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Prediction in Interacting Systems: Prediction in Interacting Systems: Applications & SimulationsApplications & Simulations
Jarett HailesNovember 1, 2002
dXt = μ(Xt)dt + σ(Xt)dBt
dx = this->mu()*dt + …
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OutlineOutline
• Refining Grid Stochastic Filter
– Description
– Characteristics
• Performer Tracking Problem
– Model
– Simulation
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Refining Grid Stochastic Filter(REST) Filter
- Given a signal that evolves on regular Euclidean subset
- Divide signal state space into a finite number of cells
In general N1 x N2 x … x Nd cells
N1
N2
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Each cell contains:
42- Particle count
- Associated Rate
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Refining Grid Stochastic Filter (REST Filter)
Particles used to approximate unnormalized conditional distribution
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1
-12-1 -2
1
Cell Rates
Cell rates are used to calculate net birth (death rate) in a cell
Rates are determined by cell’s particle count and immediate neighbour’s rates
=Net Birth Rate
+1
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Net birth rates are used to mimic particle movement in observation-dependent manner.
Net Birth Rates
O
B
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R
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T
I
O
N
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Tree Node Cell Node
4
2
1
6
1 7
3
Observation: -2 Particles
14
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N2
N1
Dynamic Cell Sizing
Zoom in: N1Zoom out: N1
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Dynamic Cell Sizing Example
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REST Advantages
- Less simulation noise than particle filters
- Dynamic cell sizing, inherent parameter estimation
- Dynamic domain problems
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Performer Problem
- Acoustic tracking system designed to have lighting equipment follow performer on large stage
- Due to mechanical lags, system must be able to predict performer’s future position based on current state
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Audience
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Performer Model
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Audience
Observation Model
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