Hidden Markov model

See also wikipedia

A Markov model where observations are dependent on a latent Markov process $X$

an HMM has an additional requirement that the outcome of $Y$ at time $t = t_0$ must be “influenced” exclusively by the outcome of $X$ at $t = t_0$ and that the outcomes of $X$ and $Y$ at $t <t_{0}$ must be conditionally independent of $Y$ at $t = t_{0}$ given $X$ at time $t = t_{0}$.