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CSE-473 Project 2 Monte Carlo Localization

CSE-473 Project 2 Monte Carlo Localization. Localization as state estimation. Motion: Perception: … is optimal under the Markov assumption. Kalman filters, Hidden Markov Models, DBN. Markov Localization as State Estimation (2). Markov!. Markov!. Kalman Filters.

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CSE-473 Project 2 Monte Carlo Localization

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  1. CSE-473 Project 2 Monte Carlo Localization

  2. Localization as state estimation

  3. Motion: Perception:… is optimal under the Markov assumption Kalman filters, Hidden Markov Models, DBN Markov Localization as State Estimation (2) Markov! Markov!

  4. Kalman Filters [Schiele et al. 94], [Weiß et al. 94], [Borenstein 96], [Gutmann et al. 96, 98], [Arras 98]

  5. Piecewise constant [Burgard et al. 96,98], [Fox et al. 99], [Konolige et al. 99]

  6. Particle Filters • Represent density by random samples • Estimation of non-Gaussian, nonlinear processes • Monte Carlo filter, Survival of the fittest, Condensation, Bootstrap filter, Particle filter • Filtering: [Handschin, 70], [Gordon et al., 93], [Kitagawa 96] • Computer vision: [Isard et al. 96, 98] • DBN: [Kanazawa et al., 95]

  7. Sample-based Density Representation • Converges to true density

  8. Importance Sampling Weight samples:

  9. Sample-based Density Representation

  10. Sensor Information: Importance Sampling

  11. Robot Motion

  12. Sensor Information: Importance Sampling

  13. Robot Motion

  14. Monte Carlo Localization (SIR) • Set of samples St = {<l1, p1>, … <lN, pN>} described by position land weight p • Initialize sample set S0according to prior knowledge • For each motion D do: • Sampling: Generate from each sample in St-1 a new sample according to motion model • For each observation s do: • Importance sampling: Re-weight each sample with the likelihood • Resampling: Draw N samples from sample set St according to their likelihood

  15. Motion Model P(l | a, l’) Model odometry error as Gaussian noise on a, b, and d

  16. Motion Model P(l | a, l’) Start

  17. Global Localization (sonar)

  18. Using Ceiling Maps for Localization [Dellaert et al. 99]

  19. P(z|x) z h(x) Vision-based Localization

  20. Vision-based Localization [CVPR-99]

  21. Comparison to Grid-based Markov Localization (2) • Office environment: 20,000 samples versus 150 million states • NMAH: Global localization in 15 seconds instead of 4 minutes • Vision-based: Can track the position in situations in which grid-based approach fails

  22. Condensation Tracking

  23. Mixed-State Tracking

  24. Tracking Multiple People

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