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Processing Sequential Sensor Data

This document delves into the complexities of processing and analyzing sequential sensor data, drawing on the insights of John Krumm. It discusses key challenges like noise, segmentation versus classification, and the "chicken and egg" problem. The text explores various methodologies including the Kalman Filter, Particle Filter, and Hidden Markov Models, emphasizing their strengths and limitations in handling noise and state inference. Practical examples illustrate how to exploit measurements and observations to infer internal states, paving the way for more accurate data-driven decisions.

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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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