mounting of rooms line in or don't know and uh and it in the because sometimes and working with this condition to in frame time so first all i will uh uh talk about the uh C uh method in the one and signal since in case and and then my i will explain all uh proposition an extension to the um the since a case which is not easy and then uh i will uh sure you some reason so uh here the problem is uh the to target detection and tracking so i see we have target uh uh if i mean in a state space oh the state is gone know that of and we know that this targets may and uh and leave these states space hundred and dates so that the uh the target but number is as a a a a round them as well these target a observe by sensor um so each sensor uh it has its own or a uh observation process we may also that the the field of use of false of these and so may yeah are that each other but this will be an important point for later the um well we'll will uh uh of a synchronised the system yeah it's time step will receive measurements from all the sensors so we we likely to have some measurement a target the association issue oh how can be it doesn't hard targets so a the classical method would be to create a uh sorry a track uh each done uh you detect and you target and to maintain this a track this will evolve according to the information you you have and the and target oh that's will focus here on number of a wait the set base sanitation a in which case the random has upon the the target number and the rip uh a round them was of the in the uh target state is a yeah that into one single uh a random object a random finite set a R S S so this this to but have F fess would be uh random variable which is defined on this the all final subset of the state space and assume here that you have uh randomness on the target state as well as the target number are the final state statistics provide us tools such as set integration said differentiation or even set a provided densities so that we are here we should be able to propagate the the uh probably to density of for are fess through time using set based but usually equation so you have a time of day question first and then the that the question so that the questions hmmm quite nice but you can see you've then in practical situations because there is a set integrals is strictly schur you need to take into account every possible number of targets site your R S S so how to simplify this well the idea is to propagate the first moment density P H D off uh i fess rather than the full density so uh we have to assume that if we T is personal which means that the target number inside a are F S is possible with parameter and then which uh like as the uh the uh uh and double a for the P H D over the whole state space and did start it's in there i S is distributed according to the number X P H D so is uh example assume that the great every yeah i cost to roughly three point two then but estimated target number will be three a but i i will eyes the is three targets along the i S speech in my uh density so you see here that the G do is defined on the state space which is a a much easier to and all than the to find it's of state subsets of the state space so but is filtering for to it with a P G framework is easier than within the rss S men work uh because we need the P G is defined as a a a a state space so we have here at that time and did equation so the first part here is uh yeah yeah we to the uh evaluation of existing targets and but a as was my out here which relates to the uh creation of new target and then the bad that a question which is a point lines to and you can see a classical notions of that of the product of detection or we likelihood here from this is quite easy but it's in the single sensor case only so no what at in the multi target at a multi sensor case this is quite uh a different and my difficult to to so so we yeah proposed um a real uh that update equations to this looks nice not nasty i now uh the chip or and here is this in the experiments you have a cross term term can it read it's a function and a and to cross too which were to deaf and shaped along every measurement points and uh uh i don't this state point two to do the that updated H G um i mean that of you hear the exact expression of the uh cost and it's in the paper i will rather try to show you what it looks like in practical situation so i assume that you have through uh since words well as you die from shake you crossed term in this state but it's missions you zero one and measures in three that but was able to a cost here yeah the that that there was a target i state X according to my uh time of the T P H D and that this target is detected by since someone and produced mission ones you one the target that was in the data and so two and was detected by since a three and that produce measurements is three i um um uh a cross term is uh a definite shaded in measurement points can me like this then uh a the resulting cross to a is a you that there is a target somewhere in the state it's but i don't know where which well to buy since so one since too but was and detected by the since of so what is it look like whether the updated is you look like and the simple example so here are yeah only two sensors first case and two measurements so one measurement per sensor if i don't example what you see here he's is a better P H D the first and here that you doing uh and denotes the uh like you that you have a target in in state but it's but it's and detected by bows answers and that um you have the this sure takes into account all the possible haitian measurement session so uh the one and the mean to here you have a linear possibility that uh oh which can and the possible to that you were to to have these two measures on the measurements on the so here because is the that's where comes from different uh uh targets and hear from the a single target you can imagine that if you increase the number of measurements are the number of target teams we grows out of control you see if i don't me had a one measurement is uh going very nasty so how can we simplify this we to to has a look on the that update equation and we found that in maybe situations uh maybe a different shaded cross terms were to vanish so that look at this example you have three sensors S one and as three at or overlapping fields and has to is isolated well i i know that a target in the recognition cannot be detected so and mm uh trust different in this measurement and i don't know a point here we have an vanish uh i i also that a type but can be detected by this sense of S one and S two so i cross term shaded in the measurement here and here will vanish two and so am so but that is that uh instead of using my uh the data that question on the whole state space i can write a use it three times and smaller uh parts of the uh state space i as well as a a of the vision without any sense well and and the the grey mission with a uh since a one and three and one and the region well since of to measurement from sensor to and i'm that the exact same results also the exact multi sensor uh P D a a a a a bit P H T but it should be uh a fast so let's look at an example so a here have uh or something like ten sensors spread or of of the state space i one you so that the the the fourth configuration is set that it should be able to P my sense the at least for parts the is this one isolated is to have a a and this through here so this that's that's this is critical because that i we have a three uh i being uh the field of you so if a target comes into this uh doc spots uh the that that the two step would be very uh compute a ah we have a out to compute so here um it is a nice and that of the time step uh in a um the number of target across time and the red the estimate number by my uh my um me a so pitch if you to so you can see that at the back of the estimation and and we as a i mean i'm high number of targets so it to this either the critical times whether the that are that should be difficult with the uh brute force approach and uh uh K any so that uh in black these a computing time of the better updates tape a across uh this you scenario a a of the brute first approach so the that that it's state of the whole state space and he yeah oh in well as the computing time further the partition ms oh the time it it's log scale here so we assume that and the we had at the um the brute force approach is exploding well i and the that and remains quite low um um as as well so a simple is as here because the target member but it is very low uh the brute first this actually but uh on the the portion that so to conclude what can we say about the partition method well uh first of all it's not an approximation because we get to have the exact is and so that a a a a a a a to question was so we can put by gate the exact value of the mid and P H D in case where the the field of you configuration is quite a can then the passion method it is likely to be much more efficient but the brute force approach but that's the passion itself other the coast that's why i we had a here a uh the passion was more a a little bit first was faster than the patch and the third if the for the feel of a come is and five or or uh what was case if it's a a a a and the uh so of used are crossing each other that the pension but them does not bring anything you and uh in to be a bit less efficient at the brute force approach but you know all in a practical situation well the field of view of the since of a spread of the state space the approximation mission can bring uh an interesting approach to if you want to provide get the truth P H D a P H D of that thank uh this if if finds that well a problem is all all and or same time yes i the why you don't have yeah ish it shouldn't have a synchronised a network then you can uh you the uh it activated directed the approximation which case you will uh you will uh use the uh single sensor uh a P G that that T questions uh second second city do one know that in the synchronized case uh if you be a product it uh it it to product that approximation then define a lattice arc approximation would depends on the order in which you you take the uh you a a process the uh sensor that's a may be a problem gosh what was the model that you're using your simulations was to dimension uh the was your house sense to was your results do a to a collection in overlapping regions sorry a what was the model you summation you mean the target model of the observation hmmm oh the target model is is quite simple weights so and and C V near constant us to model uh are the targets are created uh around the edges of the state space and the measurement i use in different kind of of sensors well some sense as of a a can the the range and the and angle of the target and you have a cushion noise and these two values and all the sensors can also uh now the uh radial velocity see and and simulation what sense there yeah we have many different kind and a yeah the sensing in as as what different for for every uh sense cool and well as as usual and the phd H the following in but it the probability detection oh you since your sense i is low then you P L O P G is likely to to crash if you in yours uh in this case it's the protein detection is quite a i but i tried to means and no uh uh uh values and eat couldn't work click i um um i used a different uh us a first on process to for every uh uh captain since so you can have a different uh class a process it works quite well except that you have the for some right will uh we'll set you will oh right estimate uh the remember but gets you will estimate would be quite a i of and than real number so we will another way to extract a target from from you you data because well i yeah a and at the beginning was but each uh a you say i again to goals of a all sits they this is my number of targets i take the the round well i the closest in to go at this is my number of targets and that will a at is um uh are the highest peaks but again can do a better thing you can try to localise in the space some place where you can extract uh the P G uh some uh in the sub region of the uh these state space uh the P such that you have a a a a a weight of one we which will note that there is a target then you extract this and you will process these two to try to extract uh a target and more questions we see have five minute what implementation the use was it think of the bayes yes and it's uh i'm it's difficult uh these uh a particular of to implementation uh "'specially" a for the creation of new uh a weight around the measurement all around oh according to the number of the of the destination so that's why in in this case the uh a target estimation the estimation of the target number was not very good at some point i should be able to to improve this uh if i use the a better article implementation you questions for the bit but uses in used seem to have fun point uh sense if you one controller positions of a there any of them is now that you would have for your of and that if i need two the sense that you have a about and fusion i do not if data point and not for sensors for target but the target are yeah yeah the sensors also they can have any particular structure the and if you in control of that would that be any optimum position you know the sense oh that's a good question uh and not as i'm working on the uh and i don't for on be solution of the sense i tried with a fixed position to control try to find the optimal uh well orientation iteration of my and my uh since and this is a a a a i think uh the big and X that for the P H D the the control part because we know that if uh there is a part of the since space which is never observed that any some now uh things were grow out of of control and it will uh the the quality of the target uh and number estimation so i'm trying to to be a a a limitation of the sensors so that i will at least look at where have that i can uh at which with a coverage and a and more questions okay let's time speaker again i