= Kalman prediction step
{c}
{title2=$m_t^-=A_tm_{t-1}+B_tu_{t-1},\quad P_t^-=A_tP_{t-1}A_t^\top+Q_t$}
The <Kalman prediction step> advances the previous <posterior mean> and <posterior covariance matrix> through the state transition:
$$
m_t^-=A_tm_{t-1}+B_tu_{t-1},\qquad
P_t^-=A_tP_{t-1}A_t^\top+Q_t.
$$
The minus superscript marks information before observing $y_t$. The <transpose> and <matrix multiplication> propagate the old uncertainty; $Q_t$ adds the uncertainty of the new <process noise>. A known <control input> changes the mean but contributes no additional <variance>. If the <control input> itself is uncertain, that uncertainty needs its own model.
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