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Motivating Markov Chain Monte Carlo for Multiple Target Tracking Krishna

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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.

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

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Single -Target Tracking : Problem Definition k -1 k k + 1 k + 2 k -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 ?

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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)

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Predicted StateObservation Kalman Filter : Specialization of Bayes Filter Assumptions of Kalman Filter:

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Multi-Target Tracking : Problem Definition k -1 k k + 1 k + 2 k -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

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Predict : Update : ? JPDAF Framework

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Predict : Update : Observation Model

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Thank You

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

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Likelihood of assignments given current states are constant for all Objects

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