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