Travel Times from Mobile Sensors

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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

Source 2007 Urban Mobility Report, Texas
Transportation Institute
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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 set of road links
  and junctions

• Each link characterized by signature
  set

Map Matching
Sequence of time stamped signatures
Locate with motion and traffic constraints
Multiple vehicles
Time Splitting
Estimates of link TT distributions for period S
Split TT between links using Sparse Network
Coding
Historic Flows

• This talk Map Matching

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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, l1,,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)

• One node per matching (n,l)

• Edge from (n,l) to (n1,l) if l in Reach(l)

Links l1,L
(n,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 recomputed
• Commit n if r gt 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 ( )
• Expected number of correct matches (
  )
• Unconstrained case

Unconstrained matching
Constrained matching
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
• Distributions of 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

Path followed from n to n1 1 if link l was used
TT between observations
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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