$\mathbf{x}\left(t\right)$	attitude of a robot at time t; $\mathbf{x}\left(t\right)={\left(\varphi \left(t\right),\theta \left(t\right),\psi \left(t\right)\right)}^T$ where $\varphi \left(t\right)$, $\theta \left(t\right)$, and $\psi \left(t\right)$
	indicate the roll, pitch, and yaw, respectively
${\widehat{\mathbf{x}}}^{-}\left(t\right)$	attitude predicted for time t, before being corrected using the measurements;
	${\widehat{\mathbf{x}}}^{-}\left(t\right)={\left({\widehat{\varphi }}^{-}\left(t\right),{\widehat{\theta }}^{-}\left(t\right),{\widehat{\psi }}^{-}\left(t\right)\right)}^T$
$\widehat{\mathbf{x}}\left(t\right)$	attitude estimated for time t through the prediction and correction procedure;
	$\widehat{\mathbf{x}}\left(t\right)={\left(\widehat{\varphi }\left(t\right),\widehat{\theta }\left(t\right),\widehat{\psi }\left(t\right)\right)}^T$
$\mathbf{a}\left(t\right)$	acceleration measured at time t in the instrument coordinate frame;
	$\mathbf{a}\left(t\right)={(a_x\left(t\right),a_y\left(t\right),a_z\left(t\right))}^T$
${\mathbf{a}}^u\left(t\right)$	normalized acceleration measurement; ${\mathbf{a}}^u\left(t\right)={(a_x^u\left(t\right),a_y^u\left(t\right),a_z^u\left(t\right))}^T=\frac{\mathbf{a}\left(\mathbf{t}\right)}{\parallel \mathbf{a}\left(t\right)\parallel }$
$\tilde{\mathbf{m}}\left(t\right)$	magnetic field measured in the instrument coordinate frame;
	$\tilde{\mathbf{m}}\left(t\right)={({\tilde{m}}_x\left(t\right),{\tilde{m}}_y\left(t\right),{\tilde{m}}_z\left(t\right))}^T$
${\mathbf{b}}_{\mathbf{m}}\left(t\right)$	bias in the magnetic field measurement $\tilde{\mathbf{m}}\left(t\right)$; ${\mathbf{b}}_{\mathbf{m}}\left(t\right)={(b_{m_x}\left(t\right),b_{m_y}\left(t\right),b_{m_z}\left(t\right))}^T$
$\mathbf{m}\left(t\right)$	magnetic field wherein the bias ${\mathbf{b}}_{\mathbf{m}}\left(t\right)$ is compensated from measurement $\tilde{\mathbf{m}}\left(t\right)$;
	$\mathbf{m}\left(t\right)={(m_x\left(t\right),m_y\left(t\right),m_z\left(t\right))}^T=\tilde{\mathbf{m}}\left(t\right)-{\mathbf{b}}_{\mathbf{m}}\left(t\right)$
${\mathbf{m}}^u\left(t\right)$	normalized magnetic field measurement; ${\mathbf{m}}^u\left(t\right)={(m_x^u\left(t\right),m_y^u\left(t\right),m_z^u\left(t\right))}^T=\frac{\mathbf{m}\left(t\right)}{\parallel \mathbf{m}\left(t\right)\parallel }$
${\mathbf{m}}_g\left(t\right)$	geomagnetic field represented in the North-East-Down (NED) coordinate frame
	appropriate for the geographical location; ${\mathbf{m}}_g\left(t\right)={(m_{g,x}\left(t\right),m_{g,y}\left(t\right),m_{g,z}\left(t\right))}^T$
${\mathbf{z}}^u\left(t\right)$	normalized field measurement at time t; ${\mathbf{z}}^u\left(t\right)={({\mathbf{a}}^u\left(t\right),{\mathbf{m}}^u\left(t\right))}^T$
$\mathbf{u}\left(t\right)$	linear velocity measured by a Doppler velocity log (DVL) in the instrument coordinate
	frame; $\mathbf{u}\left(t\right)={\left(u\left(t\right),v\left(t\right),w\left(t\right)\right)}^T$
$\mathit{\omega }\left(t\right)$	rotational (angular) velocity measured by a gyroscope in the instrument coordinate frame;
	$\mathit{\omega }\left(t\right)={(p\left(t\right),q\left(t\right),r\left(t\right))}^T$
$\mathbf{f}(·)$	motion function relating attitude $\mathbf{x}\left(t\right)$ and angular velocity $\mathit{\omega }\left(t\right)$ in the instrument
	coordinate frame to the robot’s angular velocity $\dot{\mathbf{x}}\left(t\right)$; $\dot{\mathbf{x}}\left(t\right)=\mathbf{f}\left(\mathbf{x}\left(t\right),\mathit{\omega }\left(t\right)\right)$
$\mathbf{h}(·)$	measurement function relating state $\mathbf{x}\left(t\right)$ to measurement ${\mathbf{z}}^u\left(t\right)$; ${\mathbf{z}}^u\left(t\right)=\mathbf{h}\left(\mathbf{x}\left(t\right)\right)$
$t_k$	the kth discretized sampling instant of time
$\Delta t_k$	time period between $t=t_{k-1}$ and $t=t_k$; $\Delta t_k=t_k-t_{k-1}$