$\mathbf{x}(t)$	attitude of a robot at time t; $\mathbf{x}(t)={\left(\varphi (t),\theta (t),\psi (t)\right)}^T$, where $\varphi (t)$, $\theta (t)$ and $\psi (t)$ indicate roll, pitch and yaw
$\widehat{\mathbf{x}}(t)$	attitude estimated at time t through prediction and a correction procedure; $\widehat{\mathbf{x}}(t)={(\widehat{\varphi }(t),\widehat{\theta }(t),\widehat{\psi }(t))}^T$
$\widehat{\mathbf{P}}(t)$	error covariance of the estimated attitude $\widehat{\mathbf{x}}(t)$
${\mathbf{x}}^{-}(t)$	attitude predicted at time t, before it is corrected by the measurements; ${\mathbf{x}}^{-}(t)={\left({\varphi }^{-}(t),{\theta }^{-}(t),{\psi }^{-}(t)\right)}^T$
${\mathbf{P}}^{-}(t)$	error covariance of the predicted attitude ${\mathbf{x}}^{-}(t)$
$\mathbf{a}(t)$	acceleration measured in the instrument coordinate frame; $\mathbf{a}(t)={(a_x(t),a_y(t),a_z(t))}^T$
${\mathbf{a}}_{unit}(t)$	normalized acceleration measurement; ${\mathbf{a}}_{unit}(t)={(a_x(t),a_y(t),a_z(t))}_{unit}^T=\frac{\mathbf{a}(t)}{\parallel \mathbf{a}(t)\parallel }$
$\mathbf{m}(t)$	magnetic field measured in the instrument coordinate frame; $\mathbf{m}(t)={(m_x(t),m_y(t),m_z(t))}^T$
${\mathbf{m}}_{unit}(t)$	normalized magnetic field measurement; ${\mathbf{m}}_{unit}(t)={(m_x(t),m_y(t),m_z(t))}_{unit}^T=\frac{\mathbf{m}(t)}{\parallel \mathbf{m}(t)\parallel }$
$\mathbf{z}(t)$	measurements of roll, pitch and yaw calculated from the $\mathbf{a}(t)$ and $\mathbf{m}(t)$ at time t; $\mathbf{z}(t)={(\varphi (t),\theta (t),\psi (t))}^T$
$\mathbf{v}(t)$	linear velocity of the robot in the robot coordinate frame; $\mathbf{v}(t)={\left(u(t),v(t),w(t)\right)}^T$
$\omega (t)$	rotational velocity of the robot in the robot coordinate frame; $\omega (t)={(p(t),q(t),r(t))}^T$
$g(·)$	motion model of a robot that relates the robot attitude $\mathbf{x}(t)$ and the linear velocity $\mathbf{v}(t)$ to the rotational velocity $\dot{\mathbf{x}}(t)$ of the robot; $\dot{\mathbf{x}}(t)=g\left(\mathbf{x}(t),\mathbf{v}(t)\right)$
$h(·)$	the measurement model that relates state $\mathbf{x}(t)$ to the measurement $\mathbf{z}(t)$; $\mathbf{z}(t)=h(\mathbf{x}(t))$
$t_k$	the k-th discretized sampling time instant
$\Delta t_k$	time period between $t=t_{k-1}$ and $t=t_k$; $\Delta t_k=t_k-t_{k-1}$