processing sequential sensor data the “john krumm perspective” thomas plötz november 29 th,...
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Processing Sequential Sensor Data
The “John Krumm perspective”Thomas Plötz
November 29th, 2011
Sequential Data?
Sequential Data!
Sequential Data Analysis – Challenges
• Segmentation vs. Classification“chicken and egg” problem
• Noise, noise, and noise …• … more noise
• [Evaluation – “Ground Truth”?]
Noise …
filtering trivial (technically)
- lag
- no higher level variables (speed)
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
state and observations:
Explicit consideration of noise:
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 @work
• Two-step procedure for every zi
• Result: mean and covariance of xi
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: DynamicsPrediction of next state:
Particle Filter @workGenerate random xi from p(xi | xi-1)
Sample new set of particles based on importance weights – filtering
Original goal …
Particle Filter @work
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
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p(zi | xi )
HMMs, more classical application
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