<s>
The	O
joint	O
probabilistic	O
data-association	O
filter	O
(	O
JPDAF	B-Algorithm
)	O
is	O
a	O
statistical	O
approach	O
to	O
the	O
problem	O
of	O
plot	O
association	O
(	O
target-measurement	O
assignment	O
)	O
in	O
a	O
target	O
tracking	O
algorithm	O
.	O
</s>
<s>
Like	O
the	O
probabilistic	B-Algorithm
data	I-Algorithm
association	I-Algorithm
filter	I-Algorithm
(	O
PDAF	O
)	O
,	O
rather	O
than	O
choosing	O
the	O
most	O
likely	O
assignment	O
of	O
measurements	O
to	O
a	O
target	O
(	O
or	O
declaring	O
the	O
target	O
not	O
detected	O
or	O
a	O
measurement	O
to	O
be	O
a	O
false	O
alarm	O
)	O
,	O
the	O
PDAF	O
takes	O
an	O
expected	O
value	O
,	O
which	O
is	O
the	O
minimum	B-General_Concept
mean	I-General_Concept
square	I-General_Concept
error	I-General_Concept
(	O
MMSE	O
)	O
estimate	O
for	O
the	O
state	O
of	O
each	O
target	O
.	O
</s>
<s>
However	O
,	O
unlike	O
the	O
PDAF	O
,	O
which	O
is	O
only	O
meant	O
for	O
tracking	O
a	O
single	O
target	O
in	O
the	O
presence	O
of	O
false	O
alarms	O
and	O
missed	O
detections	O
,	O
the	O
JPDAF	B-Algorithm
can	O
handle	O
multiple	O
target	O
tracking	O
scenarios	O
.	O
</s>
<s>
A	O
derivation	O
of	O
the	O
JPDAF	B-Algorithm
is	O
given	O
in	O
.	O
</s>
<s>
The	O
JPDAF	B-Algorithm
is	O
one	O
of	O
several	O
techniques	O
for	O
radar	B-Application
target	O
tracking	O
and	O
for	O
target	O
tracking	O
in	O
the	O
field	O
of	O
computer	B-Application
vision	I-Application
.	O
</s>
<s>
A	O
common	O
problem	O
observed	O
with	O
the	O
JPDAF	B-Algorithm
is	O
that	O
estimates	O
of	O
closely	O
spaced	O
targets	O
tend	O
to	O
coalesce	O
over	O
time	O
.	O
</s>
<s>
Variants	O
of	O
the	O
JPDAF	B-Algorithm
algorithm	O
have	O
been	O
made	O
that	O
try	O
to	O
avoid	O
track	O
coalescence	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
Set	O
JPDAF	B-Algorithm
uses	O
an	O
approximate	O
minimum	O
mean	O
optimal	O
sub	O
pattern	O
assignment	O
(	O
MMOSPA	O
)	O
instead	O
of	O
an	O
approximate	O
MMSE	B-General_Concept
estimator	I-General_Concept
.	O
</s>
<s>
The	O
JPDAF*	O
,	O
modifies	O
how	O
the	O
target-measurement	O
association	O
probabilities	O
are	O
computed	O
,	O
and	O
variants	O
of	O
the	O
global	O
nearest-neighbor	O
JPDAF	B-Algorithm
(	O
GNN-JPDAF	O
)	O
(	O
a	O
best-hypothesis	O
tracker	O
)	O
use	O
the	O
global	O
nearest	O
neighbor	O
(	O
GNN	O
)	O
estimate	O
in	O
place	O
of	O
the	O
mean	O
but	O
compute	O
the	O
covariance	O
matrix	O
as	O
in	O
the	O
normal	O
JPDAF	B-Algorithm
:	O
as	O
a	O
mean-squared	O
error	O
matrix	O
.	O
</s>
<s>
Matlab	B-Language
:	O
The	O
PDAF	O
,	O
JPDAF	B-Algorithm
,	O
Set	O
JPDAF	B-Algorithm
,	O
JPDAF*	O
,	O
GNN-JPDAF	O
and	O
multiple	O
other	O
exact	O
and	O
approximate	O
variants	O
of	O
the	O
JPDAF	B-Algorithm
are	O
implemented	O
in	O
the	O
singleScanUpdate	O
function	O
that	O
is	O
part	O
of	O
the	O
United	O
States	O
Naval	O
Research	O
Laboratory	O
's	O
free	O
Tracker	O
Component	O
Library	O
.	O
</s>
<s>
Python	O
:	O
The	O
PDAF	O
,	O
JPDAF	B-Algorithm
and	O
other	O
data	O
association	O
methods	O
are	O
implemented	O
in	O
Stone-Soup	O
.	O
</s>
