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Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012

Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012. Fault Prediction with Particle Filters. by David Hatfield mentors: Dr. D. Kern & Dr. J. Zalewski. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012.

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Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012

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  1. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Fault Prediction with Particle Filters by David Hatfield mentors: Dr. D. Kern & Dr. J. Zalewski

  2. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 What Is a Particle Filter? • The Particle Filter is a sequential Monte Carlo algorithm used to estimate the true state of a system given a series of measurements (which are corrupted by error) taken periodically over time.

  3. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 What Is a Monte Carlo Method? • The Monte Carlo method is an algorithm to conduct computations by random sampling of data to assess results statistically. Example of computing area under a curve: http://chc60.fgcu.edu/EN/HistoryDetail.aspx?c=6

  4. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Essential Steps in the Algorithm

  5. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Recursive Bayesian Solution • p(xk|Dk-1) denotes the Probability Density Function of the state vector given all the measurements up to time k – 1 (denoted by Dk-1). • The following are given by Bayes theorem: Prior distribution: Likelihood function: Posterior distribution:

  6. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Predicting Future States • At time k, the pdf of the state at time k + p may be calculated as follows: • The set of values the state vector may take may be classified as either normal or faulty states. Once the pdf for a future time is obtained, the probability of a fault occurring may may be calculated by integrating the pdf over the set of all faulty states.

  7. Computer Science, Software Engineering & Robotics Workshop, FGCU, April 27-28, 2012 Selected Applications • Robotics: Localization, navigation, and tracking as well as fault detection, prediction, and diagnosis. • Image and Audio Enhancement: Reduction of noise in image and audio data. • Economics and Finance: Estimation of latent variables in Econometrics.

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