[AMR] Fix residual covariance error for EKF, fixes #8

electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex

@@ -12,7 +12,7 @@ $\vec{x}_k = \mat{F}\vec{x}_{k - 1} + \mat{G}\vec{u}_k + \mat{L}\vec{w}_k$ with
 \bi{Update} Lin. meas.: $\tilde{\vec{z}}_k = \mat{H}\vec{x}_k + \vec{v}_k$ with $\vec{v_k} \sim \cN(\vec{0}, \mat{R}_k)$:
 \begin{itemize}
     \item \bi{Measurement residual}: $\vec{y}_k = \tilde{\vec{z}}_k - \mat{H} \hat{\vec{x}}_{k | k - 1}$
-    \item \bi{Residual Covariance}: $\mat{S}_k = \mat{H}\mat{P}_{k | k - 1} \mat{H}^\top \mat{R}_k$
+    \item \bi{Residual Covariance}: $\mat{S}_k = \mat{H}\mat{P}_{k | k - 1} \mat{H}^\top + \mat{R}_k$
     \item \bi{Kalman gain}: $\mat{K}_k = \mat{P}_{k | k - 1} \mat{H}^\top \mat{S}_k^{-1}$
     \item \bi{Updated mean}: $\hat{\vec{x}}_{k | k} = \hat{\vec{x}}_{k | k - 1} + \mat{K}_k \vec{y}_k$
     \item \bi{Updated Cov.}: $\mat{P}_{k | k} = (\mat{I} - \mat{K}_k \mat{H}) \mat{P}_{k | k - 1}$