Recursive Bayesian Estimation
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Recursive Bayesian estimation is a general probabilistic approach for estimating an unknown probability density function recursively over time using incoming measurements and a mathematical process model.The true state x is assumed to be an unobserved Markov process, and the measurements z are the observed states of a Hidden Markov Model (HMM). The following picture presents a Bayesian Network of a HMM. Because of the Markov assumption, the probability of the current ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Recursive Bayesian estimation is a general probabilistic approach for estimating an unknown probability density function recursively over time using incoming measurements and a mathematical process model.The true state x is assumed to be an unobserved Markov process, and the measurements z are the observed states of a Hidden Markov Model (HMM). The following picture presents a Bayesian Network of a HMM. Because of the Markov assumption, the probability of the current true state given the immediately previous one is conditionally independent of the other earlier states. p(textbf{x}_k textbf{x}_{k-1},textbf{x}_{k-2},dots,textbf{x}_0) = p(textbf{x}_k textbf{x}_{k-1} ), Similarly, the measurement at the k-th timestep is dependent only upon the current state, so is conditionally independent of all other states given the current state.
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