x(t)	pose of a robot at time t; x(t) = (x(t), y(t), θ(t))T
θ(t)	heading angle of the robot at time t
NW	number of range data measured by an LRF; in this study, NW = 19
$r_i^W\left(t\right)$	the i-th range data from a robot to the walls measured by an LRF
zW(t)	vector of the measured range data by an LRF; ${\mathbf{z}}^W\left(t\right)={(r_1^W\left(t\right),r_2^W\left(t\right),\cdots ,r_{19}^W\left(t\right))}^T$
$n_i^W\left(t\right)$	noise of measurement $r_i^W\left(t\right)$
nW(t)	noise vector of the measurement by an LRF; ${\mathbf{n}}^W\left(t\right)={(n_1^W\left(t\right),n_2^W\left(t\right),\cdots ,n_{19}^W\left(t\right))}^T$
NB	number of ultrasonic beacons; in this study, NB = 4
$r_i^B\left(t\right)$	range from a robot to an ultrasonic beacon
zB(t)	vector of the range data from a robot to the ultrasonic beacons; ${\mathbf{z}}^B\left(t\right)={(r_1^B\left(t\right),r_2^B\left(t\right),r_3^B\left(t\right),r_4^B\left(t\right))}^T$
$n_i^B\left(t\right)$	noise of measurement $r_i^B\left(t\right)$
nB (t)	noise vector of the measurements by ultrasonic beacons; ${\mathbf{n}}^B\left(t\right)={(n_1^B\left(t\right),\cdots ,n_4^B\left(t\right))}^T$
Next	number of all exteroceptive range measurement data; Next = NW + NB = 23
z(t)	exteroceptive measurement data encompassing the range data zW(t) and zB(t); $\mathbf{z}\left(t\right)={({\mathbf{z}}^B\left(t\right),{\mathbf{z}}^W\left(t\right))}^T={(r_1^B\left(t\right),\cdots ,r_4^B\left(t\right),r_1^W\left(t\right),\cdots ,r_{19}^W\left(t\right))}^T={(r_1\left(t\right),\cdots ,r_{23}\left(t\right))}^T$
n(t)	vector of exteroceptive measurement noise nW(t) and nB(t); $\mathbf{n}\left(t\right)={({\mathbf{n}}^B\left(t\right),{\mathbf{n}}^W\left(t\right))}^T={(n_1^B\left(t\right),\cdots ,n_4^B\left(t\right),n_1^W\left(t\right),\cdots n_{19}^W\left(t\right))}^T={\left(n_1\left(t\right),\cdots n_{23}\left(t\right)\right)}^T$
xBi	location of the i-th ultrasonic beacon; xBi = (xBi, yBi), i = 1, 2, 3, 4
xB	location vector of all ultrasonic beacons; xB = (xB1, xB2, xB3, xB4)T
υ(t)	linear (translational) velocity of a mobile robot at time t
ω(t)	rotational velocity of a mobile robot at time t
u(t)	robot velocity vector at time t; u(t) = (υ(t), ω(t))
nυ(t)	noise of proprioceptive data υ(t)
nω(t)	noise of proprioceptive data ω(t)
nu(t)	noise vector of proprioceptive data u(t); nu(t) = (nυ(t), nω(t))T
Q(t)	error covariance of exteroceptive measurement noise n(t)
M(t)	error covariance of proprioceptive motion noise nu(t)
Σ(t)	error covariance of state x(t) at time t
m	map of the workspace that affects the LRF measurements
g(·)	robot motion model that calculates the next robot pose from the current robot pose using linear and rotational velocities; x(ti) = g(u(t), x(ti−1))
h(·)	measurement model that maps the robot pose onto the distance to the beacons and walls; z(t) = (h(x(t), xB, m)
Z̅Bj(t)	sigma points of the predicted range to beacon Bj at time t
z̅Bj(t)	weighted mean of sigma points Z̅Bj (t)
SBj (t)	weighted error covariance of the range data to beacon Bj
K(t)	Kalman gain with which the difference between the predicted and actual measurements is multiplied to adjust the predicted pose into best estimation
Σx,z(t)	cross-error covariance between the state and measurement
S(t)	error covariance of the measurement