A PROJECT REPORT
ON
INDOOR POSITIONING SYSTEM USING WIFI
(TRILATERATION METHOD)
In partial fulfillment for the requirement of the degree of
Master of Computer Science of Assam University, Silchar
(Paper Code: MCS-1005)
Submitted By:
SONIA NAG
M.Sc (5 years)-10th sem
Roll-101611 No-02220127
Registration No: 22-110021758 of 2011-2012
UNDER THE GUIDANCE OF
Mr. Saptarshi Paul
Assistant Professor
DEPARTMENT OF COMPUTER SCIENCE
SCHOOL OF PHYSICAL SCIENCE
ASSAM UNIVERSITY SILCHAR
PIN-788011
CERTIFICATE
This is certify that SONIA NAG, the student of the Department of Computer
Science, Assam University, Silchar bearing the roll:101611 No:02220127 has
carried out her project work entitled “INDOOR POSITIONING SYSTEM USING
WIFI(TRILATERATION METHOD)” under my guidance for the partial fulfillment
of the course.
I wish her all the very best in near future.
Mr. Saptarshi Paul.
Assistant Professor
Computer Science Department,
ASSAM UNIVERSITY, SILCHAR
DEPARTMENT OF COMPUTER SCIENCE
SCHOOL OF PHYSICAL SCIENCES
ASSAM UNIVERSITY SCILHAR
A CENTRAL UNIVERSITY CONSTITUTED UNDER
ACT XIII OF 1989
ASSAM, INDIA, PIN - 788011
DECLARATION
I, Sonia Nag, student of 10th semester (M.Sc. 5 years), Department of Computer
Science do hereby solemnly declare that I have duly worked on my project entitled
“Indoor positioning using Wi-Fi” under the supervision of Mr. Saptarshi Paul,
assistant Professor, Department of Computer Science, Assam University, Silchar.
This project work is submitted in the partial fulfillment of the requirements for the
award of degree of Master of Science in computer science. The result embodied in
this thesis have not been submitted to any other university for the award of any
degree or diploma.
Place: Assam University, Silchar
(Sonia Nag,10th sem)
ACKNOWLEDGEMENT
It gives me immense pleasure to recollect the whole time and effort utilized in
making the project a grand success. First and foremost, I would like to thanks my
adored guide Mr. Saptarshi Paul, Assistant Professor, Department of Computer
Science, Assam University, Silchar, for his valuable time and for being always
supportive to my work under his guidance and giving me the freedom of thought
always.
I wish to express my deep sense of gratitude and indebtedness to Prof. Bipul Shyam
Purkayastha, Head, Department of Computer Science, Assam University, Silchar,
for providing me the opportunity to utilize the facilities of the Department of
Computer Science.
I am grateful to my parents, for their support, concern and help as and when required.
I thank all my friends and classmates for their support.
SONIA NAG
Roll-101611 No-02220127
M.Sc 10th semester
Department of computer science
Content
Certificate………………………………………………………..i
Declaration………………………………………………………ii
Acknowledgement……………………………………………….iii
Abstract…………………………………………………………..iv
Chapter-1
Introduction……………………………………………………...1
Chapter-2
Wi-Fi technology………………………………………………...2
WLAN, Wi-Fi and IEEE 802.11…………………………2.1
Chapter-3
Objective………………………………………………………….3
Requirements……………………………………………3.1
Chapter-4
Problems and disruptive factors………………………………….4
Chapter-5
Measurement Theory…………………………………………….5
Based on Proximity sensing………………………………5.1
Based on Trilateration…………………………………….5.2
Based on Triangulation……………………………………5.3
Based on Pattern recognition………………………….......5.4
Chapter-6
Methods and tools…………………………………………………6
Methods………………………………………………...6.1
Tools……………………………………………………6.2
Motivation………………………………………………6.3
Chapter-7
Advantages………………………………………………………7
Disadvantages……………………………………………7.1
Chapter-8
Trilateration positioning algorithm……………………………..8
Taylor series algorithm…………………………………..8.1
New distance based algorithm……………………………8.2
Chapter-9
Implementation ………………………………………………….9
Snapshots…………………………………………………9.1
Chapter-10
Conclusion………………………………………………………..8
Future work………………………………………………8.1
References……………………………………….………8.2
ABSTRACT
Wi-Fi positioning plays an increasingly important Role in improving performance
because good positioning can improve performance in indoor environments
without additional devices. It will make use of existing Wi-Fi infrastructure,
although this was never designed to do so.
Methods that were used for other positioning technologies can be adopted for Wi-
Fi. Whether or not these other methods work with Wi-Fi will be explained and
examined.
The increasing demand for location based services inside buildings has made
indoor positioning a significant research topic. This study deals with indoor
positioning using the Wireless Ethernet IEEE 802.11 (Wireless Fidelity, Wi-Fi)
standard that has a distinct advantage of low cost over other indoor wireless
technologies.
The aim of this study is to examine several aspects of location fingerprinting based
indoor positioning that affect positioning accuracy.
This paper also discusses the accuracy of the methods and the optimal area of
application.
Index Terms—Wi-Fi, WLAN, Positioning, Location, Position determination,
localization, Fingerprinting .
Introduction
The increasing demand for location based services inside buildings has made
indoor positioning a significant research topic. The applications of indoor
positioning are many, for instance, indoor navigation for people or robots,
inventory tracking, locating patients in a hospital, guiding blind people, tracking
small children or elderly individuals, location based advertising, ambient
intelligence etc.
Although the Global Positioning System is the most popular outdoor positioning
system, its signals are easily blocked by most construction materials making it
useless for indoor positioning. This study deals with indoor positioning using the
Wireless Ethernet IEEE 802.11 (Wi-Fi) standard that has distinct advantage of low
cost over other indoor wireless technologies – it has relatively cheap equipment
and in many areas usually a Wi-Fi network already exists as a part of the
Communication infrastructure avoiding expensive and time-consuming
Infrastructure deployment.
Most of the proposed Wi-Fi indoor positioning systems use
either proximity detection via radio signal propagation models or location
fingerprinting techniques.
By using WiFi Positioning Systems it is possible to locate the position of almost
every WiFi compatible device without installing extra software or manipulating the
hardware. In the course of time many methods that were initially used with other
positioning technologies were applied to WiFi positioning. WiFi Positioning also
allows the use of location-based services (LBS) indoors, which is interesting for
the industry. Useful applications of this technology are, for example, for indoor
navigation at shopping malls or for finding a lost child in an indoor area. Lost
devices or items can also be found with this technology. Additionally, this
technology is especially interesting for hospitals because sometimes when staff
move certain pieces of equipment it can be hard to find them again straight away.
WIFI TECHNOLOGY
WLAN, Wi-Fi and IEEE 802.11:
WLAN, WiFi and IEEE 802.11 all mean the same: they determine
the industrial standard for wireless data transmission. The latter is the most used
expression.
WiFi uses electromagnetic waves to transmit data over the airwaves. In figure 1 the
whole frequency spectrum is shown, starting with radio signals and ending with
gammarays. Looking at the illustration one can see that it operates
in broadband, on about 2,4 GHz and 5 GHz.10 Other longer distance technologies
also use frequencies in between these figures. The frequency is the number of wave
occurrences per unit of time.
In the best case, the radio waves spread out evenly and lose more and more of their
signal strength with increasing radius. This loss of signal strength is due to the
energy transformation because, in physics, energy is never lost, but instead
converted.
Consequently the amplitude of the signal becomes smaller and smaller. In an
outdoor station the radius ratio of distance to signal strength is inversely
proportional, because the decrease of the signal is log-normal.
In conclusion, if the distance to the station is increased in any direction, the signal
strength will decrease steadily. However, indoors we encounter a different
problem, because the waves bump into walls, windows, doors and so on. If a wave
bumps into a different material, it converts more energy than in the air. During this
process, the signal strength is decreased more strongly, because the energy is
transferred to the material (e.g.: in heat). Furthermore the
signal is also reflected from the material.
Fig. 1 frequency overview - A Wifi wave matches into a baseball.
1.Fundamentals for Wifi measuring: the distance between the transmitter
and the receiver has an important role in determining the position. In contrast to
GPS, WiFi, at a time measurement method, does not come into question, since
such an exact time is difficult to achieve synchronization. Finally, the path from
space to the ground is much farther than from one access point to a mobile device.
The received signal strength (RSS) and the signal noise ratio (SNR) are the most
suitable. These values can be calculated from the incoming signal.
2) Signal Strength: the signal strength is measured in dBm (decibel in
milliwatt). A Wifi station has a EIRP (Equivalent isotropically radiated power) of
100mW - 1000mW (20dBm - 30dBm).
This is how to calculate:
Lp(dBm) = 10 ∗ log p /1mW
For Example:
Lp(dBm) = 10 ∗ log100mW/1mW = 20dBm
A WiFi connection gives us information about signal strength and interference.
For example: signal strength: -52 dBm ( 0,00001 mW )
interference: -90 dBm
Because of the path loss, the signal becomes weaker and weaker the farther it is
away from its origin. Barriers may attenuate the signal (more about that later). The
property to the path loss can be used to determine the distance.
Objective
Detail study of indoor positioning system using triangulation and trilateration
methods.
Requirements
At the end of the project the following requirements were to be satisfied:
The main requirement was a system that with reasonable reliability could
estimate the position of the user, in situations where GPS and similar
satellite-based positioning systems are unreliable or unavailable.
In this case an average error of approximately 3.5 meters was considered
reasonable,although the goal was to get a much better result.
A basic functional implementation of the positioning system was to be done
for the Android platform.
Apart from these requirements there were a couple of points that were not
requirements for the project to be considered successful, but which should be
considered a bonus:
Using existing infrastructure and hardware.
Cheap infrastructure and hardware.
Problems and disruptive factors
In general, wireless radio transmission is subject to many confounding factors.
Even the sun or rain drops have an effect on the signal strength, actually even if
this disruptive factor is very low, it would still be measured. Another problem is
the electromagnetic radiation inside buildings. Additionally, many walls, doors and
floors have to be penetrated. The result of this is attenuation. An additional
problem is the wireless overlay. In an office or apartment building, there are
several dozen wireless stations that provide much interference.
1) Signal attenuation of static environment: usually hits an
electromagnetic wave on a wall or another barrier it passes through. However, the
wave becomes weaker, due to reflection that originates while striking the barrier.
Another part is absorbed and converted into heat, the factor of which is so
small that it would not be noticeable for a human. The size of the loss is related to
the material, specifically its thickness.
For example, glass has a higher attenuation effect than brick walls. These factors
are critical, especially with methods which determine a distance by the measuring
of the signal strength.
2) Signal attenuation by user: As we can see in the experiment, the presence
of a user changes the signal strength. This is especially important for the
Fingerprinting-based location method, because the mean values would be
influenced by the presence of a user. ”When the positioning system is supposed
to cater to real users, it is essential to have the user present while collecting the
RSS values for the fingerprint and to take into account the effect of the humans
body. As already mentioned, WiFi uses the frequencies of about 1,4 GHz, just
like microwaves. The effect that is used to heat up food with a microwave is a
disruptive effect with WiFi. This is because the radiation is partially absorbed by
the water in the human body and the signal is attenuated.
MEASUREMENT THEORY
There are many different approaches for locating a mobile device using WiFi
technology. In the following, the method to estimate the sought position is
described. In general, the methods need to know the position of the WiFi stations
(=access points) as a reference point that are used for the approximate position of
the mobile device.7 A prerequisite for a good-working WiFi positioning system is
an adequate coverage of the access points. This coverage is called Basic
Service Area (BSA). The expression of the BSA determines which positioning
method is the most suitable. The methods differ in the minimum required number
of stations and its accuracy. This varies between building part accuracy and room
accuracy to an accuracy of a few meters difference.
A. Based on Proximity sensing: Methods based on proximity sensing are
among the simplestand fastest, but they are also imprecise. A position
calculationcan be done with just a single station. It is hardly possible,for example,
to perform an indoor positioning that delivers the right floors in a multi-storey
building. As result, one gets only the part of the building in which the mobile
device is located. On the other hand, this kind of positioning is popular
for outdoor positioning.
B. Based on Trilateration: Lateration or trilateration is the determination of
absoluteor relative locations of points by measurement of distances,using
geometry. The ”tri in trilateration reveals that at least three fixed points are
necessary to determine a position. The idea behind the geometry is that all
trilateration methods start with calculating the distance from a station to a
device. The distance then is used as the radius from the station. Somewhere on the
edge of the resulting circuit, the position of the device is assumed. To lessen the
possibilities, a second group of results is also used from the measurements of
another station. Of course the second station has to be in the range of
the device. With the radius of the second station one receives two
points. If one imagines this in a geometrical way, one keeps two circles and two
intersection points. One of the two points is the position of the devices. To find out
which point is the right point a third station is used. An illustration of this geometry
can be seen in figure 2. In the following the methods of distance determination are
explained.
Fig. 2 Trilateration
1) Time of Arrival (ToA):
With this method time is measured,which needs a signal from a station to mobile
device and back again, and in this instance it is called the ”Round trip time (RTT).
A requirement for this method is synchronically
running clocks. According to which topology is used, only the clocks of the
stations or also the clocks of the mobile devices must run synchronically. With the
measured data of the station and the given speed of the signal, it can be calculated
how far away the mobile device is. Indeed, no time may pass with the receiving
and sending back of the signal because this would influence the measured data. As
this is not possible without modification in mobile devices, this method does not
function with WiFi.
• Positioning is based ontrilateration with measurements of time
• (-) At least three station in range of the device are necessary.
• (-) Position coordinates of station must be exact.
• (-) Does not work with Wifi.
2) Time Difference of Arrival (TDoA): Like ToA, TDoA also needs exact
clock synchronization. TDoA is more popular with commercial detection systems
than ToA. With this method, the difference is used between the arrival times of the
signals to determine the position. Because WiFi was never planned, nevertheless,
to make such exact time measurements, is also not possible to use TDoA on WiFi.
• Positioning is based ontrilateration with measurements of time difference
• (-) At least three station in range of the device are necessary.
• (-) Position coordinates of station must be exact.
• (-) Does not work with Wifi.
3) Received Signal Strength (RSS): This method uses propagation-loss of
the WiFi signals to compute the distance. The decibel version of free space path
loss equation is 10 log( s/0.001 ) (s is the signal strength in watts). By using
these measurements, which distance matches which signal power can be found out.
This method functions relatively well outdoors, but in buildings it can come to
strong divergences, because the walls reflect and attenuate the WiFi signals. These
methods work with the WiFi technology and can be used for the localisation. One
can even use all three topologies with this method, however, software must be
modified with the routers network-based topology.
• Positioning is based on trilateration with measurements of signal strength
• (-) At least three stations in range of the device are necessary.
• (-) Position coordinates of station must be exact.
• (+) Does work with Wifi
• (+) Works well outdoors
• (-) Works indoors but doesnt deliver accurate values
• (+) supports all topologies
The method Signal to Noise Ratio (SNR) is neglected here because it usually
provides poorer results than RSS. Only the fact that it exists should be mentioned.
It works on the same principle, but instead of transmitting power, the measured
interference is used.
C. Based on Triangulation
1) Angle of Arrival - AoA: In this method, the angle of the arriving signals is
determined and, using geometry, the position can be determined. At least two
stations in reach of the mobile devices are a requirement for AoA. It is suitable for
indoor and outdoor positioning and it can measure in real time. The estimation of the
angle has an inaccuracy of only degrees.
AoA is not applicable without modification of the hardware, but it returns good
results. Special antennas are mandatory for the determination of the location with
the ”Angle of Arrival method.
Fig. 3. A special directional Wifi antenna determine the position with AoA.
• Position determination with the intersection point of two lines.
• (-) needs hardware modifications / special antennas
• (+) allows Real-Time positioning
• (+) indoor + outdoor
• (-) only network-based
Comparison of Positioning Techniques-
Trilateration Triangulation • Estimates the position of an object by
measuring its
Distances from multiple reference
points.
• Estimates an object by computing
angles relative to multiple reference
points.
• The distance is computed by
multiplying the radio signal velocity
and the travel time.
• The object to be located is used as a
fixed point of a triangle.
• Usually TOA and TDOA used for
distance measuring.
• Usually AOA used for angle
measurement.
D. Based on Pattern recognition
1) Fingerprint Positioning: Fingerprinting, also called Location Patterning,
uses a previously created database of signal patterns, which need to be matched for
positioning only. Fingerprinting doesnt need modification of the hardware like, for
example, AoA. Furthermore, no time synchronisation is necessary between the
stations. Before a position can be determined, the entire area in which the positioning
is supposed to work must be recorded. This happens in Phase 1, the so called
calibration-phase, offline-phase or training-phase: The area in which the positioning
should later run, must be covered with a pattern of recording points, called
fingerprints. Step by step, for every fingerprint there must be a measurement, that
includes the information about all stations and their Received Signal Strength (RSS).
Each fingerprint is a vector R , associated with each element of a station
The number of stations must be known and may be changed only if the measurement
is repeated from phase 1. The collected data is stored in a database, called a radio
map, so that it can be retrieved later in phase 2.
Fingerprinting-based positioning algorithms
• probabilistic methods
• k-nearest neighbor
• neural networks
• support vector machine (SVM)
• smallest M-vertex polygon (SMP)
Fingerprinting-Based Positioning Methods
There are two approaches to estimate the user’s location based on the online RSS
measurements and the fingerprint database.The deterministic approach only uses
the average of the RSS time samples from each RP to estimate the location,
whereas the probabilistic approach incorporates all the RSS time samples for the
computation.
For the following section, assume the collected fingerprint database is denoted as a
set {(pi,ψi(1), . . . ,ψi(T))|i = 1, . . . ,N}, where pi is the Cartesian coordinates for
RP i, ψi(t) = [ψi;1(t), . . . , ψi;L(t)]T is the RSS readings vector for RP i at time t
with ψi;j(t) denoted as the RSS reading from AP j for RP i at time t. T is the total
number of collected time samples, N is the total number of RPs and L is the total
number of APs.
The online RSS measurement vector can be denoted as r = [r1, ...rL]T .
Figure . Location fingerprinting technique
The Positioning Procedure
The procedure for fingerprint-based positioning using the proposed joint model is
as follows, where steps 1 to 4 are the off-line data training phase and steps 5 to 7
are the on-line positioning phase:
Step1: Choose the RPs, and then collect the RSSs from all APs at each RP.
Step2: Detect the gross errors and filter them out.
Step3: Use a global search procedure to find the two peaks and the minimum value
between the two peaks. The two times minimum is compared with the sum of the
two peaks to decide between using the Gaussian model or the alternative model.
This decision rule was created based on all the data collected.
Step4: Create the fingerprint database.
Step5: RSSs are collected by the user, outliers are removed. Calculate the
probability distribution of received RSSs.
Step6: Use the fingerprint database to calculate the joint probability density for the
RSSs collected in the step 5.
Step7: Estimate the user’s location using the K weighted nearest neighbour
(KWNN) algorithm.
KWNN is a conventional algorithm used for fingerprint-based Wi-Fi positioning.
Using this algorithm, K (K ≥ 2) nearest neighbours (those with the shortest signal
distance) of a test vector are chosen. The weighted average of the co-ordinates of K
points can be used as the estimate of the user’s location. The inverse of the signal
distance defines the weight.
K-Nearest Neighbour Method (KNN)
K-nearest neighbour is a deterministic method that involves calculating a weight
based on current measurements, and possibly other factors, for each fingerprint and
then selecting the k fingerprints with the best weight, where k is pre-defined a
constant often set to 3 or 4.
The final position is often determined through using those weights to do a weighted
interpolation between the physical locations of the chosen fingerprints; this
approach is often referred to as ‘weighted k-nearest neighbour’.
The K-nearest neighbour (KNN) method is a deterministic approach that uses the
average of the RSS time samples of RPs from the fingerprint database to estimate
the user’s location. It first examines the Euclidean distance of the online RSS
measurement vector to the RPs in the database, namely:
Di = ∥r −  ̄ ψi∥
where  ̄ ψi = 1/T
ΣT_=1 ψi,1(τ ) is the average RSS vector for RP i.
K Nearest Neighbor
Lazy Learning Algorithm
Defer the decision to generalize beyond the training examples till
a new query is encountered
Whenever we have a new point to classify, we find its K
Nearest neighbors from the training data.
The distance is calculated using one of the following measures
Euclidean Distance
Minkowski Distance
Mahalanobis Distance
Simple KNN Algorithm:
For each training example <x,f(x)>, add the example to the list of
training_examples.
Given a query instance xq to be classified,
Let x1,x2….xk denote the k instances from training examples that are
nearest to xq .
Return the class that represents the maximum of the k instances.
KNN Example
If K = 5, then in this case query instance xq will be classified as negative since
three of its nearest neighbors are classified as negative.
Instance Weighted K-NN using Gradient Descent Assumptions
_ All the attribute values are numerical or real
_ Class attribute values are discrete integer values
For example: 0,1,2…..
Algorithm
_ Read the training data from a file <x, f(x)>
_ Read the testing data from a file <x, f(x)>
_ Set K to some value
_ Set the learning rate α
_ Set the value of N for number of folds in the cross validation
_ Normalize the attribute values in the range 0 to 1
Value = Value / (1+Value)
Assign random weight wi to each instance xi in the training set
Divide the number of training examples into N sets
Train the weights by cross validation
_ For every set Nk in N, do
Set Nk = Validation Set
For every example xi in N such that xi does not belong to Nk do
Find the K nearest neighbors based on the Euclidean distance Calculate the
class value as:
Σ wk X xj,k where j is the class attribute
If actual class != predicted class then apply gradient descent
Error = Actual Class – Predicted Class
For every Wk
Wk = Wk + α X Error
Calculate the accuracy as:
Accuracy = (# of correctly classified examples / # of examples in Nk) X 100
Train the weights on the whole training data set
_ For every training example xi
Find the K nearest neighbors based on the Euclidean distance
Calculate the class value as:
Σ wk X xj,k where j is the class attribute
If actual class != predicted class then apply gradient descent
Error = Actual Class – Predicted Class
For every Wk
Wk = Wk + α X Error
Calculate the accuracy as:
Accuracy = (# of correctly classified examples / # of training
examples) X 100
_ Repeat the process till desired accuracy is reached
For each testing example in the testing set
_ Find the K nearest neighbors based on the Euclidean distance
_ Calculate the class value as:
Σ Wk X xj,k where j is the class attribute
Calculate the accuracy as
_ Accuracy = (# of correctly classified examples / # of testing
examples) X 100
Example with Gradient Descent
Consider K = 3, α = 0.2, and the 3 nearest neighbors to xq are x1,x2,x3
K nearest neighbors Euclidean Distance Class Random Weight
Class of xq = 0.2 X 1 + 0.1 X 2 + 0.005 X 2 = 0.41 => 0
Correct Class of xq = 1
Applying Gradient Descent
W1 = 0.2 + 0.2 X (1 - 0) = 0.4
W2 = 0.1 + 0.2 X (1 - 0) = 0.3
W3 = 0.005 + 0.2 X (1 - 0) = 0.205
Class of xq = 0.4 X 1 + 0.3 X 2 + 0.205 X 2 = 1.41
Class of xq => 1
Simple K-NN would have predicted the class as 2
K nearest
neighbors
Euclidean
Distance
class Random Weights
X1 12 1 W1 = 0.2
X2 14 2 W2 = 0.1
X2 16 2 W3 = 0.005
Flowchart of KNN:
Methods and tools
Methods
The viability of different solutions were to be evaluated primarily through studying
paper detailing their advantages, disadvantages and difficulties, but also through
experimentation and data gathering.
As Android is built for Java, this was to be the primary programming language for
the application. However, performance demanding algorithms could have required
C and thus the Android NDK (Native Development Kit) for implementation as it
typically provides superior
performance.
It was also assumed that a simple server program had to the developed in order to
provide the client application with any static and/or pre-measured data needed for
positioning. Depending on amount and complexity of the data stored by the server,
a simple data-file might have been enough, though a relational database was
thought to most likely have been required.
Encryption of the communication between the server and the client was also meant
to be implemented, in order to protect the users’ integrity, though it was not seen as
strictly required for the project.
Tools
Eclipse with the Android Development Tools plugin was used as the development
environment for the Java code. Android SDK was used as the underlying layer
providing the actual compiler for the target platform.
Motivation
Following the achievements of satellite‐based location services in outdoor
applications the challenge has shifted to the provision of such services for the
indoor environment.
However, the ability to locate objects and people indoors remains a substantial
challenge, forming the major bottleneck preventing seamless positioning in
all environments.
Many indoor positioning applications are waiting for a satisfactory technical
solution.
Improvements in indoor positioning performance have the potential to create
unprecedented opportunities for businesses.
Advantages
Indoor positioning system technology uses radio, ultrasound or infrared
signals to more precisely track locations where GPS signals are blocked.
Low cost.
Time-consuming infrastructure.
Applications benefiting from indoor location include:
School campus
Guided tours of museums
Shopping malls
Warehouses
Airports,bus,train and subway stations
Parking lots
Social networking
Hospitals
Sports
Disadvantages
Particle filter improve accuracy.
Increased power consumption.
Trilateration Positioning Algorithms
TDOA (time difference of arrival)
TOA (time of arrival)
TDOA(TIME DIFFERENCE OF ARRIVAL)
Wireless location with TDOA is essentially to resolve non-linear estimation
problem.
In wireless location area, Taylor Series algorithm is essential to find the
solution to minimize the objective function.
A new algorithm and defines a different objective function that is the sum of
squared distances between iterative point and hyperbolas defined by TDOA.
Then Steepest Descent method is used to find the best point based on the
objective function.
The measured distance between MS and BSs is expressed as:
ri(x)= √(x-Xi)2+(y-Yi)
2, i=1,2,…N (1)
Because we measure the radio propagation time between BS and MS and
treat it as distance.
Taylor Series Algorithm:
Taylor Series algorithm for wireless location is to iteratively find the best solution to
minimize objective function - squared TDOA.
TDOA for BSi with respect to BS1 is written as:
ri1 = ri-r1+ni1TDOA = √(x-Xi)
2+(y-Yi)2 - √(x-X1)
2+(y-Y1)+ni1TDOA (2)
where i=1,2,….N
ni1TDOA is zero-mean Gaussian noise with variance 𝜎2
of the ith TDOA between BSi
and BS1.
equation (2) is expanded into Taylor
Series at the initial location (x0, y0), and the first two terms
are remained.
Then we get:
ri10+ai,x(x0,y0)x𝛿+ ai,y(x0,y0)y𝛿 = ri1+ni1
TDOA (3)
where
ri10 =√(x0-Xi)
2+(y0-Yi)2 - √(x0-X1)
2+(y0-Y1)2
ri1 is the measure TDOA between BSi with respect to BS1;
ai,x= 𝜕ri1(x,y)
𝜕𝑥, x0,y0 =
𝑋1−𝑥0
𝑟1 -
𝑋𝑖−𝑥0
𝑟𝑖
ai,y= 𝜕ri1(x,y)
𝜕𝑦, x0,y0 =
𝑌1−𝑦0
𝑟1 -
𝑌𝑖−𝑦0
𝑟𝑖
In which ri =√(x0-Xi)
2+(y0-Yi)2
It can also be rewritten as:
A𝛿 = 𝐷 + 𝑒 (4)
Where
A=[𝑎2, 𝑥 ⋯ 𝑎2, 𝑦⋮ ⋱ ⋮
𝑎𝑁, 𝑥 ⋯ 𝑎𝑁, 𝑦],𝛿 = [𝛿𝑥 𝛿𝑦]T
D=[r21-r210 r31-r31
0 …… rN1-rN10]T
e =[n21 n31…….. nN1]T
ri10=ri-r1
According to Least Square estimation, to find to
minimize the sum of squared remains, i.e.:
e2=(A𝛿-D)2=(A𝛿-D)T (A𝛿-D) (5)
The 𝛿 would be:
𝛿=(AT A)-1ATD (6)
As a summary, Taylor Series algorithm computes from
equation (6) with initial position (x0, y0), and then location
estimation is updated according to:
xk+1= xk+ 𝛿x , yk+1= yk+ 𝛿y (7)
The iteratively estimated location approaches the true
position after executing above procedures.
It is worthy to mention that after enough times of
iteration, 𝛿 will be close to 0 i.e. 𝛿 ≈0; e2 = D2. So in the
end, Taylor Series algorithm is to find the optimized solution
for objective function: sum of D2.
The new distance based Algorithm
• The proposed distance based algorithm defines a new objective function
• Then uses steepest descent method to find the optimized solution.
• The new objective function is the sum of distances from optimized location
to hyperbola defined by TDOA measurement for each BS1- BSi pair.
The new distance based algorithm follows steps as:
• Specify the initial location value θk(xk , yk) in general
coordinate and u;
• Convert θk into εk under each local coordinate defined by
BS1- BSi pair. And then get t by resolve the nonlinear
equation i.e,
by cost/sint + ax cost = C2
• Calculate each gradient (from 1 to N-1) and sum the gradients into 𝛻 θF(θk).
• get the next estimated location (xk+1,yk+1) according to equation i.e,
Θk+1 =[ 𝑥𝑘 + 1𝑦𝑘 + 1
]=θk -u 𝛻 θF(θk)
Where 𝛻 θF(θk)=𝜕𝐹
𝜕𝑥,𝜕𝐹
𝜕𝑦
• if the delta of (xk+1,yk+1) is small enough, break down;
or go to step 1 for iteration.
Advantages and disadvantages of taylor series:
When the error is small (under 300 meters) and BS number is more than five,
Taylor Series algorithm can have higher accuracy than the new distance based
algorithm.
But when BS number is less than six, the new distance based algorithm
generally performs better than Taylor Series algorithm.
Fig: FLOWCHART OF WIFI POSITIONING
Implementation
Software requirements for implementation the system:
Operating system Windows7
coding Android java
testing Android Development Tools/java
Hardware requirements for development and implementing
The system:
1. 4GB RAM
2. ANDROID MOBILE WITH KITKAT VERSION
3. WIFI ROUTER
Screenshots of trilateration distance measurement
Snapshots of detecting Wi-Fi signal
Snapshots of k nearest neighbor
Here, error rate is 28.109375%
Here the error rate is 33.21875%
Conclusion
Wi-Fi has become a wide spreading technology, a technology that has never
been designed for localization.
Nevertheless,WiFi positioning performs well in comparison to other positioning
technologies, and has the favorable advantage that it is based on an existing
infrastructure.
First, it can be said that all Wi-Fi agreed methods are based on signal strength
(except AoA).
The technique best suited for each individual Wi-Fi positioning is dependent on
the environment.
When indoors, positioning fingerprinting delivers the best results. However, it is
also associated with a lot of effort.
FUTURE WORK
To Build an application that describes the Wi-Fi trilateration method for indoor
positioning using Android-based mobile devices.
REFERENCES
1) Li, Binghao; Salter, James; Dempster, Andrew G.; Ri, Chris, Indoor Positioning
Techniques Based on Wireless LAN. Sydney: University of New South Wales,
2006. Downloaded: 2012-02-20
URL:http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.72.1265&rep=rep1
&typ e=pdf
2) "Location Based Services for Mobiles: Technologies and Standard“, ShuWang,
Jungwon Min and Byung K. Yi, IEEE International Conference on
Communication (ICC) 2008, Beijing, China.
3) Cisco Systems, Inc., Wi-Fi Location-Based Services 4.1 Design Guide San
Jose, USA: Cisco Systems, Inc. 2008. Online:
http://www.cisco.com/en/US/docs/solutions/Enterprise/Mobility/wifich2.html
4) Jami, I.; Ali, M.; Ormondroyd, R.F.; Comparision of Methods of Locating
and Tracking Cellular USA: Dept. of Aerosp. Power & Sensors, Cranfield
Univ., Swindon, 2010.
5) Martin Vossiek, Leif, Wiebking, Peter Gulden, Jan Wieghardt and
Clemens Hoffmann Wireless Location Positioning - Concepts, Solutions,
Applications Munich, Germany: Siemens Corporate Technology, 2003.
6) K. Pahlavan and P. Krishnamurthy Properties of Indoor Received Signal
Strength for Wifi Location Fingerprinting University of Pittsburgh