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# Processing Sequential Sensor Data - PowerPoint PPT Presentation

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

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

• Segmentation vs. Classification“chicken and egg” problem

• Noise, noise, and noise …

• … more noise 

• [Evaluation – “Ground Truth”?]

• filtering

• trivial (technically)

• lag

• no higher level variables (speed)

• 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

• 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)

Prediction of next state:

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

Original goal …

Sample new set of particles based on importance weights – filtering

• Kalman Filter not very accurate

• Particle Filter computationally demanding

• HMMs somewhat in-between

• Measurement model: conditional probability

• Dynamic model: limited memory; transition probabilities

HMMs, more classical application