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Institute for Software Integrated SystemsVanderbilt University
Accuracy Enhancements for TDOA Estimation on Highly
Resource Constrained Mobile Platforms
Kumar Chhokra, Ted Bapty, Jason Scott, Mitch Wilkes
March 9, 2004 2
OverviewIntroductionMotivationChallengesSolutions ResultsDemo
Supported by DARPA / IXO
March 9, 2004 3
Introduction
Increase in location aware systems and services, E911Need for close range monitoring
urban and hostile environments
Need for intelligence in hazardous areasAvailability of enabling technology
Low-cost, low-power DSPRF networksPositioning services (GPS)
March 9, 2004 4
Existing systems
Large form factorsLarge stand off / fixed locationsHigh cost
Cell phone base station ~$10,000Military units (~$50,000-100,000)
High precision, networked systemsUrban clutter“Theater” level vs. field level
Ship based TDOA
Site LOB
Image: courtesy Southwest Research Institute (SwRI ®)
March 9, 2004 5
Challenges
Effective in urban areasUniform high precision in all scenarios
Mobile = Small and low weightLongevity = low powerStealth = limited bandwidthSpatially separated = No global clockLow cost = No high precision sampling clockVarying environmental conditions
Differing radio characteristics
March 9, 2004 6
Solutions
Local processing Matched filtering with templateStealth, low power, Low bandwidth
GPS for global clock Jitter correction, introspectionLack of common global clock
Doppler and time-shift correction
Using GPS clock for local clock calibrationVarying sample ratesLow precision clock
WASPUnit
1
WASPUnit
2
WASPUnit
N
WASPBase
Station
TOAMeasurements
(low BW)
TARGETGPS
March 9, 2004 7
TOA electronics packageDSP Module
Analog Front-End
A/D Converter(2MHz)
Power SupplyGPS, RF Modem Weight : under 1 lb
4”x5”x6”
March 9, 2004 8
FRS Radio Modifications for IF
450 KHz IF (goes to A/D)
Sharp IF Filter
Frequency SynthesizerLNA Antenna
Compander
Quad Demod and Mixer
High-”Q” Filter
Audio AMP and speaker output
465MHz20MHz
Benefits:-Ability to use any radio-Cheap-Flexible
Challenges:• Phase Linearity• Poor Demod Perf.• Poor Baseband Perf.• Near Field Effects• Limited Range
March 9, 2004 9
Signal processing system architecture
SampleRate
Correct
LMS1 PPS
EstimatorGPS 1PPS
GPSLocalOsc
Count LMS Frequency estimator
Corrected GPSSlow drift
High jitter
Software Radio
50 100 150 200 250
-0.5
0
0.5
Raw IF data a fter prefiltering
0 1 2 3 4 5 6 7 8 9 10
x 105
-150
-100
-50
0
50
Frequency
Power Spectrum Magnitude (dB)
PS D of Raw IF afte r prefilte ring
-250 -200 -150 -100 -50 0 50 100 150 200 2500.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05cxy(τ)
Corre la tion lag (micros econds )
0 0.5 1 1.5 2 2.5 3 3.5 4
x 105
-1.5
-1
-0.5
0
0.5
1Baseband data after Software P LL demodulation
0 1 2 3 4 5 6 7 8 9 10
x 105
-200
-150
-100
-50
0
50
Frequency
Power Spectrum Magnitude (dB)
PS D of demod bas eband data
Radio IF
Narrow-BandFilter
420-480K
PhaseLockedLoop
(Demod)
GrossSignal
Location
GeneralizedCross
Correlation
PeakEstimation/
Interpolation
GlobalClock
CorrectionTOA Est
March 9, 2004 10
Effect of different sampling frequencies
ωb1
ωb
F ( ω)
fs1
fs2
Sampling
Sampling Reconstruction
Reconstruction
fs1
fs1
F ( ω)
ωb2’
))(()( τ−= tsftgτωωω sjesFsG −−= )/()( 1
March 9, 2004 11
Approximating frequency scaling as shifting
Doppler shift explanation Taylor series approximation
Let s = 1– a, then
if a << 1, we have (Typically, a = 20-200 ppm)
τωωω )1())1/(()1/(1)( ajeaFaG −−−−=
τωωω )1())1(()1()( ajeaFaG −−++=
0 100 200 300 400 500 600 700 800 900 1000-0.5
0
0.5
1
1.5 Scaling due to decrease in sampling frequency
Frequency in Hz
Nor
mal
ized
Mag
nitu
de
BW = 40 BW = 42.4 BW = 43.6
fs/f0 = 1 fs/f0 = 0.833 fs/f0 = 0.566
fs > f0 fs < f0
March 9, 2004 12
Doppler approximation
For narrow band signals,
where ωd = aωo = (1-s) ωo
2,0)( 0
bF ωδωδωω >=+
ωτωωω jeaFaG −++≈ ))()1()( 0
)()()( τωτ −−−≈ tj detftg
00 ,0)()( ωωδωδωωω −==+= sFsF
March 9, 2004 13
Disadvantages of Doppler shifting
Input signals modulated by complex exponential before Fourier domain correlation
Input signals become complexMemory requirement doubles
Greater memory access timesLower through putMore power consumptionMore memory / faster memory = greater cost
duetuguf tj dωτ −∞
∞−
+= ∫ )()(maxarg *
March 9, 2004 14
Alternative correction
Can we shift in time instead of frequency?Accomplished by multiplication by complex exponential in frequency domainPerformed during frequency domain correlation operations
Time and frequency are dualsShifting and approximating in time = shifting and approximating in freq
March 9, 2004 15
Time domain effects of different sampling rates
Faster sampling rate “delays” features in the sampled domainCompensate by advancing delayed signal
)2
)1(()()(~ 12 ττ sTT
stftftf od −
−−+=+=
ωτωω djeFF )()(~ =
0 10 20 30 40 50 60 70 80-5
0
5
10Effect of differeing s ample rates on cros s -correlation
cros s -correlation index
R(τ)
xcorr at Fs 1 = 500Hz, Fs 2 = 500Hzxcorr at Fs 1 = 500Hz, Fs 2 = 1000Hz
0 5 10 15 20 25 30 35 40-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
sample number
sam
pled
val
ue
f(t) = cos(20t + π/6)
Fs = 500 HzFs = 1000 Hz
March 9, 2004 16
Comparing the two
Trade-off between accuracy and performanceDoppler
Affords greater accuracyRequires more memory / computationModulates entire signal with complex cosine before xcorr
Time-shiftingProvides acceptable accuracyUses lesser memory (input signal stays real)Applies only to few significant frequency binsFaster throughput
Approximations are easy to apply)(1)exp( tjtj dd ωω +=
March 9, 2004 17
Results – Evaluating correction techniques
Comparing estimated delays vs. uncorrected when clocks are off by 10ppm
-30000
-25000
-20000
-15000
-10000
-5000
0
5000
1k 2k 3k 4k 5k
frequency of sinusoid used in Hz
erro
r in
dela
y es
timat
e in
na
no-s
econ
ds directdopplerdop approxtime shifttime approx
Corrected error is within allocated error budget for the signals of interest
Signal of interest (1Khz – 3kHz) PRNOscillator clock drift: ±100 ppm Delay in uncompensated case: ~1-10 µ-secDuration of signal of interest (template) : 0.2 secNominal sampling freq: 2 MHz
comparing errors between correction techniques
-200
-150
-100
-50
0
50
100
150
1k 2k 3k 4k 5k
Frequency of sinusoid
erro
r in
pred
icte
d de
lay
inna
no-s
econ
ds dopplerdop approxtime shifttime approx
March 9, 2004 18
Testing ResultsTime-of-arrival Consistency
Measured TOA vs Actual
0.00200.00400.00600.00800.00
1000.001200.001400.00
0 500 1000 1500Actual Distance
Mea
sure
d TO
F T
12
34
5
6
3
4
2
56
-2000.00-1000.00
0.001000.002000.003000.004000.00
1 2 3 4 5 6 7
-8000.00
-6000.00
-4000.00
-2000.00
0.00
2000.00
4000.00
6000.00
1 2 3 4 5 6 7 8 9
-8000.00
-6000.00
-4000.00
-2000.00
0.00
2000.00
4000.00
6000.00
1 2 3 4 5 6 7 8 9
-8000.00
-6000.00
-4000.00
-2000.00
0.00
2000.00
4000.00
1.00 2.00 3.00 4.00 5.00 6.00
-8000.00
-6000.00
-4000.00
-2000.00
0.00
2000.00
4000.00
6000.00
1 2 3 4 5 6 7 8
-8000.00
-6000.00
-4000.00
-2000.00
0.00
2000.00
4000.00
6000.00
1 2 3 4 5 6 7 8 9
Delta2m
103m
190m
127m
170m
1243m
March 9, 2004 19
Demo
March 9, 2004 20
Conclusion
Developed a new TDOA systemHighly constrained Solved several problems due to distributed clocksDeveloped algosTested in field
March 9, 2004 21
Questions/ Applause?
March 9, 2004 22
Road Map
OverviewPresent all the different topics we are going to talk about
IntroductionIncrease in location aware systems and services, E911Need for close range monitoring – urban and hostile environmentsNeed for intelligence in hazardous areas
MotivationCost – compare cell phone/ E911Large stand offUrban clutterTheater level vs. field level
ChallengesSaptially separated - Lack of global clockStealth + low-power - Lack of bandwidth for communicationCost - No high precision common sampling clockVarying environmental conditions – changing sample rates
March 9, 2004 23
SolutionsLocal processing – matched filtering with templateGPS for global clock – jitter correction, introspectionDoppler and time-shift correction – varying sample rates
Signal processing system architectureInsert picture here
Effect of different sampling frequenciesShow picture of how things scale with changing sampling freqShow equation
Approximating scaling with frequency shiftsDoppler shift explanation – Taylor series approximationInclude figure from Sonar signal analysis
Disadvantages of Doppler shiftingInput signals modulated by complex exponentialInput signals become complexmemory requirement doubles -> greater memory access times
March 9, 2004 24
Alternative correctionTime shiftingTime and frequency are duals
Insert picture for gate function and sinc functionShifting and approximating in time = shifting and approximating in freqInclude relevant equations here
AdvantagesReduces memory requirementsReduces access timesApproximation is easy to apply
Add equation for 1 + jwTrade-off between accuracy and performance
ResultsSimulation resultsField results
Demo
