1 / 21

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 

makara
Télécharger la présentation

Processing Sequential Sensor Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related