Hidden Markov Map Matching Through Noise and Sparseness

  • Slides: 78
Download presentation
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 Krumm Microsoft Research ACM SIGSPATIAL ’ 09 November 6 th, 2009

Agenda • • Rules of the game Using a Hidden Markov Model (HMM) Robustness

Agenda • • 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

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

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…

Except When It’s Not…

Our Test Route

Our Test Route

Three Insights 1. Correct matches tend to be nearby 2. Successive correct matches tend

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)

Mapping to a Hidden Markov Model (HMM)

Three Insights, Three Choices 1. Match Candidate Probabilities 2. Route Transition Probabilities 3. “Junk”

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

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 14 Distance Between GPS and Matched Point (meters) 16 18 20

Route Error is Exponential Distance Difference Probability 7 6 Data Histogram Exponential Distribution 5

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

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

Match Candidate Limitation • Don’t consider roads “unreasonably” far from GPS point

Route Candidate Limitation • Route Distance Limit • Absolute Speed Limit • Relative Speed

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

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

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

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.

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

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/Map. Matching. Data/data. htm

Data! http: //research. microsoft. com/en-us/um/people/jckrumm/Map. Matching. Data/data. htm

Conclusions • Map Matching is Not (Always) Trivial • HMM Map Matcher works “perfectly”

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

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

HIDDEN MARKOV MODELS OVERVIEW Markov models Hidden MarkovHIDDEN MARKOV MODELS OVERVIEW Markov models Hidden Markov
HIDDEN MARKOV MODELS OVERVIEW Markov models Hidden MarkovHIDDEN MARKOV MODELS OVERVIEW Markov models Hidden Markov
Markov Model Markov Model Markov Chain Firstorder MarkovMarkov Model Markov Model Markov Chain Firstorder Markov
Hidden Markov Models A firstorder Hidden Markov ModelHidden Markov Models A firstorder Hidden Markov Model
Hidden Markov Models A Hidden Markov Model consistsHidden Markov Models A Hidden Markov Model consists
Hidden Markov Models HMMs 1 Definition Hidden MarkovHidden Markov Models HMMs 1 Definition Hidden Markov
Hidden Markov Models A firstorder Hidden Markov ModelHidden Markov Models A firstorder Hidden Markov Model
Hidden Markov Models Hidden Markov Models HMMs XHidden Markov Models Hidden Markov Models HMMs X
Recognition Hidden Markov Models 1 Hidden Markov ModelRecognition Hidden Markov Models 1 Hidden Markov Model
Hidden Markov Models Outline Markov Chains l HiddenHidden Markov Models Outline Markov Chains l Hidden
Markov Chains and Hidden Markov Models stochastic generativeMarkov Chains and Hidden Markov Models stochastic generative
Introduction to HMMs Markov chains and Hidden MarkovIntroduction to HMMs Markov chains and Hidden Markov
Markov Chains and Hidden Markov Models stochastic generativeMarkov Chains and Hidden Markov Models stochastic generative
Artificial Intelligence Markov processes and Hidden Markov ModelsArtificial Intelligence Markov processes and Hidden Markov Models
Artificial Intelligence Markov processes and Hidden Markov ModelsArtificial Intelligence Markov processes and Hidden Markov Models
Markov Chains and Hidden Markov Models stochastic generativeMarkov Chains and Hidden Markov Models stochastic generative
Artificial Intelligence Markov processes and Hidden Markov ModelsArtificial Intelligence Markov processes and Hidden Markov Models
Artificial Intelligence Markov processes and Hidden Markov ModelsArtificial Intelligence Markov processes and Hidden Markov Models
RISET OPERASI Rantai MARKOV Rantai MARKOV Analisis MARKOVRISET OPERASI Rantai MARKOV Rantai MARKOV Analisis MARKOV
RISET OPERASI Rantai MARKOV Rantai MARKOV Analisis MARKOVRISET OPERASI Rantai MARKOV Rantai MARKOV Analisis MARKOV
Markov Chains 1 Markov Chains A Markov ChainMarkov Chains 1 Markov Chains A Markov Chain
Markov Models Markov Models Markov Models can beMarkov Models Markov Models Markov Models can be
Introduction to Hidden Markov Models Markov Models SetIntroduction to Hidden Markov Models Markov Models Set
Bioinformatics Hidden Markov Models Markov Random Processes nBioinformatics Hidden Markov Models Markov Random Processes n