diff --git a/paper/paper.org b/paper/paper.org
index 42886de..612f65b 100644
--- a/paper/paper.org
+++ b/paper/paper.org
@@ -109,7 +109,7 @@ $\tilde{n}_1$ and $\tilde{n}_2$ are white noise with unitary power spectral dens
 \begin{equation}
 \begin{split}
   \hat{x} = {}&\left( H_1 \hat{G}_1^{-1} G_1 + H_2 \hat{G}_2^{-1} G_2 \right) x \\
-              &+ \left( H_1 \hat{G}_1^{-1} N_1 \right) \tilde{n}_1 + \left( H_2 \hat{G}_2^{-1} N_2 \right) \tilde{n}_2
+              &+ \left( H_1 \hat{G}_1^{-1} G_1 N_1 \right) \tilde{n}_1 + \left( H_2 \hat{G}_2^{-1} G_2 N_2 \right) \tilde{n}_2
 \end{split}
 \end{equation}
 
@@ -123,21 +123,18 @@ Complementary Filters
   H_1(s) + H_2(s) = 1
 \end{equation}
 
-
 \begin{equation}
-  \hat{x} = x + \left( H_1 \hat{G}_1^{-1} N_1 \right) \tilde{n}_1 + \left( H_2 \hat{G}_2^{-1} N_2 \right) \tilde{n}_2
+  \hat{x} = x + \left( H_1 N_1 \right) \tilde{n}_1 + \left( H_2 N_2 \right) \tilde{n}_2
 \end{equation}
 
 Perfect dynamics + filter noise
 
-
 ** Super Sensor Noise
-
 Let's note $n$ the super sensor noise.
 
 Its PSD is determined by:
 \begin{equation}
-  \Phi_n(\omega) = \left| H_1 \hat{G}_1^{-1} N_1 \right|^2 + \left| H_2 \hat{G}_2^{-1} N_2 \right|^2
+  \Phi_n(\omega) = \left| H_1 N_1 \right|^2 + \left| H_2 N_2 \right|^2
 \end{equation}
 
 ** $\mathcal{H}_2$ Synthesis of Complementary Filters
@@ -147,18 +144,18 @@ The goal is to design $H_1(s)$ and $H_2(s)$ such that the effect of the noise so
 And the goal is the minimize the Root Mean Square (RMS) value of $n$:
 #+name: eq:rms_value_estimation
 \begin{equation}
-  \sigma_{n} = \sqrt{\int_0^\infty \Phi_{\hat{n}}(\omega) d\omega} = \left\| \begin{matrix} \hat{G}_1^{-1} N_1 H_1 \\ \hat{G}_2^{-1} N_2 H_2 \end{matrix} \right\|_2
+  \sigma_{n} = \sqrt{\int_0^\infty \Phi_{\hat{n}}(\omega) d\omega} = \left\| \begin{matrix} H_1 N_1 \\ H_2 N_2 \end{matrix} \right\|_2
 \end{equation}
 
-Thus, the goal is to design $H_1(s)$ and $H_2(s)$ such that $H_1(s) + H_2(s) = 1$ and such that $\left\| \begin{matrix} \hat{G}_1^{-1} N_1 H_1 \\ \hat{G}_2^{-1} N_2 H_2 \end{matrix} \right\|_2$ is minimized.
+Thus, the goal is to design $H_1(s)$ and $H_2(s)$ such that $H_1(s) + H_2(s) = 1$ and such that $\left\| \begin{matrix} H_1 N_1 \\ H_2 N_2 \end{matrix} \right\|_2$ is minimized.
 
 \begin{equation}
 \begin{pmatrix}
   z_1 \\ z_2 \\ v
 \end{pmatrix} = \begin{bmatrix}
-  \hat{G}_1^{-1} N_1 & -\hat{G}_1^{-1} N_1 \\
-  0                  &  \hat{G}_2^{-1} N_2 \\
-  1                  &  0
+  N_1 & N_1 \\
+  0   & N_2 \\
+  1   &  0
 \end{bmatrix} \begin{pmatrix}
   w \\ u
 \end{pmatrix}