0:00:14 | i |
---|---|

0:00:18 | i |

0:00:28 | okay okay |

0:00:29 | i will catch up |

0:00:31 | yeah |

0:00:32 | oh |

0:00:33 | um |

0:00:34 | so |

0:00:35 | you had to tie them a simple uh |

0:00:38 | we talk about this really the common filtering for caminfo to really the well known |

0:00:42 | but it is utilised |

0:00:43 | no i to our problem |

0:00:45 | okay so we establish some asymptotic |

0:00:48 | uh commanders results |

0:00:50 | uh |

0:00:51 | before i |

0:00:52 | stuff i wanted you most credit to uh sumatra and the clusters |

0:00:56 | so i do the leader in this |

0:00:58 | oh less mode you it's |

0:01:00 | the talk a little bit |

0:01:01 | so that's yeah random filter uh where things going on |

0:01:06 | i the linear regression model |

0:01:08 | so i R W is noise such that the whole lecture twice to is a lecture run them |

0:01:15 | process that's okay |

0:01:16 | so each sensor here |

0:01:18 | how a hard i but of the we score a actually in the sense that this uh of the which |

0:01:23 | a matrix is you really or |

0:01:25 | i matrix |

0:01:26 | okay |

0:01:26 | so is that it is that um can out |

0:01:29 | basically i how a good estimate of the unknown vector |

0:01:33 | we got |

0:01:35 | so |

0:01:35 | what to do so we should allow the sensors to collaborate |

0:01:39 | know this addition get the way you know other two |

0:01:42 | achieve the past |

0:01:43 | if possible i sufficient uh i estimation performance |

0:01:47 | but we don't know why they're we can achieve the same performance i L |

0:01:50 | centralized counterpart well for the example you've we have a few says are we we're you have would be a |

0:01:55 | use a matrix to stack all the most image X okay the coming or team the same performance as as |

0:02:01 | and that's as the solution |

0:02:03 | so that's or go to use that is |

0:02:06 | okay |

0:02:07 | so of course this kind of application uh okay be uh |

0:02:10 | uh applied to many and new uh |

0:02:13 | uh us such as the smart grid you do state estimation for all the |

0:02:17 | pass is |

0:02:18 | uh social networks so |

0:02:20 | okay |

0:02:22 | so for this problem might if people are uh out |

0:02:25 | where you interested and D the law of good work |

0:02:28 | uh |

0:02:29 | but you're are it this kind of a uh |

0:02:31 | these to build you guys to me G is it can there is based L |

0:02:35 | some of good out of addition based okay so i the limitation |

0:02:39 | you early the have the ability is that a gun it even worse soon |

0:02:43 | that |

0:02:46 | at each sensor |

0:02:47 | the vocal cortical billy a defect ability to not enough |

0:02:50 | and we are you assume that if we are kind it's that all the C matrix to the right you |

0:02:54 | can how certain |

0:02:56 | uh |

0:02:57 | these like really T so that so called a we call it can mobile |

0:03:00 | gullible able uh |

0:03:02 | defect really okay |

0:03:03 | basically assume the to i as a central an okay but we now it do things a locally |

0:03:09 | in that case |

0:03:10 | the you this a results |

0:03:11 | uh you dense and see this kind of iris the ability to K so called defined that will show you |

0:03:16 | remains see room later wrong okay |

0:03:18 | so |

0:03:20 | just so of this special case cases |

0:03:22 | the so some have to go that's the believe he was established but under why we stick condition |

0:03:26 | so in this work we show you were that's we just as a uh i need some very weak assumption |

0:03:32 | on the system |

0:03:33 | so we can prove |

0:03:34 | asymptotic stability for the error covariance matrix |

0:03:37 | okay |

0:03:39 | so a recently i read this is uh a previous work go for this one so same mouse there if |

0:03:44 | we same for author |

0:03:45 | assume my |

0:03:46 | so |

0:03:47 | basically you that work we assume that a model the sensors will allow |

0:03:53 | ish i each peer rate |

0:03:54 | will a a lot of one round of estimate selecting |

0:03:58 | between one pair of neighbours |

0:04:01 | okay |

0:04:02 | and and is that kind of a it were uh approach we i |

0:04:06 | prove certain |

0:04:07 | uh that's them at all because the ability for the data |

0:04:10 | okay |

0:04:11 | so a the may and needs the them then a mix system a result |

0:04:16 | okay in of or a node |

0:04:18 | so |

0:04:19 | how are do that work |

0:04:21 | we can then they use for one not a free them well he's |

0:04:24 | in addition to a lot of i C meets my be we can also a lot of the and |

0:04:29 | so okay |

0:04:31 | so you will do that |

0:04:32 | how much for we aim from and no can have |

0:04:35 | and if we do that |

0:04:37 | how fast |

0:04:38 | we can approach the central like the performance |

0:04:41 | okay |

0:04:42 | actually we we found that with this new free them |

0:04:45 | the whole analysis to we use of year cannot be applied anymore sorry |

0:04:50 | so we have to redefine re introduce there to new to to analyse the performance |

0:04:55 | yeah so has started with the side up |

0:04:58 | so let's say oh |

0:05:00 | we have a collect are you didn't or scissors okay |

0:05:03 | so we estimate of lecture |

0:05:06 | random process okay a lot of time |

0:05:09 | so we allow communication between sensors |

0:05:11 | okay |

0:05:12 | so here the ratings a |

0:05:14 | i don't want to a of and the the comedy re guy but he are really totally only uh |

0:05:18 | you value when the two to here rate |

0:05:20 | so that here defined i the link i actually |

0:05:23 | i Q we should rate so per second |

0:05:25 | how many in it |

0:05:27 | is i i okay so that's the mean may link |

0:05:30 | i'm also so the them's the come to get an scheme a long time is random |

0:05:34 | okay |

0:05:36 | okay yeah |

0:05:38 | we assume that |

0:05:40 | we we a constant uh them largest communicate a rate you can assume K so |

0:05:46 | i should be sure that i any tell that he would really easy enough |

0:05:50 | okay |

0:05:52 | so that's the main in a approach at the each moment uh P read the K okay so here's a |

0:05:57 | K K plus one so first so we do have the okay you she's as or do uh of the |

0:06:01 | region that we do communication or model scissors so the communication |

0:06:06 | you divided into two parts for us so we do i estimates well |

0:06:10 | so you each week peak run them if you go parents of neighbours to strap of their previous estimate |

0:06:16 | okay |

0:06:16 | after that |

0:06:17 | we allow multiple round of all observation |

0:06:21 | uh |

0:06:22 | we call obligation okay |

0:06:24 | so so that means you don't keep yourself |

0:06:26 | uh you always i C you only get the a neighbours but i vision means |

0:06:31 | you also keep yourself your all alone |

0:06:34 | all the we a along with neighbours okay for different that's different |

0:06:38 | a a a a and we go to do it's not total communication rate why a third an upper about |

0:06:43 | okay |

0:06:44 | so we're going to a |

0:06:46 | sure you that such kind of an estimate swiping easy enough |

0:06:49 | to guarantee a some talk "'cause" the ability of the i-th meeting error |

0:06:53 | okay |

0:06:53 | and the extra of the vision |

0:06:55 | aggregation process |

0:06:57 | can |

0:06:58 | dramatically improve |

0:07:00 | so i estimation performance in term of |

0:07:02 | the speed to converge to that's centralized |

0:07:05 | formants |

0:07:06 | okay |

0:07:07 | so |

0:07:08 | in this for local we call it's a modified |

0:07:11 | gauss safe |

0:07:12 | uh based interactive a common filter okay so um do yeah K F |

0:07:17 | so we have a certain us |

0:07:19 | us |

0:07:20 | or or side tops okay |

0:07:22 | so i that's that i want to do a a total rate of communication lies that's to upper bound |

0:07:26 | so that how many coming occasions we have we have a two times why is uh |

0:07:31 | uh uh i C made the being |

0:07:33 | okay another another E is uh all the which should exchange so the error rate just um of this the |

0:07:39 | kind of what you who's should be limit to but this are about so that's all read constraints |

0:07:44 | okay |

0:07:46 | and uh |

0:07:48 | now we a to be we use sort and uh you tell us about that is to kind of a |

0:07:53 | communication |

0:07:54 | uh in the network wise i se means way if you another ease |

0:07:58 | uh a of the which an exchange |

0:08:00 | uh or aggregation |

0:08:01 | so the first of why is ice mates so might be an |

0:08:04 | in this case we the we do is |

0:08:07 | we |

0:08:07 | we use to Q is is simple scheme okay he's not an not meeting self to this |

0:08:13 | one okay they we'll going summarise |

0:08:15 | what's a requirement for scheme to would be a reasonable you you order two |

0:08:19 | uh guarantee over result |

0:08:21 | okay |

0:08:22 | so that's a would have to go a simple scheme which all |

0:08:25 | uh |

0:08:26 | each time we actually with the link |

0:08:29 | according to our a distance metric |

0:08:31 | K is the success of a distance metrics we see that ideally drawing from all even distribution |

0:08:37 | okay so on each time of that |

0:08:38 | only one in P the active |

0:08:40 | i |

0:08:41 | if that i this is a matrix happen to be i didn't uh identity matrix which means |

0:08:46 | no node |

0:08:47 | we also have |

0:08:48 | they just keep their own i submit so that's also allowed |

0:08:51 | okay |

0:08:52 | so that's kind of what is to be a D you find |

0:08:55 | to guarantee the |

0:08:57 | for volume property okay |

0:08:59 | so if it this |

0:09:01 | if this uh |

0:09:04 | if this kind of it you to be defined |

0:09:07 | and and |

0:09:08 | this as some frames hold well basically was to that |

0:09:11 | so so called a maximum of which me |

0:09:14 | although each time a only a one to be active body we use that all the possible activity |

0:09:19 | or a long time |

0:09:20 | so that's not work to be connected of that's all row uh only requirement okay so we that |

0:09:26 | we have a fairly in fact |

0:09:28 | with a for cool okay |

0:09:30 | was as that i guess as met you matrix sequence |

0:09:33 | K |

0:09:34 | it is john and from this division D and wish discussed |

0:09:38 | okay as a result |

0:09:39 | so i |

0:09:40 | so called mean in is matrix |

0:09:43 | i about bar |

0:09:44 | is already reduce more small and uh of your all tick matrix |

0:09:47 | okay so that's all or requirement on the |

0:09:50 | properties of we do since may she sequence |

0:09:52 | okay |

0:09:53 | yeah are we have we also |

0:09:55 | can guarantee that |

0:09:57 | so rate we consume in this phase the i mates what you i i can face is lies that well |

0:10:03 | half the it remember with of how come about not we we consumed |

0:10:08 | as most come borrow two |

0:10:10 | okay |

0:10:11 | now the rest phase is the so called of their which and |

0:10:15 | uh aggregation okay |

0:10:17 | so this kind of a long words but |

0:10:20 | the message here is |

0:10:22 | when not have |

0:10:24 | oh about a lot too but it full communication between nodes okay |

0:10:28 | that we assume that the whole he we shall for in the four million a some for size |

0:10:32 | with a M to come borrow it two |

0:10:34 | but you this since the average communicate read consumption here will be less than come about or what to okay |

0:10:40 | so we don't |

0:10:41 | okay i'm cool to details but that's what do we did in the second phase |

0:10:45 | of communication |

0:10:47 | okay |

0:10:47 | so we is that of a local we can also a of the following fact |

0:10:51 | basically it for small the average |

0:10:53 | uh committee can a that we consume a the color about what to that's good because we are use of |

0:10:58 | half an now we use other half the photo total you less then |

0:11:01 | come up bar that's all that's what we were okay |

0:11:04 | i say we have a "'cause" of uh |

0:11:08 | in that |

0:11:09 | okay so this base each a use the collection be index |

0:11:12 | you know think that |

0:11:13 | i've know the and uh time K |

0:11:16 | so |

0:11:17 | what cat which a node that do you are you the regions |

0:11:20 | remember at each P are rate we all are much more round of |

0:11:24 | uh duration |

0:11:25 | exchange okay is i the results at the end of this period is should know the will how much pull |

0:11:31 | nodes was centre there |

0:11:33 | of the to to know then |

0:11:35 | okay so we you know |

0:11:36 | such a seconds of index |

0:11:38 | i as i K and |

0:11:39 | okay |

0:11:40 | actually we can show that |

0:11:42 | at the end of each period |

0:11:44 | although |

0:11:45 | we have some up to |

0:11:46 | somehow probability that you should know that we all receive the observations from other node but that probability the strictly |

0:11:52 | positive |

0:11:53 | okay so that's also critical to reestablish the our results with raw |

0:11:59 | but this is also the top apart because this sequence is a random i actually is the nonstationary |

0:12:04 | so that's give us trouble to prove things |

0:12:08 | so that's my downfall protocols for |

0:12:11 | estimator swiping and |

0:12:13 | a observation |

0:12:15 | aggregation |

0:12:16 | but when only met also have to that because |

0:12:19 | when he found out scheme to side of atherton three conditions |

0:12:22 | it's good enough |

0:12:23 | "'kay" the three conditions basically saying that |

0:12:26 | the |

0:12:27 | sec "'cause" uh of a is matrices do we used to decide activation of what links should be i D |

0:12:32 | O okay and the mean and their chicks to the beat |

0:12:34 | probably score so can guy uh reduce one of your T |

0:12:38 | right that's first requirement |

0:12:39 | okay K i can't is this sequence you know thing where you get the or a a a you want |

0:12:44 | guide observations from |

0:12:46 | should if i this uh probability constraint we should have a lot |

0:12:49 | uh up that you've probability okay to get a all other nodes of the region okay |

0:12:53 | you can be a small |

0:12:55 | so i kind of course |

0:12:56 | to |

0:12:57 | total committee can rate had to side i this constraints |

0:13:00 | you with this is a to with the uh protocol you I D then you are happy |

0:13:04 | because |

0:13:05 | then the the to all the results so we have a |

0:13:07 | i the in |

0:13:08 | okay |

0:13:10 | so no finish the |

0:13:12 | i a order |

0:13:13 | make up their wishes we finish |

0:13:15 | the estimate is we finish the observation aggregation now is time to update the or i right |

0:13:23 | so |

0:13:23 | yeah we assume that's |

0:13:25 | in the estimates to i been face what we slap a is a prediction okay based on the previous uh |

0:13:31 | uh read out to get and uh the the recall covariance matrix |

0:13:35 | so use to have this with the a well the a neighbour |

0:13:37 | okay |

0:13:39 | so which an mlp can we you know it's for the uh uh no then we need we you know |

0:13:44 | that that's than than a appear gaze and K or bar i'd |

0:13:47 | time K |

0:13:48 | okay so this is a face |

0:13:50 | then the observation aggregation give we you that |

0:13:52 | i'd and of each uh time i okay |

0:13:55 | so as and we will have a vector |

0:13:57 | oh of |

0:13:58 | all their wishes |

0:13:59 | from a a from other nodes that you have talk to |

0:14:02 | okay |

0:14:03 | so maybe from a hope to talk of multiple hot talk |

0:14:06 | you to this kind of exchange change okay |

0:14:08 | the best have this result we take the |

0:14:11 | or dicked are to one step |

0:14:13 | for there okay |

0:14:14 | so to minimize the mean square error so there's a well-known of |

0:14:17 | uh for for that |

0:14:19 | i i i i i same time we have a date data the error cornfields crimes matrix |

0:14:23 | so if i guide it's wide of the got are so we are ready for the next round iteration |

0:14:28 | right so used time we do this |

0:14:29 | you can that you can see that with this kind of predictor |

0:14:32 | we can see what we are doing in does a special case of common filter |

0:14:37 | okay |

0:14:37 | so right at we can you elements |

0:14:39 | what about doing a use the lazy in the results |

0:14:42 | you in common filter |

0:14:43 | uh |

0:14:44 | you each |

0:14:45 | okay |

0:14:45 | so |

0:14:47 | you limit the shape is not a for chorus all a "'cause" it if we don't that |

0:14:50 | what kind of probably we have |

0:14:52 | asymptotically or the i requires matrix |

0:14:55 | okay |

0:14:56 | so can show that at each node |

0:14:57 | and |

0:14:58 | okay so i i requires the matrix you malls according to a this T the person |

0:15:03 | "'kay" |

0:15:04 | it's quite complicated okay is a is itself is a random so is a random sequence of the matrices |

0:15:10 | okay |

0:15:11 | so now we about the no |

0:15:12 | you which says |

0:15:13 | asymptotically hardly this guy's table |

0:15:16 | okay |

0:15:16 | so what can we |

0:15:17 | establish regarding that |

0:15:20 | oh two |

0:15:21 | you know to do that a an a it is uh rather than they share to be the clean in |

0:15:24 | there so okay |

0:15:25 | so basically we define are are required to be a reader is the basically function being okay based on other |

0:15:31 | you used version |

0:15:32 | so |

0:15:33 | with this that each of this a particle a function we can rewrite |

0:15:37 | the a lotion of our requires a matrix of log do this or simple form |

0:15:42 | okay |

0:15:42 | so you can say that |

0:15:46 | there are the modulation factor here basically is this "'cause" of the indexes |

0:15:50 | we use you where you get |

0:15:52 | new uh where you get the of the regions from okay |

0:15:55 | and because of this segment C is analysis the and the rate this whole thing is a non-stationary |

0:16:01 | okay so that's really bad |

0:16:02 | so the result we had before kind to be used the here |

0:16:05 | okay |

0:16:06 | so |

0:16:07 | what that we can get here |

0:16:10 | so we need to make to weak assumptions |

0:16:12 | okay |

0:16:13 | yeah other to establish a main results the first why is we assume that in the uh i your regression |

0:16:19 | model for the uh a actor |

0:16:21 | so this pair of matrix |

0:16:22 | so this the the uh i've metrics remember member that's a linear regression matrix |

0:16:27 | we and of the |

0:16:28 | what noise |

0:16:29 | for matrix |

0:16:30 | so this pair is this |

0:16:32 | that uh uh |

0:16:34 | that that lights will okay |

0:16:35 | so |

0:16:37 | i course the plot that you uh that when is of this go uh are are are of noise |

0:16:41 | course to easy enough to use for that so it's not that strong |

0:16:45 | here |

0:16:45 | the second or is also not strong because for you know for central the scheme |

0:16:50 | we required this |

0:16:51 | condition K is so called a global to detect ability |

0:16:55 | so this pair of matrix |

0:16:56 | say that stack of all the small all but we should make use this |

0:16:59 | okay |

0:17:00 | so this we require |

0:17:01 | to be you tractable |

0:17:03 | "'kay" |

0:17:03 | the is enough |

0:17:05 | we only require this |

0:17:06 | similarly i that's and right the scheme to the main result okay establish is |

0:17:11 | for each node and |

0:17:13 | okay remember we are we are how we a distributed i-th emission scheme so we have to guarantee that ice |

0:17:18 | is good |

0:17:19 | at each node |

0:17:20 | okay |

0:17:21 | so for a guy show that |

0:17:23 | the error is the matrix is the stock as you body |

0:17:26 | okay so here a can be come and you know |

0:17:28 | yeah |

0:17:30 | and that there out is |

0:17:31 | i say we a but if you got a node |

0:17:34 | okay so it |

0:17:35 | can be this that can be model as the |

0:17:37 | drawing from a fusion uniformly |

0:17:39 | okay from the index |

0:17:42 | the core of the matrix |

0:17:44 | at that particular node will come or or to a description |

0:17:47 | okay |

0:17:48 | but that as well uh |

0:17:51 | that's basically come try threshold us that's we can try to |

0:17:55 | i pretty we can come roach to the theme perform as i doesn't centralized |

0:18:00 | scheme case the same this region as of less game |

0:18:02 | okay |

0:18:03 | the set the not the result is a fast we um are to centre as scheme we sure that |

0:18:08 | the screen of |

0:18:09 | a in less scheme |

0:18:11 | is the exponential or or the rate |

0:18:13 | come of K so that is a it is a full any find that even come or bar but if |

0:18:17 | we can is this one the |

0:18:19 | three at approaches and of in can be spanish exponentially fast |

0:18:23 | okay |

0:18:24 | so how do we prove this of |

0:18:28 | i mean it i just |

0:18:29 | sketch it |

0:18:30 | remember that use this guy's an null decision a so what do we do is |

0:18:34 | for one we construct a |

0:18:36 | oh as |

0:18:37 | a a to cool |

0:18:39 | process a a colour of course by modifying in this process |

0:18:42 | and that process is a stationary |

0:18:45 | okay |

0:18:45 | and with that have set go process |

0:18:48 | we can |

0:18:50 | apply apply the out you know a a a T S run them that exist systems okay |

0:18:54 | so we have a lot of an interesting without there okay |

0:18:57 | and i also show that the sole constructed |

0:18:59 | a us gender process the |

0:19:02 | which you to this R T S |

0:19:03 | the are to say R T I self |

0:19:05 | can be shown to would be so called all other pretty the ravine and a strong solve a linear |

0:19:10 | those that terms use the in the R T S you feature |

0:19:12 | okay |

0:19:14 | so |

0:19:15 | that was it |

0:19:17 | oh that some shall we have |

0:19:18 | such a at the colour about you can't really D and the the connection |

0:19:21 | a the can connectivity "'cause" that some for we have a word the network |

0:19:26 | the commercial read out for this i think a process |

0:19:29 | can be established |

0:19:30 | a a what this is not of for the or an no that right |

0:19:33 | so not the G |

0:19:34 | so basically by of uniting the fact |

0:19:39 | uh does suppose that is not station or |

0:19:42 | okay |

0:19:43 | but at the a magically a gandhi |

0:19:45 | so that's the key for beauty for us to build a connection at pretty step by step a connection between |

0:19:51 | the have a setting a process and of the or no process |

0:19:55 | then the |

0:19:56 | come as a result we got a for of this is a uh |

0:19:59 | so their or process can be you applied |

0:20:03 | so the or don't only not stationary process |

0:20:05 | okay |

0:20:06 | so |

0:20:07 | i'm collusion |

0:20:08 | basically we establish uh |

0:20:11 | it's but results |

0:20:13 | for a common three in uh |

0:20:16 | where are we only assume a week |

0:20:18 | assumptions |

0:20:19 | on global jack ability and a connective use of network |

0:20:22 | okay so this one i but that is required or a totally new approach okay |

0:20:27 | to solve this uh it hardly recursion system okay which is a stationary |

0:20:32 | okay |

0:20:33 | uh |

0:20:35 | we have some or all results on weird is established well of show that |

0:20:39 | the are |

0:20:40 | performance can approach the central the |

0:20:43 | uh from as which is optimal you can do okay |

0:20:46 | is but usually fast or or the oral communication read in the network |

0:20:51 | thank you |

0:20:53 | a |

0:20:58 | yeah |

0:21:03 | uh |

0:21:10 | yes |

0:21:11 | yes yes |

0:21:12 | i for here we uh |

0:21:15 | this for either are yeah it is a well the monophone |

0:21:19 | that |

0:21:19 | or oh |

0:21:21 | we we would like |

0:21:22 | oh |

0:21:24 | we don't call it uh a model one is to collect all that |

0:21:37 | um a a question but as concept have estimates and come from i mean |

0:21:41 | when you just keep your an estimate |

0:21:43 | oh |

0:21:44 | you mean why why uh we do |

0:21:46 | for that of |

0:21:48 | i |

0:21:49 | no you have to estimate swapping so each symbol not doesn't keep put own estimate you just get it of |

0:21:54 | your own you it basically |

0:21:55 | that |

0:21:58 | oh |

0:21:59 | hmmm |

0:22:01 | for that or |

0:22:03 | or |

0:22:04 | and |

0:22:05 | a |

0:22:06 | i |

0:22:07 | oh |

0:22:08 | and i C made we are able to come uh |

0:22:11 | is that it |

0:22:12 | i |

0:22:13 | so basis in a i don't on a method which would keep you own estimate |

0:22:17 | uh not know |

0:22:19 | we we |

0:22:21 | for |

0:22:23 | a |

0:22:24 | we |

0:22:26 | i |

0:22:27 | that's that |

0:22:28 | that |

0:23:09 | i |