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Route choice with smartphones GPS data
Michel Bierlaire
transp-or.epfl.ch
Transport and Mobility Laboratory, EPFL
Route choice with smartphones GPS data – p. 1/23
Motivation
• Travelers are equipped withsmartphones
• Smartphones are equippedwith sensors
• Can we learn mobility pat-terns from them?
Route choice with smartphones GPS data – p. 2/23
Objectives
• Focus on GPS data fromsmartphone
• Reconstruct actual paths
• Model route choice behavior
Route choice with smartphones GPS data – p. 3/23
Issues
Route choice with smartphones GPS data – p. 4/23
Issues
Route choice with smartphones GPS data – p. 5/23
Issues
• Low data collection rate to save battery
• Inaccuracy sue to technological constraints
• Smartphone carried in bags, pockets: weaker signal
• Map matching algorithms do not work with this data
Route choice with smartphones GPS data – p. 6/23
Context
• Network: G = (N,A)
• Node coordinates: xn = {lat, lon}
• Arc geometry:La : [0, 1] → R
2.
Example: straight line
La (ℓ) = (1− ℓ)xu + ℓxd.
• Model for the movement of the mobile phone:
x = S(x−, t−, t, p)
• Ideally a traffic simulator• Simpler models are used in practice• Random variable with density fx(x|x
−, t−, t, p)
Route choice with smartphones GPS data – p. 7/23
Data
One measurement: g =(t, x, σx, v, σv, h
),
• t, a time stamp ;
• x = (xlat, xlon), a pair of coordinates;
• σx, the standard deviation of the horizontal error in the locationmeasurement;
• v, a speed measurement (km/h) and,
• σv, the standard deviation of the error in that measurement;
• h, a heading measurement, that is the angle to the northdirection, from 0 to 359, clockwise.
Sequence: (g1, . . . , gT )
Route choice with smartphones GPS data – p. 8/23
Measurement equations
Objective:
• Given a path p
• Given a sequence (g1, . . . , gT )
• What is the likelihood that the sequence has been generated bya smartphone moving along path p?
• Note: different approach from map matching, which isessentially a projection procedure.
• We focus on the position only
• We derivePr(x1, . . . , xT |p),
• ... recursively
Pr(x1, . . . , xT |p) = Pr(xT |x1, . . . , xT−1, p) Pr(x1, . . . , xT−1|p).
Route choice with smartphones GPS data – p. 9/23
Recursion: first step
Pr(x1|p) =
∫
x1∈p
Pr(x1|x1, p) Pr(x1|p)dx1,
• integral spans all locations x1 on path p
• no prior information on x1
Pr(x1|p) = 1/Lp
• a smarter way would be to assign more probability in thebegining of the path
• measurement error of the device:
Pr(x1|x1, p) = Pr(x1|x1)
Route choice with smartphones GPS data – p. 10/23
Measurement error of the device
• Assume that latitudinal and longitudinal errors are i.i.d. normalwith variance σ2
• Measurement error is Rayleigh
• σ2 unknown, estimate:
σ2 = σ2
network + (σx1)2
where• σ2
network: network coding errors
• (σx1)2: GPS errors.
Pr(x1|x1) = exp
(−‖x1 − x1‖
2
2
2σ2
).
Route choice with smartphones GPS data – p. 11/23
Recursion: first step
Pr(x1|p) =1
Lp
∫
x1
exp
(−‖x1 − x1‖
2
2
2σ2
)dx1.
• Integral may be cumbersome for long paths
• Can be simplified using the concept of Domain of DataRelevance
• See Bierlaire & Frejinger (2008) and Bierlaire, Chen andNewman (2010)
Route choice with smartphones GPS data – p. 12/23
Recursion: second step
Pr(x1, x2|p) = Pr(x2|x1, p) Pr(x1|p),
Focus now on
Pr(x2|x1, p) =
∫
x2∈p
Pr(x2|x2, x1, p) Pr(x2|x1, p)dx2.
• first term = Pr(x2|x2) measurement error, same as before
• second term: predicts the position at time t2 of the traveler
Pr(x2|x1, p) =
∫
x1∈p
Pr(x2|x1, x1, p) Pr(x1|x1, p)dx1.
Route choice with smartphones GPS data – p. 13/23
Position predictor
Pr(x2|x1, p) =
∫
x1∈p
Pr(x2|x1, x1, p) Pr(x1|x1, p)dx1.
• First term: movement model
Pr(x2|x1, x1, p) = fx(x2|x1, t1, t2, p),
• Second term: Bayes rule
Pr(x1|x1, p) =Pr(x1|x1, p) Pr(x1|p)∫
x1
Pr(x1|x1, p) Pr(x1|p)dx1
.
simplifies to
Pr(x1|x1, p) =Pr(x1|x1, p)∫
x1
Pr(x1|x1, p)dx1
Route choice with smartphones GPS data – p. 14/23
Measurement equations
• Step k of the recursion based on same principles
• but requires some technical simplifications
Pr(xk−1|xk−1, p) =Pr(xk−1|xk−1, p)∫xPr(xk−1|x, p)dx
.
• Integrals can be simplified using the DDR
Route choice with smartphones GPS data – p. 15/23
Case study: true path
Route choice with smartphones GPS data – p. 16/23
Case study: path with a deviation (1)
Route choice with smartphones GPS data – p. 17/23
Case study: path with a deviation (2)
Route choice with smartphones GPS data – p. 18/23
Case study: path from map matching algo
Route choice with smartphones GPS data – p. 19/23
Case study: log likelihood from measurement equations
True path -11.3Deviation 1 -12.9Deviation 2 -13.2
Map matching −∞
• DDR simplifications assigns 0 probability on irrealistic paths
• Results are consistent with intuition
Route choice with smartphones GPS data – p. 20/23
Stochastic map matching algorithm
• Generate a set of paths candidates
• Compute for each of them the likelihood of the GPS data
• Select a subset based on this likelihood
Route choice with smartphones GPS data – p. 21/23
Summary
• We have designed a procedure that account for• the error of the GPS device• the error of the network coding• the movement of the smartphone
• It can involve complex models
• Technical simplifications are possible to make it operational onreal data
• We have also designed• a path generation algorithm (Bierlaire et al. 2010)• a procedure for the estimation of route choice models
(Bierlaire & FRejinger, 2008)
Route choice with smartphones GPS data – p. 22/23
References
• Bierlaire, M., and Frejinger, E. (2008). Routechoice modeling with network-free data,Transportation Research Part C: EmergingTechnologies 16(2):187-198.
http://dx.doi.org/10.1016/j.trc.2007.07.007
• Bierlaire, M., Chen, J., and Newman, J. P(2010). Modeling Route Choice Behavior FromSmartphone GPS data. Technical reportTRANSP-OR 101016. Transport and MobilityLaboratory, ENAC, EPFL.
http://transp-or.epfl.ch/php/abstract.php?type=1&id=BierChenNewm10
Route choice with smartphones GPS data – p. 23/23