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