Vector-Sensor Array Processing for Polarization Parameters ...
Processing Sequential Sensor Data
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Processing Sequential Sensor Data
The “John Krumm perspective”Thomas Plötz
November 29th, 2011
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Sequential Data?
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Sequential Data!
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Sequential Data Analysis – Challenges
• Segmentation vs. Classification“chicken and egg” problem
• Noise, noise, and noise …• … more noise
• [Evaluation – “Ground Truth”?]
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Noise …
filtering trivial (technically)- lag- no higher level variables (speed)
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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
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Kalman Filter
state and observations:
Explicit consideration of noise:
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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:
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Kalman Filter – Parameters
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Kalman Filter @work
• Two-step procedure for every zi
• Result: mean and covariance of xi
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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)
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Particle Filter: DynamicsPrediction of next state:
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Particle Filter @workGenerate random xi from p(xi | xi-1)
Sample new set of particles based on importance weights – filtering
Original goal …
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Particle Filter @work
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Hidden Markov Models
• Kalman Filter not very accurate• Particle Filter computationally demanding• HMMs somewhat in-between
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HMMs
• Measurement model: conditional probability
• Dynamic model: limited memory; transition probabilities
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p(zi | xi )
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HMMs, more classical application