i

i

okay okay

i will catch up

yeah

oh

um

so

you had to tie them a simple uh

we talk about this really the common filtering for caminfo to really the well known

but it is utilised

no i to our problem

okay so we establish some asymptotic

uh commanders results

uh

before i

stuff i wanted you most credit to uh sumatra and the clusters

so i do the leader in this

oh less mode you it's

the talk a little bit

so that's yeah random filter uh where things going on

i the linear regression model

so i R W is noise such that the whole lecture twice to is a lecture run them

process that's okay

so each sensor here

how a hard i but of the we score a actually in the sense that this uh of the which

a matrix is you really or

i matrix

okay

so is that it is that um can out

basically i how a good estimate of the unknown vector

we got

so

what to do so we should allow the sensors to collaborate

know this addition get the way you know other two

achieve the past

if possible i sufficient uh i estimation performance

but we don't know why they're we can achieve the same performance i L

centralized counterpart well for the example you've we have a few says are we we're you have would be a

use a matrix to stack all the most image X okay the coming or team the same performance as as

and that's as the solution

so that's or go to use that is

okay

so of course this kind of application uh okay be uh

uh applied to many and new uh

uh us such as the smart grid you do state estimation for all the

pass is

uh social networks so

okay

so for this problem might if people are uh out

where you interested and D the law of good work

uh

but you're are it this kind of a uh

these to build you guys to me G is it can there is based L

some of good out of addition based okay so i the limitation

you early the have the ability is that a gun it even worse soon

that

at each sensor

the vocal cortical billy a defect ability to not enough

and we are you assume that if we are kind it's that all the C matrix to the right you

can how certain

uh

these like really T so that so called a we call it can mobile

gullible able uh

defect really okay

basically assume the to i as a central an okay but we now it do things a locally

in that case

the you this a results

uh you dense and see this kind of iris the ability to K so called defined that will show you

remains see room later wrong okay

so

just so of this special case cases

the so some have to go that's the believe he was established but under why we stick condition

so in this work we show you were that's we just as a uh i need some very weak assumption

on the system

so we can prove

asymptotic stability for the error covariance matrix

okay

so a recently i read this is uh a previous work go for this one so same mouse there if

we same for author

assume my

so

basically you that work we assume that a model the sensors will allow

ish i each peer rate

will a a lot of one round of estimate selecting

between one pair of neighbours

okay

and and is that kind of a it were uh approach we i

prove certain

uh that's them at all because the ability for the data

okay

so a the may and needs the them then a mix system a result

okay in of or a node

so

how are do that work

we can then they use for one not a free them well he's

in addition to a lot of i C meets my be we can also a lot of the and

so okay

so you will do that

how much for we aim from and no can have

and if we do that

how fast

we can approach the central like the performance

okay

actually we we found that with this new free them

the whole analysis to we use of year cannot be applied anymore sorry

so we have to redefine re introduce there to new to to analyse the performance

yeah so has started with the side up

so let's say oh

we have a collect are you didn't or scissors okay

so we estimate of lecture

random process okay a lot of time

so we allow communication between sensors

okay

so here the ratings a

i don't want to a of and the the comedy re guy but he are really totally only uh

you value when the two to here rate

so that here defined i the link i actually

i Q we should rate so per second

how many in it

is i i okay so that's the mean may link

i'm also so the them's the come to get an scheme a long time is random

okay

okay yeah

we assume that

we we a constant uh them largest communicate a rate you can assume K so

i should be sure that i any tell that he would really easy enough

okay

so that's the main in a approach at the each moment uh P read the K okay so here's a

K K plus one so first so we do have the okay you she's as or do uh of the

region that we do communication or model scissors so the communication

you divided into two parts for us so we do i estimates well

so you each week peak run them if you go parents of neighbours to strap of their previous estimate

okay

after that

we allow multiple round of all observation

uh

we call obligation okay

so so that means you don't keep yourself

uh you always i C you only get the a neighbours but i vision means

you also keep yourself your all alone

all the we a along with neighbours okay for different that's different

a a a a and we go to do it's not total communication rate why a third an upper about

okay

so we're going to a

sure you that such kind of an estimate swiping easy enough

to guarantee a some talk "'cause" the ability of the i-th meeting error

okay

and the extra of the vision

aggregation process

can

dramatically improve

so i estimation performance in term of

the speed to converge to that's centralized

formants

okay

so

in this for local we call it's a modified

gauss safe

uh based interactive a common filter okay so um do yeah K F

so we have a certain us

us

or or side tops okay

so i that's that i want to do a a total rate of communication lies that's to upper bound

so that how many coming occasions we have we have a two times why is uh

uh uh i C made the being

okay another another E is uh all the which should exchange so the error rate just um of this the

kind of what you who's should be limit to but this are about so that's all read constraints

okay

and uh

now we a to be we use sort and uh you tell us about that is to kind of a

communication

uh in the network wise i se means way if you another ease

uh a of the which an exchange

uh or aggregation

so the first of why is ice mates so might be an

in this case we the we do is

we

we use to Q is is simple scheme okay he's not an not meeting self to this

one okay they we'll going summarise

what's a requirement for scheme to would be a reasonable you you order two

uh guarantee over result

okay

so that's a would have to go a simple scheme which all

uh

each time we actually with the link

according to our a distance metric

K is the success of a distance metrics we see that ideally drawing from all even distribution

okay so on each time of that

only one in P the active

i

if that i this is a matrix happen to be i didn't uh identity matrix which means

no node

we also have

they just keep their own i submit so that's also allowed

okay

so that's kind of what is to be a D you find

to guarantee the

for volume property okay

so if it this

if this uh

if this kind of it you to be defined

and and

this as some frames hold well basically was to that

so so called a maximum of which me

although each time a only a one to be active body we use that all the possible activity

or a long time

so that's not work to be connected of that's all row uh only requirement okay so we that

we have a fairly in fact

with a for cool okay

was as that i guess as met you matrix sequence

K

it is john and from this division D and wish discussed

okay as a result

so i

so called mean in is matrix

i about bar

is already reduce more small and uh of your all tick matrix

okay so that's all or requirement on the

properties of we do since may she sequence

okay

yeah are we have we also

can guarantee that

so rate we consume in this phase the i mates what you i i can face is lies that well

half the it remember with of how come about not we we consumed

as most come borrow two

okay

now the rest phase is the so called of their which and

uh aggregation okay

so this kind of a long words but

the message here is

when not have

oh about a lot too but it full communication between nodes okay

that we assume that the whole he we shall for in the four million a some for size

with a M to come borrow it two

but you this since the average communicate read consumption here will be less than come about or what to okay

so we don't

okay i'm cool to details but that's what do we did in the second phase

of communication

okay

so we is that of a local we can also a of the following fact

basically it for small the average

uh committee can a that we consume a the color about what to that's good because we are use of

half an now we use other half the photo total you less then

come up bar that's all that's what we were okay

i say we have a "'cause" of uh

in that

okay so this base each a use the collection be index

you know think that

i've know the and uh time K

so

what cat which a node that do you are you the regions

remember at each P are rate we all are much more round of

uh duration

exchange okay is i the results at the end of this period is should know the will how much pull

nodes was centre there

of the to to know then

okay so we you know

such a seconds of index

i as i K and

okay

actually we can show that

at the end of each period

although

we have some up to

somehow probability that you should know that we all receive the observations from other node but that probability the strictly

positive

okay so that's also critical to reestablish the our results with raw

but this is also the top apart because this sequence is a random i actually is the nonstationary

so that's give us trouble to prove things

so that's my downfall protocols for

estimator swiping and

a observation

aggregation

but when only met also have to that because

when he found out scheme to side of atherton three conditions

it's good enough

"'kay" the three conditions basically saying that

the

sec "'cause" uh of a is matrices do we used to decide activation of what links should be i D

O okay and the mean and their chicks to the beat

probably score so can guy uh reduce one of your T

right that's first requirement

okay K i can't is this sequence you know thing where you get the or a a a you want

guide observations from

should if i this uh probability constraint we should have a lot

uh up that you've probability okay to get a all other nodes of the region okay

you can be a small

so i kind of course

to

total committee can rate had to side i this constraints

you with this is a to with the uh protocol you I D then you are happy

because

then the the to all the results so we have a

i the in

okay

so no finish the

i a order

make up their wishes we finish

the estimate is we finish the observation aggregation now is time to update the or i right

so

yeah we assume that's

in the estimates to i been face what we slap a is a prediction okay based on the previous uh

uh read out to get and uh the the recall covariance matrix

so use to have this with the a well the a neighbour

okay

so which an mlp can we you know it's for the uh uh no then we need we you know

that that's than than a appear gaze and K or bar i'd

time K

okay so this is a face

then the observation aggregation give we you that

i'd and of each uh time i okay

so as and we will have a vector

oh of

all their wishes

from a a from other nodes that you have talk to

okay

so maybe from a hope to talk of multiple hot talk

you to this kind of exchange change okay

the best have this result we take the

or dicked are to one step

for there okay

so to minimize the mean square error so there's a well-known of

uh for for that

i i i i i same time we have a date data the error cornfields crimes matrix

so if i guide it's wide of the got are so we are ready for the next round iteration

right so used time we do this

you can that you can see that with this kind of predictor

we can see what we are doing in does a special case of common filter

okay

so right at we can you elements

what about doing a use the lazy in the results

you in common filter

uh

you each

okay

so

you limit the shape is not a for chorus all a "'cause" it if we don't that

what kind of probably we have

asymptotically or the i requires matrix

okay

so can show that at each node

and

okay so i i requires the matrix you malls according to a this T the person

"'kay"

it's quite complicated okay is a is itself is a random so is a random sequence of the matrices

okay

so now we about the no

you which says

asymptotically hardly this guy's table

okay

so what can we

establish regarding that

oh two

you know to do that a an a it is uh rather than they share to be the clean in

there so okay

so basically we define are are required to be a reader is the basically function being okay based on other

you used version

so

with this that each of this a particle a function we can rewrite

the a lotion of our requires a matrix of log do this or simple form

okay

so you can say that

there are the modulation factor here basically is this "'cause" of the indexes

we use you where you get

new uh where you get the of the regions from okay

and because of this segment C is analysis the and the rate this whole thing is a non-stationary

okay so that's really bad

so the result we had before kind to be used the here

okay

so

what that we can get here

so we need to make to weak assumptions

okay

yeah other to establish a main results the first why is we assume that in the uh i your regression

model for the uh a actor

so this pair of matrix

so this the the uh i've metrics remember member that's a linear regression matrix

we and of the

what noise

for matrix

so this pair is this

that uh uh

that that lights will okay

so

i course the plot that you uh that when is of this go uh are are are of noise

course to easy enough to use for that so it's not that strong

here

the second or is also not strong because for you know for central the scheme

we required this

condition K is so called a global to detect ability

so this pair of matrix

say that stack of all the small all but we should make use this

okay

so this we require

to be you tractable

"'kay"

the is enough

we only require this

similarly i that's and right the scheme to the main result okay establish is

for each node and

okay remember we are we are how we a distributed i-th emission scheme so we have to guarantee that ice

is good

at each node

okay

so for a guy show that

the error is the matrix is the stock as you body

okay so here a can be come and you know

yeah

and that there out is

i say we a but if you got a node

okay so it

can be this that can be model as the

drawing from a fusion uniformly

okay from the index

the core of the matrix

at that particular node will come or or to a description

okay

but that as well uh

that's basically come try threshold us that's we can try to

i pretty we can come roach to the theme perform as i doesn't centralized

scheme case the same this region as of less game

okay

the set the not the result is a fast we um are to centre as scheme we sure that

the screen of

a in less scheme

is the exponential or or the rate

come of K so that is a it is a full any find that even come or bar but if

we can is this one the

three at approaches and of in can be spanish exponentially fast

okay

so how do we prove this of

i mean it i just

sketch it

remember that use this guy's an null decision a so what do we do is

for one we construct a

oh as

a a to cool

process a a colour of course by modifying in this process

and that process is a stationary

okay

and with that have set go process

we can

apply apply the out you know a a a T S run them that exist systems okay

so we have a lot of an interesting without there okay

and i also show that the sole constructed

a us gender process the

which you to this R T S

the are to say R T I self

can be shown to would be so called all other pretty the ravine and a strong solve a linear

those that terms use the in the R T S you feature

okay

so

that was it

oh that some shall we have

such a at the colour about you can't really D and the the connection

a the can connectivity "'cause" that some for we have a word the network

the commercial read out for this i think a process

can be established

a a what this is not of for the or an no that right

so not the G

so basically by of uniting the fact

uh does suppose that is not station or

okay

but at the a magically a gandhi

so that's the key for beauty for us to build a connection at pretty step by step a connection between

the have a setting a process and of the or no process

then the

come as a result we got a for of this is a uh

so their or process can be you applied

so the or don't only not stationary process

okay

so

i'm collusion

basically we establish uh

it's but results

for a common three in uh

where are we only assume a week

assumptions

on global jack ability and a connective use of network

okay so this one i but that is required or a totally new approach okay

to solve this uh it hardly recursion system okay which is a stationary

okay

uh

we have some or all results on weird is established well of show that

the are

performance can approach the central the

uh from as which is optimal you can do okay

is but usually fast or or the oral communication read in the network

thank you

a

yeah

uh

yes

yes yes

i for here we uh

this for either are yeah it is a well the monophone

that

or oh

we we would like

oh

we don't call it uh a model one is to collect all that

um a a question but as concept have estimates and come from i mean

when you just keep your an estimate

oh

you mean why why uh we do

for that of

i

no you have to estimate swapping so each symbol not doesn't keep put own estimate you just get it of

your own you it basically

that

oh

hmmm

for that or

or

and

a

i

oh

and i C made we are able to come uh

is that it

i

so basis in a i don't on a method which would keep you own estimate

uh not know

we we

for

a

we

i

that's that

that

i