$p={\left[p_{\mathrm{N}}{p}_{\mathrm{E}}{p}_{\mathrm{D}}\right]}^T$	position with respect to the NED coordinate frame.
$v={\left[v_{\mathrm{N}}{v}_{\mathrm{E}}{v}_{\mathrm{D}}\right]}^T$	velocity with respect to NED coordinate frame.
$g={\left[00g_z\right]}^T$	gravity acceleration vector, where $g_z=9.81$ m/s${}^2$.
${\mathcal{R}}_{\mathrm{b}}^{\mathrm{NED}}$	rotation matrix between the body coordinate frame and the NED coordinate frame.
$u_k$	input vector.
$a_{\mathrm{m},k}$	accelerometer measurement.
$e_{\mathrm{m},k}$	orientation measurement in unit quaternion.
${\beta }_{a,k}$	accelerometer bias.
$q_{a,k}$	acceleration measurement noise.
$q_{\beta ,k}$	random walk noise.
$q_{e,k}$	orientation measurement noise.
${\stackrel{`}{p}}_k^c$	cloned state vector.
$x_k$	state vector.
$y_k$	output measurement.
$p_{\mathrm{m},k}$	position measurement given by GNSS.
$v_{\mathrm{m},k}$	velocity measurement given by GNSS.
$r_{p,k}$	position measurement noise.
$v_{p,k}$	velocity measurement noise.
${\delta }_{\mathrm{m},k}$	relative measurement given by LO.
$r_{\delta ,k}$	relative measurement noise.
$f(·)$	process model.
$h(·)$	observation model.
${\widehat{x}}_k$	state estimate.
$P_k^{xx}$	covariance matrix of state estimate.
$q_k$	process noise.
$Q_k$	covariance matrix of process noise.
$r_k$	output measuremnt noise.
$R_k$	covariance matrix of output measurement noise.
$R_0$	nominal covariance matrix of output measurement noise.
${\widehat{R}}_k$	estimate of the covariance matrix of output measurement noise.
${\nu }_k$	innovation.
${ϵ}_{k,i}^{\nu }$	normalized innovation squared.
${\xi }^{\prime }$	MAV’s path.
$\vartheta$	vector field