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Processing Sequential Sensor Data

Processing Sequential Sensor Data. The “John Krumm perspective” Thomas Plötz November 29 th , 2011. Sequential Data?. Sequential Data!. Sequential Data Analysis – Challenges. Segmentation vs. Classification “chicken and egg” problem Noise, noise, and noise … … more noise 

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Processing Sequential Sensor Data

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  1. Processing Sequential Sensor Data The “John Krumm perspective”Thomas PlötzNovember 29th, 2011

  2. Sequential Data?

  3. Sequential Data!

  4. Sequential Data Analysis – Challenges • Segmentation vs. Classification“chicken and egg” problem • Noise, noise, and noise … • … more noise  • [Evaluation – “Ground Truth”?]

  5. Noise … • filtering • trivial (technically) • lag • no higher level variables (speed)

  6. States vs. Direct Observations • Idea: Assume (internal) state of the “system” • Approach: Infer this very state by exploiting measurements / observations • Examples: • Kalman Filter • Particle Filter • Hidden Markov Models

  7. Kalman Filter state and observations: Explicit consideration of noise:

  8. Kalman Filter – Linear Dynamics State at time i: linear function of state at time i-1 plus noise: System matrix describes linear relationship between i and i-1:

  9. Kalman Filter – Parameters

  10. Kalman Filter @work • Two-step procedure for every zi • Result: mean and covariance of xi

  11. Generalization: Particle Filter • No linearity assumption, no Gaussian noise • Sequence of unknown state vectors xi, and measurement vectors zi • Probabilistic model for measurements, e.g. (!): • … and for dynamics: PF samples from it, i.e., generates xi subject to p(xi | xi-1)

  12. Particle Filter: Dynamics Prediction of next state:

  13. Particle Filter @work Generate random xi from p(xi | xi-1) Original goal … Sample new set of particles based on importance weights – filtering

  14. Particle Filter @work

  15. Hidden Markov Models • Kalman Filter not very accurate • Particle Filter computationally demanding • HMMs somewhat in-between

  16. HMMs • Measurement model: conditional probability • Dynamic model: limited memory; transition probabilities

  17. HMMs, more classical application

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