[PPT] - DATAMAN MOBILE COMPUTING LABORATORY VOR Base Stations for Indoor PowerPoint Presentation

SLIDE 1

DATAMAN

MOBILE COMPUTING LABORATORY

VOR Base Stations for Indoor 802.11 Positioning

Dragos ¸ Niculescu and Badri Nath {dnicules,badri}@cs.rutgers.edu

SLIDE 2

indoor positioning

☞

existing systems require either:

❍ extra infrastructure

+ good accuracy

instrumentation
specialized beacons, badges
LOS

❍ signal strength (SS) map

+ existing 802.11 base stations

map depends on people, furniture, ...
centralized database

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 3

signal strength map (example) ☞

= basestations = sample point 25m (0,0) 56m

RADAR project (Microsoft)

1. build SS map:

❍ for each point, measure SS to all 5 BS

2. query:

❍ measure SS to 5 BS⇒best match in the map

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 4

VORBA - VOR BAse stations

☞

goals:

❍ no signal strength map ❍ less infrastructure ❍ move complexity to the 802.11 base station ❍ use: − angles − ranges − angles and ranges

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 5

VORBA prototype

☞

IR sender IR receiver

antenna

IR sender

802.11 card 802.11 card

0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330°

− 4 0− 3 − 1 − 3 0 − 2 −4 0− 3 − 1 − 3 0 − 2

prototype base station directional antenna pattern

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 6

basic idea

☞

−78 −76 −74 −72 −70 −68 −66 −64 −62 mean SS signal strength [dBm]

π 2 π 2 3π 2 3π 2

π π 2π 2π

signal strength variation = SS(α) 1.SS(α) 2. peak → angle mean → range 3. angle and/or range → position

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 7

experiments

☞

❍ 32 measurement points ❍ 5 + 2 base stations ❍ N/E/S/W measurements of 3-4 revolutions each

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 8

angles only positioning

☞

0.25 0.5 0.75 1 2 4 6 8 10 12 14 16

cumulative probability error in meters using best angle using first two angles

❍ 3.5m median position error ❍ 3m if we knew the best peak

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 9

quantized angles

☞

−400 −200 200 400 600 800 1000 1200 1400 −400 −200 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 −500 500 1000 1500 −500 500 1000 1500 2000 2500 + 1650x794 1776x130 218x178 552x908 814x358

+ + +

+

+ +

−400 −200 200 400 600 800 1000 1200 1400 −400 −200 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 −500 500 1000 1500 −500 500 1000 1500 2000 2500 + 1650x794 1776x130 218x178 552x908 814x358

+ +

❍ measurements rounded to the nearest 45◦

❍ simulation ❍ little degradation for 45◦ and 22.5◦ quantizations

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 10

angles & ranges

☞

A M

σr σx σa σy r ❍ angle error σa = 0.4 radians ≃ 21◦ ❍ range error σr = 0.2r ❍ approximate uncertainty as an ellipse ❍ error ellipse increases with distance

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 11

angles & ranges uncertainty

☞

how to combine several readings? Kalman filter.

α1 ρ1

BS1 BS2 BS3

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 12

angles & ranges positioning

☞

0.25 0.5 0.75 1 2 4 6 8 10 12 14 16 cumulative probability error in meters 7 BS 5 BS 3 BS 1 BS

❍ more base stations ⇒ better positions ❍ 2.1m median position error (all 7 BS)

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 13

summary

☞

❍ VORBA = VOR base station ❍ complexity into the base station − less infrastructure − no SS map ❍ revolving basestation measures SS(α) to derive − discrete angles − angle distributions − ranges ❍ works with quantized angles as well ❍ can achieve 2.1m - 4m median error

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 14

index

☞

❍ indoor positioning − angulation/lateration − SS map example ❍ VOR BAse station − prototype − basic idea − experiment setup ❍ angles only positioning − discrete angles − quantized angles ❍ angles and ranges − uncertainty − performance ❍ summary

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 15

trilateration

☞

M B C A N N N

α β γ

(xM − xA)2 + (yM − yA)2 = MA2 (xM − xB)2 + (yM − yB)2 = MB2

solve for (xM, yM)

(xM − xC)2 + (yM − yC)2 = MC2 ❍ MA, MB, MC are affected by errors ❍ several methods available

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 16

triangulation

☞

M B C A N N N

α β γ

(xM − xA) sin α = (yM − yA) cos α (xM − xB) sin β = (yM − yB) cos β

solve for (xM, yM)

(xM − xC) sin γ = (yM − yC) cos γ ❍ α, β, γ -affected by errors (Gaussian) ❍ several methods available

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 17

ranges and angles

☞

M B C A N N N

α β γ

xM = xA + MA cos α = xB + MB cos β = xC + MC cos γ yM = yA + MA sin α = yB + MB sin β = yC + MC sin γ ❍ one base station is theoretically enough ❍ α, β, γ, MA, MB, MC - affected by errors

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 18

best peak distribution

☞

−1 0.6 0.6 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8

probability

peak rank number of peaks

30%

histogram of number of peaks Histogram of SS rank

f best peak

mean = 4.5 peaks

60%

❍ 4.5 peaks on average ❍ best peak is first/second 90% of the time

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 19

ther peak distribution

☞

true direction

π −π

π 4

− π

4

15% true direction 33%

π 4

− π

4 π 2

− π

2

❍ other peaks point away from true direction

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 20

triangulation analysis

☞

0.001 0.002 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 simulation lower bound

1 λ

Var[x]

0.01 0.02 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 simulation lower bound

σ2 a Var[x]

0.01 0.02 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 simulation lower bound

1 ln R Rm Var[x]

V ar[x] > σ2

a

λπ ln R

Rm ❍ V ar[x] - standard dev. of positioning error ❍ λ - density of basestations / m2 ❍ to improve positioning:

1. decrease measurement error σa
2. use more basestations

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 21

angle distribution

☞

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 22

quantized angles

☞

0.25 0.5 0.75 1 2 4 6 8 10 12 14 cumulative probability error in meters best angle (non quantized) quantization 45 quantization 22.5 quantization 90 ❍ little degradation for − 16 directions (22.5◦) − 8 directions (45◦)

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 23

range inference

☞

❍ open space attenuation: SS[dBm] = SS0[dBm] − log10( d

d0 )n

❍ d(SS) − obtained through fitting − known to be unreliable ❍ we obtain it from integration of SS(α) ❍ 5-fold cross validation − corridor basestations - waveguide effect − median range error 2.8m

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 24

positioning w. ranges

☞

0.25 0.5 0.75 1 2 4 6 8 10 12 14 cumulative probability error in meters

❍ trilateration 5 base stations ❍ median position error 4.5m

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning

SLIDE 25

discussion

☞

❍ triangulation with large outliers ❍ use more than two angles? ❍ no correlation between − angle error and distance − angle error and SS ❍ corridors ⇒ waveguides ❍ revolving signal at the mobile? ❍ data performance?

Dragos ¸ Niculescu – VOR Base Stations for Indoor 802.11 Positioning