Tracking with Viterbi Algorithm

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Tracking with Viterbi Algorithm

• Yang Jinghong

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Viterbi Algorithm

• Apply to discrete time, memoryless systems
• Observed in memoryless noise
• Optimal in the sense of minimizing error
  probability.

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Viterbi Tracking (Continuous state space)
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Viterbi Tracking (Continuous state space)
t 1 t 2 t 3
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Viterbi Tracking (Discrete state space)

• Quantize continuous states

• Methodology trellis diagram

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Initial and Ending States

• Knowledge of initial state is not crucial
• Ending state
• - Optimal estimates if ending state is known
• - If allow sufficient long delay, estimates can
  approach optimal.

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Pros and Cons

• Pros
• No requirements for linearility on process and
  observation models
• Cons
• - Transition probabilities, and observations
  dependency on state should be attainable.

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Comparations with Kalman Filter

• Kalman filter
• Extended Kalman Filter
• Viterbi Algorithm

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Example
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Thank You !
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Reference

• 1 The Viterbi Algorithm, G. DAVID FORNEY, JR.
  1973
• 2 Manoeuvring-target tracking with the Viterbi
  algorithm in the presence of interference, Kerim
  Demirbag, 1989
• 3 Comparison of Kalman Filter Estimation
  Approaches for State Space Models with Nonlinear
  Measurements, Fredrik Orderud

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Kalman Filter

• Linear dynamic systems
• (wide-Sense) Markov chain
• Additive, white, Gaussian noise
• Continuous state space

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Extended Kalman Filter (EKF)

• Non-linear dynamic systems
• (wide-Sense) Markov chain
• (Additive) Gaussian noise
• Continuous state space
• Notes.
• Linearization First order Taylor approximation
• Diverge over time (unstable)