Hidden Markov Map Matching Through Noise and Sparseness Paul Newson and John Krumm Microsoft...
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Hidden Markov Map Matching Through Noise and Sparseness Paul Newson and John Krumm Microsoft Research ACM SIGSPATIAL ’09 November 6 th , 2009
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Transcript of Hidden Markov Map Matching Through Noise and Sparseness Paul Newson and John Krumm Microsoft...
Hidden Markov Map Matching Through Noise and Sparseness
Paul Newson and John KrummMicrosoft ResearchACM SIGSPATIAL ’09November 6th, 2009
Agenda
• Rules of the game• Using a Hidden Markov Model (HMM)• Robustness to Noise and Sparseness• Shared Data for Comparison
Rules of the GameSome 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)
0 2 4 6 8 10 12 14 16 18 200
0.02
0.04
0.06
0.08
0.1
0.12
GPS Difference Probability
Data Histogram Gaussian Distribution
Distance Between GPS and Matched Point (meters)
Route Error is Exponential
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
1
2
3
4
5
6
7
Distance Difference Probability
Data Histogram Exponential Distribution
abs(great circle distance - route distance) (meters)
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
1 2 5 10 20 30 45 60 90 120
180
240
300
360
420
480
540
600
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Error vs. Sampling Period
Sampling Period (seconds)
Rout
e M
ismat
ch F
racti
on
Robustness to Sparse Data
1 2 5 10 20 30 45 60 90 120
180
240
300
360
420
480
540
600
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Error vs. Sampling Period
Sampling Period (seconds)
Rout
e M
ismat
ch F
racti
on
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 NoiseAt 30 second sample period
4.07 10 15 20 30 40 50 75 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Accuracy vs. Measurement Noise
Noise Standard Deviation (meters)
Frac
tion
of R
oute
Inco
rrec
t
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 KrummMicrosoft ResearchACM SIGSPATIAL ’09November 6th, 2009
