INDOOR LOCATION OF WIRELESS DEVICESBrian 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

x

y

Range2

Range3

Range1

Source estimation from signal circle intersection (trilateration method)

Trilateration Visualized

Problem Description: Range Estimation Using Hardware

Communication Protocol Between AP and Source

Start: Source sends a ‘Ready To Send’ (RTS) Frame to AP

Finish: AP responds with a ‘Clear to Send’ (CTS) Frame to Source

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

x

y

r2

r3

r1

(x, y)

Trilateration Visualized

(x3, y3)

(x2, y2)

(x1, y1) 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

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 equationsLLS Algorithm

x= (ATA)-1ATb

where,

x2-x1 y2-y1 x-x1 b21A = x3-x1 y3-y1 x = y-y1 b = b31

and,

bij = ½(rj2 – ri

2 + 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

x

y

(x3, y3)

(x2, y2)

(x1, y1)

Overlap region boundary points

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

(represented by blue square in plot)

Source estimate from LLS method

(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

(xEST, yEST)

Region boundary points

MSE ComparisonSimulated 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 SupervisorsPatricio La Rosa

Graduate Student (ESE)

Professor Paul MinAssociate Professor (ESE)