1. Motivating Markov Chain Monte Carlo for Multiple Target Tracking
Krishna

2. 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.

3. Basic Concepts Law of Total Probability Markov Process
Locating an Object
Bayes Rule
Observation
Prior
Posterior

4. Single -Target Tracking : Problem Definition
Consider tracking 1 Object.
state of a single object at time k
Noisy observation- time k
is the sequence of all measurements upto time k
How to estimate the state for observations ?

5. 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)
Update :
P(Current State | Current & previous observations)
P(Current Observation | Current State)
Observation Model !
P(Current State | previous observations)

6. Kalman Filter : Specialization of Baye’s Filter
Assumptions of Kalman Filter:
Predicted State
Observation

7. Multi-Target Tracking : Problem Definition
Consider tracking T Objects.
State of these objects at time k :
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

8. JPDAF Framework
Predict :
Update : ?

9. Predict : 1 2
Observation Model
Update : 3

15. Thank You

23. Recall Markov Process Chicken egg problem : State of objects  θ
Approximation by the belief about predicted state of objects

24. Likelihood of assignments given current states are constant for all Objects