a a good morning everyone now um P to tom plus this paper performance of for tracking the multi part in my um my name is such and the con and then the i've from you need to mobile one um a those of this paper are a what and a bit more and and still so this is the outline of the talk huh oh issue see here i have don't a typical multi party environment so you can see a the target transmit uh the sensor so in pink colour i have a detect but so as you can see in addition to the to but you get a lot of multiple part you is uh um the beatings so building so um no in this paper are what we are interested in is uh finding the performance well or also i find in the lower bound for the mean squared error in estimate in these time to it in this but one and R so well can measure rate that systems assume line of communication and then you should you like uh a one of this uh previous that um presentations a well um i form like a a B i the type church treat them as a interference and try to me to get them right and um no in it right now a great line an open in back and you really can't guarantee that line sight is always be there and the from that you the only clapped a you get lots of reflection so if you think about it and different way that at the reflections a multiple reflections my can be in somebody's additional information so that has laid down um that has been a really um i D research topic in the recent past so um T via a a no existing work uh you can see big is assumptions a for example what wall locations are known beforehand um or if that you did the known um you assume the number of of this to be known and sometimes a like in the the each are like the the assume to X basically john metric or used for example the walls becoming um most panel to be a each other the or you are drama to is an our kernel so what we you wanna do he a try to um as much as possible type to the um really it relax these assumptions and another thing to note is that in this uh and this filtering in is preceded by of you can just H for example what that movie is strong in this that rate animation as you free to be can feed that into detect S C H use of the diffusion in stage and this detection outcome is fed the filtering algorithm no it has been shown to the that um for for probably of be the channel less then one did it a time you very a so so this is a although some jazz an extensions well in the um clean finding being these a a on a so we assume that that our target is a point scatterer and you to look at locations are known how um we have a meter reflections and uh be uh we B are used to got high order reflections cell use multiple transmitters and receivers and uh is receiver consists of stuff phase there and an R a a number of elements and a be model building a um because like is that's that was and of a and a not that would be done is like each part we side to it to um random a she why get the in that is because even though we assume that the building locations are no for example you might have a map in wires but it might be the case that there could be some uncertainty associated with that for example the map may be accurate for a couple of sending so if you are using or um if you using a a a a a um a read and say has a range we have a a a a a solution in a couple of centimetres so yeah a on that it could be quite significant so in a stance by what do this um and a fish you yeah in that aren't in on one so our model because more and uh so yeah yeah using a pretty detection mission ones for P what that mean is uh C be at right that you can read of this stage H and you can if or a mission was filtering algorithm and uh we don't impose any restriction on this drama to that set up so um no restrictions whatsoever so let's more the model hmmm so i stays with can part the three components them target dynamics consisting of uh uh a light look at in the car scene playing and the corresponding video C D's that by X stuff and by dot and we have a a this more reflect that you used in a by is it and its collection of random a face ships um thereby by side K or so this how our state you also have a time list is the was a but in the a fashion um and is it the collection of uh while if that Q the em model that so we have more them as a a a gaussian random really mean music and covariance P Z and site K the collection of uh uh phase shift is well modelled as a uniform this which no measurement model of so for seem the a hash shown on to a a one single transmit is your pay yeah a uh and uh and only two parts so but that you can be a less to multiple transmit is you pair as and um multiple pots so this measurement function G contains things like a generation delay don't to uh and steering vector and this exponential to a is the one that uh i this of that but yeah we got in the face you based she now what the where gets he's the summation of all those come of components and it up at the sense uh so that mean a to this plot was to do came around a little but also oh P C B for short um if let's see X is that and um back to suck at a friend of pat is and Y be a vector of mission data and if G a why use an estimate of makes we have this uh the will bound on this estimate estimation you and by uh this inverse of this information may G is this information make "'cause" and site is key and he's uh a team of uh proposed to because you met that to find the is um P C R B and that's the i'm at the to you that you are using to oh in our setup no mean value of time tie "'cause" is meant that it turns out that certain quantities that not quite so straightforward to got so let's see how we have gone on about finding that um so this is you end up with the set of fee questions a like this i don't want to some discuss these the equation um they are included in the paper so things like these gradients yeah a lot of straight for to calculate so uh no this is a typical a from a top but to this for the top but the of store this only one half of of the pot so are not that um part which i have not sure he X is from the trance meet up to the top that's that's was there are capital L number of uh well as and uh for each word be C a a difference point and we choose is such that it is the um it is the what was point of the wall that uh in case in case the vol is i to the horizontal axis to be choose the um if most point and this distance from this if point to the deflection point we D it by D such L no one because we assume that the job a in locations are known we know this and that this more makes with the horizontal axis and B no this point brown this a reference point so using this distance we can parameterize this reflection point S that shown here no turns out that the quantities be need to have a little need to well find a speech is yeah B can be expressed in this for bad this fine uh if a we need to calculate positivity to use a is like this yeah they yeah um they are in turn a function as of these distances D you want to do yeah and there's a one to the is the corresponding distance from the at the part that i have not shown here um um so by using the chain rule you can find is a T is C by use this method now once again to find now this still in be need be the need to find this context even by these down would be or without X and are but did a a will topics not so still it's remains to find these condo so this is how we do that now remember we have had a mean address this point using this the distance so using these two points i can write an expression for this and a use these two points which i short here then you can do this the M T uh four a point immediately after the top and finally but the and of for i well uh shown here know what we do is you take the first eight picks plus question and then so um salt this full um a such a capital is and you end up with the function of X Y N T so you do the same thing for these the and um and so it for the sub to simple a and you end up with a function of the at class of or and T are and finally um obviously this fines and fine finding is it's of is uh uh function enough this this do you want now we can X press that because you relationship between the partial the every two years by so by um by a um expressing the of the positive in this for yeah yeah as five a and you get that related to um do F file plus one and get plus one using this uh relationship and you can start the recursion by um as as a few couple then it to a of a scene using this i so um i you find a have a one and you can my you can easily work but to find D and but or do but X and was of back to find a point these that you need so let me just to it so you start the by and a a um subject got L any to such and and you were back until you find out from underneath of or and want to find those to can you can is you can um uh find out what do you do what a but X using this issue no once you for one to find that so you can now you have all the quantities needed to it the uh terms on the left hand side which is all we need do to find you find that of data so let me give you the real stupid the new make a was so here you get see that a and the blue line score one to some to was and you had the charter trajectory to by dashed line and then you you had the transmit and receive receiver so this is the P C R B for position estimate so this is a blue line "'cause" to the P C R B B my to and the a it line be top might but so as i mean do inside it's um we have a lower bound the all bound is low for um the case speak much what we side is that uh there is some additional information which we can exploit for our advantage and this is the same graph four willow cd estimation and so in future we want to implement of filter for this up quite challenging because like we have introduce more parameters well modelled like them then um um um vol effect is and faces is so it's a quite challenging to find of a to implement a few then we won't want to also look at a but i was it was the a number of targets that's and the and delay assumption that of locations and that known and probably look at wave forms that can be uh you but the results and also we to do the problem so is worth microphone you oh you are assumed but um all the points of of at all the boards not exactly know right all the one location and even given the ball could you flick most of the beginning or the end i mean yes but in a john made to you an easy using or a job or to work of bits point you um those if that combines a like a a racing type of yes that and locates that then the common would be actually in a you frequency five remotes that the most obvious affect was in or scenes are actually traffic signed and not pull multiples so one of three does exactly the same but you might wanna look to this and you is that they are if you're put more like point scatterer not like a like don't not want to be used meter if three that would be a that i don't with vectors but for think it's a i just a calm the questions you assume a isotropic tradition yes is related to the previous question how can make sure of the number of times that you have a the most controls that you have a way a you basically do a a a a a great a model a and but that before hand hmmm so that's how we will uh okay this so is the session to and the thing you for time um is one you know the speaker from another