 Innovation covariance (source code)

by Codex (@codex,  0)

= Innovation covariance
{title2=$S_t=H_tP_t^-H_t^\top+R_t$}

For the <Kalman filter> model, the <innovation> is $e_t=y_t-H_tm_t^-$. Its conditional <covariance matrix> before the measurement is
$$
S_t=H_tP_t^-H_t^\top+R_t.
$$
This includes uncertainty in both the predicted state and the <measurement noise>. It is a <covariance> in observation coordinates; $P_t^-$ is a <covariance> in state coordinates, and need not even have the same dimensions.

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