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