Motivating Markov Chain Monte Carlo for Multiple Target Tracking Krishna.
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Transcript of Motivating Markov Chain Monte Carlo for Multiple Target Tracking Krishna.
Motivating Markov Chain Monte Carlo for Multiple Target Tracking
Krishna
Overview
• Single Target Tracking : Bayes filter.
• Multiple Target Tracking : Extending Bayes filter to Joint Probabilistic Data Association Filter (JPDAF).
• JPDAF is NP Hard. Extend JPDAF to MCMC.
Prior
Posterior
Basic Concepts
Observation
Law of Total Probability
Markov Process
Bayes Rule
Locating an Object
Single -Target Tracking : Problem Definition
k -1 k k + 1 k + 2k -2
Consider tracking 1 Object.
is the sequence of all measurements upto time k
state of a single object at time k
Noisy observation- time k
How to estimate the state for observations ?
Bayes Filters
Motion Model
Observation Model
Predict :
Update : P(Current State | previous observations)P(Current State | Previous State)
Motion Model !
P(Previous State | Previous Observations)
P(Current State | Current & previous observations)P(Current Observation | Current State)
Observation Model !
P(Current State | previous observations)
Predicted State Observation
Kalman Filter : Specialization of Baye’s Filter
Assumptions of Kalman Filter:
1 , where (0, )
, where (0, )t t t t t t
t t t t t t
x A x w w N Q
z C x v v N R
Multi-Target Tracking : Problem Definition
k -1 k k + 1 k + 2k -2
State of these objects at time k :
Consider tracking T Objects.
is the state space of a single object.
is observation at time k is one such observation.is the sequence of all observations upto time k
How to assign the observed observations to individual objects ?Simultaneously Assign and Track
Predict :
Update :
?
JPDAF Framework
Predict :
Update :
1
2
3
Observation Model
Thank You
Markov Process
Recall
Approximation by the belief about predicted state of objects
Chicken egg problem : State of objects θ
State of objectsθ
Likelihood of assignments given current states are constant for all Objects