Pedestrian Localisation for Indoor Environments
Oliver Woodman
Computer Laboratory
University of Cambridge
ojw28@cam.ac.uk
Robert Harle
Computer Laboratory
University of Cambridge
rkh23@cam.ac.uk
ABSTRACT
Location information is an important source o f context for
ubiquitous computing systems. This paper looks at how a
foot-mounted inertial unit, a d etailed building model, and
a particle filter can be co mbined to provide absolute posi-
tioning, despite th e presence o f drift in the inertial unit and
without knowledge of the user’s initial location. We show
how to handle multiple floors and stairways, how to handle
symmetry in the env ironment, and how to initialise the local-
isation algorithm using WiFi signal strength to reduce initial
complexity.
We evaluate the en tire system experimentally, using an inde-
pendent tracking system for ground truth. Our results show
that we can track a user throughout a 8725 m
2
building span-
ning three floors to within 0.5 m 75% of the time, and to
within 0.73 m 95% of the time.
ACM Clas sification Keywords
D.2.8 Mathematics of Com puting: Probability and Statis-
tics—probabilistic algorithms
General Terms
Algorithms, measurement, experimentation
Author Keywords
Inertial tracking, particle filters, loca lisation
INTRODUCTION
Some of the first ubiquitous computin g systems to come out
of research labor atories made use of lo cation information
to provide useful clu es as to the context a person or device
was situated within. Today, GPS provides localisation out-
doors, but precise indoor tracking o f people remains an open
research problem. We have seen indoor location systems
based on infra-red, ultrasoun d, narr owband radio, WiFi sig-
nal strength, UWB, vision, and many others [11]. However,
few can be easily deployed over large buildings whilst still
providing accurate localisation.
c
ACM, (2008). This is the author’s version of the work. It is posted here
by permission of ACM for your personal use. Not for redistribution. The
definitive version was published in UbiComp’08
UbiComp’08, September 21-24, 2008, Seoul, Korea.
To minimise deployment and infrastructur e costs, we wish
to develop a wearable location system that can position itself
absolutely within a complex structure. The imme diate paral-
lel is with robotics, where mobile devices typically use iner-
tial sensors, laser range-finders and computer vision to pro -
vide accurate localisation without the requirement of fixed
infrastructure. A pplying the same systems to peo ple is, how-
ever, fraught with difficulties; laser range-finders and cam-
eras are impractical, we lose the ability to control the sub-
ject to maximise our chances of precise lo c alisation, and the
techniques are usually developed with a single floor in mind
(and ce rtainly no stairs!). One type o f sensor which does
seem applicable to people tracking is inertial measurement
units (IMUs). Recent advances in micro-electro-mechanical
systems ( MEMS) technologies have made such units smaller
and cheape r, however also m ore prone to e rror. Accurate
people tracking in a general environment using small and
wearable inertial sensors has yet to be reliably shown, al-
though previous attempts have been made [8, 9].
In this paper we demonstrate how to locate and track a per-
son in a building for which we have an accurate model, us-
ing an off-the-shelf wearable inertial system and a particle
filter to tac kle the traditional drift problems associated with
inertial trac king. With this setup, we find that we are able
to track a person throughout a 8725 m
2
building to within
0.73 m 95% of the time, all without the user providing any
explicit initialisation information. Sin ce the system requires
very little fixed infrastructure, the monetary cost is propor-
tional to the number of users, rather than to the coverage area
as is the case for traditional indoor location systems. We
propose that such a system could be used to enable the de-
ployment of location-aware applications in large buildings,
where the installation of a high accuracy absolute location
system is either too expensive or impractical.
The structure of this paper is as follows. We first review rel-
evant literature a nd how a foot-mounted IM U might be used
to provid e a sequence of relative lo cations. We the n dis-
cuss a compu ta tional model for the representation of build-
ings, and how such models ar e inpu t to our particle filter,
along with the relative locations, to derive absolute posi-
tions. We discuss how to g ather initialisation information
autonomously, and describe a WiFi-based scheme to reduce
the computational overheads involved at the start of the lo-
calisation process. Finally, we evaluate our system exper-
imentally, by quantitatively comparing it with an indepen-
dent, high -accuracy tracking system installed in the build-
ing.
RELATED WORK
Localisation is a problem often encountered in mobile robots,
where sensor-based localisation has been recognised as a key
problem [ 7]. In the robot localisation problem a robot is
placed at an unknown lo c ation in a known enviro nment. By
sensing the environment the robot must determ ine its abso-
lute location. Robots used in localisation research typically
sense their environment using a laser range-finder, which
measures the distance to the nearest obstruction in the di-
rection in which it is pointed.
Solutions to the robot localisation problem have been imple-
mented using b oth grid [4] and p article-based [7] Baye sian
filters. Both are able to track the multimodal d istributions
that often arise durin g localisation due to symmetry in the
environment. Particle filters are preferred beca use they re-
quire significantly less computation and have a smaller mem-
ory footprint than comparable grid-based filters [7].
There are severa l differences between robot and pedestrian
localisation as presented in this paper. Firstly, the robots
used in existing literatur e have bee n unable to climb stairs.
As a result, a 2-dimensional map of the envir onment has
been sufficient. Secondly, the movement of a robot can be
actively controlled. This is clearly not possible in a pedes-
trian localisation sy stem. Thirdly, robot localisation is typ-
ically solved k nowing both the relative movement of the
robot and me asurements obtained from a laser range finder.
In contrast, we use only relative movement information (in
the form of step events) to solve the pedestrian localisation
problem.
Aside from their use in robot localisation, particle filters
have also been a pplied in absolute lo cation systems. Most
notable are The Location Stack [10, 12] and Placelab [13],
which use particle filters to update the location of a user
based on measurements received from a variety o f different
sensor systems. This work differs to our approach because
they deal with absolute measurements and do not use the
environment to constrain the user’s movement. In contrast
we use relative lo cation info rmation and environmental con-
straints to locate and track a user.
TRACKING USING A FOOT MOUNTED IMU
An IMU contains three orthogonal rate-gyroscopes and ac-
celerometer s, which report angular velocity and acceleration
respectively. In principle, it is possible to track the orienta-
tion of the IMU by integrating the angular velocity signals.
This can then be used to resolve th e acceleration samples
into the global frame of refer ence, from which acce leration
due to gr avity is subtracted. The remaining acceleration can
then be integrated twice to track the position of the IMU rel-
ative to a known starting point and heading [18].
Unfortu nately the error, or ‘drift’ in th e calculated position
grows rapidly w ith time. The main cause of drift is small er-
rors perturbing the gyroscope signals, wh ic h cause gr owing
tilt errors in the tracked orientation. A small tilt error causes
a compone nt of ac celeration due to gravity to be projecte d
onto the globally horizontal axes. This residu al is double in-
Figure 1. A foot mounted IMU trace (dashed red line) obtained by
descending a flight of stairs, and the corresponding step events (solid
black lines separated by dots) reported by the inertial navigation com-
ponent. Grid size = 1 m
2
.
tegrated, causing an e rror in position which grows cubically
in time in the shor t term [8]. The drift inc urred by a high end
MEMS IMU will typically exceed 100 metres after 1 minute
of operation [19].
For f oot-mounted IMUs the cubic-in-time drift problem can
be reduced by detecting whe n the foot is in the stationary
stance phase (i.e. in contact with the ground) during each
gait cycle. Zero velocity updates (ZVUs) can be applied dur-
ing this phase, in which the known direction of acceleration
due to gravity is used to correct tilt errors wh ich have accu-
mulated during the previous step. The applicatio n of such
constraints replaces the cubic-in-time error growth with an
error ac cumulation that is linear in the number of steps [8].
The detection of stationary stance phases an d the a pplica-
tion of ZVUs is documented extensively in the literature [8 ,
3, 15, 9] and hence is not discussed further here.
In this paper we consider the inertial navigation component
to be a black box . This component performs inertial navi-
gation (with ZVUs), and segments the integrated trace into
step events corre sponding to strides taken by the pedestrian,
as shown in Figure 1. The i
th
step event is rep orted as a tuple
u
i
= (l, δz, δθ) (1)
in which l is the horizontal step length, δz is the change in
height over the step, and δθ is the change in heading between
the pr evious and current steps. The pedestrian localisation
problem is then to use these (noisy) step events to determine
and track the absolute position of the user in a known envi-
ronment, as shown in Figure 2. Note that the initial position
and orientation of the user are unknown.
Figure 2. The pedestrian localisation problem: To determine the abso-
lute location of a pedestrian given a path of step events describing their
relative movement, and a map of the environment.
2.5D BUILDING REPRESENTATION
There are many obstacles th a t limit the possible movement
of a pedestrian within a building. In pa rticular walls are im-
passable obstacles.
In order to enforce such constraints it is ne cessary to have a
computer-readable plan of the building. Since it is rea son-
able to assume that a pedestrian’s foot is constrained to lie
on the floor during the stance phase of th e gait cycle, a 2.5-
dimensional description of the building (in which each ob-
ject has a vertical position but no depth) is sufficient. Hence
we define a map to be a collection of plan ar floor polygons.
Each floor polygon corresponds to a surface in the building
on which a pedestrian’s foot may be grounded. Each edge of
a floor polygon is either an impassable wall or a connection
to the edge of another polygon. Connected e dges must coex-
ist in the (x,y) pla ne, however they may be separated in the
vertical direction to allow the representation of stairs. It is
possible to represent even complex rooms using this format,
such as the lecture theatre shown in Figure 3.
The use of a 2.5D format avoids the additional complex-
ity that would be required to construct and use a fully 3-
dimensional map.
PARTICLE FILTERS
Bayesian filters probabilistically estimate the state of a dy-
namic system based on noisy measurements. A Bayesian
filter represents its belief about a system at time t as a prob-
ability distribution over the state space
Bel(s
t
) = p(s
t
|z
1
, ..., z
t
) (2)
where s
t
is a state and z
1
, ..., z
t
are no isy measurements
made up to (and including) time t.
Under the Markov assumption Bel(s
t
) can be calculated by
Figure 3. The 2.5D representation of a lecture theatre. The edges sepa-
rating adjacent rows of seating are considered as walls (solid blue lines),
whereas the edges between stairs in the aisle are connections (dashed
green lines). Grid size = 1 m
2
.
updating Bel(s
t−1
), allowing a Bayesian filter to track the
state of a dynamic system through time. To do this the belief
is first propagate d according to a m otion model; a probabil-
ity distribution wh ic h defines the possible transitions from
one state to the next. Th e propaga te d belief is then corrected
using measurements of the system. Each measurement has
a corresponding measu rement model; a probability distribu-
tion defining the likelihood of observing the measurement
given that the system is in a particular state at the same point
in time.
To update th e belief it is first propagated forward according
to a motion model p(s
t
|s
t−1
, c
t
) to obtain the prior:
Bel
−
(s
t
) =
Z
p(s
t
|s
t−1
, c
t
)Bel(s
t−1
) ds
t−1
. (3)
where c
t
is control information describing the transition from
the previous to the current state (for pedestrian localisation
step events can be used). Th e updated posterior is calculated
from the prior as
Bel(s
t
) = α
t
p(z
t
|s
t
)Bel
−
(s
t
) (4)
where p(z
t
|s
t
) is th e measurement model corresponding to
the measurement z
t
, and α
t
is a normalisation factor.
Particle filters approximate the posterior d istribution as a set
of weighted samples (‘particles’)
S
t
= hs
i
t
, w
i
t
i i = 1, ..., n (5)
where s
i
t
is the state and w
i
t
is the weight of the i
th
particle.
A par ticle filter update co nsists of genera ting the set S
t
from
the previous posterior S
t−1
. Each new particle hs
j
t
, w
j
t
i is
generated as follows [5] :
1. Re-sampling: Sample a state s
i
t−1
from the prior S
−
t
ac-
cording to the distribution defined by the weights w
i
t−1
.
2. Propagation: Sample s
j
t
from the motion model distribu-
tion p(s
t
|s
i
t−1
, u
t
), where s
i
t−1
is from the re-sampling
step.
3. Correction: Sample w
j
t
from the measurement model
distribution p(z
t
|s
j
t
), wh ere z
t
is the measurement re-
ceived at time t.
This procedure is repeated n times, where n is the number
of particles in the new posterior. T he value o f n can be fixed
or varied at each step according to an adaptive resampling
scheme.
In our loc a lisation f ramework each particle has a state s
t
at
time t
s
t
= (x
t
, y
t
, θ
t
, poly
t
) (6)
where (x
t
, y
t
) is the horizontal position, θ
t
is the heading
and poly
t
is the floor polygon to which the par ticle is cur-
rently constrained. Since the particle is defined to lie on the
surface of poly
t
, it is not ne cessary to explicitly store the
vertical position of the particle in the state vector.
We now outline in detail the prop agation, correction and re-
sampling steps used by our localisation filter.
Particle propagation
The prop agation step g e nerates the state s
t
of a new particle
by sampling fro m the motion model distribution p(s
t
|s
t−1
, c
t
),
where s
t−1
is a previous state selected during resampling
and c
t
= u
t
is the step event for the interval (t − 1,t).
First, w e perturb the step according to an uncertainty model,
which describes unc ertainty that has built up over the step
due to noise perturbing the IMU measurements. We u se a
simplified mo del in which it is a ssumed that both the length
and the change in heading of the step are perturbed by Gaus-
sian ra ndom variables, drawn from N
0,σ
l
and N
0,σ
θ
respec-
tively. The deviations were chosen e mpirically to be σ
l
=
0.15 m a nd σ
θ
= 0.6
◦
. The perturbed step parameters are
l
′
= l + X (7)
δθ
′
= δθ + Y (8)
where X and Y ar e drawn from N
0,σ
l
and N
0,σ
θ
respectively.
The new heading an d position are then calculated from the
previous state and the perturbed step parameters:
θ
t
= θ
t−1
+ δθ
′
(9)
x
t
= x
t−1
+ l
′
· cos θ
t
(10)
y
t
= y
t−1
+ l
′
· sin θ
t
(11)
It is also necessary to de termine the floor polygon poly
t
to
which the propgated particle is constrain e d. We initially as-
sume that the floor polygon in which the particle resides is
unchanged by the update:
poly
t
= poly
t−1
(12)
In order for the particle to have exited this floor polygon ,
the step vector must intersect one of its edges in the (x, y)
plane. Let A = (x
t−1
, y
t−1
) and B = (x
t
, y
t
) be th e start
and end poin ts of the step vector in the (x, y) plane. We find
the first intersection between
−−→
AB and the edges of poly
t
in
the (x,y) plane, using it to update poly
t
accordin g to one of
three cases:
1. No intersection point is found. The particle must still be
constrained to the same polygon.
2. The first intersection C is with a wall. In this case th e
particle’s weight should be set to equal 0 in the correction
step, enforcing the constraint that walls are impassable.
3. The first intersection C is with an edge connecting to an-
other polygon (given by GetDstPoly(C)). In this case
we update the current polygon
poly
t
= GetDstPoly(C) (13)
Since a single step may span multiple connections, the in-
tersection test is repeated between the remainder of the
step vector (
−−→
CB) and the updated polygon. This process
continues rec ursively until one o f the first two cases ap-
plies.
Particle correction
The c orrection step sets the weight w
t
of a propagated parti-
cle. We use this step to enforce wall constra ints. If a wall is
intersected during the propagation step used to generate the
state of the particle, then it is assigned a weight
w
t
= 0 (14)
If a wall is not intersected, th e particle is assigned a weight
based on the difference between the h eight change δz of the
current step and the d ifference in height between the start
and en d floor polygons. The height change according to the
map is given by
δz
poly
= Height(poly
t
) − Height(poly
t−1
) (15)
We assign the particle a weight
w
t
= N
0,σ
h
(|δz − δz
poly
|) (16)
where σ
h
was chosen empirically as 0.1 m. Here we are
using the change in height reported in the current step as a
measurement in the Bayesian framework. Particles whose
change in heig ht over the step closely matches the cha nge
in height reported in the step event a re assign e d stronger
weights. This allows localisation to occur quickly when the
user climbs or descends stairs. Particles wh ic h are not lo-
cated on stairs will have a height change δz
poly
= 0 accord-
ing to the map. This will not be close to the height cha nge re-
ported in the step event, causing the particles to be assigned
small weights relative to particles that are located on stairs.
This will make them less likely to be resampled, resulting in
rapid convergence of Bel(s) to stair regions.
The comb ined propagation and correction algorithm is shown
in Algorithm 1.
Algorithm 1 Update - Applies the propagation and corre c -
tion algorithms to generate a particle at time t from a sam -
pled state at time (t − 1).
1: procedure UPDATE(
s
t−1
= (x
t−1
, y
t−1
, θ
t−1
, poly
t−1
) ,
u
t
= (l, δz, δθ) )
// Model step noise
2: δθ
′
← δθ + X
3: l
′
← l + Y
// Calculate the new xy-position
4: θ
t
← θ
t−1
+ δθ
′
5: x
t
← x
t−1
+ l
′
· cos θ
t
6: y
t
← y
t−1
+ l
′
· sin θ
t
// Initialisation for the intersection algorithm
7: poly
t
← poly
t−1
8: A ← (x
t−1
, y
t−1
)
9: B ← (x
t
, y
t
)
10: done ← false
11: kill ← false
// Determine the new constraining polygon
12: while ¬done do
13: C ← Intersect(
−−→
AB, poly
t
)
14: if C = null then
15: done ← true
16: else if Type(C) = Wall then
17: // Note the wall intersection
18: kill ← true
19: done ← true
20: else if Type(C) = Connection then
21: poly
t
← GetDstPoly(C)
22: A ← C
23: end if
24: end while
// Correction step
25: if kill then
26: w
t
← 0
27: else
28: δz
poly
← Height(poly
t
) − Height(poly
t−1
)
29: w
t
← N
0,σ
h
(|δz − δz
poly
|)
30: end if
// Return the updated particle
31: return h(x
t
, y
t
, θ
t
, poly
t
), w
t
i
32: end procedure
Re-sampling
The number of particles need e d to represent Bel(s) to a
given level of accuracy depends on the complexity of the dis-
tribution, which can vary drastically over time. As a result it
can be highly inefficient to use a fixed number of particles.
This is particularly true for localisation prob lems, where the
number of p articles required to track an object a fter conver-
gence is typically only a small fraction of the number re-
quired to adequately describe the distribution in the early
stages of localisation [5].
Several sch emes have been proposed for dynamically adapt-
ing the number of particles used to represent th e distribution,
such as likelihood-based adaptation [7], Kullback-Leibler
divergence (KLD) sampling [5] and variants [17]. We u se
KLD-sampling in ou r framework since likelihood-based adap-
tation is not well suited for pr oblems where Bel(s) ca n be a
multimodal distribution, as is often the case during indoor
localisation due to symmetry in the environment [5].
The idea of KLD-sampling is to generate a number of par-
ticles at each step such that the approximation error intro-
duced by using a sample-based repre sentation of Bel(x) re-
mains below a specified threshold ǫ. KLD-sampling assumes
that the sample-based representation of the propaga te d be-
lief can be used as a n estimate for the posterior [6], an d that
the true posterior can be repre sented b y a discr e te piecewise
constant distribution consisting of a set of multidimensional
bins. Since the propagation step in our framework uses con-
trol information (in the form of step events), the propagated
belief is a reasonable estimate of the posterior. The second
assumption requires that we spec ify a bin size, which was
chosen empirically to be 1 m
3
in position and 10
◦
in head-
ing.
INITIALISATION AND LOCALISATION
To test our framework a hip-mounted ultra mobile PC (UMPC)
was used to log data obtained from a foot-mounted Xsens
Mtx IMU. The logs we re then postprocessed on a deskto p
machine. In the future we envisage that the system will con-
sist of only a fo ot-mounted component, containing the IMU,
battery, and WiFi capability to offload the data for real-time
processing.
Figure 4 shows an example application of our f ramework in
our lab, a three storey building with a floo r area of 8725 m
2
(93915 sqft). Figu re 4(a) depicts the route taken by th e pedes-
trian and th e steps generated by the inertial navigation com-
ponen t. Note that the trace has been manually aligned with
the map to have the correct initial location and orientation,
both of which are unknown to the loc alisation algorithm.
Figure 4(b) shows the initial collection of particles, drawn
from the prior Bel(s
0
). Since the initial location of the pedes-
trian is unknown, we use a uniform distribution over the en-
tire floor surface. The initial heading is also unknown, hence
the particle headings are distributed uniformily in all direc-
tions. Figure 4(c) sh ows the particles after the pedestrian has
taken five steps. Figures 4(d) and 4(e) show the distribution
just before and just after the pedestrian starts to descend a
flight of stairs. Note how the pedestrian is quickly lo calised
to stair regions due to the use of height change measurements
in the corr e ction step of the particle filter.
The example presented illustrates two prob le ms commonly
faced dur ing localisation tasks: symmetry of the e nviron-
ment and scalability.
Environmental symmetry
Symmetry in the environment can delay or prevent c onver-
gence to a single cluster of pa rticles. Rotational a nd transla-
tional symme try cause multimodal d istributions to a rise dur-
ing the localisation process. Such distributions consist of a