Nonparametric generalized belief propagation based on pseudo-junction tree for cooperative localization in wireless networks

EURASIP Journal on Advances in Signal Processing

Table 1 Summary of notation

C _i	Clique i
S _{i j}	Separator set between cliques C _i and C _j
G _t	Set of neighbors of node t
$G_{C_{i}}$	Set of neighbors of C _i
x _t	Random variable for position of node t
X _a	Position of anchor node a
$x_{C_{i}}$	Random variable for position of C _i
$x_{S_{ij}}$	Random variable for position of S _{i j}
d _{t u}	Distance between nodes t and u
p _v	Noise distribution of the measured distance
R	Transmission radius
ψ _t(x _t)	Single potential (prior) of node t
ψ _{t u}(x _t,x _u)	Pairwise potential between nodes t and u
$ψ_{C_{i}} (x_{C_{i}})$	Potential of clique i
M _t(x _t)	Belief of node t
m _{t u}(x _u)	Message from node t to node u
$M_{i}^{m} (x_{C_{i}})$	Belief of C _i at iteration m
$m_{ij}^{m} (x_{S_{ij}})$	Message from C _i to C _j at iteration m
$M_{ij}^{m} (x_{C_{j}})$	Joint message from C _i to C _j at iteration m
$q_{C_{i}}^{m} (x_{C_{i}})$	Importance density function of C _i at iteration m
$X_{C_{i}}^{k, m}$	Particle k from $M_{i}^{m} (x_{C_{i}})$
$W_{C_{i}}^{k, m}$	Weight of particle k from $M_{i}^{m} (x_{C_{i}})$
$X_{S_{ij}}^{k, m}$	Particle k from $m_{ij}^{m} (x_{S_{ij}})$
$W_{S_{ij}}^{k, m}$	Weight of particle k from $m_{ij}^{m} (x_{S_{ij}})$