Kamin Whitehouse David Culler WSNA, September

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Presentation transcript:

Kamin Whitehouse David Culler WSNA, September 28 2002 Macro-calibration Kamin Whitehouse David Culler WSNA, September 28 2002

Introduction r* = f(r, ß) Light Sensor Response Stimulus Observed Desired Light Sensor

Introduction

Introduction Macro-Calibration Calibrate the network, not the devices Exploit sensor redundancy Global optimization

Talk Outline Distance estimation Traditional (micro-)calibration Iterative calibration Macro-calibration Joint calibration

Calamari Overview Antenna Speaker Tone Detector Microphone

Acoustic Time of Flight Calamari Overview Transmit Time Receive Time Acoustic Time of Flight

Experimental Setup

No Calibration: 74.6% Error

Traditional Calibration Time Adjust transmitter and receiver to minimize error Observed Desired Distance

Chicken or Egg? TOF Transmit Receive Tns Receive TOF Transmit Rcv TOF

Iterative Calibration Tref T T R R

Iterative Calibration: 19.7%

Naive Calibration: 21% Error

Calibration as Parameter Estimation Stimulus Response Observed r* = f(r, ß) Desired

Parameter Estimation r*1 = ß1 + ß2r1 + ß3r21 r*2 = ß1 + ß2r2 + ß3r22 Stimulus Response r* = f(r, ß) r*1 = ß1 + ß2r1 + ß3r21 r5 r*2 = ß1 + ß2r2 + ß3r22 r*6 r4 r*3 = ß1 + ß2r3 + ß3r23 r*5 r3 r*4 r*4 = ß1 + ß2r4 + ß3r24 r2 r*3 r1 r*5 = ß1 + ß2r5 + ß3r25 r*2 r*1

Joint Calibration Tk, Rk Ti, Ri dik = f(tik, Ti, Rk)

Joint Calibration

Joint Parameter Estimation d12 = f(t12, T1, R2) d13 = f(t13, T1, R3) 2n parameters d14 = f(t14, T1, R4) n2 equations … d21 = f(t21, T2, R1) d23 = f(t23, T1, R2)

Joint Calibration: 10.1%

Conclusions Iterative Joint Calibration Micro-calibration One-by-one Observed each device Macro-calibration All-at-once Observed system Single Reference Propogates Noise Exploits Redundancy Cancels Noise Greedy Optimizes each device Global maximum Optimizes system

Future Work Non-linear parameter estimation Other sensor domains EM MCMC Other sensor domains Auto-calibration Post-deployment Unknown distances

Auto-calibration f(tik, Ti, Rk) = f(tki, Tk, Ri) dik = dki Tk Rk Rk Tk TOF Rk Tk TOF

Auto Calibration dik <= dhk + dhk dik <= dkh + dhk dik dhk dkh

Auto-calibration Choose parameters that maximize consistency while satisfying all constraints A quadratic program arises Minimize: Σik |dik – dki| Subject to: dih + djk - dhk >=0 for all trianglehik

Joint Calibration Revisited d12 = f(t12, T1, R2) 2n parameters d13 = f(t13, T1, R3) n2 equations d14 = f(t14, T1, R4) Up to n2-2n distances can be unknown … d21 = f(t21, T2, R1) d23 = f(t23, T1, R2)