Presentation on theme: "Motivating Markov Chain Monte Carlo for Multiple Target Tracking Krishna."— 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.
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 + 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 ?
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 StateObservation Kalman Filter : Specialization of Bayes Filter Assumptions of Kalman Filter:
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
Predict : Update : ? JPDAF Framework
Predict : Update : Observation Model
Markov Process Recall Approximation by the belief about predicted state of objects Chicken egg problem : State of objects θ State of objects θ
Likelihood of assignments given current states are constant for all Objects