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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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**Basic Concepts Law of Total Probability Markov Process**

Locating an Object Bayes Rule Observation Prior Posterior

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**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 ?

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

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**Kalman Filter : Specialization of Baye’s Filter**

Assumptions of Kalman Filter: Predicted State Observation

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**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

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JPDAF Framework Predict : Update : ?

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Predict : 1 2 Observation Model Update : 3

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Thank You

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**Recall Markov Process Chicken egg problem : State of objects θ**

Approximation by the belief about predicted state of objects

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**Likelihood of assignments given current states are constant for all Objects**

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