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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