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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

Processing Sequential Sensor Data

The “John Krumm perspective”Thomas PlötzNovember 29th, 2011




Sequential data analysis challenges
Sequential Data Analysis – Challenges

  • Segmentation vs. Classification“chicken and egg” problem

  • Noise, noise, and noise …

  • … more noise 

  • [Evaluation – “Ground Truth”?]


Noise
Noise …

  • filtering

  • trivial (technically)

  • lag

  • no higher level variables (speed)


States vs direct observations
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


Kalman filter
Kalman Filter

state and observations:

Explicit consideration of noise:


Kalman filter linear dynamics
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:


Kalman filter parameters
Kalman Filter – Parameters


Kalman filter @work
Kalman Filter @work

  • Two-step procedure for every zi

  • Result: mean and covariance of xi


Generalization particle filter
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)


Particle filter dynamics
Particle Filter: Dynamics

Prediction of next state:


Particle filter @work
Particle Filter @work

Generate random xi from p(xi | xi-1)

Original goal …

Sample new set of particles based on importance weights – filtering



Hidden markov models
Hidden Markov Models

  • Kalman Filter not very accurate

  • Particle Filter computationally demanding

  • HMMs somewhat in-between


HMMs

  • Measurement model: conditional probability

  • Dynamic model: limited memory; transition probabilities


Hmms more classical application
HMMs, more classical application


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