# Modified Bryson-Frazier (MBF) smoother explain

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