0:00:14mounting of rooms line in or don't know and uh
0:00:17and it in the because sometimes
0:00:20and working with this condition to in frame
0:00:25time
0:00:26so first all i will uh uh talk about the uh
0:00:29C uh method in the one and signal since in case
0:00:33and and then my i will explain all uh proposition an extension to the um the since a case which
0:00:39is not easy
0:00:40and then uh i will uh
0:00:42sure you some reason
0:00:45so uh here the problem is uh the to target detection and tracking
0:00:50so i see we have target
0:00:52uh uh if i mean in a state space
0:00:54oh
0:00:56the state is gone know that of and
0:00:59we know that this targets may and uh and leave these states space hundred and dates
0:01:04so that the uh the target but number is as a a a a round them as well
0:01:09these target
0:01:10a observe by sensor
0:01:13um
0:01:15so each sensor uh it has its own or a
0:01:18uh observation process
0:01:20we may also that the the field of use of false of these and so may yeah
0:01:24are that each other
0:01:26but this will be an important point for later
0:01:30the um
0:01:31well we'll will uh uh of a synchronised the system
0:01:34yeah it's time step will
0:01:36receive measurements from all the sensors so we
0:01:39we likely to have some measurement a target the association issue
0:01:45oh how can be it doesn't hard targets
0:01:47so a the classical method would be to create a uh
0:01:52sorry
0:01:53a track
0:01:54uh each done uh you detect and you target and to maintain this a track
0:01:59this will evolve according to the information you you have
0:02:03and the and target
0:02:05oh that's will focus here on number of a
0:02:08wait
0:02:09the set base
0:02:10sanitation a in which case
0:02:12the random has upon the
0:02:14the target number and the rip uh a round them was of the
0:02:18in the uh target state is a yeah that into one single uh a random object
0:02:23a random finite set a R S S
0:02:27so this this to but have F fess would be uh
0:02:30random variable which is defined on this
0:02:32the all final subset of the state space
0:02:35and assume here that
0:02:37you have
0:02:38uh randomness on the target state as well as the target number
0:02:45are the final state statistics provide us tools
0:02:48such as set integration said differentiation or
0:02:52even set a
0:02:53provided densities
0:02:55so that we are here we should be able to propagate the
0:03:00the uh
0:03:01probably to density of for are fess through time
0:03:04using set based but usually equation
0:03:06so you have a time of day question first
0:03:09and then the that the question
0:03:11so that the questions
0:03:13hmmm
0:03:13quite nice
0:03:14but you can see you've then in practical situations
0:03:18because there is a set integrals is strictly schur you need to
0:03:22take into account every possible number of targets
0:03:25site your R S S
0:03:28so how to simplify this
0:03:31well
0:03:32the idea is to propagate
0:03:34the first moment density P H D
0:03:36off uh i fess rather than the full density
0:03:41so uh we have to assume that if we T is personal
0:03:44which means that the target number inside a are F S
0:03:47is possible
0:03:48with parameter and then which uh like as the uh
0:03:52the uh uh
0:03:53and double a for the P H D over the whole state space
0:03:57and did start it's in there i S is distributed according to the number X P H D
0:04:02so is
0:04:04uh example assume that the great every yeah i cost to roughly three point two
0:04:09then but estimated target number will be three
0:04:12a but i i will eyes
0:04:14the is three targets
0:04:15along the i S speech in my uh density
0:04:19so you see here that
0:04:20the G do is defined on the
0:04:22state space which is a a much easier to and all than the to find it's of state
0:04:26subsets of the state space
0:04:30so but is filtering for to it with a P G framework is easier than within the rss S men
0:04:36work
0:04:38uh because we need the P G is defined as a a a a state space
0:04:43so we have here at that time and did equation
0:04:45so the first part here
0:04:47is uh
0:04:48yeah yeah we to the uh evaluation of existing targets and but a as was my out here
0:04:54which relates to the uh creation of new target
0:04:58and then the bad that a question which is a point lines to and you can see a classical notions
0:05:03of that of the
0:05:04product of detection or we likelihood here
0:05:09from this is quite easy but it's in the single sensor case only
0:05:13so no what at in the multi target at a multi sensor case
0:05:17this is quite uh a different
0:05:19and my difficult to
0:05:21to so
0:05:23so we yeah proposed um
0:05:25a real uh that update equations
0:05:29to this looks nice not nasty i now
0:05:32uh the chip or and here is this
0:05:34in the experiments you have a
0:05:36cross term term can it read it's a function and a and to cross too
0:05:40which were to deaf and shaped along every measurement points and uh uh i don't this state point two
0:05:46to do the that updated H G
0:05:49um i mean that of you hear the exact expression of the uh cost and it's
0:05:54in the paper
0:05:55i will rather try to show you what it looks like in practical situation
0:06:01so i assume that you have through uh since words
0:06:05well as you die from shake you crossed term in this state but it's
0:06:10missions you zero one and measures in three
0:06:12that but was able to a cost here
0:06:15yeah the
0:06:17that that there was a target
0:06:19i state X according to my uh time of the T P H D
0:06:23and that
0:06:24this target is detected by since someone
0:06:26and produced mission ones you one
0:06:29the target that was in the data and so two
0:06:32and was detected by since a three
0:06:34and that produce measurements is three
0:06:38i
0:06:39um um
0:06:41uh a cross term is uh a definite shaded in
0:06:45measurement points can me
0:06:47like this
0:06:48then uh a
0:06:49the resulting cross to a is a you that there is a target somewhere in the state it's but i
0:06:54don't know where
0:06:55which
0:06:56well to buy since so one since too but was and detected by the
0:07:01since of
0:07:05so what is it look like whether the updated is you look like and the simple example so here are
0:07:09yeah only two sensors
0:07:11first case and two measurements so one measurement per sensor if i don't example
0:07:16what you see here he's is a better P H D
0:07:19the first and here that you doing uh
0:07:21and denotes the uh
0:07:23like you that you have a target in in state but it's but it's and detected by bows answers
0:07:29and that
0:07:30um you have
0:07:31the this sure takes into account all the possible
0:07:35haitian measurement session
0:07:37so uh the one and the mean to here you have a linear
0:07:41possibility that uh
0:07:44oh
0:07:45which can
0:07:46and the possible to that you were to to have these two measures on the measurements on the
0:07:51so
0:07:52here
0:07:52because is the that's where
0:07:54comes from different uh
0:07:56uh
0:07:57targets and hear from the
0:07:59a single target
0:08:02you can imagine that if you increase the number of measurements are the number of target
0:08:06teams we grows out of control you see if i don't me
0:08:10had a one measurement is
0:08:11uh
0:08:13going very nasty
0:08:14so how can we simplify this
0:08:17we to to has a look on the
0:08:20that update equation
0:08:21and we found that in maybe situations uh maybe a different shaded cross terms were to vanish
0:08:28so that look at this example you have three sensors S one and as three at or overlapping fields
0:08:34and has to is isolated
0:08:36well i i know that a target in the recognition cannot be detected
0:08:40so and mm uh trust different in
0:08:43this measurement and i don't know a point here
0:08:46we have an vanish
0:08:48uh i i also that a type but can be detected by this sense of S one and S two
0:08:54so i cross term shaded in the
0:08:57measurement here and here will vanish two
0:09:00and so am
0:09:02so
0:09:03but that is that
0:09:05uh
0:09:07instead of using my uh the data that question on the whole state space
0:09:12i can write a
0:09:13use it three times and smaller
0:09:15uh parts of the uh state space
0:09:18i as well as a a of the vision without any sense
0:09:22well
0:09:23and and the the grey mission with a uh since a one and three and one and the region
0:09:28well since of to measurement from sensor to
0:09:31and i'm that the exact same results also the exact multi sensor uh
0:09:35P D a a a a a bit P H T
0:09:37but it should be uh a fast
0:09:41so let's look at an example
0:09:43so a here have uh or something like ten sensors spread or of of the state space
0:09:49i one you so that the the the fourth configuration is set that it should be able to
0:09:54P my sense the at least
0:09:56for parts
0:09:57the is
0:09:58this one isolated is to have a a and this through here
0:10:01so this that's that's this is critical because that i we have a three uh i being uh the field
0:10:06of you so if a target
0:10:08comes into this
0:10:09uh doc spots
0:10:10uh the
0:10:12that that the two step would be very uh
0:10:15compute a ah
0:10:16we have a out to compute
0:10:19so here um
0:10:22it is a nice and that of the time step
0:10:24uh in a um the number of target across time and the red the estimate number by my uh my
0:10:31um
0:10:32me
0:10:33a so pitch if you to so you can see that at the back of the estimation and and we
0:10:40as a
0:10:41i mean i'm high number of targets so
0:10:43it
0:10:43to this either the critical times whether the that are that should be difficult with the
0:10:48uh brute force approach
0:10:52and uh uh K any so that
0:10:54uh in black these a computing time of the better updates tape
0:10:58a across
0:10:59uh this you scenario
0:11:00a a of the brute first approach so
0:11:03the that that it's state of the whole state space
0:11:06and he yeah
0:11:07oh in well as the computing time further the partition ms
0:11:10oh the time it it's log scale here
0:11:13so we assume that
0:11:14and the we had at the um the brute force approach is exploding
0:11:18well i and the that and remains quite low
0:11:22um um as as well so a simple is as
0:11:25here because the target member but it is very low
0:11:28uh the brute first this actually but uh on the the portion that
0:11:34so to conclude what can we say about the partition method
0:11:37well uh first of all it's not an approximation because we get
0:11:41to have the exact is and so that a a a a a a a to question was so we
0:11:45can put by gate
0:11:46the exact value of the mid and P H D
0:11:50in case where the the field of you configuration is quite a can then the passion method it is likely
0:11:56to be much more efficient
0:11:57but the brute force approach
0:12:00but that's the passion itself other the coast
0:12:02that's why i
0:12:04we had a here a uh the passion was more
0:12:08a a little bit first was faster than the patch and the third
0:12:12if the for the feel of a come is and five or or uh what was case if
0:12:17it's a a a a and the uh
0:12:19so of used are
0:12:20crossing each other
0:12:22that the pension but them does not bring anything you and uh
0:12:25in to be a bit less efficient at the brute force approach
0:12:28but you know all
0:12:30in a practical situation well the field of view of the
0:12:33since of a spread of the state space
0:12:35the approximation mission can bring uh
0:12:38an interesting approach to
0:12:39if you want to provide get the truth
0:12:42P H D a P H D of that
0:12:45thank
0:13:02uh
0:13:02this if if finds that well
0:13:04a problem is all all and
0:13:06or same time
0:13:09yes
0:13:10i the why you don't have
0:13:12yeah ish
0:13:12it shouldn't have a synchronised a network
0:13:15then you can uh you the uh
0:13:17it activated directed the
0:13:19approximation
0:13:20which case you will uh
0:13:22you will uh use the uh
0:13:24single sensor uh a P G
0:13:26that that T questions uh
0:13:28second second city
0:13:30do one know that in the synchronized case
0:13:32uh if you be a product it uh it it to product that approximation
0:13:37then define a lattice arc approximation would depends on the order in which you you take the uh
0:13:43you a a process the uh sensor that's
0:13:46a may be a problem
0:13:50gosh
0:13:58what was the model that you're using your simulations was to dimension
0:14:02uh the was your house sense to was your results
0:14:05do a to a collection
0:14:07in overlapping regions
0:14:10sorry
0:14:10a what was the model
0:14:13you summation
0:14:14you mean the target model of the
0:14:16observation
0:14:18hmmm
0:14:19oh the target model is is quite simple weights so and and C V near constant us to model
0:14:24uh are the targets are created uh around the edges of the state space
0:14:28and
0:14:29the measurement i use in different kind of of sensors
0:14:32well
0:14:33some sense as of a a can the the range
0:14:37and the and angle
0:14:38of the target and you have a cushion noise
0:14:41and these two values
0:14:42and all the sensors can also uh
0:14:45now the uh radial velocity
0:14:47see
0:14:48and and simulation what sense
0:14:50there
0:14:50yeah we have many different kind and a yeah
0:14:53the sensing in as as what different for for every uh sense
0:14:59cool
0:15:01and
0:15:01well as as usual and the phd H
0:15:03the following in but it the probability detection
0:15:06oh you since your sense i is low
0:15:09then you
0:15:09P L O P G is likely to to crash
0:15:12if you in yours
0:15:15uh in this case it's the protein detection is quite a i but i tried to means and no uh
0:15:20uh uh values and eat
0:15:22couldn't work
0:15:23click
0:15:24i
0:15:25um um i used a different uh us a first on process to for every uh uh captain
0:15:31since so you can have a different uh
0:15:34class a process it works quite well
0:15:37except that you have
0:15:38the for some right will uh we'll set you will
0:15:41oh right estimate
0:15:42uh
0:15:43the remember but gets you will estimate would be quite a i of and than real number
0:15:48so we will another way to extract
0:15:50a target from from you you data
0:15:52because well i yeah a and at the beginning was
0:15:55but each
0:15:56uh a you say
0:15:57i again to goals of a all sits they this is my number of targets
0:16:01i take the
0:16:02the round well i the closest in to go at this is my number of targets
0:16:06and that will a at is um uh are the highest peaks
0:16:09but again can do a better thing
0:16:11you can try to localise in the space
0:16:14some place where you can extract
0:16:16uh
0:16:17the P G uh
0:16:19some
0:16:21uh in the sub region of the uh these state space
0:16:24uh
0:16:25the P such that you have a a a a a weight of one
0:16:28we which will
0:16:29note that there is a target then you
0:16:31extract this and you will process these two to try to extract uh
0:16:35a target
0:16:38and more questions we see have five minute
0:16:54what implementation the use was it think of the bayes yes
0:16:59and it's uh i'm
0:17:00it's difficult uh these uh a particular of to implementation
0:17:04uh "'specially" a for the creation of new uh a weight around the measurement all around
0:17:09oh according to the number of the of the destination
0:17:13so that's why in in this case the uh a target estimation the estimation of the target number was not
0:17:18very good at some point
0:17:20i should be able to
0:17:21to improve this uh if i use the
0:17:23a better article implementation
0:17:29you questions
0:17:34for the bit but uses in used seem to have fun
0:17:36point
0:17:37uh sense
0:17:38if you one controller positions of
0:17:40a
0:17:41there any of them is now that you would have
0:17:44for your of and that
0:17:45if i need two
0:17:47the sense that you have a about
0:17:49and
0:17:50fusion
0:17:51i do not if data point
0:17:53and not for sensors for target
0:17:55but the target are yeah
0:17:56yeah
0:17:56the sensors also they can have any particular structure
0:17:59the and if you in control of that would that be any
0:18:01optimum position you know the sense
0:18:03oh that's a good question uh and not as i'm working on the uh and i don't for on be
0:18:09solution of the sense i tried with a fixed position to control
0:18:12try to find the optimal uh
0:18:15well orientation iteration of my and my uh since
0:18:17and
0:18:18this is a a a a i think uh
0:18:20the big and X that for the P H D the the control part
0:18:24because we know that if
0:18:26uh there is a part of the since space which is never observed that any some
0:18:30now uh things were grow out of of control and it will uh
0:18:34the the quality of the target uh and number estimation so i'm trying to
0:18:41to be a a a limitation of the sensors
0:18:43so that i will
0:18:44at least look at
0:18:46where have that i can uh
0:18:47at which with a coverage and
0:18:49a
0:18:51and more questions
0:18:55okay let's time speaker again
0:18:57i