mounting of rooms line in or don't know and uh
and it in the because sometimes
and working with this condition to in frame
time
so first all i will uh uh talk about the uh
C uh method in the one and signal since in case
and and then my i will explain all uh proposition an extension to the um the since a case which
is not easy
and then uh i will uh
sure you some reason
so uh here the problem is uh the to target detection and tracking
so i see we have target
uh uh if i mean in a state space
oh
the state is gone know that of and
we know that this targets may and uh and leave these states space hundred and dates
so that the uh the target but number is as a a a a round them as well
these target
a observe by sensor
um
so each sensor uh it has its own or a
uh observation process
we may also that the the field of use of false of these and so may yeah
are that each other
but this will be an important point for later
the um
well we'll will uh uh of a synchronised the system
yeah it's time step will
receive measurements from all the sensors so we
we likely to have some measurement a target the association issue
oh how can be it doesn't hard targets
so a the classical method would be to create a uh
sorry
a track
uh each done uh you detect and you target and to maintain this a track
this will evolve according to the information you you have
and the and target
oh that's will focus here on number of a
wait
the set base
sanitation a in which case
the random has upon the
the target number and the rip uh a round them was of the
in the uh target state is a yeah that into one single uh a random object
a random finite set a R S S
so this this to but have F fess would be uh
random variable which is defined on this
the all final subset of the state space
and assume here that
you have
uh randomness on the target state as well as the target number
are the final state statistics provide us tools
such as set integration said differentiation or
even set a
provided densities
so that we are here we should be able to propagate the
the uh
probably to density of for are fess through time
using set based but usually equation
so you have a time of day question first
and then the that the question
so that the questions
hmmm
quite nice
but you can see you've then in practical situations
because there is a set integrals is strictly schur you need to
take into account every possible number of targets
site your R S S
so how to simplify this
well
the idea is to propagate
the first moment density P H D
off uh i fess rather than the full density
so uh we have to assume that if we T is personal
which means that the target number inside a are F S
is possible
with parameter and then which uh like as the uh
the uh uh
and double a for the P H D over the whole state space
and did start it's in there i S is distributed according to the number X P H D
so is
uh example assume that the great every yeah i cost to roughly three point two
then but estimated target number will be three
a but i i will eyes
the is three targets
along the i S speech in my uh density
so you see here that
the G do is defined on the
state space which is a a much easier to and all than the to find it's of state
subsets of the state space
so but is filtering for to it with a P G framework is easier than within the rss S men
work
uh because we need the P G is defined as a a a a state space
so we have here at that time and did equation
so the first part here
is uh
yeah yeah we to the uh evaluation of existing targets and but a as was my out here
which relates to the uh creation of new target
and then the bad that a question which is a point lines to and you can see a classical notions
of that of the
product of detection or we likelihood here
from this is quite easy but it's in the single sensor case only
so no what at in the multi target at a multi sensor case
this is quite uh a different
and my difficult to
to so
so we yeah proposed um
a real uh that update equations
to this looks nice not nasty i now
uh the chip or and here is this
in the experiments you have a
cross term term can it read it's a function and a and to cross too
which were to deaf and shaped along every measurement points and uh uh i don't this state point two
to do the that updated H G
um i mean that of you hear the exact expression of the uh cost and it's
in the paper
i will rather try to show you what it looks like in practical situation
so i assume that you have through uh since words
well as you die from shake you crossed term in this state but it's
missions you zero one and measures in three
that but was able to a cost here
yeah the
that that there was a target
i state X according to my uh time of the T P H D
and that
this target is detected by since someone
and produced mission ones you one
the target that was in the data and so two
and was detected by since a three
and that produce measurements is three
i
um um
uh a cross term is uh a definite shaded in
measurement points can me
like this
then uh a
the resulting cross to a is a you that there is a target somewhere in the state it's but i
don't know where
which
well to buy since so one since too but was and detected by the
since of
so what is it look like whether the updated is you look like and the simple example so here are
yeah only two sensors
first case and two measurements so one measurement per sensor if i don't example
what you see here he's is a better P H D
the first and here that you doing uh
and denotes the uh
like you that you have a target in in state but it's but it's and detected by bows answers
and that
um you have
the this sure takes into account all the possible
haitian measurement session
so uh the one and the mean to here you have a linear
possibility that uh
oh
which can
and the possible to that you were to to have these two measures on the measurements on the
so
here
because is the that's where
comes from different uh
uh
targets and hear from the
a single target
you can imagine that if you increase the number of measurements are the number of target
teams we grows out of control you see if i don't me
had a one measurement is
uh
going very nasty
so how can we simplify this
we to to has a look on the
that update equation
and we found that in maybe situations uh maybe a different shaded cross terms were to vanish
so that look at this example you have three sensors S one and as three at or overlapping fields
and has to is isolated
well i i know that a target in the recognition cannot be detected
so and mm uh trust different in
this measurement and i don't know a point here
we have an vanish
uh i i also that a type but can be detected by this sense of S one and S two
so i cross term shaded in the
measurement here and here will vanish two
and so am
so
but that is that
uh
instead of using my uh the data that question on the whole state space
i can write a
use it three times and smaller
uh parts of the uh state space
i as well as a a of the vision without any sense
well
and and the the grey mission with a uh since a one and three and one and the region
well since of to measurement from sensor to
and i'm that the exact same results also the exact multi sensor uh
P D a a a a a bit P H T
but it should be uh a fast
so let's look at an example
so a here have uh or something like ten sensors spread or of of the state space
i one you so that the the the fourth configuration is set that it should be able to
P my sense the at least
for parts
the is
this one isolated is to have a a and this through here
so this that's that's this is critical because that i we have a three uh i being uh the field
of you so if a target
comes into this
uh doc spots
uh the
that that the two step would be very uh
compute a ah
we have a out to compute
so here um
it is a nice and that of the time step
uh in a um the number of target across time and the red the estimate number by my uh my
um
me
a so pitch if you to so you can see that at the back of the estimation and and we
as a
i mean i'm high number of targets so
it
to this either the critical times whether the that are that should be difficult with the
uh brute force approach
and uh uh K any so that
uh in black these a computing time of the better updates tape
a across
uh this you scenario
a a of the brute first approach so
the that that it's state of the whole state space
and he yeah
oh in well as the computing time further the partition ms
oh the time it it's log scale here
so we assume that
and the we had at the um the brute force approach is exploding
well i and the that and remains quite low
um um as as well so a simple is as
here because the target member but it is very low
uh the brute first this actually but uh on the the portion that
so to conclude what can we say about the partition method
well uh first of all it's not an approximation because we get
to have the exact is and so that a a a a a a a to question was so we
can put by gate
the exact value of the mid and P H D
in case where the the field of you configuration is quite a can then the passion method it is likely
to be much more efficient
but the brute force approach
but that's the passion itself other the coast
that's why i
we had a here a uh the passion was more
a a little bit first was faster than the patch and the third
if the for the feel of a come is and five or or uh what was case if
it's a a a a and the uh
so of used are
crossing each other
that the pension but them does not bring anything you and uh
in to be a bit less efficient at the brute force approach
but you know all
in a practical situation well the field of view of the
since of a spread of the state space
the approximation mission can bring uh
an interesting approach to
if you want to provide get the truth
P H D a P H D of that
thank
uh
this if if finds that well
a problem is all all and
or same time
yes
i the why you don't have
yeah ish
it shouldn't have a synchronised a network
then you can uh you the uh
it activated directed the
approximation
which case you will uh
you will uh use the uh
single sensor uh a P G
that that T questions uh
second second city
do one know that in the synchronized case
uh if you be a product it uh it it to product that approximation
then define a lattice arc approximation would depends on the order in which you you take the uh
you a a process the uh sensor that's
a may be a problem
gosh
what was the model that you're using your simulations was to dimension
uh the was your house sense to was your results
do a to a collection
in overlapping regions
sorry
a what was the model
you summation
you mean the target model of the
observation
hmmm
oh the target model is is quite simple weights so and and C V near constant us to model
uh are the targets are created uh around the edges of the state space
and
the measurement i use in different kind of of sensors
well
some sense as of a a can the the range
and the and angle
of the target and you have a cushion noise
and these two values
and all the sensors can also uh
now the uh radial velocity
see
and and simulation what sense
there
yeah we have many different kind and a yeah
the sensing in as as what different for for every uh sense
cool
and
well as as usual and the phd H
the following in but it the probability detection
oh you since your sense i is low
then you
P L O P G is likely to to crash
if you in yours
uh in this case it's the protein detection is quite a i but i tried to means and no uh
uh uh values and eat
couldn't work
click
i
um um i used a different uh us a first on process to for every uh uh captain
since so you can have a different uh
class a process it works quite well
except that you have
the for some right will uh we'll set you will
oh right estimate
uh
the remember but gets you will estimate would be quite a i of and than real number
so we will another way to extract
a target from from you you data
because well i yeah a and at the beginning was
but each
uh a you say
i again to goals of a all sits they this is my number of targets
i take the
the round well i the closest in to go at this is my number of targets
and that will a at is um uh are the highest peaks
but again can do a better thing
you can try to localise in the space
some place where you can extract
uh
the P G uh
some
uh in the sub region of the uh these state space
uh
the P such that you have a a a a a weight of one
we which will
note that there is a target then you
extract this and you will process these two to try to extract uh
a target
and more questions we see have five minute
what implementation the use was it think of the bayes yes
and it's uh i'm
it's difficult uh these uh a particular of to implementation
uh "'specially" a for the creation of new uh a weight around the measurement all around
oh according to the number of the of the destination
so that's why in in this case the uh a target estimation the estimation of the target number was not
very good at some point
i should be able to
to improve this uh if i use the
a better article implementation
you questions
for the bit but uses in used seem to have fun
point
uh sense
if you one controller positions of
a
there any of them is now that you would have
for your of and that
if i need two
the sense that you have a about
and
fusion
i do not if data point
and not for sensors for target
but the target are yeah
yeah
the sensors also they can have any particular structure
the and if you in control of that would that be any
optimum position you know the sense
oh that's a good question uh and not as i'm working on the uh and i don't for on be
solution of the sense i tried with a fixed position to control
try to find the optimal uh
well orientation iteration of my and my uh since
and
this is a a a a i think uh
the big and X that for the P H D the the control part
because we know that if
uh there is a part of the since space which is never observed that any some
now uh things were grow out of of control and it will uh
the the quality of the target uh and number estimation so i'm trying to
to be a a a limitation of the sensors
so that i will
at least look at
where have that i can uh
at which with a coverage and
a
and more questions
okay let's time speaker again
i