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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

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Presentation Transcript
motivation for project
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

y

x

Problem Description

Trilateration Visualized

Range1

Range2

Range3

Source estimation from signal circle intersection (trilateration method)

problem description range estimation using hardware
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
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

y

x

Problem Description: Tracking Algorithm Using Range Estimates

Trilateration Visualized

(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

r1

r2

r3

(x3, y3)

(x, y)

static source
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
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,

x2-x1 y2-y1 x-x1 b21

A = x3-x1 y3-y1 x = y-y1 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
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
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 method1
Static Source: Noise Estimation Method

(x1, y1)

(x2, y2)

Overlap region boundary points

y

Source estimation (average of three boundary points)

(x3, y3)

x

example lls and nls
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
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
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
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
Special Thanks

Project Supervisors

Patricio La Rosa

Graduate Student (ESE)

Professor Paul Min

Associate Professor (ESE)