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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> |
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The forward algorithm is easily modified to account for observations from variants of the hidden Markov model as well, such as the |
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]]. |