High Quality Content by WIKIPEDIA articles! 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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