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Specification, estimation and validation of a
pedestrian walking behavior model
Gianluca Antonini
Michel Bierlaire
Javier Cruz
Thomas Robin
14th March 2008
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Motivation
● Model the pedestrian behaviour
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Motivation
● Use of econometric models
● Calibration on real data
● Model of the pedestrian behaviour
visibility and control of the specification
incorporate the model in more global models
estimated parameters values
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State of the art
pedestrian modelling
huge estimation data setlimited estimation data set
continuous modelsdiscrete models
- flexible - postulate equations
use of machine
learning methods
disaggregate behaviouraggregate level
Flow problems
- few number of parameters- lot of parameters
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Objectives
● Model the pedestrian behaviour at operational level
● Develop a specification with ‘constrained’ and
‘unconstrained’ parameters
● Estimate the model
● Validate the model
● Implement the model in a simulator
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Outline
● Introduction
● Discrete choice models
● Model specification
● Model estimation
● Model validation
● Simulator
● Conclusion
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Introduction
● Microscopic model : capture the behavior of each pedestrian
● Concept of personal space : interactions with other pedestrians
Strategical : destination
Leader follower
Collision avoidance
● Different behavioral levels :
Tactical : route choice
Operational level : short range behavior
instantaneous decisions
Fixed
Discrete choice model
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● Introduction
● Discrete choice models
● Model specification
● Model estimation
● Model validation
● Simulator
● Conclusion
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Discrete choice models : introduction
● Econometric models developped since the 50’s
● A choice theory defines :
- a decision maker : each pedestrian
- alternatives : possible immediate future steps
- attributes of alternatives : characteristics
- decision rule : utility maximisation theory
● Disagregate model
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Discrete choice model : our context
● Example : only considering distance toward destination
Alt. 2
Alt. 1
Alt. 3
destination
Decision maker nAlternatives, choice set
(set of possible next steps)
Dist 1
Alternatives
characteristics
Which alternative will he choose?
● At each step the pedestrian has to choose the next step in a choice set
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Discrete choice model : decision rule
● Association of a function, called utility to each alternative
● Utility maximisation theory
● It depends on the alternative i , and on the decision maker n
Alt. 2
Alt. 1
Alt. 3
The decision maker n will choose the alternative i which has the
higher utility
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Discrete choice model : utility function
● Utility is a latent concept
● It can not be directely observed
● Decision maker: stochastic decision rules
● Analyst: Lack of information Uncertainty
: deterministic part of the utility of alternative i for individual n
: error term, different assumptions can be made on its distribution
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Discrete choice model : utility specification
● Example : depends only on the distance toward the destination
: unknown parameter, has to be estimated from the data
: distance between alternative i and the final destination
How do we estimate ?
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Discrete choice model : error term
● Example : suppose independent and identically distributed (iid)
with an extreme value distribution
Multinomial Logit model
: probability for the individual n to choose the alternative i
: Choice set, depends on the individual n
Decision maker
Alt.1 Alt.2 Alt.3
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Discrete choice model : estimation data
start
Data set
destination
1s
Pedestrian trajectories
Observation Choice dist.1 dist.2 dist.3
1
2
3
4
5
6
2
2
2
2
3
2
1
1
2
3
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Discrete choice model : likelihood
● Maximisation of the likelihood function
● In practice use of the log-likelihood (numerical reasons)
: indicator equals to 1, if individual n has choosen alternative i, 0 otherwise
: set of individuals in the population
estimated from the data
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Why using a discrete choice model?
● Disaggregate
● Flexible
● Estimation
capture the behaviour of each pedestrian
easy to add behavioural modules
easy to add pedestrians characteristics
estimation on a real data set by likelihood
maximisation
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● Introduction
● Discrete choice models
● Model specification
● Model estimation
● Model validation
● Simulator
● Conclusion
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Model specification : the space discretization
Choice set : discretization of the visual space
Pedestrian visual space
At each step the choice set depends on the pedestrian speed and direction
Dynamic choice set
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Model specification : the choice set
11 directions3 speed regimes
33 alternatives
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Model specification : cross nested structure
● Hypothesis : alternatives correlated along speed regimes and directions
Nesting based on
direction
Nesting based on
speed regime
Cross Nested Logit model
● Cross Nested structure : each alternative belongs to 2 nests
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Model specification : cross nested structure
central
Decision maker
non central decelerate constant accelerate
alt. 17alt. 1 alt. 33
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Model specification : cross nested structure
● Probability of choosing the alternative i :
: choice set
: utility of alternative i
: membership degree of alternative j in the nest n
: parameter of the nest m
: number of nests
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Model specification : utility specification
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Model specification : utility specification
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Model specification : utility specification
● Keep direction (unconstrained) :
<0 <0<0
-0.0252
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Model specification : utility specification
● Toward destination (unconstrained) :
distance direction
<0 <0
-0.0790-1.55
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Model specification : utility specification
● Free flow acceleration (unconstrained) :
- Acceleration :
Low speed High speed
0.358-7.474.16-4.97
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Model specification : utility specification
● Free flow acceleration (unconstrained) :
- Deceleration :-2.41-0.0630
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Model specification : utility specification
● Leader follower (constrained) :
stimulus stimulussensitivity sensitivity
0.652-0.6633.69-0.1710.625-0.4890.942
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Model specification : utility specification
● Collision avoidance (constrained) :
stimulussensitivity
non significative0.239-0.00639
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● Introduction
● Discrete choice models
● Model specification
● Model estimation
● Model validation
● Simulator
● Conclusion
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The Japanese data set : video sequence
● Collected in Sendaï, Japan, on August 2000, large pedestrian crossing road
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The Japanese data set : data processing
● Tracking from video sequence: 2 observations per second
● Pedestrians trajectories extracted using 3D-calibration (DLT algorithm)
● For each pedestrian trajectory :
190 pedestrians, 9281 observations
framesff-1 f+2
Observed choiceCurrent frame
frame used to calculatespeed and direction
1s0.5s
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The Japanese data set : pedestrian trajectory
● 4 alternatives are never chosen: 1, 12, 23, 33
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Model estimation : general diagnosis
● Estimation made using the free Biogeme package (biogeme.epfl.ch)
● Estimation results :
● Parameters values consistent with hypothesis
Number of estimated parameters : 24
Init log-likelihood : -32451
Final log-likelihood : -13997.27
Likelihood ratio test : 36907
= 0.568
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Model estimation : parameters values
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● Introduction
● Discrete choice models
● Model specification
● Model estimation
● Model validation
● Simulator
● Conclusion
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Model validation : methodology
● Validation of the specification :
Developpment of a model with constants only (ASC model)
Simulation on the Japanese data set
Cross validation on the Japanese data set
● Validation of the model :
Simulation on an experimental Dutch data set, not used for model
estimation
Comparison of the proposed model with the ASC model
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Model validation : model constants-only
● The simplest model : utility of each alternative represented only
by an alternative specific constant (ASC)
● This model with only constants (ASC model) estimated on the
Japanese data set.
● It reproduces the aggregated observations proportions of the
Japanese data set
● The ASC model used for comparison (for example the number
of outliers)
28 parameters (33, minus 4 never chosen,
minus 1 for normalization)
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Model validation : simulation on the Japanese
data set (Aggregate level)● The proposed model is applied to the Japanese data set (used for
estimation)
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Model validation : simulation on the Japanese
data set (Disaggregate level)● Outlier : Observation with predicted probability less than 1/33 (hazard)
Number of outliers: 7.13% for proposed model
19.90% for ASC model
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Model validation : Cross-validation on the
Japanese data set● Japanese data splited into 5 subsets, each containing 20% of the
observations
● Number of outliers (compared with the ASC model cross validation)
5 experiments :1 subset saved for validation
estimation of the model on the 4 remaining
Robust specification
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The Dutch data set : video sequence
● Collected at Delft university, in 2000-2001, 2 pedestrians crossing flows
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The Dutch data set : general information
● Experimental data set
● Video sequence recorded at 10 frames per second
● Pedestrians trajectories extracted from the video sequence
● For each pedestrian trajectory :
724 pedestrians, 47481 observations
framesff-1 f+10
Observed choiceCurrent frame
frame used to calculatespeed and direction
1s0.1s
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The Dutch data set : comparison with
the Japanese data set● Normalized observations distribution among alternatives
● Observations repartitions inside the nest (Japanese / Dutch)
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The Dutch data set : comparison with
the Japanese data set
● Quite similar observations proportions in the direction’s cones (not for
speed regime)
● Speed distributions have different shapes (experimental design of Dutch
data set)
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Model validation : simulation on the Dutch
data set (Aggregate level)● The proposed model is applied to the Dutch data set ( NOT used
for estimation)
Overprediction of acceleration and deceleration
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Model validation : simulation on the Dutch
data set (Disaggregate level)● Outlier : Observation with predicted probability less than 1/33 (hazard)
Number of outliers: 2.48%
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Model validation : Comparison with the ASC
model on the Dutch data set (Aggregate level)
● The ASC model is applied to the Dutch data set and compared to the
proposed model)
Proposed modelASC model
Equivalent for direction (logical, due to proportions)
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Model validation : simulation on the Japanese
data set (Disaggregate level)● Outlier : Observation with predicted probability less than 1/33 (hazard)
Number of outliers: 2.48% for proposed model
10.31% for ASC model
Superiority of the proposed model
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● Introduction
● Discrete choice models
● Model specification
● Model estimation
● Model validation
● Simulator
● Conclusion
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Simulator
● Implementation of the developped specification in a simulator
● Simulation of 2 pedestrian crossing flows with the model
● Examples :
- Start : random speed and direction
- Simulation of 300s
Ex1 : low density, 2 pedestrians per second entering
Ex2 : high density, 5 pedestrians per second entering
- Finish : random destination
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Simulator
● Low density :
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Simulator
● High density :
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Conclusions and Perspectives
● Conclusions :
Discrete choice model for pedestrian walking behavior with ‘unconstrained‘ and
‘constrained’ parameters
Model estimated on a real data set, parameters values consistent with hypothesis
Model validated on a real data set, not used for estimation
Operating Simulator
● Perspectives :
Improve the acceleration and deceleration patterns
Incorporate physical characteristics of the pedestrians
Model the strategical and tactical behavioural levels
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