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Processing Sequential Sensor Data The “John Krumm perspective” Thomas Plötz November 29 th,...
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Transcript of Processing Sequential Sensor Data The “John Krumm perspective” Thomas Plötz November 29 th,...
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
€
p(zi | xi )
HMMs, more classical application