Causal state filtering
= Causal state filtering
{title2=$\mathbb E[x_t\mid y_1,\ldots,y_t]$}
<Causal state filtering> estimates the current state of a <dynamical system> from observations up to the current time. Under <quadratic loss>, the <conditional expectation> is an optimal estimate. A <Kalman filter> obtains this estimate recursively for a linear <Gaussian> <state-space model>, without using future observations.