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You’re about to leave…… and you’re addicted to TripCheck. So you
go and check it out and see this:
What’s wrong with this picture?
What’s wrong with this picture?
Gray is not the new black!
Estimation may be betterthan no data on final products
• Data may not be displayed for various reasons– Sensor failure– Data quality
• May prefer to estimate the system state instead of displaying gray areas
• Not enough sensors – but may still be able to recover information.
• Must be careful with estimation – at least report a confidence factor.
System State Estimation
• Must carefully choose good sources of correlated data
• Every sensor station has its own estimator• The PORTAL project does a great job at
archiving data – this makes statistical regressors for state estimation a good alternative.
• May consider to rely on observed features from the past in addition to well-known transportation theory.
Regression
• Find a description of data in terms of a function
• Example: height (H) and weight (W) data transformed into a function F(H) = W.
Which functional family?
• May consider a linear family first…
… which can easily be derived (Least squares). May also consider the expected value of a conditional Gaussian:
• A conditional Gaussian buys us statistics: The conditional mean is a linear regressor! Plus, estimating the joint is easy.
bmxy +=
)()]|([2| xx
xyyxy xxypE μ
σσ
μμ −+==
Which functional family?
• May also want to consider non-linear functions. A good first approach is an Artificial Neural Network
Experimental results
• Looked at rush hour (06:00 – 10:30) data from a “typical” Portland week, from US 26 E (Oct. 16 – Oct. 20 2006)
• Found a segment that is typically shown gray (it is my commute, so I notice these things)
• Inputs: current measurements of speed at nearby stations
• Goal: come up with a good enough estimate to color the TripCheck map
Segment
Confusion matrices
0 0 0
0 55 0
0 0 0
14 5 0
0 9 0
0 6 21
0 0 0
0 55 0
0 0 0
Milepost 73.62 Milepost 71.37
Linear
ANN 17 2 0
2 7 0
0 2 25
Prediction R Y G
Observed
R
Y G
Prediction R Y G
Prediction R Y G
Prediction R Y G
Observed
R
Y G
Observed
R
Y G
Observed
R
Y G
80%
89%100%
100%
Future work
• May still be able to recover system information with a nonlinear model from far away stations
• Still need to explore other segments and build a representative amount of model regressors (20% ?) to demonstrate effectiveness of the approach
• What keeps us from using this approach to estimate intermediate location states?
Future work
• May want to consider regressors with more inputs (shifted speeds, time, etc.)
• If nonlinear regressors are effective, we may want to use Gaussian Mixture Models (cheaper to train, statistically rich)
• Addressing quality in data presentation can be a sub-product of a more general problem: construct a framework for reliable system state estimation.