Transcript Indoor Location of Wireless Devices

INDOOR LOCATION OF
WIRELESS DEVICES
Brian Murphy
Motivation for Project

Location Based Services (LBS)
 GPS
most prominent yet ineffective for indoor
positioning

Need for indoor positioning technology growing
 Simple

and Inexpensive methods preferable
Goal: Use trilateration via signal radii from three
WLAN APs to estimate source terminal position in
indoor environment
 For
both a static and mobile source terminal
Problem Description
Trilateration Visualized
Range1
Range2
Range3
y
x
Source estimation from signal circle
intersection (trilateration method)
Problem Description: Range Estimation
Using Hardware
Communication Protocol Between AP and Source
Finish: AP responds with a
‘Clear to Send’ (CTS)
Frame to Source
Start: Source sends a
‘Ready To Send’ (RTS)
Frame to AP
Time Elapsed between RTS and receipt of CTS equals Round Trip Time (RTT)
Problem Description: Range Estimation
Using RTT



AP Signal travels at speed of light (c=2.998 x 108)
Distance between source and AP is signal range
RTT is time elapsed between source sending signal
and source receiving signal from AP
Distance = Rate x Time
Signal Range= Speed of Light x RTT
Problem Description: Tracking
Algorithm Using Range Estimates
Trilateration Visualized
(x2, y2)
(x1, y1)
r1
System of Equations
(x1-x)2 + (y1-y)2 = r12
(x2-x)2 + (y2-y)2 = r22
(x3-x)2 + (y3-y)2 = r32
3 equations, 2 unknowns and
(xi, yi), ri for i=1,2,3 are given
r2
r3
y
(x3, y3)
x
(x, y)
Static Source

Before tracking a mobile source terminal, need to
effectively estimate static source position.
 With

and without measurement noise
Methods for static source calculation
 Linear
Least Least Squares
 Nonlinear Least Squares
 Noise Estimation Method
Static Source: Linear Least Squares
(LLS) Method

Accuracy decreases as more APs are added to the experiment
 Arbitrarily eliminate constraint to linearize system of
equations
LLS Algorithm
x= (ATA)-1ATb
where,
A=
x2-x1
x3-x1
y2-y1
y3-y1
x=
x-x1
y-y1
b21
b = b31
and,
bij = ½(rj2 – ri2 + dij2), (i=2,3 and j=1)
*dij is distance between APi and APj
Static Source: Nonlinear Least Squares
(NLS) Method

Iterative algorithm supposed to improve accuracy
of LLS estimate
 Executes
until diff. between previous and current
iteration is less than threshold (δ)
Rk+1 = Rk – (JkTJk)-1JkT fk
Static Source: Noise Estimation Method

Measurement error introduced
 Causes
signal expansion only
 Signal retraction means we can not guarantee an
intersection and thus can not derive a source estimation

Signal expansion means signal overlap as opposed
to perfect intersection
 Union
of three circles (overlap) is region where source
may exist
 Noise Estimation method takes the average of three
points that form boundary of overlap region
Static Source: Noise Estimation Method
(x1, y1)
(x2, y2)
Overlap region
boundary points
y
(x3, y3)
x
Source estimation (average
of three boundary points)
Example (LLS and NLS)
Three APs centered at: (x1,y1)=(0,0), (x2,y2)=(0,1), and (x3,y3)=(1, 1)
With signal radii : r1=2/3, r2=3/4, and r3=3/4
Source estimate from NLS method
Source estimate from LLS method
(represented by blue square in plot)
(represented by red star in plot)
Example (Noise Estimate Method)
Three APs centered at: (x1,y1)=(0,0), (x2,y2)=(0,1), and (x3,y3)=(1, 1)
With signal radii : r1=2/3, r2=3/4, and r3=3/4 and σi = 0.1 for i=1,2,3
Region boundary points
(xEST, yEST)
MSE Comparison
Simulated one thousand distinct realizations of our experimental setup with
variances from 0 to 0.2 and measured the mean squared error
Future Work

Kalman Filter for mobile source tracking
 Assumes
measurement noise
 Takes weighted average of position estimate and
position measurement

Hardware and Experimental Design
 Lego
Mindstorm technology can be used for our source
terminal (cheap and easy to assemble)
 Experiment with placement of APs to determine optimal
location
Special Thanks
Project Supervisors
Patricio La Rosa
Graduate Student (ESE)
Professor Paul Min
Associate Professor (ESE)