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Bluetooth Triangulation Bluetooth Triangulation
Authors:Authors:
AndreiAndrei
TrungTrung
JonathanJonathan
BluetoothBluetooth
u Short range (10 m), low power consumption, 2.45 GHz ISM
u Voice and data transmission, approx. 1 Mbit/s gross data
rate, including system overhead
u Two Bluetooth devices within 10m of each other can share
up to 720 kbps of capacity
u Universal radio interface for ad-hoc wireless connectivity
u Designed to operate with up to 8 devices communicating in
a small network called piconet
u Interconnecting computer and peripherals, handheld
devices, PDAs, cell phones – replacement of IrDA
u Embedded in other devices, such as audio headsets,
speakers, printers, digital cameras
Idea Idea
Ant Ant
Ant
Device
Antenna
1.Scan for Bluetooth device
2.RedFang can brute force MAC
address if needed
3.Determine signal strength
4.Get location via GPS device
5.Send packets to a server
containing location and signal
strength
6.Map signal strength to a
distance and find difference in
GPS location in meters.
7.Triangulate to find the
position of the Device.
Server
Bluetooth device
data relayed to
small computer to
calculate
triangulation.
EquipmentEquipment
uu 2.4 GHz ISM Band2.4 GHz ISM Band
uu IEEE 802.11b and 802.11g Wireless LANIEEE 802.11b and 802.11g Wireless LAN
uu Directional and multipoint applicationsDirectional and multipoint applications
uu Bluetooth®Bluetooth®
uu Public Wireless HotspotPublic Wireless Hotspot
uu WiFiWiFi
uu Light weightLight weight
uu All weather operationAll weather operation
uu UVUV--stable, UL flame ratedstable, UL flame rated radomeradome
2.4 GHz 14.5 dBi Radome Enclosed Wireless LAN Yagi Antenna
How did we get the Signal?How did we get the Signal?
uu BlueZBlueZ -- An implementation of theAn implementation of the
Bluetooth™ wireless standardsBluetooth™ wireless standards
specifications for Linuxspecifications for Linux
uu BluezBluez is included in every kernelis included in every kernel
from 2.4, we compiled our ownfrom 2.4, we compiled our own
distribution ofdistribution of BlueZBlueZ to tie our sourceto tie our source
code into the system callcode into the system call
How did we get GPS coordinates? How did we get GPS coordinates?
uu GPSTK is a GPS toolkit for LinuxGPSTK is a GPS toolkit for Linux
uu 110 if (110 if (raimSolver.isValidraimSolver.isValid())())
111 { 112111 { 112 coutcout << setprecision(12) <<<< setprecision(12) <<
raimSolver.Solution[0] << " " ;raimSolver.Solution[0] << " " ;
113 113 coutcout << raimSolver.Solution[1] << " ";<< raimSolver.Solution[1] << " ";
114 114 coutcout << raimSolver.Solution[2];<< raimSolver.Solution[2];
115 115 coutcout <<<< endlendl ;;
The above code merely writes the positionThe above code merely writes the position
calculation to standard output in Degreescalculation to standard output in Degrees
minutes.minutes.
Software we programmed Software we programmed
uu ClientClient –– reused sample text chatreused sample text chat
client from 152B. Converted it toclient from 152B. Converted it to
send signal datasend signal data
uu ServerServer –– reused sample text chatreused sample text chat
server from 152B. Converted it to doserver from 152B. Converted it to do
parsing and triangulationparsing and triangulation
uu GUIGUI
Limiting Factor in Project Limiting Factor in Project
uu Need accurate signal to distanceNeed accurate signal to distance
ratio in order to triangulate.ratio in order to triangulate.
Measurements Measurements
uu How: At first we checked the signal at everyHow: At first we checked the signal at every
meter from the antenna.meter from the antenna.
uu Bad idea.Bad idea. Took too long and wasn’t efficientTook too long and wasn’t efficient
(signal didn’t change much over a given distance)(signal didn’t change much over a given distance)
uu Better idea:Better idea: we used the GPS device to get ourwe used the GPS device to get our
distance relative to the antenna.distance relative to the antenna. Then, weThen, we
measured the signal strength at various points.measured the signal strength at various points.
Performed multiple tests at same distance andPerformed multiple tests at same distance and
averaged results.averaged results. Planned on using linearPlanned on using linear
regression to derive an equation for our signal toregression to derive an equation for our signal to
distance ratios.distance ratios. We could then use the equationWe could then use the equation
to approximate the distance of the antennato approximate the distance of the antenna relative to the device.relative to the device.
Triangulation Calculation Triangulation Calculation
uu By using the distance formula, we canBy using the distance formula, we can
come up with three equations:come up with three equations:
A: (PxA: (Px –– R0_x)^2 + (R0_x)^2 + (P yP y –– R0_y)^2 = D0^2R0_y)^2 = D0^ B: (PxB: (Px –– R1_x)^2 + (R1_x)^2 + (P yP y –– R1_y)^2 = D1^2R1_y)^2 = D1^ C: (PxC: (Px –– R2_x)^2 + (R2_x)^2 + (PyPy –– R2_y)^2 = D2^2R2_y)^2 = D2^
And we reduce them to 2 equations inAnd we reduce them to 2 equations in
the form of:the form of:
AA –– B:B: aPx + baPx + bPyPy = e= e BB –– C: cPx + dC: cPx + dPyPy = f= f
Where a, b, c, d, e, f are just someWhere a, b, c, d, e, f are just some
constants.constants.
D
D
D
R2_x, R2_y
R0_x, R0_y
R1_x, R1_y
Px, Py
Solving the Linear Equations Solving the Linear Equations
uu aPx + baPx + bPyPy = e= e
uu cPx + dcPx + dPyPy = f= f
These two equations can be solved by using the Cramer’sThese two equations can be solved by using the Cramer’s
RuleRule
DetDet(( )) DetDet(( ))
Px =Px = PyPy ==
DetDet(( )) DetDet(( ))
e b
f c
a b
c d
a e
c f
a b
c d
Code SegmentCode Segment
uu Actual code used to figure out the location of theActual code used to figure out the location of the BlueToothBlueTooth devicedevice
public static Point2D.Doublepublic static Point2D.Double computeGPS(doublecomputeGPS(double a1, double b1, double d1, double a2, double b2, doublea1, double b1, double d1, double a2, double b2, double d2, double a3, double b3, double d3){d2, double a3, double b3, double d3){ double A, B, C, D, E, F, X, Y,double A, B, C, D, E, F, X, Y, DetXDetX,, DetYDetY,, DetDet;; A =A = --2a1 + 2a2;2a1 + 2a2; B =B = --2b1 + 2b2;2b1 + 2b2; C =C = --2a2 + 2a3;2a2 + 2a3; D =D = --2b2 + 2b3;2b2 + 2b3; E = Math.pow(d1, 2)E = Math.pow(d1, 2) -- Math.pow(d2, 2)Math.pow(d2, 2) --Math.pow(a1, 2) + Math.pow(a2, 2)Math.pow(a1, 2) + Math.pow(a2, 2) -- Math.pow(b1, 2) +Math.pow(b1, 2) + Math.pow(b2, 2);Math.pow(b2, 2); F = Math.pow(d2, 2)F = Math.pow(d2, 2) -- Math.pow(d3, 2)Math.pow(d3, 2) --Math.pow(a2, 2) + Math.pow(a3, 2)Math.pow(a2, 2) + Math.pow(a3, 2) -- Math.pow(b2, 2) +Math.pow(b2, 2) + Math.pow(b3, 2);Math.pow(b3, 2);
//Using Cramer’s Rule//Using Cramer’s Rule DetDet = AD= AD -- BC;BC; DetXDetX = ED= ED -- BF;BF; DetYDetY = AF= AF -- EC;EC;
return new Point2D.Double(DetX/Det,return new Point2D.Double(DetX/Det, DetY/DetDetY/Det);); }}
Blame the equipment!!! Blame the equipment!!!
Better yet, blame the guy that Better yet, blame the guy that
suggested this lame projectsuggested this lame project
Possible ProblemsPossible Problems
uu Connection QualityConnection Quality-- BluezBluez could havecould have
been operating based on a thresholdbeen operating based on a threshold
for the minimum connection qualityfor the minimum connection quality
necessary to transmit data (i.e. a file)necessary to transmit data (i.e. a file)
uu Signal strength didn’t go below 200Signal strength didn’t go below 200
(on a scale from 1 to 255) and others(on a scale from 1 to 255) and others
have detected a signal at approx. ahave detected a signal at approx. a
km with the same antenna.km with the same antenna.
Possible solutionsPossible solutions
uu Hardware scanner thatHardware scanner that syncronizessyncronizes
withwith bluetoothbluetooth spreadspread--spectrumspectrum
hopping and returns any active SNR,hopping and returns any active SNR,
not just usable link SNR.not just usable link SNR.
Milling the stock Milling the stock
Constructing the enclosure Constructing the enclosure
Painting and fitting Painting and fitting
The end.The end.
uu Demo the scanner and GUIDemo the scanner and GUI
