Transcript Document

Travel Times from Mobile Sensors
Ram Rajagopal, Raffi Sevlian and Pravin Varaiya
University of California, Berkeley
Singapore Road Traffic Control
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Complex System Challenges: Urban Traffic
1982 to 2001:
– 20% population increase
– 236% travel time increase
Congestion costs per year:
– $78 billion
– 4.2 billion lost hours
– 2.9 billion gallons of wasted gas
Highways operated at 100% efficiency can reduce this by
40%
Providing drivers with travel time estimates will help
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Source: 2007 Urban Mobility Report, Texas Transportation Institute
Challenges for Travel Time (TT) Measurements
Street TT distributions poorly
characterized by means and
variances
Need to measure individual
vehicle travel times
Need real-time estimates
Travel times in a typical link
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Proposed Approach
Localization signatures from vehicle probes:
– GPS from navigation devices
– Received Signal Strength Indicators from GSM phones
Existing work maps each signature to a location causing:
– Large individual localization errors (RSSI) (90 m median error)
– Localization errors propagate
Proposed approach maps signature sequence to paths--inspired
by bio-sequence matching and Viterbi algorithms
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Description of Method
Road map
Each link
: set of road links
and junctions
characterized by signature set
Map
Matching
Sequence of time
stamped signatures
Estimates of link TT
distributions for period S
Locate with motion and
traffic constraints
Time
Splitting
Split TT
between links using
Sparse Network Coding
This talk: Map Matching
Multiple
vehicles
Historic
Flows
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Map Matching (MM)
Split GIS map into L links of size U (e.g. U = 20m)
Data given by signature distance matrix:
Estimate matching
Performance metrics
Prob. of
Error
Meter
Error
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Signature Distance
Database of GIS-signature
pairs for each link:
Distance:
e.g.: Euclidean norm (RSSI)
Statistical model:
Distributions from
experimental data
RSSI measurement for
base station r
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Statistical Model for MM
Conditional on true , independent links, data D distributed as:
Minimize negative log-likelihood, using a proper prior
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Constrained MM (Routes)
Consider a route 1, …, l, l+1,…,L
Statistical model does not incorporate motion constraints
Vehicles only move forward on the route, speed limits, giving
constraint
is the furthest link reachable using multiple of speed limit
during time
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Matching Graph (Routes)
Edit graph representation
(N,|L|)
Links l=1,|L|
• One node per matching
(n,l)
(n’,l’)
• Edge from (n,l) to (n+1,l’)
if l’ in Reach(l)
• Diagonal edge weights
(n,l)
• Vertical edge weights = 0
• Vertical edge weights = 0
Samples n = 1, N
Viterbi decoding = shortest path on matching graph
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Example of Signature Distance Matrix
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Real-Time Matching
Error correction: future positions constrain past positions
Real-time matching: future continuously updated
Estimate when sample r arrives:
Edit graph updated:
– Columns added for new observations
– Columns deleted for committed matches
– Matching
Commit n’ if
recomputed
r>R
or if
n’
Real time matching
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Beyond Routes
Assign a weight for each road section:
– distance, frequency of use, …
– Vehicle takes shortest weight route between observations
Match graph (“edit graph”) still valid:
– Reachable set defined by map graph constraints
– Furthest reachable node computed with all-pairs shortest path in
map graph
Heuristics used to avoid calculating every
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Performance Bound (“High SNR”)
Size of search space (
):
Unconstrained matching
Constrained matching
 Expected number of correct matches (
Unconstrained case:
):
Under (n,l) being true match
Goes to zero for N large
(“Large map, long path”)
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Experimental Data
Data collected for a route: RSSI
and corresponding GPS, every 2
seconds
Route is 8 Km long
Road sections are 9m long
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Error Distribution
10-fold cross-validation, database = 8 route logs
Database is the prerecorded set of signatures for a map
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Error for Varying Sample Separations
Vary sampling rate: no benefit below 3 m/sample
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Position Dependency of Error
Error peaks at entrance of
highway section and parking
For single track: dependency of
meter-error and distance to previous
observation
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GPS Interpolation Performance
Periodically use GPS, in between use RSSI
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Time Splitting

is section travel time R.V. for fixed period
If observations are infrequent:
TT between
observations
Distributions of
Path followed from n to
n+1: 1 if link l was used
from such observations?
Issue: few observations, but history is available as
Idea: for most l,
close to
, e.g.
ML Deconvolution, LASSO, Sparse Sum Decoding
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Mobile Travel Time Problem (unified view)
Factor Model (v is vehicle)
Observation Model
Assumptions
Goals
and/or
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Conclusions and Future Work
Analogy with coding/decoding powerful
Constraints reduce search space
1/SNR error behavior suggests using multiple measurements
Compute mean-field approximation for probability of error
Compute achievable error rate for Mobile Travel Time
problem
Large Scale Field Test algorithms with data from Dubai and
New Delhi
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