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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

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Indoor Location of Wireless Devices

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  1. Indoor Location of Wireless Devices Brian Murphy

  2. 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

  3. y x Problem Description Trilateration Visualized Range1 Range2 Range3 Source estimation from signal circle intersection (trilateration method)

  4. 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)

  5. 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

  6. 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)

  7. 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

  8. 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

  9. 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

  10. 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

  11. Static Source: Noise Estimation Method (x1, y1) (x2, y2) Overlap region boundary points y Source estimation (average of three boundary points) (x3, y3) x

  12. 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)

  13. 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)

  14. MSE Comparison Simulated one thousand distinct realizations of our experimental setup with variances from 0 to 0.2 and measured the mean squared error

  15. 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

  16. Special Thanks Project Supervisors Patricio La Rosa Graduate Student (ESE) Professor Paul Min Associate Professor (ESE)

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