A. Acronyms
BO	Bearing-only
OOSM	Out-of-sequence measurement
IPDA	Integrated probabilistic data association
IPDA-EKF	Integrated probabilistic data association-extended Kalman filter
LIPDA	Local integrated probabilistic data association
DIPDA-FPFD	Distributed integrated probabilistic data association-forward prediction fusion and decorrelation
SPRT	Sequential probability ratio test
PTE	Probability of target existence
LOS	Line-of-sight
RMSE	Root mean square error
DIPDA-Re	Distributed integrated probabilistic data association-reprocessing
DIPDA-D	Distributed integrated probabilistic data association-discarding
CFT	Confirmed false track
CTT	Confirmed true track
Gmix	Gaussian mixture
pdf	Probability density function
B. Notations
$p_{11}$	The probability that target exists at time k given that it existed at time $k-1$
$\Delta T_{k,k-1}$	The time interval of two consecutive scans
$T_{ave}$	The averaged target existence duration
${\chi }_k$	The event of target existence at time $t_k$
${\mathbf{x}}_k$	The target kinematic state at time $t_k$, with position component ${\mathbf{x}}_k^p$ and velocity component ${\mathbf{x}}_k^v$
${\mathbf{B}}_k$	The pseudo track state at time $t_k$
${\mathbf{F}}_{k,k-1}$	The kinematic state transition matrix from time $t_{k-1}$ to $t_k$
${\tilde{\mathbf{F}}}_{k,k-1}$	The measurement state transition matrix from time $t_{k-1}$ to $t_k$
${\mathbf{w}}_k$	The process noise of target dynamic model, with zero mean and covariance ${\mathbf{Q}}_{k,k-1}$
${\tilde{\mathbf{w}}}_k$	The process noise of measurement state model, with zero mean and covariance ${\tilde{\mathbf{Q}}}_{k,k-1}$
${\mathbf{Z}}_k^s$	The set of measurements received by sensor s at time $t_k$ with cardinality $M_k^s$
${\mathbf{Z}}_{k,i}^s$	The ith measurement of ${\mathbf{Z}}_k^s$
${\mathbf{Z}}^{k,s}$	The set of sensor s received measurements up to and including time $t_k$
${\mathbf{Z}}^k$	The set of measurements collected by all sensors up to and including time $t_k$
${\mathbf{z}}_k$	The set of selected measurements at time $t_k$, with cardinality $m_k$
${\mathbf{z}}_{k,i}$	The ith measurement of ${\mathbf{z}}_k$
${\widehat{\mathbf{Z}}}_k^s$	The set of refined bearing measurements of sensor s at time $t_k$
${\widehat{\mathbf{Z}}}^k$	The set of refined bearing measurements collected by all sensors up to and including time $t_k$
$P_D$	Target detection probability
${\mathbf{s}}_k$	The sensor kinematic state at time $t_k$, with position component ${\mathbf{s}}_k^p$ and velocity component ${\mathbf{s}}_k^v$
${\mathbf{v}}_k$	The sensor noise with zero mean and covariance ${\mathbf{R}}_k$
$N(\mathbf{x};\widehat{\mathbf{x}},\mathbf{P})$	The Gaussian distribution of variable $\mathbf{x}$ with mean $\widehat{\mathbf{x}}$ and its error covariance $\mathbf{P}$
$({\widehat{\mathbf{x}}}_{k-1|k-1},{\mathbf{P}}_{k-1|k-1})$	Mean and covariance of posterior kinematic state estimate at time $t_{k-1}$
$({\widehat{\mathbf{x}}}_{k|k-1},{\mathbf{P}}_{k|k-1})$	Mean and covariance of predicted kinematic state estimate at time $t_k$
$p_{k,i}$	The likelihood of measurement ${\mathbf{z}}_{k,i}$
$P_G$	The probability that target measure falls into the validation gate
${\rho }_{k,i}$	The clutter measurement density of ${\mathbf{z}}_{k,i}$
${\beta }_{k,i}$	The association probability that each measurement ${\mathbf{z}}_{k,i}$ originates from the target
$\left({\widehat{\mathbf{x}}}_{k|k,i},{\mathbf{P}}_{k|k,i}\right)$	Mean and covariance of kinematic state updated using ${\mathbf{z}}_{k,i}$ at time $t_k$
$({\widehat{\mathbf{B}}}_{k|k},{\Gamma }_{k|k})$	Mean and covariance of posterior local measurement state estimate at time $t_k$
${\mathbf{i}}_x$	The unit vector of the X-axis of the sonar s local Cartesian coordinate
${\mathbf{i}}_s$	The unit vector of the sonar s position vector in the global Cartesian coordinate
$(v_{max}^t,v_{max}^s)$	The maximum velocity of target and sonar s, respectively
$({\overline{\mathbf{x}}}_{k|b}^c,{\overline{\mathbf{P}}}_{k|b}^c)$	Mean and covariance of predicted kinematic state of central track c from $t_b$ to $t_k$
$({\widehat{\mathbf{x}}}_{\tau |b,\tau }^c,{\mathbf{P}}_{\tau |b,\tau }^c)$	Mean and covariance of track c kinematic state updated by ${\widehat{\mathbf{Z}}}_{\tau }^s$ at time $t_{\tau }$
$({\overline{\mathbf{x}}}_{k|b,\tau }^c,{\overline{\mathbf{P}}}_{k|b,\tau }^c)$	Mean and covariance of track c predicted kinematic state from time $t_{\tau }$ to $t_k$
$({\widehat{\mathbf{x}}}_{k|\tau }^c,{\mathbf{P}}_{k|\tau }^c)$	Mean and covariance of track c kinematic state purely updated by ${\widehat{\mathbf{Z}}}_{\tau }^s$ at time $t_k$
$({\widehat{\mathbf{x}}}_{k|k,\tau }^c,{\mathbf{P}}_{k|k,\tau }^c)$	Mean and covariance of fused track c kinematic state at time $t_k$