0:00:13 | yes |
---|---|

0:00:13 | right once |

0:00:15 | uh a for my first our right |

0:00:18 | notation |

0:00:18 | what i wanna do is that wanna to talk about |

0:00:23 | so uh |

0:00:24 | i i do i |

0:00:26 | i |

0:00:26 | i |

0:00:27 | a fixed and by the um |

0:00:31 | is more than a to like extent by some stuff that was done in tracking you in particular the first |

0:00:35 | presentation this morning what you saw was some people talking about a H T talk on the at thought |

0:00:41 | a a a a filter is a a a label agnostic filter doesn't care which is which you don't doesn't |

0:00:46 | has the question where target one words target to |

0:00:49 | you ask the question where other targets |

0:00:51 | that really the motivation for dealing with side with such thing |

0:00:55 | i actually the the idea of this goes back a lot of or their some work pilots a and to |

0:00:59 | people i even drown was not thing other people doing things he was saying well |

0:01:03 | what's suppose that we have a target tracker or of more than in an H T a really good target |

0:01:08 | tracker that |

0:01:08 | can track multiple target |

0:01:10 | and it's supposed to find a target ones over there and target to over there but hey made a mistake |

0:01:16 | target to is that it has to the target to use where target one a to be |

0:01:20 | and the S of where target |

0:01:21 | well i'm is is where target to one |

0:01:24 | so do you use a at the end of it all that that's a terrible estimator |

0:01:29 | because the error target one target to or a part can be extremely high |

0:01:34 | well |

0:01:34 | yeah it's not good i mean you you as opposed to know where the various targets are |

0:01:38 | is is in both the word target one is |

0:01:40 | but |

0:01:41 | on the other hand if you are able to necessarily mean and all that much of the start if you |

0:01:45 | just that a guess is the which is which is not a terrible track |

0:01:49 | so the idea is that |

0:01:51 | first of all let's a problem get put some uh cut with that but suppose let's i've to get the |

0:01:56 | credit to |

0:01:57 | should but one we came up with this or was he a metric which all talk about was second |

0:02:01 | uh_huh |

0:02:02 | i came up with a we use a a a a way to measure the performance of trackers that do |

0:02:08 | not necessarily know which target we've which you that we couldn't care which a which are a target with which |

0:02:13 | so here we go |

0:02:15 | uh yeah was so out the side but metric is this and it was a very nice paper by few |

0:02:19 | back or thousand eight they to a generalization of the drum and thing to result um was only the case |

0:02:24 | where you do the right number target space leap for the sign |

0:02:28 | i i idea basically a this is a mathematical looking me this talk about every second of |

0:02:32 | uh if you assume that are gonna one was you are talking to see sorry |

0:02:36 | saying this right like to use my |

0:02:38 | i think or |

0:02:40 | a one is a target to is here you estimates are slightly different from that okay a here to here |

0:02:45 | well this estimates close to try one see that what i think is where |

0:02:48 | and the the estimate to is close to target to where you can compute the beach these square that |

0:02:54 | you can also compute the cross errors if you exchange the link on that arg |

0:02:58 | to but to do is you gotta take the minimum those two and that's essentially what is always was he |

0:03:03 | a metric does |

0:03:05 | so bit more general that a little bit more of one that because it it allows them |

0:03:10 | and a in the number of a targets the number of objects |

0:03:14 | that you to make a so in T if you estimate that there are more targets is actually only three |

0:03:19 | they you don't get P light with an infinite at |

0:03:22 | no if has to make their only two targets there what is actually three |

0:03:26 | so it actually has a clamp that's you that number C the you talk that you can see there |

0:03:30 | uh that up is that upper bound you model family can get for making that sort of the state |

0:03:36 | one the beautiful things but this paper is that it was shown that it was a metric in the mathematical |

0:03:40 | sense |

0:03:40 | that's important thing because that means we can do some a stuff with with it |

0:03:44 | so that's the a was up out assignment uh uh D |

0:03:48 | uh a in this paper that we're not gonna worry about the number of target ask target estimated |

0:03:54 | being different in the number of targets are there |

0:03:56 | and also you want to on the slide like do need to mention |

0:03:59 | and i uh |

0:04:01 | if i can get this to work |

0:04:02 | but states and targets |

0:04:04 | so this X here |

0:04:06 | the acts to is does not have a source good on it is gonna represent the stacked vector or all |

0:04:12 | the states |

0:04:13 | so if you mentioned for example a a like and he was doing we high dimensional states |

0:04:18 | and you had to draw gets then this is gonna be of dimension eight |

0:04:21 | and when i talk about exchanging the labeling i'm talking about it's changing the labelling of the top word with |

0:04:26 | a bottom or in that case |

0:04:28 | is one like stage all the states |

0:04:30 | oh of the cost quite to the target side keeping the ones together |

0:04:34 | the cards quite to take your definition of the state or that particular meeting |

0:04:40 | so you it was this and uh for some reason michael a lot of the you're press will be the |

0:04:44 | cross as a side you know a lot of was to talk about or was he a make my |

0:04:49 | uh uh a slide per present by uh it's changing between or was and all E and i don't go |

0:04:54 | back and yelled a bit later on |

0:04:56 | uh but he's like he's called a case these this is only for always the error |

0:05:00 | we in this case years as france the is actually the uh what if we know the number of objects |

0:05:05 | are out there |

0:05:06 | but i don't have to worry about a thing though those extra penalty |

0:05:09 | but i have to really about so every collection of the them it's finding the best match |

0:05:14 | between those estimates the target |

0:05:16 | a few people know a target tracking did association what a like to it's not an algorithm is a two |

0:05:21 | dimensional were problem the figure that out it's easy okay |

0:05:24 | so uh a this work for equal to this uh any equal to so i and uh |

0:05:29 | uh a just to a back here for second |

0:05:31 | and corresponds to it's not written down you well uh a and in this case card once the experiment and |

0:05:37 | the air so for a will the to just where there are people to fill with a you talking about |

0:05:41 | two is a a power error |

0:05:43 | okay so that's what the meaning and |

0:05:45 | um so one can talk about uh minimizing the uh as well as talk that a second of uh |

0:05:51 | i would like to try your to to something which will explain your minds are able you minds or or |

0:05:55 | or just a general what you |

0:05:57 | uh this is somehow as you might wanna take between traditional estimation what i want talk about a good additional |

0:06:03 | estimation and when i thought but the estimation i mean |

0:06:06 | basically you of estimation then i would have a a measure which would be this where are in many cases |

0:06:12 | where interested in |

0:06:13 | i what's so i i don't that's estimate uh i i'm label estimation on the estimation |

0:06:19 | a a in that case the measure of the performance for a particular on is gonna be the L a |

0:06:24 | a one a such but |

0:06:26 | but the criterion we coming up with good estimate it is to minimize was so is the mean square error |

0:06:31 | that's that that's that that's the measure goodness or are estimate or whatever it is |

0:06:36 | it had a vision of labeled estimation set |

0:06:39 | member from a the estimation things about how did it |

0:06:42 | and if i choose not to worry about my body willing then i i i'm gonna be minimize the was |

0:06:47 | so i got be dealing with the criterion |

0:06:49 | i be maybe i was a almost a |

0:06:51 | now that's as got one M two it now if i wanted to have a good estimate |

0:06:56 | in the traditional sense and then to talk about the in minimum be a minimum mean square error estimate and |

0:07:02 | i Z |

0:07:03 | or M S |

0:07:04 | yeah yeah S E |

0:07:05 | which is a very much more so that then the minimum |

0:07:09 | mean was a measure memory estimate |

0:07:12 | which is what i to talk about the day that's out what popular as well |

0:07:16 | i think that acronym |

0:07:17 | i have tried i of wrestling in with michael a lot is to make it a little bit more pronounced |

0:07:22 | able i tried to suggest the most to them but they |

0:07:24 | still are sticking around most but |

0:07:26 | so that we have |

0:07:28 | most ever by |

0:07:30 | so that was used for a what i wanna do is a one size for just a little bit because |

0:07:35 | as |

0:07:35 | this |

0:07:36 | uh if you imagine that in uh |

0:07:40 | that i estimation problem is actually a a um |

0:07:45 | an optimization problem |

0:07:46 | okay so the optimization is optimization of the criteria |

0:07:50 | mean square error is well used to but this case it's M S P A |

0:07:53 | uh a the criterion is the the the this the test it's the measure of you the you want to |

0:07:57 | get that you want to a |

0:07:59 | have the best you can get them mean square error for example is what you traditionally used to deal |

0:08:04 | oh are you are going to say a a target one are target to that if you like |

0:08:09 | that this that that to the first elements is talking one second on its is target to |

0:08:14 | that you stay mind all that you could think that as a constraint |

0:08:18 | well you got rid of that constraint |

0:08:21 | a mention you do the estimation now i'm as you the optimization and you remove the constraint |

0:08:26 | or you can do worse than you did with a constraint |

0:08:28 | we can do worse |

0:08:29 | and my plane in it is and there are some results showing this and and not for that this presentation |

0:08:34 | show in that you actually can do better in terms not just to |

0:08:38 | and S P A which is kind of a |

0:08:41 | a if you're the general you worried about a if you got not some place but in terms of real |

0:08:45 | matters has in but i just that there should down some point you can actually show you can do a |

0:08:49 | little better |

0:08:50 | in terms of estimation your probability will be higher |

0:08:53 | by removing that constraints of it but i would the constraint i could do a little bit that |

0:08:58 | okay okay |

0:08:59 | uh_huh |

0:09:00 | so i some uh that different things you think about here a a a a we have some uh a |

0:09:03 | a work uh which is being submitted a the you all that'll be accepted |

0:09:07 | and B is invited for a super resolution of the always "'cause" the direction of arrival estimation you can say |

0:09:13 | that the unlabeled label "'cause" you the knows which is which |

0:09:15 | a a a a a i think i could use but a lot to talk about things like the uh |

0:09:20 | the P H D other |

0:09:21 | dataset set based that method small |

0:09:23 | is our motivation to where we started doing this stuff |

0:09:27 | i was used that that the diffusion conference in the two thousand nine |

0:09:31 | and this well as where we first scale class the idea now the sir |

0:09:34 | in this case or first to set in a model are sets the random finite sets set |

0:09:39 | a a and the have to be so see an example of to target |

0:09:42 | you can see one of them |

0:09:43 | coming in from the top left someone of coming in from the bottom left |

0:09:47 | so i get bottom left |

0:09:49 | but the bad one |

0:09:50 | a a that's the that's a the track colours |

0:09:52 | a a kind of a why actually separating |

0:09:55 | and a red and the black score to the tracks that we do have from them using R J P |

0:10:00 | D A have estimate |

0:10:02 | for a couple of you of the audience gets the white all be embarrassed |

0:10:05 | we don't know what a G yeah yeah is me just give you a a a a very quick sketch |

0:10:09 | of it |

0:10:10 | yeah is to have of this like a a lot of these a tracker to trivial to you hear that |

0:10:13 | explain easily be proof that you problem is always in the implementation of a |

0:10:18 | J yeah basically is a skin and scan and was the estimator basic are used to up with a gaussian |

0:10:23 | prior for that are pretty a to as you tried |

0:10:26 | but are the target you do a couple version |

0:10:28 | and you uh a create a a multivariate or so i multi mode |

0:10:33 | gaussian posterior "'cause" trying to all the association that the case for example i two targets |

0:10:38 | and two measurements i have by the posterior |

0:10:42 | which corresponds to |

0:10:44 | this this association this association could be right |

0:10:48 | and then the J U S as a relative to |

0:10:52 | um so my gaussian posterior |

0:10:54 | and i two and then |

0:10:57 | according to a minimum mean square error estimate that's gonna undefined the mean and the final covariance and then pretend |

0:11:03 | that that was just a gaussian yeah |

0:11:05 | ready for my next estimation |

0:11:08 | alright so you want to do that we use most estimator at each stage |

0:11:13 | you come up with something called the sites such a pda a for S J P D A |

0:11:17 | that's a thing these C down the bottom |

0:11:19 | the set you use as a as a posterior estimator and what do not to it doesn't take a lead |

0:11:25 | which is which |

0:11:26 | and if you don't do is very quickly here |

0:11:29 | a performance nine are quickly let's like then a wow with it |

0:11:32 | but the for so that was a very represent the performance of the J P D A in this case |

0:11:36 | you are we actually have a a high probability detection i don't even know we have any clutter at all |

0:11:40 | of them in or in this case at that maybe we do have some uh at some clutter |

0:11:45 | uh because of the fact that happens at the end of so as to what happens the J P D |

0:11:48 | A comes together |

0:11:49 | and because times an mmse estimators hence their bats the talk but that a second |

0:11:53 | the mse estimators |

0:11:55 | do are they call S in the middle they uh don't be a they're not able to track the targets |

0:12:00 | separately at a and at the and then not the targets are not able to separate and to have it |

0:12:06 | is becomes overwhelming and they got a separate that perform |

0:12:10 | the has to be D and the other hand because i because the characteristics of the or was be a |

0:12:15 | metric are able that are able to put one target i top of one |

0:12:20 | estimated target roughly on top of whether targets are you're not forced to be in the middle you're not gonna |

0:12:24 | be liable to a a of the same sense |

0:12:27 | but i is part of a right the doing |

0:12:32 | same as |

0:12:33 | same as over here |

0:12:34 | right and |

0:12:35 | there |

0:12:36 | is an exchange available |

0:12:38 | as a metric to about that notice that perhaps and yes i can do something with elaine hasn't to this |

0:12:45 | plan to talk about this in that in this |

0:12:48 | but yeah that's it makes a mistake |

0:12:50 | but does the tracks and that's the good thing about okay so |

0:12:54 | ah |

0:12:55 | that tracking for a second i've been back about track |

0:12:58 | you that's good i can i make a a or about that |

0:13:00 | um |

0:13:01 | i want to a estimation |

0:13:03 | and what i wanna do as i want to mmospa estimate a estimation um estimation |

0:13:09 | and you can see from the for a this task to me |

0:13:13 | or the estimation problem this kind here |

0:13:16 | and and and a have to choose the past or in the object you trying to estimate |

0:13:22 | that's a so and about to solve a case i can be something you could do a usually a and |

0:13:26 | the of this time is the come up with a by approximate that come up with a reasonable performance |

0:13:32 | a a a a and of the fusion two thousand ten at a conference we had a couple of things |

0:13:36 | you here one of things the most day is we show that in fact a and i'm a estimate |

0:13:41 | well as the and M S E estimator for a specific adult a weighted |

0:13:46 | a joint density function we calling it P to a i'll give about that the second or two |

0:13:50 | um |

0:13:52 | and uh i it is a a big with at present we one here where the uh as a uh |

0:13:56 | uh actually a yes with post where for special cases of but is explicit solution for that |

0:14:01 | not work in this case you are one do something a bit more a but more general |

0:14:05 | that's a set a and a finite sets then state with talked but it's one of the basically you need |

0:14:10 | to really there for every actually need to really of the a labels |

0:14:15 | such that the P at such that be a a um and i T a it basically cut a cost |

0:14:20 | as to minimize that this is the D where you expect to be where was for every yeah |

0:14:25 | like to do but uh a least in there are you can be done however all which is uh just |

0:14:30 | okay that you know this is a |

0:14:32 | but and means is if you want to get the and then wise B A estimator |

0:14:36 | you have to find that density and then you do to traditional |

0:14:39 | i expect shall expectation like you would do for them in a mean square error estimator it works |

0:14:45 | is what you got that they you can use a traditional easy technique easy well okay |

0:14:50 | the approximating the approximate in an estimation is not that it easy a a is a letter review also a |

0:14:56 | for example if you knew how to do these things if you know what you are these density functions |

0:15:01 | you can create something the look you have like equation ten you of the markov chain monte carlo technique where |

0:15:06 | you have a words weights of that that we going W use here |

0:15:08 | we would prefer to talk about the discrete as in the density would of course you can do it any |

0:15:12 | kind of |

0:15:13 | uh dimensional space of um |

0:15:15 | you could come up with a a a that are in fact was up and down here of a curse |

0:15:20 | of way to figure out the what the mmospa estimate a is in a in an arbitrary situation |

0:15:26 | i i to have a good the uh that equation and is at a certain a mathematics cancelling out terms |

0:15:31 | which don't matter |

0:15:32 | uh so |

0:15:33 | the are too much about by bottom line message here is that in the ear a is like getting done |

0:15:39 | two minutes left okay so i have only each two slides less all of them are very quickly a K |

0:15:43 | you put on you glass |

0:15:45 | oh |

0:15:45 | as a do i mention it's not that the stuff here |

0:15:48 | a a a a a a a a would we done not to talk about that |

0:15:50 | uh a a a a one to talk to think about the concept uh |

0:15:55 | the uh |

0:15:56 | the mean a B M is as the estimation and i'm as the estimation |

0:16:01 | a the case of the mean of a bimodal density function you see you have a P D a lot |

0:16:06 | but like that the mean of close to them that's what you'd expect to be for a bimodal density function |

0:16:11 | this is a a what you see on the right is the marginalised case where you based project a things |

0:16:15 | are to the uh on the ball |

0:16:17 | i one the two axes |

0:16:18 | a for the a finite set of densities |

0:16:20 | for the mmospa estimate a a you get much better performance you get one and it does not have a |

0:16:26 | small because you are small because |

0:16:28 | they are can exchange that's point |

0:16:31 | and so that i yeah was be estimator is much better what not here is |

0:16:36 | but but we talk about is for any equal to two that's mean square error |

0:16:40 | i'm a time but here that to use for any that's where the error as a power and and try |

0:16:45 | to be much easier to work with |

0:16:46 | because as |

0:16:48 | well i this year the sewage uh is with the china out i can make a turn out to get |

0:16:52 | it training like in the gaussian mixture case |

0:16:56 | here |

0:16:56 | is the thing we gonna use these standard back yeah i i want was to at sure that you're not |

0:17:02 | data charge about because got a fixed the did it |

0:17:05 | if we split the experiment between the two terms in this |

0:17:08 | we can and that i might minimizing not yeah as the not exactly the uh |

0:17:14 | the uh the product but it's not exactly society |

0:17:17 | by and so on and to the quality while the panel of the quantity |

0:17:22 | and we can also be in two |

0:17:24 | like that |

0:17:25 | which give us exactly the end to that we need to get a and we have explicit solution in the |

0:17:30 | gaussian mixture case for the for this i'm not we normally want but hey because of a good performance |

0:17:35 | and this is sort of basically last likes your or choice so sort K C showing that we get |

0:17:40 | in this case you X one X two are still objects ones or on the right we're getting |

0:17:44 | something like the correct performance |

0:17:46 | yeah you can see where |

0:17:48 | and is in the right of and everything we don't want that for the unlabeled case we very close the |

0:17:53 | most best but with the equal to two |

0:17:55 | that's right basically that |

0:17:56 | i told you of the last minute quickly |

0:18:06 | why |

0:18:07 | thank |

0:18:11 | a a do i need to know the number of a a a a lot of text the implementation in |

0:18:16 | the mathematics to have as we do we have to we have a a we had to have object we |

0:18:22 | have to know that what there to a picked out there |

0:18:24 | a a i mean i thinking about this is many wondering doing it the be extended to the case of |

0:18:29 | a merge and a distance function but the milk yeah that's be a a a a a right now but |

0:18:34 | it's sounds like an to growl |

0:18:39 | okay the thing speaker again |