Innovation covariance ($S_t=H_t{P}_t^{-}{H}_t^{\top }+R_t$)

For the Kalman filter model, the innovation is $e_t=y_t-H_t{m}_t^{-}$. Its conditional covariance matrix before the measurement isThis 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.