Traffic Estimation withSpace-Based Data
Mark R. McCord
NCRST-FThe Ohio State University
Workshop on
Satellite Based Traffic Measurement
Berlin, Germany
9-10 September 2002
Satellite Imagery forVehicle Identification
High Resolution RequiredCars 1m - 2m panchromatic
Trucks 4m panchromatic
High Resolution=> Low orbits => Limited temporal sampling
(dynamic traffic) => Long time scale, geographically
extensive applications
=> Traffic Monitoring Average Annual Daily Traffic (AADT) Vehicle Kilometers Traveled (VKT)
Improved AADT and VKTEstimation from High-Resolution
Satellite Imagery
AcknowledgmentsP. Goel, Z. Jiang, B. Coifman,
Y. Yang,C. Merry, Past Students
National, Regional Network Coverage AADT and VKT
Average Annual Daily TrafficVehicle Kilometers Traveled
AADT: Traffic on a highway segment
AADTs Σ=1,365 V24s, / 365
V24s, 24-hour volume, segment s, day
VKT: Travel over the network
(avg daily) VKT = Σs=1,S Lengths * AADTs
Estimating AADT on System
(Permanent) Automatic Traffic Recorders
V24s, , = 1, 2, …, 365, s Spatr
~3% segments equipped with PATRs
=> Calculate AADTs s Spatr
=> Estimate temporal variability
(“expansion factors”)
e.g., EF() = EFMD[m(),d()], m() = 1,2, …, 12
d() = 1, 2, …, 7
Estimating AADT on System (cont.)
Moveable ATRs (Coverage Counts) V24
s, , V24s, +1, {1, 2, …, 364},sSmatr
~33% segments per year
=> Estimate AADTs s Smatr
AADTests = f[V24
s, , V24s, +1, EF(), EF(+1)]
e.g. AADTests = [V24
s, /EF()+V24s,+1/EF(+1)]/2
Estimating AADT on System (cont.)
Unsampled Segments in Year, Suns (S= Spatr Smatr Suns)
AADTs Suns = f[AADTs’, s’ SpatrSmatr], s Suns
e.g. AADTs Suns = Average[AADTs’, s’ SpatrSmatr]
AADTs Suns = f[AADTs sampled in previous year, network growth factors]
AccuracySampling, Estimation Methodology
CostLarge Labor and Equipment Expenses
Satellite Imagery
Potential Added Data
Off-the-Road
Spatial Perspective
Access of Remote Areas
Difficulty Unfamiliar (Density Based)
Potential Error (“Short Interval” Observation)
OriginalImage
Binary Image
Flowest(x,t+t) = Density(x+x,t)*Velocity(x+x,t) Flowest(x,t+t) [vph]
t short (3-15 minutes)
V24,ests, = f[Flowest(x,t+t; s,), EFh(h(t))]
e.g., V24,ests, = 24*Flowest(x,t+t; s,) / EFh(h(t))
EFh: hourly expansion factor
V24,ests, = f[Flowest(x,t+t; s,), EFh(h(t))]
AADTimgs = f[ V24,est
s, , EFMD[m(),d()] ] EFMD: seasonal factor (month-of-year, day-of-week)
Relative Error
(AADT Image-based – AADTTrue) / AADTTrue
AADTTrue AADTGround-based
Higher LOSSegment Number of Segment Density in "higher
No Descripton FC* Image Date Time Images Length (km) (pcplpkm) direction"
1 I-71: @US62 11 Aerial 11/30/95 10:13 am 13 12.02 5.70 A
2 I-270: @I-70 11 Aerial 11/30/95 10:21 am 6 4.95 6.51 A
… … … … … … … … … …
17 I-475: SALISBURY RD. to SR2 11 Satellite 10/22/01 12:32 pm 1 3.49 4.98 A
18 I-475: SR2 to US20 11 Satellite 10/22/01 12:32 pm 1 6.97 6.26 A
*Functional Classification: 1=Rural Interstate, 11= Urban Interstate **Assumed 10-11am
Duration of Image- Ground-Simulated based based
Segment Segment Number of Space-Mean Count Interval AADT AADT Relative ErrorNumber Length, L (mi) Cars Nc , Trucks Nt Speed Us (kmph) RE
1 12.02 98, 88 96.97 7.44 30248 30178** 0.0023
2 4.95 143, 33 101.57 2.92 78358 77497* 0.0111
… … … … … … … …
17 3.49 127,2 104.34 2.01 79610 70722* 0.1257
18 6.97 296,9 104.11 4.02 93943 84844** 0.1072
*: based on published AADT and growth factors
**: based on PATR data
imgAADT(mins)t dur grd
AADT
D u r a t i o n o f I m a g e - G r o u n d -S i m u l a t e d b a s e d b a s e d
S e g m e n t S e g m e n t N u m b e r o f S p a c e - M e a n C o u n t I n t e r v a l A A D T A A D T R e l a t i v e E r r o rN u m b e r L e n g t h , L ( m i ) C a r s N c , T r u c k s N t S p e e d U s ( m p h ) R E
1 7 . 4 7 9 8 , 8 8 6 0 . 2 7 7 . 4 4 3 0 2 4 8 3 0 1 7 8 * * 0 . 0 0 2 32 3 . 0 7 1 4 3 , 3 3 6 3 . 1 3 2 . 9 2 7 8 3 5 8 7 7 4 9 7 * 0 . 0 1 1 13 4 . 7 5 7 2 , 5 1 6 5 . 8 5 4 . 3 3 3 2 7 7 8 4 5 9 5 5 * - 0 . 2 8 6 74 1 3 . 0 1 2 3 3 , 9 2 6 2 . 1 7 1 2 . 5 5 2 8 8 8 1 3 0 1 1 2 * * - 0 . 0 4 0 95 3 . 8 2 2 1 9 , 2 5 6 3 . 9 8 3 . 5 8 8 2 5 6 6 7 8 9 7 0 * 0 . 0 4 5 56 1 0 . 7 6 2 0 6 , 1 3 0 6 6 . 1 3 9 . 7 7 4 2 4 1 0 4 7 9 3 1 * - 0 . 1 1 5 27 1 . 4 3 4 8 , 1 0 6 3 . 2 8 1 . 3 6 4 3 8 5 0 5 1 6 0 4 * - 0 . 1 5 0 38 2 . 8 5 1 0 8 , 2 6 6 3 . 0 6 2 . 7 1 5 0 6 5 8 4 7 8 5 2 * 0 . 0 5 8 69 3 . 7 4 1 3 7 , 4 5 6 2 . 5 3 3 . 5 9 5 1 9 8 9 4 5 2 8 8 * 0 . 1 4 8 0
1 0 2 . 1 0 8 3 , 8 6 9 . 1 2 1 . 8 2 3 8 1 5 2 4 1 9 2 0 * - 0 . 0 8 9 91 1 3 . 4 5 1 3 9 , 8 6 9 . 4 6 2 . 9 8 3 7 7 1 0 4 2 2 1 0 * - 0 . 1 0 6 61 2 0 . 6 3 6 0 , 3 6 4 . 5 2 0 . 5 9 1 8 2 4 3 0 1 3 9 4 6 0 * 0 . 3 0 8 11 3 2 . 2 4 1 8 0 , 2 6 4 . 8 9 2 . 0 7 1 5 0 4 0 1 1 4 5 1 2 0 * * 0 . 0 3 6 41 4 2 . 1 9 1 7 1 , 0 6 5 . 0 0 2 . 0 2 1 4 4 4 0 6 1 3 4 0 2 0 * 0 . 0 7 7 51 5 1 . 8 0 1 1 4 , 1 8 6 3 . 6 4 1 . 7 0 9 1 1 7 6 6 7 5 9 2 * 0 . 3 4 8 91 6 1 . 8 7 8 3 , 4 6 4 . 5 4 1 . 7 4 6 1 8 1 8 6 0 9 4 2 * * 0 . 0 1 4 41 7 2 . 1 7 1 2 7 , 2 6 4 . 8 4 2 . 0 1 7 9 6 1 0 7 0 7 2 2 * 0 . 1 2 5 71 8 4 . 3 3 2 9 6 , 9 6 4 . 7 0 4 . 0 2 9 3 9 4 3 8 4 8 4 4 * * 0 . 1 0 7 2
* : b a s e d o n p u b l i s h e d A A D T ( a n d g r o w t h f a c t o r s )* * : b a s e d o n P A T R d a t a
imgAADT(mins)t dur grd
AADT
Relative Errors, RE
N = 18N(RE > 0) = 12N(RE < 0) = 6
Sample Mean = 0.03Sample St. Dev. = 0.15
RELATIVELY UNBIASED
Relative Errors, RE
Sample St. Dev. (w. mean = 0) = 0.15Maximum RE = 0.34
Lower RE with better AADTGr-based
Equiv. Count Interval: 0.6 – 12.6 mins
SURPRISING, PROMISING PERFORMANCE
RE Decreases with Increased Simulated Time Interval
1.51.00.50.0
0.3
0.2
0.1
0.0
1/tdur
Ab
solu
te v
alu
e of
RE
R-Sq = 34.8 %
Absolute value of RE = 0.0462 + 0.136 1/tdur
Regression Plot
NETWORK LEVEL ANALYSIS
Computer Simulation
Inputs- Traffic Patterns
• AADT distribution, Link Lengths, EFM, EFD
- Ground-Based Sampling• % Permanent ATR’s (PATR’s)• % Coverage Counts (MATR’s)
- Satellite-Based Sampling*- Variability/Error/Random Terms**
Outputs- AADT and VKT (VMT) Estimation Error
• Ground-Based Data Only• Satellite- and Ground-Based Combination
Satellite-Based Sampling* Physical Relations
FCD[lat1,lat2] = 2(1-Fnpgt)*NPIX*RES*NORB*L[lat1,lat2;i, NORB])10-3)/EAR[lat1, lat2] (5)
NORB = 8,681,665.8/ (R+H)1.5 [orbits/day] (9) H > 200 km => NORB < 16.3 [orbits/day] (10) H = (FL/WPI)(RES)(103) [km] (12) NORB>8,681,665/((FL/WPI)max(RES(103)+6371)1.5 [orb/day] (14) Vsg = 0.4633(NORB) [km/sec] (17) DBR = 3.706(NORB)(NPIX)(10-3)/(RES*COMP) [Mbits/sec] (18) (NPIX)( NORB) < 269.8(RES)(DBR*COMP)max (20)
Satellite-Based Sampling*Maximal Coverage
(P1) Max: Z1=NORB*NPIX*L[lat1,lat2;i,NORB] NORB,NPIX,i
s.t. 90 < i < 180
8,681,665.8/((FL/WPI)max RES(103)+6371)1.5 < NORB < 16.3
0 < NPIX < NPIXmax
(NPIX)(NORB) < 269.8(RES)(DBR*COMP)max
Satellite-Based Sampling*: Daily Coverage vs.
Resolution and Inclination Angle
Variability/Error/Random Terms**
- Ground-based sample: (gr)
V24(gr)s, = AADTs*EFM
M()-1 *EFD
D()-1
* exp((gr) - (gr)2/2), (gr) ~ N(0, (gr))
(gr): Daily deviation from deterministic model
- Satellite-based sample: (sat)
V24(sat)s, = AADTs*EFM
M()-1 *EFD
D()-1
* exp((sat) - (sat)2/2),
(sat) ~ N(0, (sat)) (sat): Error in Expanding Short-Duration Counts
and Daily Variability
Mean Squared Relative Error in AADT estimates
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0% 10% 20% 30% 40% 50%Percentage of Segments Sampled Annually with Ground Counts
Mea
n Sq
uare
d R
elat
ive
Err
or
Ground data onlyStd. Dev of Relative Error = 0.1Std. Dev of Relative Error = 0.2Std. Dev of Relative Error = 0.4Std. Dev of Relative Error = 0.6Std. Dev of Relative Error = 0.8Std. Dev of Relative Error = 1.0Std. Dev of Relative Error = 1.2Std. Dev of Relative Error = 1.4
Mean Squared Relative Error in VMT estimates
0
0.05
0.1
0.15
0.2
0.25
0% 10% 20% 30% 40% 50%Percentage of Segments Sampled Annually with Ground Counts
Mea
n Sq
uare
d R
elat
ive
Err
or
Ground data onlyStd. Dev of Relative Error = 0.1Std. Dev of Relative Error = 0.2Std. Dev of Relative Error = 0.4Std. Dev of Relative Error = 0.6Std. Dev of Relative Error = 0.8Std. Dev of Relative Error = 1.0Std. Dev of Relative Error = 1.2Std. Dev of Relative Error = 1.4
a. AADT errors vs. ESC (MATR=33%)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.5 1 1.5 2 2.5 3 3.5 4
ESC
MS
RE
in
AA
DT
est
imat
e
Impact of Satellite Supply — Equivalent Satellite Coverage (ESC)
Mean Squared Relative Error in AADT estimates
0
0.2
0.4
0.6
0.8
1
1.2
0% 10% 20% 30% 40% 50%Proportion of Moveable ATR
Mea
n Sq
uare
d R
elat
ive
Err
or
Ground data only
Ground and Sat data, ESC=0.5
Ground and Sat data, ESC=1.0
Ground and Sat data, ESC=2.0
Extensions
• More image- vs. ground-based comparisons• Expansion of short-interval flows
– Improved hourly factors– Quantification of uncertainty in sub-hour expansion
• Bayesian and model-based estimation• Spatial correlations • Satellite and air-based sampling strategies• Other Uses of Volume Data
– Statewide truck OD estimation– Screening tool: growth factors, ground-based
sample strategies• Implementation strategies• …