Recursive Bayesian estimation: Difference between revisions

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Because of the Markov assumption, the true state is conditionally independent of all earlier states given the immediately previous state.
 
:<math>p(\textbf{x}_k|\textbf{x}_0,...,\textbf{x}_{k-1}) = p(\textbf{x}_k|\textbf{x}_{k-1} )</math>
 
Similarly the measurement at the ''k''-th timestep is dependent only upon the current state and is conditionally independent of all other states given the current state.