Přepis řeči - MULTI-SENSOR PHD: CONSTRUCTION AND IMPLEMENTATION BY SPACE PARTITIONING

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

MULTI-SENSOR PHD: CONSTRUCTION AND IMPLEMENTATION BY SPACE PARTITIONING

Target Detection and Localisation

Přednášející: Emmanuel Delande, Autoři: Emmanuel Delande, CNRS, France; Emmanuel Duflos, Philippe Vanheeghe, Ecole Centrale de Lille, France; Dominique Heurguier, Thales Communications, France