SAMSI Discussion Session Random Sets Point Processes in MultiObject Tracking: Vo

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SAMSI Discussion SessionRandom Sets/ Point
Processes in Multi-Object Tracking Vo
Dr Daniel ClarkEECE DepartmentHeriot-Watt
University UK
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Multi-object filtering with point processes
observation space
observation produced by targets
state space
target motion
Xk
Xk-1
3 targets
5 targets

• Number of states and their values are (random)
  variables
• Need to estimate the number of target states and
  their state vectors online

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PHD filters
state space
vk
vk-1
PHD filter
PHD prediction
PHD update
vkk-1(xkZ1k-1)
vk-1(xk-1Z1k-1)
vk(xkZ1k)
???
???
prediction
pk-1(Xk-1Z1k-1)
pk(XkZ1k)
pkk-1(XkZ1k-1)
update
???
???
Multi-object Bayes filter
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Approximation Strategies

• PHD assumes that the prior intensity is Poisson
• MeMBer assumes multi-Bernoulli i.e. each target
  is assumed to be Bernoulli with probability of
  target existence
• PHD/CPHD filters propagate an intensity function
  of a point process

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Problems

• How do we estimate single/ multiple target states
  from a multi-modal particle density?
• - Clustering algorithms such as k-means and EM
  can be unreliable

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Problems

• Complexity
• How does the complexity/ reliability of the
  approach scale with the number of targets?
• Poisson PP meanvar

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Problems

• SMC implementations for filtering propagate
  intensity functions not probability densities
• Usual convergence properties of SMC algorithms of
  probability distributions needs modifying.
• Non Feynman-Kac model.

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Problems

• How do we obtain tracks/ trajectories of
  individual targets?
• - Possible solutions include track id in the
  state / find greatest intersection of particles