0:00:13right once
0:00:15uh a for my first our right
0:00:18what i wanna do is that wanna to talk about
0:00:23so uh
0:00:24i i do i
0:00:27a fixed and by the um
0:00:31is more than a to like extent by some stuff that was done in tracking you in particular the first
0:00:35presentation this morning what you saw was some people talking about a H T talk on the at thought
0:00:41a a a a filter is a a a label agnostic filter doesn't care which is which you don't doesn't
0:00:46has the question where target one words target to
0:00:49you ask the question where other targets
0:00:51that really the motivation for dealing with side with such thing
0:00:55i actually the the idea of this goes back a lot of or their some work pilots a and to
0:00:59people i even drown was not thing other people doing things he was saying well
0:01:03what's suppose that we have a target tracker or of more than in an H T a really good target
0:01:08tracker that
0:01:08can track multiple target
0:01:10and it's supposed to find a target ones over there and target to over there but hey made a mistake
0:01:16target to is that it has to the target to use where target one a to be
0:01:20and the S of where target
0:01:21well i'm is is where target to one
0:01:24so do you use a at the end of it all that that's a terrible estimator
0:01:29because the error target one target to or a part can be extremely high
0:01:34yeah it's not good i mean you you as opposed to know where the various targets are
0:01:38is is in both the word target one is
0:01:41on the other hand if you are able to necessarily mean and all that much of the start if you
0:01:45just that a guess is the which is which is not a terrible track
0:01:49so the idea is that
0:01:51first of all let's a problem get put some uh cut with that but suppose let's i've to get the
0:01:56credit to
0:01:57should but one we came up with this or was he a metric which all talk about was second
0:02:02i came up with a we use a a a a way to measure the performance of trackers that do
0:02:08not necessarily know which target we've which you that we couldn't care which a which are a target with which
0:02:13so here we go
0:02:15uh yeah was so out the side but metric is this and it was a very nice paper by few
0:02:19back or thousand eight they to a generalization of the drum and thing to result um was only the case
0:02:24where you do the right number target space leap for the sign
0:02:28i i idea basically a this is a mathematical looking me this talk about every second of
0:02:32uh if you assume that are gonna one was you are talking to see sorry
0:02:36saying this right like to use my
0:02:38i think or
0:02:40a one is a target to is here you estimates are slightly different from that okay a here to here
0:02:45well this estimates close to try one see that what i think is where
0:02:48and the the estimate to is close to target to where you can compute the beach these square that
0:02:54you can also compute the cross errors if you exchange the link on that arg
0:02:58to but to do is you gotta take the minimum those two and that's essentially what is always was he
0:03:03a metric does
0:03:05so bit more general that a little bit more of one that because it it allows them
0:03:10and a in the number of a targets the number of objects
0:03:14that you to make a so in T if you estimate that there are more targets is actually only three
0:03:19they you don't get P light with an infinite at
0:03:22no if has to make their only two targets there what is actually three
0:03:26so it actually has a clamp that's you that number C the you talk that you can see there
0:03:30uh that up is that upper bound you model family can get for making that sort of the state
0:03:36one the beautiful things but this paper is that it was shown that it was a metric in the mathematical
0:03:40that's important thing because that means we can do some a stuff with with it
0:03:44so that's the a was up out assignment uh uh D
0:03:48uh a in this paper that we're not gonna worry about the number of target ask target estimated
0:03:54being different in the number of targets are there
0:03:56and also you want to on the slide like do need to mention
0:03:59and i uh
0:04:01if i can get this to work
0:04:02but states and targets
0:04:04so this X here
0:04:06the acts to is does not have a source good on it is gonna represent the stacked vector or all
0:04:12the states
0:04:13so if you mentioned for example a a like and he was doing we high dimensional states
0:04:18and you had to draw gets then this is gonna be of dimension eight
0:04:21and when i talk about exchanging the labeling i'm talking about it's changing the labelling of the top word with
0:04:26a bottom or in that case
0:04:28is one like stage all the states
0:04:30oh of the cost quite to the target side keeping the ones together
0:04:34the cards quite to take your definition of the state or that particular meeting
0:04:40so you it was this and uh for some reason michael a lot of the you're press will be the
0:04:44cross as a side you know a lot of was to talk about or was he a make my
0:04:49uh uh a slide per present by uh it's changing between or was and all E and i don't go
0:04:54back and yelled a bit later on
0:04:56uh but he's like he's called a case these this is only for always the error
0:05:00we in this case years as france the is actually the uh what if we know the number of objects
0:05:05are out there
0:05:06but i don't have to worry about a thing though those extra penalty
0:05:09but i have to really about so every collection of the them it's finding the best match
0:05:14between those estimates the target
0:05:16a few people know a target tracking did association what a like to it's not an algorithm is a two
0:05:21dimensional were problem the figure that out it's easy okay
0:05:24so uh a this work for equal to this uh any equal to so i and uh
0:05:29uh a just to a back here for second
0:05:31and corresponds to it's not written down you well uh a and in this case card once the experiment and
0:05:37the air so for a will the to just where there are people to fill with a you talking about
0:05:41two is a a power error
0:05:43okay so that's what the meaning and
0:05:45um so one can talk about uh minimizing the uh as well as talk that a second of uh
0:05:51i would like to try your to to something which will explain your minds are able you minds or or
0:05:55or just a general what you
0:05:57uh this is somehow as you might wanna take between traditional estimation what i want talk about a good additional
0:06:03estimation and when i thought but the estimation i mean
0:06:06basically you of estimation then i would have a a measure which would be this where are in many cases
0:06:12where interested in
0:06:13i what's so i i don't that's estimate uh i i'm label estimation on the estimation
0:06:19a a in that case the measure of the performance for a particular on is gonna be the L a
0:06:24a one a such but
0:06:26but the criterion we coming up with good estimate it is to minimize was so is the mean square error
0:06:31that's that that's that that's the measure goodness or are estimate or whatever it is
0:06:36it had a vision of labeled estimation set
0:06:39member from a the estimation things about how did it
0:06:42and if i choose not to worry about my body willing then i i i'm gonna be minimize the was
0:06:47so i got be dealing with the criterion
0:06:49i be maybe i was a almost a
0:06:51now that's as got one M two it now if i wanted to have a good estimate
0:06:56in the traditional sense and then to talk about the in minimum be a minimum mean square error estimate and
0:07:02i Z
0:07:03or M S
0:07:04yeah yeah S E
0:07:05which is a very much more so that then the minimum
0:07:09mean was a measure memory estimate
0:07:12which is what i to talk about the day that's out what popular as well
0:07:16i think that acronym
0:07:17i have tried i of wrestling in with michael a lot is to make it a little bit more pronounced
0:07:22able i tried to suggest the most to them but they
0:07:24still are sticking around most but
0:07:26so that we have
0:07:28most ever by
0:07:30so that was used for a what i wanna do is a one size for just a little bit because
0:07:36uh if you imagine that in uh
0:07:40that i estimation problem is actually a a um
0:07:45an optimization problem
0:07:46okay so the optimization is optimization of the criteria
0:07:50mean square error is well used to but this case it's M S P A
0:07:53uh a the criterion is the the the this the test it's the measure of you the you want to
0:07:57get that you want to a
0:07:59have the best you can get them mean square error for example is what you traditionally used to deal
0:08:04oh are you are going to say a a target one are target to that if you like
0:08:09that this that that to the first elements is talking one second on its is target to
0:08:14that you stay mind all that you could think that as a constraint
0:08:18well you got rid of that constraint
0:08:21a mention you do the estimation now i'm as you the optimization and you remove the constraint
0:08:26or you can do worse than you did with a constraint
0:08:28we can do worse
0:08:29and my plane in it is and there are some results showing this and and not for that this presentation
0:08:34show in that you actually can do better in terms not just to
0:08:38and S P A which is kind of a
0:08:41a if you're the general you worried about a if you got not some place but in terms of real
0:08:45matters has in but i just that there should down some point you can actually show you can do a
0:08:49little better
0:08:50in terms of estimation your probability will be higher
0:08:53by removing that constraints of it but i would the constraint i could do a little bit that
0:08:58okay okay
0:09:00so i some uh that different things you think about here a a a a we have some uh a
0:09:03a work uh which is being submitted a the you all that'll be accepted
0:09:07and B is invited for a super resolution of the always "'cause" the direction of arrival estimation you can say
0:09:13that the unlabeled label "'cause" you the knows which is which
0:09:15a a a a a i think i could use but a lot to talk about things like the uh
0:09:20the P H D other
0:09:21dataset set based that method small
0:09:23is our motivation to where we started doing this stuff
0:09:27i was used that that the diffusion conference in the two thousand nine
0:09:31and this well as where we first scale class the idea now the sir
0:09:34in this case or first to set in a model are sets the random finite sets set
0:09:39a a and the have to be so see an example of to target
0:09:42you can see one of them
0:09:43coming in from the top left someone of coming in from the bottom left
0:09:47so i get bottom left
0:09:49but the bad one
0:09:50a a that's the that's a the track colours
0:09:52a a kind of a why actually separating
0:09:55and a red and the black score to the tracks that we do have from them using R J P
0:10:00D A have estimate
0:10:02for a couple of you of the audience gets the white all be embarrassed
0:10:05we don't know what a G yeah yeah is me just give you a a a a very quick sketch
0:10:09of it
0:10:10yeah is to have of this like a a lot of these a tracker to trivial to you hear that
0:10:13explain easily be proof that you problem is always in the implementation of a
0:10:18J yeah basically is a skin and scan and was the estimator basic are used to up with a gaussian
0:10:23prior for that are pretty a to as you tried
0:10:26but are the target you do a couple version
0:10:28and you uh a create a a multivariate or so i multi mode
0:10:33gaussian posterior "'cause" trying to all the association that the case for example i two targets
0:10:38and two measurements i have by the posterior
0:10:42which corresponds to
0:10:44this this association this association could be right
0:10:48and then the J U S as a relative to
0:10:52um so my gaussian posterior
0:10:54and i two and then
0:10:57according to a minimum mean square error estimate that's gonna undefined the mean and the final covariance and then pretend
0:11:03that that was just a gaussian yeah
0:11:05ready for my next estimation
0:11:08alright so you want to do that we use most estimator at each stage
0:11:13you come up with something called the sites such a pda a for S J P D A
0:11:17that's a thing these C down the bottom
0:11:19the set you use as a as a posterior estimator and what do not to it doesn't take a lead
0:11:25which is which
0:11:26and if you don't do is very quickly here
0:11:29a performance nine are quickly let's like then a wow with it
0:11:32but the for so that was a very represent the performance of the J P D A in this case
0:11:36you are we actually have a a high probability detection i don't even know we have any clutter at all
0:11:40of them in or in this case at that maybe we do have some uh at some clutter
0:11:45uh because of the fact that happens at the end of so as to what happens the J P D
0:11:48A comes together
0:11:49and because times an mmse estimators hence their bats the talk but that a second
0:11:53the mse estimators
0:11:55do are they call S in the middle they uh don't be a they're not able to track the targets
0:12:00separately at a and at the and then not the targets are not able to separate and to have it
0:12:06is becomes overwhelming and they got a separate that perform
0:12:10the has to be D and the other hand because i because the characteristics of the or was be a
0:12:15metric are able that are able to put one target i top of one
0:12:20estimated target roughly on top of whether targets are you're not forced to be in the middle you're not gonna
0:12:24be liable to a a of the same sense
0:12:27but i is part of a right the doing
0:12:32same as
0:12:33same as over here
0:12:34right and
0:12:36is an exchange available
0:12:38as a metric to about that notice that perhaps and yes i can do something with elaine hasn't to this
0:12:45plan to talk about this in that in this
0:12:48but yeah that's it makes a mistake
0:12:50but does the tracks and that's the good thing about okay so
0:12:55that tracking for a second i've been back about track
0:12:58you that's good i can i make a a or about that
0:13:01i want to a estimation
0:13:03and what i wanna do as i want to mmospa estimate a estimation um estimation
0:13:09and you can see from the for a this task to me
0:13:13or the estimation problem this kind here
0:13:16and and and a have to choose the past or in the object you trying to estimate
0:13:22that's a so and about to solve a case i can be something you could do a usually a and
0:13:26the of this time is the come up with a by approximate that come up with a reasonable performance
0:13:32a a a a and of the fusion two thousand ten at a conference we had a couple of things
0:13:36you here one of things the most day is we show that in fact a and i'm a estimate
0:13:41well as the and M S E estimator for a specific adult a weighted
0:13:46a joint density function we calling it P to a i'll give about that the second or two
0:13:52and uh i it is a a big with at present we one here where the uh as a uh
0:13:56uh actually a yes with post where for special cases of but is explicit solution for that
0:14:01not work in this case you are one do something a bit more a but more general
0:14:05that's a set a and a finite sets then state with talked but it's one of the basically you need
0:14:10to really there for every actually need to really of the a labels
0:14:15such that the P at such that be a a um and i T a it basically cut a cost
0:14:20as to minimize that this is the D where you expect to be where was for every yeah
0:14:25like to do but uh a least in there are you can be done however all which is uh just
0:14:30okay that you know this is a
0:14:32but and means is if you want to get the and then wise B A estimator
0:14:36you have to find that density and then you do to traditional
0:14:39i expect shall expectation like you would do for them in a mean square error estimator it works
0:14:45is what you got that they you can use a traditional easy technique easy well okay
0:14:50the approximating the approximate in an estimation is not that it easy a a is a letter review also a
0:14:56for example if you knew how to do these things if you know what you are these density functions
0:15:01you can create something the look you have like equation ten you of the markov chain monte carlo technique where
0:15:06you have a words weights of that that we going W use here
0:15:08we would prefer to talk about the discrete as in the density would of course you can do it any
0:15:12kind of
0:15:13uh dimensional space of um
0:15:15you could come up with a a a that are in fact was up and down here of a curse
0:15:20of way to figure out the what the mmospa estimate a is in a in an arbitrary situation
0:15:26i i to have a good the uh that equation and is at a certain a mathematics cancelling out terms
0:15:31which don't matter
0:15:32uh so
0:15:33the are too much about by bottom line message here is that in the ear a is like getting done
0:15:39two minutes left okay so i have only each two slides less all of them are very quickly a K
0:15:43you put on you glass
0:15:45as a do i mention it's not that the stuff here
0:15:48a a a a a a a a would we done not to talk about that
0:15:50uh a a a a one to talk to think about the concept uh
0:15:55the uh
0:15:56the mean a B M is as the estimation and i'm as the estimation
0:16:01a the case of the mean of a bimodal density function you see you have a P D a lot
0:16:06but like that the mean of close to them that's what you'd expect to be for a bimodal density function
0:16:11this is a a what you see on the right is the marginalised case where you based project a things
0:16:15are to the uh on the ball
0:16:17i one the two axes
0:16:18a for the a finite set of densities
0:16:20for the mmospa estimate a a you get much better performance you get one and it does not have a
0:16:26small because you are small because
0:16:28they are can exchange that's point
0:16:31and so that i yeah was be estimator is much better what not here is
0:16:36but but we talk about is for any equal to two that's mean square error
0:16:40i'm a time but here that to use for any that's where the error as a power and and try
0:16:45to be much easier to work with
0:16:46because as
0:16:48well i this year the sewage uh is with the china out i can make a turn out to get
0:16:52it training like in the gaussian mixture case
0:16:56is the thing we gonna use these standard back yeah i i want was to at sure that you're not
0:17:02data charge about because got a fixed the did it
0:17:05if we split the experiment between the two terms in this
0:17:08we can and that i might minimizing not yeah as the not exactly the uh
0:17:14the uh the product but it's not exactly society
0:17:17by and so on and to the quality while the panel of the quantity
0:17:22and we can also be in two
0:17:24like that
0:17:25which give us exactly the end to that we need to get a and we have explicit solution in the
0:17:30gaussian mixture case for the for this i'm not we normally want but hey because of a good performance
0:17:35and this is sort of basically last likes your or choice so sort K C showing that we get
0:17:40in this case you X one X two are still objects ones or on the right we're getting
0:17:44something like the correct performance
0:17:46yeah you can see where
0:17:48and is in the right of and everything we don't want that for the unlabeled case we very close the
0:17:53most best but with the equal to two
0:17:55that's right basically that
0:17:56i told you of the last minute quickly
0:18:11a a do i need to know the number of a a a a lot of text the implementation in
0:18:16the mathematics to have as we do we have to we have a a we had to have object we
0:18:22have to know that what there to a picked out there
0:18:24a a i mean i thinking about this is many wondering doing it the be extended to the case of
0:18:29a merge and a distance function but the milk yeah that's be a a a a a right now but
0:18:34it's sounds like an to growl
0:18:39okay the thing speaker again