Motivating Markov Chain Monte Carlo for Multiple Target Tracking

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Presentation transcript:

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.

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

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 ?

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)

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

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

JPDAF Framework Predict : Update : ?

Predict : 1 2 Observation Model Update : 3

Thank You

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

Likelihood of assignments given current states are constant for all Objects