined by the
contextual floormap. We characterize this correspondence via a function
M:R4→R
which assigns
a specific context
mk
for
zk
. The tracking problem can be viewed as a statistical filtering problem
where
zk
is to be estimated based on a set of noisy measurements
y1:k={y1
,
···
,
yk}
up to time
k
.
Specifically,
yk
is the measurements available at time
k
, and, in our case, it includes measurements
from multiple sensors,
{yn
k}Ns
n=1
where
Ns
is total number of sensors deployed in the space of interest.
We model the uncertainty about the observations and the states by treating them as random variables
and assigning certain probability distribution to each random variable. In this setting, we want to
compute the posterior distribution of the state given the measurements up to time k,i.e.,p(zk|y1:k).
The impact of introducing context as an auxiliary state variable is manifold. Firstly, the transition
of contexts
mk−1
to
mk
determines the type of motion executed during the time interval
(k−
1,
k]
.
For instance, if the context remains the same, then the occupant should follow the motion type defined
by the two identical contexts; on the contrary, if the context varies during
(k−
1,
k]
, then the occupant
would execute the motion that is defined by neither of the contexts. For simplicity, we will assume a
free motion. That is, the position/velocity state at time
k
,
zk
, depends on not only the past state
zk−1
and
mk−1
, but also the current context
mk
stochastically. Moreover, there is a deterministic mapping
between
zk
and
mk
as is specified by the contextual map. In order to facilitate visualization and
analysis of the complex dependencies among the variables, we use a factor graph to represent the
states, observations and the functions bridging these variables, as illustrated in Figure 4.
A factor graph has two types of nodes, variable node for each variable and function node for
each local function, which are indicated by circles and squares, respectively. The edges in the graph
represents the “is an argument of” relation between variables and local functions. For example, the
function
Tk
has four arguments,
zk
,
zk−1
,
mk−1
and
mk
. Three types of local functions are involved in
our model:
•Tk(zk
,
zk−1
,
mk
,
mk−1) = p(zk|zk−1
,
mk
,
mk−1)
: transition model, or the prior information on the
state evolution over time. Inspired by Variable Structure Multiple Model Estimator in [
23
], we
propose CDKM to capture the context-dependent characteristics of occupants’ motion in the
indoor space.
•Ok(zk
,
yk) = p(yk|zk)
: observation model, or how the unknown states and sensor observations
relate. We will introduce PSMM where the relationship between locations and sensor observations
is characterized by certain conditional probabilities and multiple sensor observations are combined
via Bayes’ theorem.
Sensors 2016,16, 472 7 of 19
•Ck(zk,mk): characteristic function that checks the validity of the correspondence between zkand
mkusing the contextual floormap.
Note that the prior knowledge abstracted from the floormap is inherently accommodated to
this problem by defining characteristic function and parameterizing the transition model as will be
elaborated in the following section.
zk−1
yk−1
yk
yk+1
zk
zk+1
mk−1
mk
mk+1
Ck1
Ck
Ck+1
Ok1
Ok
Tk
Tk+1
Ok+1
Figure 4.
A factor graph model representation of the dependencies among location, velocity, context
and observation.
3.2. Context-Dependent Kinematic Model
We assume that given
zk−1
,
mk−1
and
mk
, the current position/velocity
zk
follows a Gaussian
distribution, of which the mean and covariance matrix are specified as
p(zk|zk−1,mk,mk−1)∼ N(F(mk−1,mk)zk−1,GQ(mk−1,mk)G0)(2)
The equivalent state space model of Equation (2) is given by
zk=F(mk−1,mk)zk−1+Gv(mk−1,mk)(3)
v(mk−1,mk)∼ N(0, Q(mk−1,mk))
where F(mk−1,mk)∈R4×4determines the mean of the distribution of the next state. Let adenote the
acceleration, we have the following kinematic equations,
xk=xk−1+˙
xk−1T+1
2aT2(4)
˙
xk=˙
xk−1+aT (5)
where
T
is the sampling period. We will assume constant velocity in this paper, and model
a
as a
Gaussian noise term. If we manipulate Equations (4) and (5) into matrix forms, then it can be identified
that F(mk−1,mk)has two possible values corresponding to moving or remaining static,
F0=
1 0 T0
0 1 0 T
0 0 1 0
0 0 0 1
,F1=
1000
0100
0000
0000
(6)
F1
imposes the velocity component of the state
zk
to be zero and
F=F1
when the context remains
to be static space, i.e.,mk−1=mk=SS; otherwise, F=F0.
Sensors 2016,16, 472 8 of 19
The matrix Gis given by
G=
T2/2 0
0T2/2
T0
0T
(7)
Q(mk−1
,
mk)
stands for the process noise and, as the notation indicates, it is also a function
of the context transition from
k−
1 to
k
. We will adopt the concept of directional noise to handle
the constraints imposed by the contextual map. To see this, note that occupants in the free space
(
mk−1=mk=FS
) can move in any direction with equal probability, therefore using equal process
noise variance in both xand ydirection, i.e.,
Q0="σ2
f0
0σ2
f#(8)
For occupants moving on the constrained space (
mk−1=mk=CSi
,
∀i=
1,
···
,
R
) such as
corridors, more uncertainty exists along than orthogonal to the corridor. Denote the variances along
and orthogonal to the corridor by
σ2
a
and
σ2
o
(
σ2
a>σ2
o
), respectively, and the canonical direction of the
constrained space
CSi
is specified by the angle
φi
(measured clockwise from y-axis). Then the process
noise covariance matrix corresponding to the motion in the constrained space is given by
Qi="−cos φisin φi
sin φicos φi#" σ2
o0
0σ2
a#" −cos φisin φi
sin φicos φi#(9)
The preceding model specification incorporates the scenarios where the context remains the same
during the time interval
[k−
1,
k]
and the occupant will keep the motion type defined by the two
identical contexts. On the contrary, if the context switches during the time interval
[k−
1,
k]
, we will
assume a free motion pattern, i.e.,
F=F0
,
Q=Q0
. Table 2summarizes our model given all possible
context transitions.
Table 2. Context-dependent kinematic models.
Context Transition Model Specification
F(mk−1,mk)Q(mk−1,mk)
mk−1=mk=FS F0Q0
mk−1=mk=CSiF0Qi
mk−1=mk=SS F1Q0
mk−16=mkF0Q0
3.3. Probabilistic Sensor Measurement Model
We construct probabilistic models for each sensor and multisensor fusion can be performed via
Bayes’ rule. Assuming that
Ns
different sensors function independently, then the observation model
p(yk|zk)can be factored as
p(yk|zk) =
Ns
∏
n=1
p(yn
k|zk)(10)
This actually forms a convenient and unified interface to combine distinctive sensor data by
projecting the heterogeneous measurements (
yn
) to the probability space via likelihood function,
p(yn|z)
.
If one more sensor is added into the system, then the observation model can be simply updated by
Sensors 2016,16, 472 9 of 19
multiplying the corresponding likelihood. Different likelihood functions requires being trained for
different types of sensors.
WiFi Measurement.
In the free space, the WiFi signal strength is a log linear function of the
distance between the transmitter and receiver. However, due to the multipath effect caused by
obstacles and moving objects in the indoor environments, the log linear relationship no longer holds.
Previous work has proposed to adding a Gaussian noise term to account for the variations arising
from the multipath effect; however, the simple model-based method can hardly guarantee a reasonable
performance in practice. Another popular way is to construct a WiFi database comprising WiFi
measurements at known locations to fingerprint the space of interest, but it requires onerous calibration
to ensure the accuracy. We propose a novel WiFi modeling method based on a relatively small WiFi
training set to accommodate for the complex variations of WiFi signals in the indoor space. The key
insight is to use Gaussian process (GP) to model the WiFi signal where the simple model-based method
provides a prior over the function space of GP.
We collect WiFi signal strength data at
Nw
reference points over the space and let
{lj
,
yj
w}Nw
j=1
denote the training dataset, where
lj
is a vector containing the distances of
j
th reference point to each
of the WiFi APs deployed in the field and
yj
w
is the observed WiFi signal strengths. Assume the WiFi
observations are drawn from the GP,
yw∼ GPµ(l),k(l,l0)(11)
where the mean function
µ(·)
is imposed to be a linear model with the parameters adapted to the
training samples. The covariance function k(·,·)takes the squared exponential form,
k(l,l0) = σ2
fexp(−1
2r2(l−l0)2) + σ2
n(12)
where
σ2
n
stands for the variance of the additive Gaussian noise term in the observation process, and
σ2
f
and
r
are the hyperparameters of the GP. These parameters can be tweaked according to the training
data, and we set
σn=
4,
σf=
2,
r=
5 in our experiments. At an arbitrary point
l∗
in the space of
interest, the posterior mean and variance of the WiFi signal y∗are
¯
y∗=µ(l∗) + K(l∗,L)[K(L,L) + σ2
nI]−1yw(13)
cov(y∗) = K(l∗,l∗)−K(l∗,L)[K(L,L) + σ2
nI]−1K(L,l∗)(14)
where
L
and
yw
are the vectors concatenated by
{lj}Nw
j=1
and
{yj
w}Nw
j=1
, respectively.
K(l∗
,
L)
denotes the
1
×Nw
matrix of the covariances evaluated at all pairs of training and testing points, and similarly for
the other entries
K(L
,
L)
and
K(L
,
l∗)
. In previous work using GP to model the WiFi signal strength [
24
],
the WiFi signal is assumed to follow the Gaussian distribution with the mean and variance given by
Equations (13) and (14), respectively. However, the posterior variance derived from GP is a indicator
of estimation confidence. It depends largely on the density of training samples in the vicinity of
the evaluated position. That is, if the evaluated point
l∗
happens to fall into the area that is densely
calibrated, then the posterior variance will be relatively small. The posterior variance derived from GP
cannot truly reflect the variations of WiFi signals over time. Therefore, instead of using the posterior
Variance (14) in classical predictive equations, we model the likelihood as
y∗∼ N(¯
y∗,σ2
n)(15)
Ultrasonic Measurement.
Essentially, each of the ultrasonic sensors in the ultrasonic station
can output the distance to the occupant passing in front of it. However, due to the missing data
and measurement noise, the distance measurement is not always steady. Here, we will consider the
Sensors 2016,16, 472 10 of 19
ultrasonic station to be a binary sensor to indicate the occupancy in its detection zone. To be specific,
the likelihood function is modeled as
p(yk<η|zkin the detection zone) = 1 (16)
where ηis the threshold for ultrasonic measurements.
3.4. Characteristic Function
The characteristic function imposes constraints on the correspondence between the position
and the context, and embodies the prior knowledge available from the floormap. In the preceding
section, we have defined a function
M
that sets up the relationship between the context and the
position/velocity, i.e.,
mk=M(zk)
, and
M
can be readily read out from the contextual map. We
thereby define the characteristic function to be
Ck(zk,mk) = I[M(zk)−mk=0](17)
where
I[·]
is an indicator function. In other words, the characteristic function enforces the local
correspondence defined by M.
4. Context-Augmented Particle Filter
In this section, we will discuss how to perform inference on the underlying factor graph of the
tracking problem we formulated previously. The particle filter is a technique for implementing a
recursive Bayesian filter by Monte-Carlo simulations [
25
]. The key idea of particle filter is to represent
the required posterior density function by a set of random samples or “particles” associated with
discrete probability mass, and compute the state estimate based on these “particles”. The original
particle filter proposed by Gordon et al. [
26
] was designed for a simple hidden Markov chain, which is
also a cycle-free factor graph, using the Sampling Importance Resampling (SIR) algorithm to propagate
and update the particles. However, the factor graph in our problem, as illustrated in Section 4, does
have cycles due to the introduction of the context variable, and only approximate inference algorithms
exist. We present a recursive approximate inference method for the cyclic factor graph by extending
the particle filter and the resulting algorithm is termed Context-Augmented Particle Filter (CAPF).
To see the operation of the CAPF, consider a set of particles
{zi
k−1
,
mi
k−1}N
i=1
that represents the
posterior distribution
p(zk−1
,
mk−1|y1:k−1)
of the state. Note that
mi
k−1
can be uniquely determined by
zi
k−1
via the characteristic function. At time
k
, we have some new measurement
yk
. It is required to
construct a new set of particles
{zi
k
,
mi
k}N
i=1
which characterizes the posterior distribution
p(zk
,
mk|y1:k)
.
Now, suppose we have an “oracle" that is capable of providing the context value
mi
k
of the corresponding
zi
keven before we generate zi
k’s, then our task is equivalent to draw samples from the distribution
p(zk|mk,y1:k)(18)
This can be carried out in two steps: First, the historical density
p(zk−1
,
mk−1|y1:k−1)
is propagated
via the transition model p(zk|zk−1,mk,mk−1)to produce the prediction density
p(zk|mk,y1:k−1) = Zp(zk|zk−1,mk)p(zk−1|y1:k−1)dzk−1(19)
where
p(zk|zk−1
,
mk) = p(zk|zk−1
,
mk
,
mk−1)
since
mk−1
is completely determined conditioning on
zk−1
. Second, our interested density
p(zk|mk
,
y1:k)
can be updated from the prediction density using
Bayes’ theorem,
Sensors 2016,16, 472 11 of 19
p(zk|mk,y1:k) = p(yk|zk)p(zk|mk,y1:k−1)
p(yk|y1:k−1,mk)(20)
=γp(yk|zk)p(zk|mk,y1:k−1)(21)
where
γ
is a normalization constant. Thus, Equations (19) and (20) form a recursive solution to
Equation (18). In particle filter framework, the aforementioned prediction and update steps are
performed by propagating and weighting the random samples.
Prediction Step. In the prediction phase, we generate the predicted particles by
ezi
k∼p(zk|zi
k−1,e
mi
k,mi
k−1)(22)
where
{e
mi
k}N
i=1
is a set of particles representing the estimates of
mk
produced by the “oracle”. Given
the different possible values of
mi
k−1
and
e
mi
k
,
ezi
k
will be sampled from different models, detailed in
Table 2. We will then perform sanity check on newly generated particles, where the particles
ezi
k
absent
from the reachable set of zi
k−1will be eliminated.
Update Step.
To update, each predicted particle
ezi
k
is assigned with a weight proportional to
its likelihood.
e
wi
k=p(yk|ezi
k)(23)
The weight is then normalized by
wi
k=e
wi
k
∑N
i=1e
wi
k
(24)
We resample
N
times with replacement from the set
{ezi
k}N
i=1
using weights
{wi
k}N
i=1
to obtain a
new set of samples
{zi
k}N
i=1
such that
p(zi
k=ezi
k) = wi
k
. Correspondingly, the contexts
mi
k
’s are obtained
through the characteristic function, i.e.,
mi
k=M(zi
k)(25)
“Oracle” Design.
The oracle is supposed to be able to answer the query about the next
possible contexts
mk
, based upon which the position/velocity component of the state can be properly
propagated according to different transition models. For computational efficiency, we adopt a simple
discriminative model to produce
e
mk
’s. Given a small database of WiFi fingerprints, we apply the
K-Nearest Neighbors (K-NN) algorithm and a modified distance weighted rule to generate an empirical
distribution of the context. To be specific, let the WiFi database be denoted by
{(mj
,
yj
w)}Nw
j=1
, and
Nw
is
the number of WiFi fingerprints. When the new WiFi observation
yk
is querying the possible contexts,
the
K
nearest neighbors of
yk
are found among the given training set. Let these
K
nearest neighbors
of
yk
, with their associated context, be given by
{(mj0
,
yj0
w)}K
j0=1
. In addition, let the corresponding
distances of these neighbors from
yk
be given by
dj0
,
j0=
1,
···
,
K
. The weight attributed to the
j0
th
nearest neighbor is then defined as
e
qj0=dK−dj0
dK−d1,j0=1, ··· ,K(26)
We then normalize the weights,
qj0=e
qj0
∑K
j0=1e
qj0
, and sample the context according to the following
discrete probability distribution,
Sensors 2016,16, 472 12 of 19
P(e
mk=mj0) = (qj0(1−α) + α,mj0=mk−1
qj0(1−α),mj06=mk−1
(27)
where
α
is a context resilience factor and
α∈[
0, 1
]
. We incorporate
α
to accommodate for the prior
knowledge that the context will not change too often and to make the “oracle” more robust to the
observation noise. Moreover, for the particles on the boundary of distinctive contexts,
e
mk
is equally
probable to be these contexts. The pseudo-code of the CAPF algorithm is provided in Algorithm 1.
Algorithm 1 Context-Augmented Particle Filter
function CAPF(y1:T,wi f i_database,reachable_set)
Initialization:
Uniformly generate Nsamples {zi
0}N
i=1
Set mi
0=M(zi
0),wi
0=N−1,i=1, ··· ,N
for k=1, ··· ,Tdo
for i=1 : Ndo
Context Estimate:
if zi
k−1on the boundary of {mb}B
b=1then
Uniformly sample e
mi
kfrom {mb}B
b=1
else
Sample e
mi
kfrom Equation (27)
end if
Prediction Step:
ezi
k∼p(zk|zi
k−1,e
mi
k,mi
k−1)
Discard particles ezi
k6∈ reachable_set(zi
k−1)
Update Step:
Compute weight e
wi
k=p(yk|ezi
k)
end for
Normalize weights: wi
k=e
wi
k
∑N
i=1e
wi
k
Resampling:
Select Nparticle indices i0∈ {1, ··· ,N}according to weights {wi
k}N
i=1
Set zi
k=ezi0
kand wi
k=N−1
Set mi
k=M(zi
k)
Estimate:
ˆzk=∑N
i=1wi
kzi
k
end for
return ˆz1:T
end function
5. Performance Evaluation
Our experiment was carried out in the Singapore–Berkeley Building Efficiency and Sustainability
in the Tropics (SinBerBEST) located in CREATE Tower at the National University of Singapore campus,
which is a typical office environment consisting of cubicles, individual offices, corridors and obstacles
like walls, desks, etc. The total area of the testbed is around 1000 m
2
. There are 10 WiFi routers and
four ultrasonic stations deployed in the testbed in total. We utilize TP-LINK TL-WDR4300 Wireless
N750 Dual Band Routers (manufactured in Shenzhen, China) as WiFi APs and HC-SR04 Ultrasonic
Sensors (manufactured in Shenzhen, China) as the components of ultrasonic stations. The floormap
and the corresponding contextual map are shown in Figure 5. Different contexts are colored differently
in the contextual map. The static space contains the seating areas in the cubicles and offices, where
occupants hardly move. The corridors of horizontal and vertical directions are considered to be
two types of constrained spaces (HCS and VCS, respectively). The free space includes the open areas
where occupants can freely move. We seek to answer the questions including how well MapSentinel is
Sensors 2016,16, 472 13 of 19
able to track the occupant, and whether the map information exploited by way of MapSentinel can
bring additional benefits to the tracking performance.
WiFi Routers
Ultrasonic Stations
Ground Truth Walking Trajectories
45.6 m
31.1 m
2
1
3
FS
SS
Vertical CS (VCS)
Horizontal CS (HCS)
Obstacle
Figure 5.
The floormap (
top
) and corresponding contextual map (
bottom
) of the testbed. Four different
contexts (FS, SS, VCS, HCS) are defined and color coded as illustrated in the legend.
Experimental methodology.
In a real-world setting, we expect the occupant to carry the
smartphone as they walk through various sections of an indoor space. Moreover, occupants are
unlikely to walk continuously; they would walk between locations of special interest and dwell at
certain locations for a significant length of time. Our experiment aims at emulating these practical
scenarios in an office environment and incorporating all the contexts defined in our model. Therefore,
the following routes were designed as the ground truth for evaluation: (1) A enters the office from
the front gate and walks through the corridors to find her colleague (different CSs are included);
(2) B enters the office from the side door, walks to her own seat, stays there for a while and exits the
office from the front gate (CSs, SS are included); (3) C enters the office from the front gate, walks
through corridors, takes some time at her office and goes to the open area (CSs, SS, FS are included).
We asked the experimenter to behave as usual when walking in the space. At the same time, the WiFi
APs and ultrasonic stations constantly collect the measurements and send them to the central server.
Sensors 2016,16, 472 14 of 19
To obtain the ground truth at the sampling time of the tracking system, we mark the ground with a 1 m
grid on the pre-specified route and ask the experimenter to create lap times with a stopwatch when
happening to be on the grid. By recording the starting time of the experiment, we can obtain the time
stamp of each grid and then interpolate the ground truth at the sampling time.
Does the “oracle” work?
The current context estimation done by the “oracle” is critical to the
CAPF algorithm, as the tuple of the current and previous context jointly steer the states in our model.
Here, we would like to evaluate the context prediction performance of the “oracle” we constructed in
light of several design rules presented in the Section 4. Figure 6illustrates the result of the context
estimation for different walks. Since the context estimates are represented by a set of particles in the
algorithm, we visualize the context estimate by the purple lines centered at the possible contexts,
and the lengths of the purple lines are scaled by the proportions of the particles of different contexts.
Ideally, the purple cloud should scatter around the ground truth context. Figure 6suggests that
the estimates given by the “oracle” can generally capture the ground truth. Evidently, the context
estimate is not perfect, especially for the static space (SS). However, these approximate “ground truths”
essentially present other possibilities of the current context and avoids particles trapping in the static
space. We define the context estimation accuracy to be the ratio of the number of particles with correct
context estimate to the total number of particles. The context estimation accuracy is calculated for
each time step of the experiments, and the empirical distribution of the context estimation accuracy is
illustrated in Figure 7, where the mean accuracy is 52.41%. With this noisy “oracle”, the system can
achieve median tracking error of 1.96 m, while the tracking error would be 1.84 m if a perfect “oracle”
was utilized. Therefore, our work has the potential to be further improved with a more advanced
“oracle” design.
FS
HCS
VCS
SS
Time
1st Walk 2nd Walk 3rd Walk
Ground Truth of Contexts Estimate of Contexts
Figure 6.
The context estimate produced by the “oracle" versus the ground truth context. The radius of
the purple cloud is proportional to the number of particles of the estimated context which the cloud is
centered around.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Context Estimation Accuracy
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Frequency
Normalized Histogram of Context Estimation Accuracy
Figure 7.
Normalized histogram of context estimation accuracy of the “oracle”. The mean accuracy
is 52.41%.
Sensors 2016,16, 472 15 of 19
Figure 8demonstrates some snapshots of the CAPF algorithm in progress. At the beginning,
the particles are initialized to be uniformly distributed in the space. In addition, the spread of the
particles shrinks as the new WiFi observations come. When the ultrasonic station reports a detection,
the particles are concentrated in the corresponding detection zone. As the occupant exits the detection
zone, the particles spread out along the direction of the corridor. When the occupant sits in the
cubicle, the particles distribute over the seating area as well as some possible routes through which
the occupant might leave the seating area. The particles distribute evenly along different directions
when the occupant is moving in the free space, in which case our model is identical to the traditional
constant velocity dynamic model for the particle filter.
(a) t=0. Initialization. (b) t=3. Particles shrink. (c) t=
5. Passing the
ultrasonic station.
(d) t=
15. Moving in the
constrained space.
(e) t=
53. Seating in the
static space.
(f) t=
205. Moving in the
free space.
Figure 8.
The snapshots of the intermediate steps of the CAPF algorithm visualized. The location
estimate, ground truth location, particles are presented by the red cross, blue circle, green dots,
respectively. As before, the black square and white triangles give the positions of WiFi routers and
ultrasonic stations.
MapSentinel’s tracking performance.
We aggregate the data from different walks and compare
the performance of MapSentinel against the fusion system of WiFi and ultrasonic station without
leveraging the floormap information, as well as the purely WiFi-based tracking system. The tracking
error distributions are depicted in Figure 9. As can be seen, the MapSentinel achieves an essential
performance improvement, 31.3% over the WiFi tracking system and 29.1% over the fusion scheme.
Note that adding the ultrasonic calibration into the WiFi system is able to realize a small amount of
accuracy increment. Due to the high degree of uncertainty of WiFi signals, the effect of ultrasonic
calibration will not last for long. The map information elongates the effect of the ultrasonic calibration
via imposing additional constraints to the motion, and that is why MapSentinel greatly enhances the
tracking performance compared with the purely WiFi-based system. We also evaluate the tracking
performance in different contexts, and the result is shown by boxplots in Figure 10. Here, “without
map” means using the WiFi and ultrasonic sensing systems without taking into account the reachable
set as well as the context-dependent kinematic model. A unified dynamical model, the free space
model, is applied in this case, and a traditional particle filter is implemented to estimate the location.
Sensors 2016,16, 472 16 of 19
As can be readily read from the figure, the MapSentinel performs better in all contexts. More significant
increase is achieved in constrained spaces and static spaces, as expected.
Tracking Error (m)
0123456789
CDF
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1MapSentinel
WiFi+US
WiFi
Figure 9.
Tracking performance of MapSentinel, the fusion system of WiFi and ultrasound sensor, the
pure WiFi system. The median tracking accuracy of the MapSentinel is 1.96 m, MapSentinel can achieve
the performance improvement of 31.3% over the purely WiFi-based tracking system, 29.1% over the
fusion system.
Context-wise Tracking Error
Figure 10. Tracking error in different contexts for the MapSentinel and the WiFi+Ultrasound system.
Figure 11 compares the performance of tracking systems with distinctive floormap usage.
MapSentinel exploits the floormap information in two folds: first, MapSentinel integrates the context
information into the kinematic model, and the movement patterns of people on different locations of
the map are better captured. Secondly, MapSentinel takes into account the speed restrictions as well
as physical obstacles in the indoor space by checking if the particles fall inside the reachable set at
each time step. The second fold of the floormap information has been widely utilized in the previous
work, while the context information is less explored. We therefore compare the tracking error of our
system with the one that merely uses the reachable conditions. Figure 11 shows that incorporating
information about physical constraints, as the previous work did, is surely beneficial to the tracking
system. Particularly, the performance can be further improved by 19.8% by introducing the context
information into the tracking system.
Sensors 2016,16, 472 17 of 19
0 1 2 3 4 5 6 7 8 9
Tracking Error (m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CDF
MapSentinel (Context+RSC)
RSC
w/out Map
Figure 11.
Tracking performance of different usage of floormap information. “RSC” stands for reachable
set check. MapSentinel extracts the context information from the floormap, and simultaneously
eliminates the particles falling outside the reachable set. MapSentinel is compared with the tracking
system without using context information (i.e., only performing RSC) and the one without using the
map information at all. The median tracking errors of MapSentinel, the system only performing RSC,
and the one without exploiting the floormap information are 1.96 m, 2.44 m and 2.77 m, respectively.
To better understand how the map helps improve the location estimation, we demonstrate the
velocity estimation of different tracking schemes in Figure 12. Typically, the occupants will not perform
complex motions in the indoor space due to the constraints of the wall and other barricades. The more
the velocity estimate deviates from the canonical directions defined by the indoor environment, the
worse the tracking performance can be. Using the fusion schemes of WiFi and ultrasonic calibration,
only the location is the observable state. The velocity estimates depend largely on the location
estimate and it has little effect in smoothing out the location estimate. Hence, extensive research has
been focusing on using inertial measurements to perform dead reckoning, which makes the velocity
observable. Analogously, the MapSentinel creates a virtual inertial sensor for the occupant, which
mimics the actual inertial sensor to provide the possible walking speed and directions. As is shown in
Figure 12, the velocity estimation without map information tends to point to any direction while the
MapSentinel constrains the velocity via the context-dependent kinematic model.
MapSentinel
w/out Map
Velocity Estimate w/ or w/out Map Information
Figure 12.
The velocity estimation for the MapSentinel and the WiFi+Ultrasound system. The vector
indicates the speed and direction of the estimated motion.
Sensors 2016,16, 472 18 of 19
6. Conclusions
This paper presents MapSentinel, a system for real-time location tracking that emphasizes both
non-intrusiveness and accuracy. The non-intrusive sensing networks comprise the modified WiFi
access points and the ultrasonic calibration stations. The MapSentinel makes novel attempts to exploit
the floormap information by categorizing the indoor space into different contexts to capture the
diversity of typical motion characteristics. This mimics having an inertial sensor attached to the
occupant to obtain the knowledge of velocity. We formalize the fusion of floormap information as well
as the noisy sensor readings using the Factor Graph, and develop the Context-Augmented Particle
Filtering algorithm to efficiently solve real-time walking trajectories. Our evaluation in the large typical
office environment shows that MapSentinel can achieve the performance improvement of 31.3% over
the purely WiFi-based tracking system. MapSentinel is among the early attempts to obviate the need
for the inertial sensors in indoor tracking, and our results are promising.
For future work, we would like to explore multiple occupant tracking. The ultrasonic sensor
is essentially anonymous and cannot identify the occupant entering its detection zone. The WiFi
access points are able to identify the occupant from the MAC address of the mobile device and can
approximately tell which occupant is approaching the ultrasonic station. The ultrasonic calibration
will work if the occupant can be identified with the MAC information without ambiguity; however,
if the identity of the occupant within the range cannot be uniquely determined, as in the crowded
scenario, the calibration may not work effectively. Further work to reliably track multiple occupants is
necessary. Moreover, we would like to integrate our tracking method to the control of lighting and
ventilation systems to improve energy efficiency of buildings.
Acknowledgments:
This research is funded by the Republic of Singapore’s National Research Foundation through
a grant to the Berkeley Education Alliance for Research in Singapore (BEARS) for the Singapore–Berkeley Building
Efficiency and Sustainability in the Tropics (SinBerBEST) Program. BEARS has been established by the University
of California, Berkeley as a center for intellectual excellence in research and education in Singapore.
Author Contributions:
Ruoxi Jia proposed the information fusion framework; Ruoxi Jia, Ming Jin, Han Zou
and Yigitcan Yesilata conducted the experiment. Lihua Xie and Costas Spanos supervised the work and revised
the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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