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

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

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

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