hidden markov map matching through noise and sparseness

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