0:00:13a a good morning everyone now
0:00:15um P to tom plus this paper performance of for tracking the multi part in my
0:00:20my name is such and the con and then the i've from you need to mobile one
0:00:25a those of this paper are a what and a bit more and and still
0:00:31so this is the outline of the talk huh
0:00:34oh issue see here i have don't a typical multi party environment so
0:00:39you can see a the target transmit uh the sensor
0:00:43so in pink colour i have a detect but so as you can see
0:00:46in addition to the to but you get a lot of multiple part you is uh
0:00:51the beatings so building
0:00:53so um
0:00:55no in this paper are what we are interested in is uh finding the performance well or also i find
0:01:00in the lower bound for the mean squared error
0:01:03in estimate in these time to it
0:01:06in this but one and R
0:01:10so well
0:01:11can measure rate that systems assume line of communication and then you should you like uh
0:01:15a one of this uh previous that um
0:01:18presentations a
0:01:21um i form like a a B i the type church treat them as a interference and try to me
0:01:26to get them
0:01:26right and um
0:01:29in it right now a great line an open in back and you really can't guarantee that line sight is
0:01:34always be there and the from that
0:01:36you the only clapped a you get lots of reflection
0:01:39so if you think about it and different way
0:01:43at the reflections a multiple reflections my can be in somebody's additional information so
0:01:49that has laid down
0:01:51that has been a really um
0:01:52i D research topic in the recent past
0:01:55so um
0:01:57T via a a
0:01:58no existing work
0:02:01you can see big is assumptions a for example what wall locations are known beforehand um
0:02:06or if that you did the known
0:02:08um you assume the number of of this to be known and
0:02:11sometimes a like in the
0:02:12the each are like
0:02:13the the assume to X basically john metric or used for example the walls becoming
0:02:19um most panel to be a each other the or
0:02:23you are drama to is an our kernel
0:02:25so what we you wanna do he a
0:02:28try to um
0:02:30as much as possible type to the um really it relax these assumptions
0:02:34and another thing to note is that in this uh
0:02:37and this
0:02:38filtering in is preceded by of you can just H for example what that movie is
0:02:42strong in this that rate animation as you free to be can feed that into detect S C H
0:02:48use of the diffusion in stage and this detection outcome is fed
0:02:52the filtering algorithm
0:02:53no it has been shown to the that
0:02:56for for probably of be the channel less then one
0:02:59did it a time you very a
0:03:05so this is a
0:03:06although some jazz an extensions
0:03:09well in the um
0:03:11finding being these a
0:03:12a on
0:03:13a so we assume that that our target is a point scatterer
0:03:17and you to look at locations are known how um
0:03:19we have a meter reflections
0:03:21and uh be
0:03:23we B are used to got high order reflections cell
0:03:27use multiple transmitters and receivers and uh
0:03:29is receiver consists of stuff phase there and an R
0:03:33a a number of elements
0:03:35and a be model building a um because like is that's that was and of a
0:03:40a not that would be done is like
0:03:43each part we side to it to um
0:03:46random a she
0:03:48why get the in that is because even though we assume that the building locations are no
0:03:54for example you might have a map in wires
0:03:56but it might be the case that there could be some uncertainty associated with that for example the map may
0:04:02be accurate for a couple of sending
0:04:05so if you are using or um
0:04:08if you using a a a a a um a read and say has a range
0:04:12we have a a a a a solution in a couple of centimetres
0:04:17yeah a on that it could be quite significant so in a stance by what do this
0:04:21and a fish you yeah in that aren't in on one so our model because more
0:04:27and uh
0:04:29yeah yeah using a pretty detection mission ones for P what that mean is uh
0:04:33C be at right that you can read of this stage H and you can if or a mission was
0:04:38filtering algorithm
0:04:40and uh we don't impose any restriction on this drama to that set up so
0:04:45no restrictions whatsoever
0:04:48so let's more the model
0:04:49hmmm so i
0:04:51stays with can part the three components them target dynamics consisting of uh
0:04:58uh a light look at in the car scene playing
0:05:00and the corresponding video C D's that by X stuff and by dot
0:05:04and we have a a this more reflect that you used in a by is it
0:05:08and its collection of random a face
0:05:12thereby by side K
0:05:16so this how our state you also have a time list is the was a
0:05:21in the a
0:05:22fashion um
0:05:24and is it the collection of uh
0:05:27while if that Q the em model that so we have more them as a
0:05:31a a gaussian random really mean music and covariance P Z
0:05:35and site K the collection of uh
0:05:39phase shift
0:05:40is well modelled as a uniform this which
0:05:45no measurement model of so for seem the a hash shown on to a a one single transmit is your
0:05:50pay yeah a uh and uh
0:05:53and only two parts
0:05:55so but that you can be a less to multiple transmit is you pair as and um multiple pots
0:06:01this measurement function G contains
0:06:04things like a generation delay don't to
0:06:08and steering vector
0:06:09and this exponential to a is the one that uh i this of that but yeah we got in the
0:06:14face you based she
0:06:17now what the where
0:06:19gets he's the summation of all those come of components
0:06:24and it up at the sense
0:06:29so that mean
0:06:30a to this plot was to do came around a little but also
0:06:33oh P C B for short
0:06:36let's see X is that and um back to suck at a friend of pat is and Y be a
0:06:41vector of mission data
0:06:43if G
0:06:44a why use an estimate of makes
0:06:46we have this uh the will bound on this estimate estimation
0:06:49you and by uh this inverse
0:06:52of this information may
0:06:54G is this information make
0:06:56"'cause" and
0:06:57site is key and he's uh a team of uh proposed to because you met that to find the
0:07:02is um
0:07:03P C R B
0:07:04and that's the
0:07:05i'm at the to you that you are using to oh in our setup
0:07:10mean value of time tie "'cause" is meant that it turns out that certain quantities that
0:07:15not quite so straightforward to got so let's see how we have gone
0:07:19on about finding that
0:07:21so this is you end up with the
0:07:24set of fee questions a like this i don't want to some
0:07:27discuss these the equation
0:07:30they are included in the paper
0:07:32things like these gradients
0:07:33yeah a lot of straight for to calculate
0:07:40this is a typical a from a top but to this
0:07:44for the top but the of store
0:07:46this only one half of of the pot so are not that
0:07:48um part which i have not sure he X is from the trance meet up to the top
0:07:53that's that's was there are capital L number of uh well as
0:07:57and uh
0:07:59for each word be C a a difference point and we choose is such that it is the um
0:08:05it is the what was point of the wall
0:08:08that uh
0:08:09in case
0:08:10in case the vol is i to the horizontal axis to be choose the um if most point
0:08:16and this distance from this if point to the deflection point we D it by D such L
0:08:21no one because we assume that the job a in locations are known
0:08:26we know this and that this more makes with the horizontal axis
0:08:29and B no this point brown this
0:08:31a reference point
0:08:32so using this distance we can parameterize this reflection point
0:08:38S that
0:08:39shown here
0:08:42no turns out
0:08:44that the quantities be need to have a little need to well find a speech is yeah B
0:08:49can be expressed in this for bad this fine uh if
0:08:53a we need to calculate positivity to use
0:08:56a is like this
0:08:57yeah they yeah
0:09:00they are in turn a function as of these distances D you want to do yeah
0:09:04and there's a one to the is the corresponding distance from the at the part that i have not shown
0:09:11um um
0:09:11so by using the chain rule you can find is a T is
0:09:15C by
0:09:16use this method now
0:09:18once again to find
0:09:20now this still in be
0:09:22need be the need to find this context
0:09:24even by these down would be or without X and are but
0:09:27did a a will topics
0:09:30so still it's remains to find these condo
0:09:33so this is how we do that
0:09:36remember we have had a mean address this point using this
0:09:40the distance so using
0:09:43these two points
0:09:44i can write an expression for this and a
0:09:47use these two points which i short here
0:09:51then you can do this the M T
0:09:53uh four
0:09:54a point immediately after the top
0:09:56and finally but the and of for i well
0:10:00shown here
0:10:02know what we do is you take the first eight picks
0:10:05plus question
0:10:07and then so um salt this full
0:10:11a such a capital is and you end up with the function of X Y N T
0:10:16so you do the same thing for these the and um
0:10:19and so it for the sub to simple a and you end up with a function of the at class
0:10:23of or and T are
0:10:26and finally um obviously this
0:10:28fines and fine finding is
0:10:31it's of is uh uh
0:10:32function enough
0:10:33this this do you want
0:10:34now we can
0:10:36press that because you relationship between the partial the every two years by so
0:10:40by um
0:10:43by a um
0:10:44expressing the of the positive in this for
0:10:47yeah yeah as five a and you get that related to
0:10:52do F file plus one and get plus one using this
0:10:55uh relationship
0:10:56you can start the recursion
0:10:59by um
0:11:00as as a few couple then it to a of a scene using this
0:11:05i so um
0:11:07i you find a have a one and you can my you can easily work
0:11:12to find D and but or do but X and was of back to find a point these that you
0:11:17so let me just to it so you start the by
0:11:20and a a um
0:11:21subject got L any to such
0:11:24and you were back until
0:11:26you find out from underneath of or
0:11:28and want to find those to can you can is you can um
0:11:33find out what do you do what a but X
0:11:36using this issue
0:11:38no once you for one to find that
0:11:41so you can now you have all the quantities needed to it
0:11:44the uh terms on the left hand side
0:11:46which is all we need do to find you find that of data
0:11:51so let me give you the real
0:11:53stupid the new make a was so here you get
0:11:56see that a
0:11:58and the blue line score one to some
0:12:01to was and you had the charter trajectory to by dashed line
0:12:05and then you you had the
0:12:07transmit and receive receiver
0:12:09so this is the P C R B for position estimate
0:12:12so this is a blue line "'cause" to the P C R B B
0:12:16my to and the a it line be top might but so as i mean do inside it's
0:12:21um we have a lower bound
0:12:23the all bound is low
0:12:24for um the case speak much what
0:12:27we side is that uh there is some additional information which we can exploit for our advantage
0:12:33and this is the same graph four willow cd estimation
0:12:37so in future we want to implement of filter for this
0:12:41quite challenging because like we have introduce more parameters well modelled like them
0:12:46then um um
0:12:48um vol effect is and faces is so it's a quite challenging to find of a to implement a few
0:12:53then we won't want to also look at a but i was it was the a number of targets that's
0:12:57and the and delay
0:12:59assumption that of locations and that known and probably look at wave forms that can be
0:13:05uh you but the results and also
0:13:07we to do the problem
0:13:23is worth microphone
0:13:29you are assumed but um
0:13:31all the points of of at all the boards not exactly know
0:13:36all the one location
0:13:38and even given the ball could you flick most of the beginning or the end i mean yes but in
0:13:42a john made to you an easy using or a job or to work of bits
0:13:46point you um those if that combines a
0:13:49like a a racing type of
0:13:51yes that
0:13:53and locates that
0:13:54then the common would be actually in a you frequency five remotes that
0:13:58the most obvious affect was in or scenes are actually traffic signed and not pull multiples
0:14:04so one of three does exactly the same but you might wanna look to this and you is that they
0:14:08are if you're put more like point scatterer not like a
0:14:13don't not want to be used meter if three that would be a that i don't with vectors but for
0:14:18think it's a
0:14:20just a calm
0:14:24the questions
0:14:31you assume a
0:14:33isotropic tradition yes is related to the previous question
0:14:37how can make sure of the number of times that you have a the most controls that you have a
0:14:43a you basically do a a a a a great a model
0:14:46a and but that before hand
0:14:48hmmm so that's how we will uh
0:14:58okay this so is the session to and the thing you for time um is one you know the speaker
0:15:03from another