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CSSE463: Image Recognition Day 31

Explore the concept of Kalman filtering for tracking, a probabilistic model that merges noisy measurements with the expected object trajectory, overcoming occlusion challenges. Learn motion models for accurate tracking and find relevant resources for a practical understanding. Discover how Kalman filtering applies to scenarios like tracking a missile or observing planets. Gain insights into trajectory inference for dynamic systems, despite noisy measurements, with examples and formalism breakdown. Delve into iterative algorithm processes, limitations of linear systems and Gaussian noise, as well as diverse applications beyond traditional tracking.

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CSSE463: Image Recognition Day 31

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  1. CSSE463: Image Recognition Day 31 • This week • Today: Intro to Kalman filtering for tracking • Tomorrow: Project workday, status report due • Questions?

  2. Motion models for tracking The Kalman filter is a probabilistic model that combines noisy measurements with the expected trajectory of the object. It works even with occlusion. Ideas presented here are from • http://www.cs.unc.edu/~welch/kalman/ • chapter 15.4 of Russell and Norvig, Artificial Intelligence: A Modern Approach, ed 2: Prentice Hall, 2003 • Chapter 16.6 of Sonka et al. • Kevin Murphy’s toolbox: http://www.cs.ubc.ca/~murphyk/Software/Kalman/kalman.html

  3. Scenarios Imagine: • Viewing a small bird flying through a forest • Tracking a missile given a blip every few seconds • Tracking planets, given intermittent observations

  4. Scenarios • Imagine: • Viewing a small bird flying through a forest • Tracking a missile given a blip every few seconds • Tracking planets, given intermittent observations • In each case: • The observations are noisy • But we can formulate an expectation about the trajectory

  5. Goal • We are trying to infer the state, X, of a dynamic system, given only noisy measurements, Z, over time Q1

  6. Example • Trajectory of a particle with acceleration due to gravity • State: • Position, velocity, and acceleration • Observations • Position only, corrupted by Gaussian noise Q2

  7. Formalism of model A linear system with Gaussian noise: and noisy measurements: Q3,4

  8. Algorithm • Give initial estimates of Iteratively: Predict Correct Q3-4

  9. Limitations • Must be a linear system • Noise must be Gaussian

  10. Applications and Extensions • Beyond just tracking and physical control…any system with continuous state variables and noisy measurements: • Economies! • Ecosystems! • To overcome linearity constraint: • Extended Kalman filters • Switching Kalman filters • Particle filters: Monte Carlo method

  11. Demos • Projectile motion (courtesy of Nathan Sickler) • Accelerometers:http://www.youtube.com/watch?v=AWAFFZ7rPDc • Tracking:http://www.youtube.com/user/rfengr (bright colors)http://www.youtube.com/watch?v=86UeUvI7pLQ (ES453: uniform ribbon)http://www.youtube.com/watch?v=U1L0X4cts8o (RC car) • Balancing robots:http://www.youtube.com/watch?v=46FswYw-m6o (inverted pendulum)http://www.youtube.com/watch?v=_TXfXoKyMzc&NR=1 (Boston Scientific’s Big Dog)

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