Wireless Indoor Localization with Dempster-Shafer Simple Support Functions

Wireless Indoor Localization with Dempster-Shafer
Simple Support Functions∗
Vladimir Kulyukin Amit Banavalikar John Nicholson
Computer Science Assistive Technology Laboratory
Department of Computer Science
Utah State University
Logan, Utah, U.S.A
{vladimir.kulyukin}@usu.edu

Abstract— A mobile robot is localized in an indoor envi-
ronment using IEEE 802.11b wireless signals. Simple support
functions of the Dempster-Shafer theory are used to combine ev-
idence from multiple localization algorithms. Emperical results
are presented and discussed. Conclusions are drawn regarding
when the proposed sensor fusion methods may improve perfor-
mance and when they may not.

Index Terms— localization, sensor fusion, Dempster-Shafer
theory

I. I NTRODUCTION
In May 2003, the Assistive Technology Laboratory of
the Department of Computer Science (CS) of Utah State
Univeristy (USU) and the USU Center for Persons with
Disabilities (CPD) started a collaborative project whose ob-
jective is to build an indoor robotic guide for the visually
impaired in dynamic and complex indoor environments, such
as grocery stores and airports. A proof-of-concept prototype
has been deployed in two indoor environments: the USU CS
Department and the USU CPD. The guide’s name is RG,
which stands for “robotic guide.”

A. RFID-based localization Fig. 1. RG: A Robotic guide for the visually impaired.
RG, shown in Fig. 1, is built on top of the Pioneer 2DX
commercial robotic platform from the ActivMedia Corpo-
ration (See Fig. 1). What turns the platform into a robotic objects in the environment or worn on clothing. They do not
guide is a Wayfinding Toolkit (WT) mounted on top of the require any external power source or direct line of sight to
platform and powered from the on-board batteries. As can be detected by the RFID reader. The tags are activated by
be seen in Fig. 1, the WT resides in a polyvinyl chloride the spherical electromagnetic field generated by the RFID
(PVC) pipe structure and includes a Dell T M Ultralight X300 antenna with a radius of approximately 1.5 meters. Each tag
laptop connected to the platform’s microcontroller, a laser is programmatically assigned a unique ID.
range finder from SICK, Inc., and to a radio-frequency RFID tags are viewed as stimuli that trigger or dis-
identification (RFID) reader. The TI Series 2000 RFID reader able specific behaviors, e.g., follow-wall, turn-left, turn-right,
is connected to a square 200mm × 200mm antenna. The avoid-obstacle, make-u-turn, etc. The robot’s knowledge base
upper left part of Fig. 1 depicts a TI RFID Slim Disk consists of a connectivity graph of the environment, tag to
tag attached to a wall. These tags can be attached to any destination mappings, and behavior trigger/disable scripts as-
sociated with specific tags. Each node of the graph represents
∗ This work is supported, in part, by NSF Grant IIS-0346880 and, in part,
a location marked with a tag. The robot’s location with
by two Community University Research Initiative (CURI) grants (CURI
2003 and CURI 2004) from the State of Utah. Copyright c 2005 USU respect to the graph is updated as soon as RG detects a tag.
Computer Science Assistive Technology Laboratory (CSATL). During experimental runs described elsewhere [6], the

RFID tags were successfully detected with the exception of been much debated in the literature [17], [21], [5]. Attempts
three runs in crowded environments. During these runs, the were made to reduce DST to the fundamental axioms of
robot missed a total of five RFID tags, because it had to classical probability theory [10]. However, belief functions,
navigate around groups of people standing near the tags. The a fundamental concept underlying DST, were shown not to
detection failures happened when the tags were outside of be probability distributions over sample spaces [13].
the effective range of the robot’s RFID antenna. The robot DST was chosen for three reasons. First, in DST, it
successfully navigated around each group of people using its is unnecessary to have precise a priori probabilities. This
obstacle avoidance routines. However, the obstacle avoidance was considered an advantage, because the propagation of
maneuver would put a blocked tag outside of the RFID wireless signals indoors is affected by dead spots, noise,
antenna’s electromagnetic sphere, which caused the robot to and interference. Second, Laplace’s Principle of Insufficient
miss an important maneuver, e.g., turn in the right direction Reason, i.e., a uniform distribution of equal probability to all
or make a u-turn [8]. Consequently, the robot would become points in the unknown sample space, is not imposed and,
lost and would have to stop and re-plan its path after detecting as a consequence, there is no axiom of additivity. Third,
that it had become lost. DST evidence combination rules have terms indicating when
multiple observations disagree.
B. Wireless localization
To overcome RFID detection failures in crowded environ- C. Related work
ments, it was decided to supplement RFID-based localization The research presented in this paper contributes to the body
with wireless localization. The working hypothesis was that of work on indoor localization done by assistive technology
indoor localization can be done by using wireless signals and robotics researchers. Ladd et al. [12] used Bayesian
already available in many indoor environments due to the reasoning combined with Hidden Markov Models (HMMs)
ubiquitous use of wireless Wi-Fi (IEEE 802.11b) Ethernet to determine the orientation and position of a person using
networks. One advantage of this approach is that it does not wireless 802.11b signals. The person wore a laptop with a
require any modification of the environment, e.g., deployment wireless card and was tracked in an indoor environment. The
of extra sensors or chips, which may disrupt routine activities assumption was made that people were minimally present in
of organizations and expose the robot to potential vandalism. the environment.
It should be noted that wireless localization is similar to Serrano [19] uses IEEE 802.11b wireless network signals
RFID-based localization in that it localizes the robot to a to determine the position of a robot inside a building. The
location. No attempt is made to determine the robot’s pose conducted experiments show that wireless indoor localization
(x, y, θ). In keeping with the principles of the Spatial Seman- may not be possible without a preconstructed sensor signal
tic Hierarchy [9] on which RG’s knowledge representation is map. However, if a motion model is available, Markov
based, once the robot is localized to a location, the location localization techniques can be used to localize the robot
specific behavior scripts are triggered to achieve a global accurately. Howard et al. [4] also investigated the use of
navigation objective [7]. Markov localization techniques in wireless robot localization.
Kismet, an open source wireless network analyzer, was Talking SignsT M is an infrared localization technology
used to detect and digitize wireless signal strengths. The developed at the Smith-Kettlewell Eye Research Institute in
software runs on the robot’s Dell T M Ultralight X300 laptop San Francisco [2]. The system is based on infrared sensors
equipped with the Orinoco T M Classic Gold PC 802.11b card. and operates like the infrared remote control device for
D-LinkT M 802.11b/2.4GHz wireless access routers were television channel selection. Infrared beams carry speech
used as access points, i.e., signal sources. A set of locations signals embedded in various signs to hand-held receivers that
is selected in a target environment. The wireless signature of speak those signals to users. Marston and Golledge [14] used
each location consists of a vector of signal strengths from Talking SignsT M in their Remote Infrared Audible Signage
each access point detected at that landmark. At run time, (RIAS) system. RIAS was installed at the San Francisco
signal strengths are classified to a location. CalTrain station to conduct several field tests with legally
While much effort has been put into modelling wireless blind individuals.
radio signals, no single consistent model exists that can The BAT system is an indoor localization system de-
reliably describe the behavior of wireless signals indoors[12]. veloped at the AT&T Cambridge Research Laboratory [1].
Consequently, it was decided to use sensor fusion to localize The system uses ultrasonic sensors that are placed on the
the robot. Sensor fusion is a post-processing technique that ceiling to increase coverage and obtain sufficient accuracy.
combines and refines initial sensor readings. The Dempster- The receiver detects ultrasonic signals and uses triangula-
Shafer theory (DST) of evidence [20] was chosen as a tion to position itself. The Atlanta Veterans Administration
theoretical framework for sensor fusion. The relative advan- (VA) R&D Center proposed the concept of Talking Braille
tages and disadvantages of DST and Bayesian theory have infrastructure [18]. Talking Braille is a method for providing

access to Braille/Raised Letter (BRL) signage at a distance. as its subset. Formally, a simple support function S : 2 Θ →
Talking Braille is an adaptation of electronic infrared badge [0, 1], A = , A ∈ Θ, is defined as S(B) = 0, if ¬(A ⊆ B);
technology developed by Charmed Technologies, Inc. The S(B) = s, 0 ≤ s ≤ 1, if A ⊆ B, and B = Θ; S(B) = 1,
infrastructure consists of small digital circuits embedded in if B = Θ. If S is focused on A, S’s BPAs are defined as
standard BRL signs. Small badges worn by users remotely follows: m(A) = S(A); m(Θ) = 1 − S(A); m(B) = 0,
trigger signs in the user’s vicinity. Using buttons on the B = A and B ∈ Θ. A separable support function is the
badge, the user requests that signs either voice their message orthogonal sum of two or more simple support functions.
or transmit their message to the user’s device over an infrared Simple support functions can be homogeneous or hetero-
beam. geneous. Homogeneous simple support functions focus on
As regards sensor fusion, the research presented here the same subset of Θ, whereas heterogeneous simple support
contributes to the body of work done by robotics researchers functions focus on different subsets of Θ.
who used DST to fuse information from multiple robotic Let S1 and S2 be two simple support functions focused on
sensors. In particular, Murphy [16] used DST as a framework A so that S1 (A) = s1 and S2 (A) = s2 . It can be shown that
for the Sensor Fusion Effects (SFX) architecture. In the SFX, the BPA m corresponding to S 1 ⊕ S2 is defined as follows:
the robot’s execution activities used DST beliefs generated m(A) = 1 − (1 − s1 )(1 − s2 ) and m(Θ) = (1 − s1 )(1 − s2 ).
from a percept to either proceed with a task, terminate the If S1 is focused on A and S 2 is focused on B = A, then
task, or conduct more sensing. Other robotics researchers also it can be shown that the BPA m corresponding to S 1 ⊕ S2
used DST for sensor fusion [3]. depends on whether A ∩ B = . If A ∩ B = , m(A) =
The remainder of this paper is organized as follows. s1 (1 − s2 ); m(A ∩ B) = s1 s2 ; m(B) = s2 (1 − s1 ); and
First, a brief review of the salient aspects of DST is given. m(Θ) = (1 − s1 )(1 − s2 ), which gives rise to the following
Second, the details of the proposed approach to wireless support function:
indoor localization are presented. Third, the results of the ⎧
experiments are discussed. ⎪ 0
⎪
⎪
⎪ s1 s2
⎪
⎪
II. D EMPSTER -S HAFER T HEORY ⎨
s1
S(C) = (2)
In DST, knowledge about the world is represented as a ⎪ s2
⎪
⎪
⎪ 1 − (1 − s1 )(1 − s2 )
set of elements, Θ, called the frame of discernment (FOD). ⎪
⎪
⎩
Each element of Θ corresponds to a proposition. For example, 1 .
Θ = {θ1 , θ2 } can be a FOD for a coin tossing experiment The first case arises when ¬(A ∩ B ⊆ C); the second case
so that θ1 is heads and θ2 is tails. Each subset of Θ can be arises when A ∩ B ⊆ C ∧ ¬(A ⊆ C) ∧ ¬(B ⊆ C); the
assigned a number, called its basic probability number, that third case arises when A ⊆ C ∧ ¬(B ⊆ C); the fourth case
describes the amount of belief apportioned to it by a reasoner. arises when B ⊆ C ∧ ¬(A ⊆ C); the fifth case arises when
The assignment of basic probability numbers is governed A ⊆ C, B ⊆ C∧ = Θ; the sixth case arises when C = Θ.
by a basic probability assignment (BPA) m : 2 Θ → [0, 1] so If A ∩ B = , S1 ⊕ S2 has the following BPA: m(A) =
that m( ) = 0 and ΣA⊆Θ m(A) = 1. Each BPA describes a s1 (1 − s2 )/(1 − s1 s2 ); m(B) = s2 (1 − s1 )/(1 − s1 s2 );
belief function over Θ. A subset A of Θ is a focal point of a m(Θ) = (1 − s1 )(1 − s2 )/(1 − s1 s2 ), which corresponds
belief function Bel if m(A) > 0. Suppose that m 1 and m2 to the following support function:
are two BPAs for two belief functions Bel 1 and Bel2 over Θ,
respectively. Let A1 , A2 , ..., Ak , k > 0 be the focal points of ⎧
Bel1 and B1 , B2 , ..., Bn , n > 0 be the focal points of Bel 2 . ⎪ 0
⎪
⎪
⎪ s1 (1 − s1 )/(1 − s1 s2 )
Then Bel1 and Bel2 can be combined through the orthogonal ⎨
sum Bel1 ⊕ Bel2 whose BPA is defined as follows: S(C) = s2 (1 − s1 )/(1 − s1 s2 ) (3)
⎪
⎪ (s1 (1 − s2 ) + s2 (1 − s1 ))/(1 − s1 s2 )
⎪
⎪
⎩
ΣAi ∩Bj =A m1 (Ai )m2 (Bj ) 1
m(A) = (1)
1 − ΣAi ∩Bj = m1 (Ai )m2 (Bj )
The first case arises when ¬(A ⊆ C) ∧ ¬(B ⊆ C); the
Once the pairwise rule is defined, one can orthogonally second case arises when A ⊆ C ∧ ¬(B ⊆ C); the third case
sum several belief functions. A fundamental result of the DST arises when B ⊆ C ∧ ¬(A ⊆ C); the fourth case arises when
is that the order of the individual pairwise sums has no impact A ⊆ C ∧ B ⊆ C ∧ C = Θ; the fifth case arises when C = Θ.
on the overall result [20].
A simple support function S provides evidential support III. W IRELESS L OCALIZATION
for one specific subset A of Θ. S is said to be focused on The target environment for localization experiments was
A. The function provides no evidential support for any other the USU CS Department. The department occupies an indoor
subset of Θ unless that set is implied by A, i.e., contains A area of approximately 6,590 square meters. The floor contains

example, if a hall’s orientation was from north to south, two
sets of samples were collected: one facing north, the other
facing south. A set of samples consisted of two minutes
worth of data. An individual sample was a set of five
wireless signal strengths, one from each wireless access
point in the department. Samples were collected at a rate of
approximately one sample every ten microseconds. Different
sets of data for a single collection position were collected on
different days in order to see a wider variety of signal strength
patterns. Each collection position and direction combination
had 10 total sets of data, which amounted to a total of twenty
minutes worth of data. Therefore, the total data collection
Fig. 2. Wi-Fi access points at the USU CS Department. time was 260 minutes, which resulted in a total of 1,553,428
samples. These samples were used for training purposes.
To obtain the validation data, RG was made to navigate
the route that contained all the selected locations 5 times in
each direction. Four pieces of masking tape were placed at
each collection position: two at 0.5 meter from the collection
position and two at 1 meter from the collection position. The
pieces of tape marked the proximity to the collection position,
i.e., the robot is within 0.5 meter of the collection position
and the robot is within 1 meter of the collection position. As
the robot crossed a tape, a human operator following the robot
Fig. 3. Data collection at a location. would press a key on a wearable keypad to mark this event
electronically. Thus, in the validation file, the readings at each
position were marked with the proximity to that position.
23 offices, 7 laboratories, a conference room, a student Unlike in the wireless localization experiments conducted
lounge, a tutor room, two elevators, several bathrooms, and by Ladd et al. [12], people were present in the environment
two staircases. during the robot runs.
Five wireless access points were deployed at various A. Localization algorithms
offices in the USU CS Department. The offices are shown The following algorithms were used for localization:
in Fig. 2 with black circles. The offices were selected on Bayesian, C4.5, and an artificial neural network (ANN) [15].
the basis of their availability. No other strategy was used The Bayesian algorithm considered the access points to be
for choosing the offices. Five locations were then selected. independent of each other. At each location, the priors were
Each location was at a corner. Corners were selected because acquired for the probabilities of specific signal strengths
in indoor environments they are very useful decision points. from each sensor at that location, i.e., P (s i |L), where si
In Fig. 2, the locations are shown as circles with crosses. is the signal strength from the i-th sensor at location L.
Each location had several (two or more) collection positions At run time, the standard Bayes rule was used to classify
marked. A collection position was the actual place where received signal strengths with respect to a specific location.
wireless signal strengths were collected. Each collection posi- The C4.5 algorithm inductively constructed a decision tree
tion was located 1.5 meters away from a corner. Fig. 3 shows for classifying the signal strengths into five locations. One
how wireless signal strength data were collected at a hall backpropagation ANN was trained for each location. Each
corner. The bullets represent three collection positions. The ANN had 5 input nodes, i.e., 1 node for each access point,
width of the hall determined how many collection positions 2 hidden layers of 10 nodes each, and 1 output node. At
were needed. If the hall was narrow (width < 2 meters), run time, the outputs from each ANN were taken and the
only one collection position was chosen in the middle of the final classification was decided by the activation levels of
hall. If the hall was wider than 2 meters, then there were the output nodes of the individual ANNs. The winner ANN
two collection positions, which were positioned to divide the determined the result location.
hall width into thirds. A total of 13 collection positions was
chosen for the five selected locations. Thus, each location B. Two evidence combination algorithms
corresponded to at least two collection positions. Evidence from the algorithms was combined as follows.
Two sets of samples were taken at each collection position, Let Θ = {L1 , L2 , L3 , L4 , L5 }, where Li , 1 ≤ i ≤ 5,
one for each direction of the hall’s orientation. So, for corresponds to the proposition that the robot is at location

Algorithm Position
Li . Let X be a vector of wireless signal strength readings 1 2 3 4 5
such that X = [s1 , s2 , s3 , s4 , s5 ], where 0 ≤ si ≤ 130. BAY 0.98 0.95 0.79 0.65 0.91
Let A be a localization algorithm such that X is its input C45 0.94 0.95 0.77 0.67 0.95
ANN 0.98 0.94 0.81 0.72 0.88
so that A(X) ∈ Θ, i.e., the output of A is a possibly
DST1 1.00 0.97 0.84 0.84 0.99
empty set of locations. Let T be the target location, i.e., the DST2 1.00 0.98 0.79 0.67 0.99
current location of the robot. Let all available algorithms be
enumerated as A1 , ..., An , n > 0. TABLE I
The performance of each localization algorithm at L i can TABLE I: PPV AT 0.5 METER .
Ai
be represented as a simple support function S B={Li } , where
B = {Li } is the focus of S and A i is a localization algorithm. Algorithm Position
For example, if there are five locations and three localization 1 2 3 4 5
algorithms, there are fifteen simple support functions: one BAY 0.93 0.91 0.82 0.68 0.91
simple support function for each location and each localiza- C45 0.87 0.91 0.78 0.64 0.95
ANN 0.92 0.93 0.82 0.67 0.89
tion algorithm. DST1 0.72 0.89 0.82 0.80 0.99
At run time, given X, A j (X) is computed for each L i DST2 0.91 0.90 0.81 0.68 0.97
and for each localization algorithm A j . If Aj (X) is greater
Aj TABLE II
than the threshold, S {Li } ({Li }) = sij , where sij is the basic
Aj TABLE II: PPV AT 1.0 METER .
probability number with which S {Li } supports its focus. Oth-
Aj
erwise, S{Li } ({Li }) = 0. The support for L i is computed as
A1 Aj
S{Li } ⊕...⊕S{Li} . After such orthogonal sums are computed
Let T P , T N , F P , and F N be the number of true
for each location, the location whose orthogonal sum gives it
positives, true negatives, false positives, and false negatives,
the greatest support is selected. This method of combination
respectively. Using T P , T N , F P , and F N , one can define
is called homogeneous insomuch as the orthogonal sums are
four evaluation statistics: sensitivity, specificity, positive pre-
computed of simple support functions with the same focus.
dictive value (PPV), negative predictive value (NPV) [11].
There is another possibility of evidence combination. From
Sensitivity, T P/(T P + F N ), estimates the probability of A
preliminary tests it is possible to find the best localization
saying that the signal receiver is at location L given that
algorithm for each location according to some criterion C.
the signal receiver is at location L, i.e., P [A(X) = L|T =
Suppose that A1 , ..., An are the best localization algorithms
L]. Specificity, defined as T N/(T N + F P ), estimates the
for each of the n locations. Note that the same algorithm
probability of A saying that the signal receiver is not at L
can be best for several locations. Suppose further that
given that the signal receiver is not at L, i.e., P [A(X) =
these algorithms are represented as simple support function
L|T = L]. PPV, defined as T P/(T P + F P ), estimates the
S{L1 } , ..., S{Ln } . Given X, Ai (X) is computed for each L i ,
probability that the receiver is at L given that A says that the
where Ai (X) is the output of the best algorithm for L i . If
receiver is at L, i.e., P [T = L|A(X) = L]. Finally, NPV,
Ai (X) is greater than some threshold, S {Li } ({Li }) = si .
defined as TN/(TN + FN), estimates the probability that the
Once each of the n support degrees are computed, the
signal receiver is not at L given that the algorithm says that
orthogonal sum S = S {L1 } ⊕ ... ⊕ S{Ln } is computed. The
the receiver is not at L, i.e., P [T = L|A(X) = L].
result sum is heterogeneous, because each simple support
The PPV was chosen as the metric for computing basic
function has a different focus. The best location is the
probability numbers, because it simulates the run-time per-
location with the highest degree of support according to S.
formance of a localization algorithm. In particular, the PPV
estimates the likelihood of the signal receiver being at L
C. Assigning basic probability numbers
when the algorithm states that the receiver is at L.
If one is to represent each localization algorithm as a
simple support function, the question arises as to how to IV. E XPERIMENTS
assign the basic probability numbers with which each simple Tables I and II show the PPV numbers computed from the
support function supports the location on which it is focused. robot’s validation runs. Table I shows the PPV numbers for
One possibility is to compute the basic probability numbers in the 0.5 meter proximity and Table II shows the PPV numbers
terms of true and false positives and true and false negatives. for the 1 meter proximity. In both tables, DST1 denotes the
A true positive is defined as A(X) = L and T = L, where homogeneous combination of simple support functions while
T is the true location and L is a location output by the DST2 denotes the heterogeneous combination. To analyze the
algorithm. A true negative is defined as A(X) = L and results, it was agreed to discretize the performance R of each
T = L. A false positive is defined as A(X) = L and T = L. algorithm into three intervals: strong (0.90 ≤ R), average
A false negative is defined as A(X) = L and T = L. (0.80 ≤ R < 0.90), and weak (R < 0.80).

The following observations were made. First, when the term sensor fusion in the presented conclusions refers only
performance of all three algorithms is strong, DST1 and to the sensor fusion methods described in this paper, i.e.,
DST2 either maintained the same level of performance or when the fused algorithms are represented as DST simple
slightly improved it. For example, Table I column 1 shows support functions that subsequently are fused homogeneously
that, at location 1, the three algorithms, i.e., Bayesian, C4.5, or heterogeneously.
and ANN, performed at 0.98, 0.94, and 0.98, respectively.
The performance numbers for DST1 and DST2 at the same R EFERENCES
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not to confound wireless signals. It should be noted that these Report: Departmento de Informatica, Estadistica y Telematica, Univer-
sidad Rey Juan Carlos, Mostoles, Spain, 2003.
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[21] P. Smets, “The Combination of Evidence in the Transferrable Belief
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