A New Coarse Gating Strategy Driven Multidimensional Assignment for Two-Stage MHT of Bearings-Only Multisensor-Multitarget Tracking

. 2022 Feb 24;22(5):1802. doi: 10.3390/s22051802

Notations	Definitions
S	Number of sensors
s	Sensor index, $s = 1, 2, \dots, S$
i	Target index
k	Time index
$j_{s}$	Bearing measurement index acquired by sensor s
$N_{s}$	Number of bearing measurements acquired by sensor s
$z_{k}^{s, j_{s}}$	The $j_{s}$ th bearing measurement acquired by sensor s at time k
$β_{k}^{s, i_{s}}$	True bearing between target i and sensor s
${\tilde{z}}_{k}^{j_{s}}$	False measurements
$x_{k}^{i}$	State vector of target i at time k
$p_{k}^{s}$	Position vector of sensor s
$F_{k}$	State transition matrix at time k
$w_{k}^{i}$	Process noise vector of target i at time k
$v_{k}^{s, j_{s}}$	Measurement noise of sensor s at time k
$σ_{s}^{2}$	Measurement noise variance of sensor s
$Z_{k}^{j_{1} j_{2} \dots j_{S}}$	An S-tuple of measurements, one from each sensor
$c_{k}^{j_{1} j_{2} \dots j_{S}}$	Cost of associating S-tuple of measurements with a target
$ρ_{k}^{j_{1} j_{2} \dots j_{S}}$	Binary decision variables
$P_{D_{s}}$	Detection probability of sensor s
$ψ_{s}$	Volume of the field of view of sensor s
$u (j_{s})$	Binary indicator function
l	iteration index
$z_{k}^{j_{1} j_{2} \dots j_{S}}$	Stacked measurement vector corresponding to S-tuple $Z_{k}^{j_{1} j_{2} \dots j_{S}}$
$p_{k}^{i}$	Position vector of target i
${\hat{p}}_{k}^{i, 0}$	Initial position estimate of target i
${\hat{p}}_{k}^{i, l}$	Position estimation of target i after iteration l
$R_{k}^{i, l}$	Covariance matrix corresponding to the position estimate ${\hat{p}}_{k}^{i, l}$
$J_{k}^{l}$	Jacobian matrix
$d_{k}^{i, l}$	Mahalanobis distance
T	Threshold