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I'm reading about MBF smoother on Wikipedia.

I'm confused of the quantity $\hat{\lambda}_k$ and $\tilde{\lambda}_k$. What does they really mean intuitively ? Why the update formula has the form

$\hspace{3.0cm} \hat{\textbf{x}}_{k|n} = \hat{\textbf{x}}_{k|k} - \textbf{P}_{k|k} \hat{\lambda}_k$

or (as stated in the article)

$\hspace{3.0cm} \hat{\textbf{x}}_{k|n} = \hat{\textbf{x}}_{k|k-1} - \textbf{P}_{k|k-1} \tilde{\lambda}_k$

Can anyone explain it intuitively for me ?

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