0:00:28okay okay
0:00:29i will catch up
0:00:35you had to tie them a simple uh
0:00:38we talk about this really the common filtering for caminfo to really the well known
0:00:42but it is utilised
0:00:43no i to our problem
0:00:45okay so we establish some asymptotic
0:00:48uh commanders results
0:00:51before i
0:00:52stuff i wanted you most credit to uh sumatra and the clusters
0:00:56so i do the leader in this
0:00:58oh less mode you it's
0:01:00the talk a little bit
0:01:01so that's yeah random filter uh where things going on
0:01:06i the linear regression model
0:01:08so i R W is noise such that the whole lecture twice to is a lecture run them
0:01:15process that's okay
0:01:16so each sensor here
0:01:18how a hard i but of the we score a actually in the sense that this uh of the which
0:01:23a matrix is you really or
0:01:25i matrix
0:01:26so is that it is that um can out
0:01:29basically i how a good estimate of the unknown vector
0:01:33we got
0:01:35what to do so we should allow the sensors to collaborate
0:01:39know this addition get the way you know other two
0:01:42achieve the past
0:01:43if possible i sufficient uh i estimation performance
0:01:47but we don't know why they're we can achieve the same performance i L
0:01:50centralized counterpart well for the example you've we have a few says are we we're you have would be a
0:01:55use a matrix to stack all the most image X okay the coming or team the same performance as as
0:02:01and that's as the solution
0:02:03so that's or go to use that is
0:02:07so of course this kind of application uh okay be uh
0:02:10uh applied to many and new uh
0:02:13uh us such as the smart grid you do state estimation for all the
0:02:17pass is
0:02:18uh social networks so
0:02:22so for this problem might if people are uh out
0:02:25where you interested and D the law of good work
0:02:29but you're are it this kind of a uh
0:02:31these to build you guys to me G is it can there is based L
0:02:35some of good out of addition based okay so i the limitation
0:02:39you early the have the ability is that a gun it even worse soon
0:02:46at each sensor
0:02:47the vocal cortical billy a defect ability to not enough
0:02:50and we are you assume that if we are kind it's that all the C matrix to the right you
0:02:54can how certain
0:02:57these like really T so that so called a we call it can mobile
0:03:00gullible able uh
0:03:02defect really okay
0:03:03basically assume the to i as a central an okay but we now it do things a locally
0:03:09in that case
0:03:10the you this a results
0:03:11uh you dense and see this kind of iris the ability to K so called defined that will show you
0:03:16remains see room later wrong okay
0:03:20just so of this special case cases
0:03:22the so some have to go that's the believe he was established but under why we stick condition
0:03:26so in this work we show you were that's we just as a uh i need some very weak assumption
0:03:32on the system
0:03:33so we can prove
0:03:34asymptotic stability for the error covariance matrix
0:03:39so a recently i read this is uh a previous work go for this one so same mouse there if
0:03:44we same for author
0:03:45assume my
0:03:47basically you that work we assume that a model the sensors will allow
0:03:53ish i each peer rate
0:03:54will a a lot of one round of estimate selecting
0:03:58between one pair of neighbours
0:04:02and and is that kind of a it were uh approach we i
0:04:06prove certain
0:04:07uh that's them at all because the ability for the data
0:04:11so a the may and needs the them then a mix system a result
0:04:16okay in of or a node
0:04:19how are do that work
0:04:21we can then they use for one not a free them well he's
0:04:24in addition to a lot of i C meets my be we can also a lot of the and
0:04:29so okay
0:04:31so you will do that
0:04:32how much for we aim from and no can have
0:04:35and if we do that
0:04:37how fast
0:04:38we can approach the central like the performance
0:04:42actually we we found that with this new free them
0:04:45the whole analysis to we use of year cannot be applied anymore sorry
0:04:50so we have to redefine re introduce there to new to to analyse the performance
0:04:55yeah so has started with the side up
0:04:58so let's say oh
0:05:00we have a collect are you didn't or scissors okay
0:05:03so we estimate of lecture
0:05:06random process okay a lot of time
0:05:09so we allow communication between sensors
0:05:12so here the ratings a
0:05:14i don't want to a of and the the comedy re guy but he are really totally only uh
0:05:18you value when the two to here rate
0:05:20so that here defined i the link i actually
0:05:23i Q we should rate so per second
0:05:25how many in it
0:05:27is i i okay so that's the mean may link
0:05:30i'm also so the them's the come to get an scheme a long time is random
0:05:36okay yeah
0:05:38we assume that
0:05:40we we a constant uh them largest communicate a rate you can assume K so
0:05:46i should be sure that i any tell that he would really easy enough
0:05:52so that's the main in a approach at the each moment uh P read the K okay so here's a
0:05:57K K plus one so first so we do have the okay you she's as or do uh of the
0:06:01region that we do communication or model scissors so the communication
0:06:06you divided into two parts for us so we do i estimates well
0:06:10so you each week peak run them if you go parents of neighbours to strap of their previous estimate
0:06:16after that
0:06:17we allow multiple round of all observation
0:06:22we call obligation okay
0:06:24so so that means you don't keep yourself
0:06:26uh you always i C you only get the a neighbours but i vision means
0:06:31you also keep yourself your all alone
0:06:34all the we a along with neighbours okay for different that's different
0:06:38a a a a and we go to do it's not total communication rate why a third an upper about
0:06:44so we're going to a
0:06:46sure you that such kind of an estimate swiping easy enough
0:06:49to guarantee a some talk "'cause" the ability of the i-th meeting error
0:06:53and the extra of the vision
0:06:55aggregation process
0:06:58dramatically improve
0:07:00so i estimation performance in term of
0:07:02the speed to converge to that's centralized
0:07:08in this for local we call it's a modified
0:07:11gauss safe
0:07:12uh based interactive a common filter okay so um do yeah K F
0:07:17so we have a certain us
0:07:20or or side tops okay
0:07:22so i that's that i want to do a a total rate of communication lies that's to upper bound
0:07:26so that how many coming occasions we have we have a two times why is uh
0:07:31uh uh i C made the being
0:07:33okay another another E is uh all the which should exchange so the error rate just um of this the
0:07:39kind of what you who's should be limit to but this are about so that's all read constraints
0:07:46and uh
0:07:48now we a to be we use sort and uh you tell us about that is to kind of a
0:07:54uh in the network wise i se means way if you another ease
0:07:58uh a of the which an exchange
0:08:00uh or aggregation
0:08:01so the first of why is ice mates so might be an
0:08:04in this case we the we do is
0:08:07we use to Q is is simple scheme okay he's not an not meeting self to this
0:08:13one okay they we'll going summarise
0:08:15what's a requirement for scheme to would be a reasonable you you order two
0:08:19uh guarantee over result
0:08:22so that's a would have to go a simple scheme which all
0:08:26each time we actually with the link
0:08:29according to our a distance metric
0:08:31K is the success of a distance metrics we see that ideally drawing from all even distribution
0:08:37okay so on each time of that
0:08:38only one in P the active
0:08:41if that i this is a matrix happen to be i didn't uh identity matrix which means
0:08:46no node
0:08:47we also have
0:08:48they just keep their own i submit so that's also allowed
0:08:52so that's kind of what is to be a D you find
0:08:55to guarantee the
0:08:57for volume property okay
0:08:59so if it this
0:09:01if this uh
0:09:04if this kind of it you to be defined
0:09:07and and
0:09:08this as some frames hold well basically was to that
0:09:11so so called a maximum of which me
0:09:14although each time a only a one to be active body we use that all the possible activity
0:09:19or a long time
0:09:20so that's not work to be connected of that's all row uh only requirement okay so we that
0:09:26we have a fairly in fact
0:09:28with a for cool okay
0:09:30was as that i guess as met you matrix sequence
0:09:34it is john and from this division D and wish discussed
0:09:38okay as a result
0:09:39so i
0:09:40so called mean in is matrix
0:09:43i about bar
0:09:44is already reduce more small and uh of your all tick matrix
0:09:47okay so that's all or requirement on the
0:09:50properties of we do since may she sequence
0:09:53yeah are we have we also
0:09:55can guarantee that
0:09:57so rate we consume in this phase the i mates what you i i can face is lies that well
0:10:03half the it remember with of how come about not we we consumed
0:10:08as most come borrow two
0:10:11now the rest phase is the so called of their which and
0:10:15uh aggregation okay
0:10:17so this kind of a long words but
0:10:20the message here is
0:10:22when not have
0:10:24oh about a lot too but it full communication between nodes okay
0:10:28that we assume that the whole he we shall for in the four million a some for size
0:10:32with a M to come borrow it two
0:10:34but you this since the average communicate read consumption here will be less than come about or what to okay
0:10:40so we don't
0:10:41okay i'm cool to details but that's what do we did in the second phase
0:10:45of communication
0:10:47so we is that of a local we can also a of the following fact
0:10:51basically it for small the average
0:10:53uh committee can a that we consume a the color about what to that's good because we are use of
0:10:58half an now we use other half the photo total you less then
0:11:01come up bar that's all that's what we were okay
0:11:04i say we have a "'cause" of uh
0:11:08in that
0:11:09okay so this base each a use the collection be index
0:11:12you know think that
0:11:13i've know the and uh time K
0:11:17what cat which a node that do you are you the regions
0:11:20remember at each P are rate we all are much more round of
0:11:24uh duration
0:11:25exchange okay is i the results at the end of this period is should know the will how much pull
0:11:31nodes was centre there
0:11:33of the to to know then
0:11:35okay so we you know
0:11:36such a seconds of index
0:11:38i as i K and
0:11:40actually we can show that
0:11:42at the end of each period
0:11:45we have some up to
0:11:46somehow probability that you should know that we all receive the observations from other node but that probability the strictly
0:11:53okay so that's also critical to reestablish the our results with raw
0:11:59but this is also the top apart because this sequence is a random i actually is the nonstationary
0:12:04so that's give us trouble to prove things
0:12:08so that's my downfall protocols for
0:12:11estimator swiping and
0:12:13a observation
0:12:16but when only met also have to that because
0:12:19when he found out scheme to side of atherton three conditions
0:12:22it's good enough
0:12:23"'kay" the three conditions basically saying that
0:12:27sec "'cause" uh of a is matrices do we used to decide activation of what links should be i D
0:12:32O okay and the mean and their chicks to the beat
0:12:34probably score so can guy uh reduce one of your T
0:12:38right that's first requirement
0:12:39okay K i can't is this sequence you know thing where you get the or a a a you want
0:12:44guide observations from
0:12:46should if i this uh probability constraint we should have a lot
0:12:49uh up that you've probability okay to get a all other nodes of the region okay
0:12:53you can be a small
0:12:55so i kind of course
0:12:57total committee can rate had to side i this constraints
0:13:00you with this is a to with the uh protocol you I D then you are happy
0:13:05then the the to all the results so we have a
0:13:07i the in
0:13:10so no finish the
0:13:12i a order
0:13:13make up their wishes we finish
0:13:15the estimate is we finish the observation aggregation now is time to update the or i right
0:13:23yeah we assume that's
0:13:25in the estimates to i been face what we slap a is a prediction okay based on the previous uh
0:13:31uh read out to get and uh the the recall covariance matrix
0:13:35so use to have this with the a well the a neighbour
0:13:39so which an mlp can we you know it's for the uh uh no then we need we you know
0:13:44that that's than than a appear gaze and K or bar i'd
0:13:47time K
0:13:48okay so this is a face
0:13:50then the observation aggregation give we you that
0:13:52i'd and of each uh time i okay
0:13:55so as and we will have a vector
0:13:57oh of
0:13:58all their wishes
0:13:59from a a from other nodes that you have talk to
0:14:03so maybe from a hope to talk of multiple hot talk
0:14:06you to this kind of exchange change okay
0:14:08the best have this result we take the
0:14:11or dicked are to one step
0:14:13for there okay
0:14:14so to minimize the mean square error so there's a well-known of
0:14:17uh for for that
0:14:19i i i i i same time we have a date data the error cornfields crimes matrix
0:14:23so if i guide it's wide of the got are so we are ready for the next round iteration
0:14:28right so used time we do this
0:14:29you can that you can see that with this kind of predictor
0:14:32we can see what we are doing in does a special case of common filter
0:14:37so right at we can you elements
0:14:39what about doing a use the lazy in the results
0:14:42you in common filter
0:14:44you each
0:14:47you limit the shape is not a for chorus all a "'cause" it if we don't that
0:14:50what kind of probably we have
0:14:52asymptotically or the i requires matrix
0:14:56so can show that at each node
0:14:58okay so i i requires the matrix you malls according to a this T the person
0:15:04it's quite complicated okay is a is itself is a random so is a random sequence of the matrices
0:15:11so now we about the no
0:15:12you which says
0:15:13asymptotically hardly this guy's table
0:15:16so what can we
0:15:17establish regarding that
0:15:20oh two
0:15:21you know to do that a an a it is uh rather than they share to be the clean in
0:15:24there so okay
0:15:25so basically we define are are required to be a reader is the basically function being okay based on other
0:15:31you used version
0:15:33with this that each of this a particle a function we can rewrite
0:15:37the a lotion of our requires a matrix of log do this or simple form
0:15:42so you can say that
0:15:46there are the modulation factor here basically is this "'cause" of the indexes
0:15:50we use you where you get
0:15:52new uh where you get the of the regions from okay
0:15:55and because of this segment C is analysis the and the rate this whole thing is a non-stationary
0:16:01okay so that's really bad
0:16:02so the result we had before kind to be used the here
0:16:07what that we can get here
0:16:10so we need to make to weak assumptions
0:16:13yeah other to establish a main results the first why is we assume that in the uh i your regression
0:16:19model for the uh a actor
0:16:21so this pair of matrix
0:16:22so this the the uh i've metrics remember member that's a linear regression matrix
0:16:27we and of the
0:16:28what noise
0:16:29for matrix
0:16:30so this pair is this
0:16:32that uh uh
0:16:34that that lights will okay
0:16:37i course the plot that you uh that when is of this go uh are are are of noise
0:16:41course to easy enough to use for that so it's not that strong
0:16:45the second or is also not strong because for you know for central the scheme
0:16:50we required this
0:16:51condition K is so called a global to detect ability
0:16:55so this pair of matrix
0:16:56say that stack of all the small all but we should make use this
0:17:00so this we require
0:17:01to be you tractable
0:17:03the is enough
0:17:05we only require this
0:17:06similarly i that's and right the scheme to the main result okay establish is
0:17:11for each node and
0:17:13okay remember we are we are how we a distributed i-th emission scheme so we have to guarantee that ice
0:17:18is good
0:17:19at each node
0:17:21so for a guy show that
0:17:23the error is the matrix is the stock as you body
0:17:26okay so here a can be come and you know
0:17:30and that there out is
0:17:31i say we a but if you got a node
0:17:34okay so it
0:17:35can be this that can be model as the
0:17:37drawing from a fusion uniformly
0:17:39okay from the index
0:17:42the core of the matrix
0:17:44at that particular node will come or or to a description
0:17:48but that as well uh
0:17:51that's basically come try threshold us that's we can try to
0:17:55i pretty we can come roach to the theme perform as i doesn't centralized
0:18:00scheme case the same this region as of less game
0:18:03the set the not the result is a fast we um are to centre as scheme we sure that
0:18:08the screen of
0:18:09a in less scheme
0:18:11is the exponential or or the rate
0:18:13come of K so that is a it is a full any find that even come or bar but if
0:18:17we can is this one the
0:18:19three at approaches and of in can be spanish exponentially fast
0:18:24so how do we prove this of
0:18:28i mean it i just
0:18:29sketch it
0:18:30remember that use this guy's an null decision a so what do we do is
0:18:34for one we construct a
0:18:36oh as
0:18:37a a to cool
0:18:39process a a colour of course by modifying in this process
0:18:42and that process is a stationary
0:18:45and with that have set go process
0:18:48we can
0:18:50apply apply the out you know a a a T S run them that exist systems okay
0:18:54so we have a lot of an interesting without there okay
0:18:57and i also show that the sole constructed
0:18:59a us gender process the
0:19:02which you to this R T S
0:19:03the are to say R T I self
0:19:05can be shown to would be so called all other pretty the ravine and a strong solve a linear
0:19:10those that terms use the in the R T S you feature
0:19:15that was it
0:19:17oh that some shall we have
0:19:18such a at the colour about you can't really D and the the connection
0:19:21a the can connectivity "'cause" that some for we have a word the network
0:19:26the commercial read out for this i think a process
0:19:29can be established
0:19:30a a what this is not of for the or an no that right
0:19:33so not the G
0:19:34so basically by of uniting the fact
0:19:39uh does suppose that is not station or
0:19:43but at the a magically a gandhi
0:19:45so that's the key for beauty for us to build a connection at pretty step by step a connection between
0:19:51the have a setting a process and of the or no process
0:19:55then the
0:19:56come as a result we got a for of this is a uh
0:19:59so their or process can be you applied
0:20:03so the or don't only not stationary process
0:20:07i'm collusion
0:20:08basically we establish uh
0:20:11it's but results
0:20:13for a common three in uh
0:20:16where are we only assume a week
0:20:19on global jack ability and a connective use of network
0:20:22okay so this one i but that is required or a totally new approach okay
0:20:27to solve this uh it hardly recursion system okay which is a stationary
0:20:35we have some or all results on weird is established well of show that
0:20:39the are
0:20:40performance can approach the central the
0:20:43uh from as which is optimal you can do okay
0:20:46is but usually fast or or the oral communication read in the network
0:20:51thank you
0:21:11yes yes
0:21:12i for here we uh
0:21:15this for either are yeah it is a well the monophone
0:21:19or oh
0:21:21we we would like
0:21:24we don't call it uh a model one is to collect all that
0:21:37um a a question but as concept have estimates and come from i mean
0:21:41when you just keep your an estimate
0:21:44you mean why why uh we do
0:21:46for that of
0:21:49no you have to estimate swapping so each symbol not doesn't keep put own estimate you just get it of
0:21:54your own you it basically
0:22:01for that or
0:22:08and i C made we are able to come uh
0:22:11is that it
0:22:13so basis in a i don't on a method which would keep you own estimate
0:22:17uh not know
0:22:19we we
0:22:27that's that