Transcript Hidden Markov Map Matching Through Noise and Sparseness Paul Newson and John Krumm Microsoft Research ACM SIGSPATIAL ’09 November 6th, 2009

Hidden Markov Map Matching
Through Noise and Sparseness
Paul Newson and John Krumm
Microsoft Research
ACM SIGSPATIAL ’09
November 6th, 2009
Agenda
•
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Rules of the game
Using a Hidden Markov Model (HMM)
Robustness to Noise and Sparseness
Shared Data for Comparison
Rules of the Game
Some Applications:
• Route compression
• Navigation systems
• Traffic Probes
Map Matching is Trivial!
“I am not convinced to which
extent the problem of path
matching to a map is still
relevant with current GPS
accuracy”
- Anonymous Reviewer 3
Except When It’s Not…
Our Test Route
Three Insights
1. Correct matches tend
to be nearby
2. Successive correct
matches tend to be
linked by simple
routes
3. Some points are junk,
and the best thing to
do is ignore them
Mapping to a Hidden Markov Model
(HMM)
Three Insights, Three Choices
1. Match Candidate
Probabilities
2. Route Transition
Probabilities
3. “Junk” Points
Match Error is Gaussian (sort of)
GPS Difference Probability
0.12
0.1
Data Histogram
Gaussian Distribution
0.08
0.06
0.04
0.02
0
0
2
4
6
8
10
12
Distance Between GPS and Matched Point (meters)
14
16
18
20
Route Error is Exponential
Distance Difference Probability
7
6
Data Histogram
Exponential Distribution
5
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
abs(great circle distance - route distance) (meters)
1.2
1.4
1.6
1.8
2
Three Insights, Three Choices
1. Match Candidate
Probabilities
2. Route Transition
Probabilities
3. “Junk Points”
Match Candidate Limitation
• Don’t consider roads
“unreasonably” far
from GPS point
Route Candidate Limitation
• Route Distance Limit
• Absolute Speed Limit
• Relative Speed Limit
Robustness to Sparse Data
Error vs. Sampling Period
1
0.9
0.8
Route Mismatch Fraction
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
600
540
480
420
360
300
240
180
120
90
60
45
30
20
10
5
2
1
Sampling Period (seconds)
Robustness to Sparse Data
Error vs. Sampling Period
1
0.9
0.8
Route Mismatch Fraction
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
600
540
480
420
360
300
240
180
120
90
60
45
30
20
10
5
2
1
Sampling Period (seconds)
30 second sample period
90 second sample period
30 second sample period
90 second sample period
30 second sample period
90 second sample period
Robustness to Noise
At 30 second sample period
Accuracy vs. Measurement Noise
1
0.9
Fraction of Route Incorrect
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
4.07
10
15
20
30
40
Noise Standard Deviation (meters)
50
75
100
30 seconds, no added noise
30 seconds, 30 meters noise
30 seconds, no added noise
30 seconds, 30 meters noise
30 seconds, no added noise
30 seconds, 30 meters noise
30 seconds, no added noise
30 seconds, 30 meters noise
30 seconds, no added noise
30 seconds, 30 meters noise
Data!
http://research.microsoft.com/en-us/um/people/jckrumm/MapMatchingData/data.htm
Conclusions
• Map Matching is Not (Always) Trivial
• HMM Map Matcher works “perfectly” up to
30 second sample period
• HMM Map Matcher is reasonably good up to
90 second sample period
• Try our data!
Questions?
Hidden Markov Map Matching Through Noise and Sparseness
Paul Newson and John Krumm
Microsoft Research
ACM SIGSPATIAL ’09
November 6th, 2009