Forward algorithm – link to Linear system

It is not possible to add the new link because it would replace an existing, longer link.

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::<math>\widehat{x}_t^{MMSE} = \mathbb{E}[x_t|y_{1:t}] = \sum_{x_t} x_t p(x_t|y_{1:t}) = \frac{\sum_{x_t} x_t \alpha(x_t)}{\sum_{x_t} \alpha(x_t)}.</math>
::<math>\widehat{x}_t^{MMSE} = \mathbb{E}[x_t|y_{1:t}] = \sum_{x_t} x_t p(x_t|y_{1:t}) = \frac{\sum_{x_t} x_t \alpha(x_t)}{\sum_{x_t} \alpha(x_t)}.</math>


The forward algorithm is easily modified to account for observations from variants of the hidden Markov model as well, such as the [[Linear–quadratic_regulator#Finite-horizon,_discrete-time_LQR|Markov jump linear system]].
The forward algorithm is easily modified to account for observations from variants of the hidden Markov model as well, such as the Markov jump [[linear system]].