Recursive Bayesian estimation: Difference between revisions

Revision as of 17:37, 8 March 2014

Revision as of 12:24, 5 May 2014

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The true state <math>x</math> is assumed to be an unobserved [[Markov process]], and the measurements <math>z</math> are the observed states of a [[Hidden Markov Model]] (HMM). The following picture presents a Bayesian Network of a HMM.

[[Image:HMM_Kalman_Filter_DerivationHMM Kalman Filter Derivation.svg|Hidden Markov Model|center]]

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.

:<math>p(\textbf{x}_k|\textbf{x}_{k-1},\textbf{x}_{k-2},\dots,\textbf{x}_0) = p(\textbf{x}_k|\textbf{x}_{k-1} )</math>

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== Applications ==

* [[Kalman filter]], a recursive Bayesian filter for [[multivariate normal distribution]]s

* [[Particle filter]], a sequential Monte Carlo (SMC) based technique, which models the [[Probability_density_functionProbability density function|PDF]] using a set of discrete points

* '''Grid-based estimators''', which subdivide the PDF into a discrete grid