0:00:15or or known is the probably one of the most all of the stuff but still
0:00:20what the leaves
0:00:21approach to the in track and the state estimation and control
0:00:26and that is a problem to meet here use so she that to noise that can what was
0:00:31be B goes on
0:00:33it can have a all lives and industrial applications will become
0:00:37a a tail
0:00:38so that the colour field of
0:00:40but it was lunch
0:00:42it's this presentation i'm going to show that that was it not only two
0:00:45is based on the finite impulse
0:00:48is if you for i'm going to the present a doesn't require a the knowledge about noise
0:00:54and initial conditions
0:00:55and a is it by uh
0:00:58in control
0:00:58a a car you know that
0:01:00use that workers
0:01:04you of the skulls as you
0:01:06just a a a and a a a a a a a you give a finally several important but
0:01:11most the scene
0:01:12vacations for too few
0:01:16so what can this so if you have to
0:01:19you you know that she some data base of some points that in
0:01:23well as and for the in if
0:01:26initial one in a to the present point
0:01:29we can apply the averaging procedure and the provide a few per use a you step
0:01:35a a a a a a a P she is zero small so
0:01:40a it you've
0:01:52uh this you know get you've in V B is keep the T V can you to you to be
0:01:56capable of the model
0:01:58um and uh and the
0:02:01it is a finite impulse response estimate or can be designed
0:02:05is it is a H four
0:02:06or in the iterative comma like form the day to can find
0:02:11but to it by change in a a pretty will be can also solves the problems so pretty Q
0:02:16i fight i you are and all smooth and i for a few
0:02:21what is the difference between the the colour you are in the fight a few
0:02:27if you need to extract some a of this uh uh uh the slide for example
0:02:33a a and you know have or in are the initial conditions and noise exactly that's how much you for
0:02:38starts to some initial points and the
0:02:42do the step by step but also have produce and it
0:02:45at each new step is that it's to that is very
0:02:48close your related to the truck and before ones
0:02:52because you know almost everything here
0:02:55in control the F i i feel the that does
0:02:58oh yeah it's on a are shown
0:03:00that's that you in you voice and the initial conditions
0:03:04it's not a
0:03:04um the unknown points and the state by state
0:03:09or the average and eyes and of an optimal point
0:03:12go goes to that
0:03:13last last point and and does also work the related to the actual value and uh
0:03:19actually is a common estimate of that if i a estimates a of articles your
0:03:25if you have of the Q sort of the column few buttons the T V O
0:03:29i and that of the original work of calm on and column be C
0:03:33the a field or
0:03:34"'cause" test to or what
0:03:36a are many midi if occasions related implications of the common field or two
0:03:41to the problems use not gaussian white noise
0:03:44we is the in set for systems
0:03:46these is linearity as uh
0:03:48for a large matrix is in many a a like quite problem solves that he finally
0:03:53that it finds that
0:03:55they come up to four as a part of the estimation as you not remote control
0:04:00in the come like for we need only
0:04:04this a result most most important results and that if i a area
0:04:09uh a type of but come on a and B if used for and that
0:04:13also the same or or or was a C parcels
0:04:16really too
0:04:17the modification of of the common structure to be a a fight a
0:04:21and also is they just a an it the F if are that each right you've if like a a
0:04:26you know a such as that is the construct structure for deterministic models and my are on but that
0:04:34but start with the
0:04:38you have the the this model in is usual for but
0:04:42as as lead to
0:04:43the real time problem not to the can problem
0:04:47a a and the
0:04:48all of the matrix is also the vectors that can be describe which a state space
0:04:54uh a a correctly
0:04:56uh a and a long of this model
0:04:58or all
0:05:00two vectors actors uh the vector of the system noise and the vector of that
0:05:04at separation noise to get an you covariance matrix a so noise to have any distribution and the
0:05:10"'cause" variance
0:05:11send me
0:05:13apply to the
0:05:16the standard can um
0:05:19which for two provides a a a what and and drive it's the final results also problem from the is
0:05:25if have the model
0:05:27you would like to design a a general P achieved
0:05:30and people like
0:05:31this uh is to make a would be a of the come like
0:05:35for or if used to the to solve the problems so a few or be you're pretty should you are
0:05:40that you one small and be a negative you
0:05:42or discrete time
0:05:43very state space models of this
0:05:45no requirements for noise and initial conditions
0:05:49but is the estimate a must be i by that that's exactly necessary to project
0:05:54the that have or use the minimum shift
0:06:00let's a back to the model
0:06:02if you get this model that you'd
0:06:04that yeah
0:06:05translate or or a to pretty the became or from the in minus one point of one step back to
0:06:11the present one
0:06:12but if it lies a if i i approach is that we need
0:06:16much more or since the model so we need to consider a the X
0:06:20and it model start them from some last point to the present one so the this stays this model a
0:06:26needs to be midi file two
0:06:28somehow two
0:06:30in in a all all the spy since yeah
0:06:35that can be done if you can the that's it is the original model the uh use the for for
0:06:40ten times solutions so if you can see that
0:06:43step by step back a better down to the your or and all the equations and combined to the
0:06:50a a a a to the expanded state is model
0:06:53do find a like yeah right it is this
0:06:55for four in which all of the
0:06:57the back for some matrix is R
0:06:59and determinant
0:07:01so we have
0:07:03uh a a state vector was that
0:07:05in well
0:07:06the a region of it them from that
0:07:09initial point up to the present one the same for measurement and the same for
0:07:14and they also have a or was that matters is inside describe it
0:07:18or the average of her rise of off
0:07:20and point
0:07:22if you also introduce some it usual matrix is here
0:07:27yeah can that
0:07:28you can be in need to describe
0:07:30i in a more correct way that
0:07:32the only the matrix B and then use the
0:07:35combinations of of of the matrix presentations to describe the model find then
0:07:44in chi
0:07:45or that and by to it as the
0:07:48and by that if i estimator can but it if you is high now how sound
0:07:55estimation matrix eight that actually is the gain matrix for all our measurement that wrote
0:08:01all the cries and fall
0:08:02a point and a to the present brilliant
0:08:05and that uh it you know why it is it's this state space
0:08:09a a representation
0:08:11and then uh
0:08:12a can see it is uh
0:08:14it you should in each
0:08:16X to this to do it was that the
0:08:18estimate estimate and the parent and and plus P in which you be takes positive because a prediction this is
0:08:25your it's a a a a a real time
0:08:27or in and and uh is to negative it's small soon
0:08:30and if it sounds uh it lies and by that this can you sense that this principle point here because
0:08:36you would like as if you few to be and by it
0:08:39so that if you it lies this condition
0:08:42and the uh then the provides a a ever chance and it finally
0:08:46oh i've uh the at the very simple relation
0:08:50that means that the mean value of over is to make use
0:08:54but is that cool to some image matrix
0:08:57we see that
0:08:59modified expanded matrix
0:09:01the measurement equation and X
0:09:04yeah represents the state in the initial points that places of a cost or in
0:09:09uh and uh on the averaging horizon of the endpoint
0:09:16we also need to describe the correctly with the ever issues that the
0:09:22in case two
0:09:24a she
0:09:24used image relates to
0:09:26a chance this for
0:09:29yeah your presents the problem
0:09:30for all of the
0:09:32system and to them from the initial one up to the present one at the point and
0:09:38and a if a a a a a way to to to a question
0:09:41to results in accordance with the and by that this condition it finally arrive
0:09:46and it is that is
0:09:48the it also gives us the and buys a gain in which case we have a
0:09:54also also property is
0:09:56or of the state space model it's that said to be a last
0:10:00information about noise and the initial condition
0:10:05now we are right at the fierce you
0:10:07given uh
0:10:08in a to put the cause and the second equation as that's it's model a zero-mean mutually uncorrelated and independent
0:10:16and noise component
0:10:17a a would distributions and known covariance functions
0:10:21is if you are in is your P like small and be negative and P step prediction you you
0:10:26can be probably a data and at and plus key use and data taken from
0:10:31a a two and by the page if i a a and by the estimator as follows
0:10:36so we have now the trust result
0:10:39that time for
0:10:40also information about of the that the state space model or but be a last noise and initial and you
0:10:47but i
0:10:48the yeah
0:10:49it you can do this
0:10:50because is there is a very important G phones in the harmonic here was that doesn't across a few
0:10:56you have a a few of the trucks
0:10:58on this very large number of the points
0:11:01you know is that the white gaussian noise is reduced by the federal and the variance of the noise is
0:11:07reduced by the factor of and
0:11:09so if you're right
0:11:10the advice if you are in a frame can be a dramatically in the F I F you reduce the
0:11:16variance of the loss
0:11:18but the is the problem is this
0:11:20is the problem is this
0:11:22a that to
0:11:24so has
0:11:25and how of matrix as
0:11:28is that uh
0:11:30a just let's it is the advantages and disadvantages that than about the problem
0:11:35so a in the time varying of like estimator read with noise and initial conditions it have the form of
0:11:41bit back just
0:11:43it it slice
0:11:44there is no no no no king jeez
0:11:48but but at all
0:11:49of course
0:11:50"'cause" that of very strong engineering feature
0:11:53a a a as a as a a hand when and and number of the points of yours to the
0:11:57one is the estimated and vectors to a optimal model one
0:12:01"'cause" an part to but also because of are important disadvantage is that actually is a computational problem
0:12:08but be do you is of a like to matter "'cause" of where two dimensions that we
0:12:12in in color to the problem of
0:12:15or computation
0:12:17the is that the whole of this your and suggest just are right fusion colour like for presents
0:12:24uh so uh
0:12:26if you have that and by that the uh if you the re is uh the structure if fight a
0:12:31then a F but that the kind of like for all of this estimator is the form of in
0:12:36a representation
0:12:37it is it i one you
0:12:40in H
0:12:40this part represents presents a how about gain free of noise and the initial conditions
0:12:46and that all of the just are described it
0:12:49but is the only difference is used as a common that the the band can she if it the the
0:12:54set yes us to use for G from male are useful future and
0:12:57yeah prediction and small and in this case we have a unified
0:13:02we can use it
0:13:03but we just to select P problem
0:13:07a in that case
0:13:08we need to use calls the data base and how about that chief in case of the noise is the
0:13:14nonstationary or
0:13:19i noise is a stationary
0:13:21then is can use
0:13:22that that for for eyes and car yeah why it is that is
0:13:26that that require uh the horizon rise in it
0:13:29the works is as the point so it "'cause" much more attractive engineering feat feature
0:13:36uh what's more important for all and F I i feel for we can also form in a very simple
0:13:42way that
0:13:43a bounds of shows
0:13:45house if you for the
0:13:47a a what is a an hour was if you of the time
0:13:51uh and C so the bomb can be produce the crumbs enormous problem came and has a form of
0:13:56the free C one noise bone
0:14:01a is the speech of follows uh the can and so the optimal if i a few and we
0:14:07the a wise upon souls that
0:14:09one can see is that
0:14:10when and if yours to be more than saudi so is almost no difference between to few or and that
0:14:16i was position
0:14:17to try a a a a noise an initial conditions of used to be a
0:14:21car wreck for practical applications
0:14:25now or let's consider several
0:14:26the it's samples
0:14:29in insists is it to stay model uh a V is uh uncertainty certainty temporal and seventy you is channel
0:14:36in inside
0:14:37a junior is a process and probably lies a common standard kalman field and there
0:14:42uh you introduce it to that if like a come by
0:14:47but then this C
0:14:49a was the became a a a time but the cable are all of the model of is and T
0:14:54and to you know was demonstrated the
0:14:57the G from the
0:14:59uh a different be hit are in the
0:15:02time invariant case
0:15:03the most you want and G froze between the common and or and if we uh ones that
0:15:08F F i a a a a two side like to it's conference so
0:15:12the show the trends in
0:15:13you controls the common few or "'cause" it for a discussion about larger trained
0:15:18but the is the time you where in case both futile bottles
0:15:22a a of the same project so as as the difference between two field of it's much more information
0:15:28if is the same effect
0:15:30it it
0:15:30well i but sure the trains and and
0:15:33and that if i a few or but the a filter "'cause"
0:15:37it it's a to try in but for a extra
0:15:41the same for the second stage
0:15:45if you uh but the less now assume that we can describe a core right "'cause" a model of that
0:15:51does it cheap people for vacations for example i don't know how to this type right "'cause" the noise in
0:15:56the velocity of the moving object
0:15:58or or in in the next orange
0:16:00if it had miss some and house in that noise disk action for the common few or and for that
0:16:06if i have few problems set so out to be a
0:16:09like you and so does a very well reproduceable reproducible result
0:16:14the common field are instantly demonstrate like to scarf
0:16:18kind of instability in the you
0:16:20or or is that if i if i a few
0:16:23is your in sensitive to noise
0:16:26i you do not can use
0:16:28not descriptions of okay
0:16:31and this is uh a for all the time for case
0:16:36several of those of prediction
0:16:38if you
0:16:40do the same for all the model of that this type of a champ of and so to do and
0:16:45some time in
0:16:47and compared prior to know was that in town sounds it is a common few problems that
0:16:51i i i a few
0:16:53a produce almost was the same prediction is that
0:16:56but a small difference is that i i few for has a big
0:17:00uh a we have a yeah or it for was for the at comparison of the red and black
0:17:05i else
0:17:06but if it means some
0:17:08and and you know that uh a and is the matrix connection
0:17:13is the common field or part was much like yeah O
0:17:16especially in this case the became a a a a is a it in contrast to the will be
0:17:25let's in use now seven our planners
0:17:28it was a a a a a a while but also house and it again in a plane to a
0:17:33few hours
0:17:34as and so the it does this is to fess use of i have set seven out sliders here
0:17:39uh a for one side to a a a a to all as the same
0:17:44at the same
0:17:45a a will the
0:17:47real behaviour or down to real became so that's of how to feel or
0:17:52or or X to the out of players
0:17:55because a noise it make it in the description of the for the common few hours of covariance matrix as
0:18:01i a realise is that how one field or game but a better watch it's cars
0:18:05it but also the common like one that has a a fixed extent
0:18:11and it a second stage the as a results more impressive there was almost no sensitivity in that F a
0:18:17few or to i'll by so that X that the but to as a cup few you forced to produce
0:18:25so so to uh what can we say a of the source so
0:18:28the don't known like and by it if i i estimator and noise noise and initial the is really and
0:18:34two for the optimal estimation and denotes listen
0:18:38and if H just for trick can state estimation and uh
0:18:41in a a a for the control problem
0:18:43the estimator i can i'll be O forms a common field or if
0:18:48noise and initial and uses and not a on exactly so if you do not know noise and it if
0:18:54you have problems and more descriptions that's
0:18:57try to use this you are your realise that it can
0:19:00provide a better result and the output
0:19:03a a it was this system and measurement noise components need to be if you
0:19:07if per out
0:19:08so are several problems that you need to few for power
0:19:12but was lost components form that uh state this model in this case that i five a few times more
0:19:19my and the match to the models i'm never it in the non about phone
0:19:23a data or our for just our noise invited and insist case again
0:19:29averaging procedure is more open for a
0:19:33and that models have ten probably and so
0:19:37that a month of about and times to computation time required by
0:19:43the iteration procedure but no
0:19:46do not be necessary if you designs the field or in are little computer for every new point you just
0:19:52need to provide in part
0:19:54but the computation of the next for the next step
0:19:57so that this model computers because a not is a problem
0:20:01so that's all sent
0:20:09a for this become
0:20:20now it's some quite you to that you are do not use a minimal by sec
0:20:27minimum Y
0:20:28sense so it "'cause" i i'm by
0:20:39yes is this your there
0:20:41as this field or is not great converse
0:20:43it is a a a to she you are so it does it have i a structure finite impulse response
0:20:49in each case we can no feedback
0:21:01i can not included this is a consist presentation because of limited time but seven as the sort and and
0:21:06you are descriptions that was that L
0:21:09equation to cook to is that the the final as a a a a a a a it's its output
0:21:14for it's still it not small
0:21:16you can use the is a a as as we see my sense and the
0:21:20uh the is that yeah this to
0:21:23so but is it a comparison is a common to for house that sake of almost the same performance in
0:21:28that i do or it could be a case
0:21:30you can all have or in the about
0:21:32about the model
0:21:33absolute absolute have as and the to few course provides or was the same result
0:21:41i is uh
0:21:49and standard standard and once we speaker
0:21:51in in in the is like
0:21:53so we are talking remote featuring problem
0:21:57given that the whole last
0:22:00all data from that
0:22:01from the in finding blast test at meeting and we and variance estimate uh
0:22:06so you you've can lean to but you are feature in you know way that
0:22:09not the whole plus testifying to don't top last
0:22:13it's that tool there actually use a finite impulse response so it works is a finite number of the points
0:22:19and the past not use as a bus
0:22:21yeah that in contrast to the common to those it those
0:22:24the infinity in
0:22:26that that's that's what i am trying to get that
0:22:29we can interpret your three get as a a
0:22:32up to feature a minimum variance feature
0:22:36given a if i a blast
0:22:38not that in fine but
0:22:40well that
0:22:42is this presentation of leads to the and buys a finite impulse response you come like um C
0:22:48so was and that's of a a a a few it just a more as a minimum mean square error
0:22:54sense so so that
0:22:55it just and was the same like a
0:22:57the common few uh in the minimum
0:22:59the likelihood function so
0:23:02it is the same but a is this presentation leads to and buys a field
0:23:07i know what you're want to come now
0:23:09you can find and might be a a a a a what it takes time
0:23:14but can say in the case of that up to a few of we need to solve a take equation
0:23:21but i and the averaging horizon out
0:23:23much larger numbers of support
0:23:27more questions
0:23:32the i think it can be easily extended to nonlinear ten so as like extend colour of yeah if i
0:23:39was yes exactly S of course you just must apply the standard extended kalman filter
0:23:45uh approach to use a that and apply to a nonlinear problems not problem
0:23:49at all
0:23:55and more question
0:23:59oh have you applied this to G P S
0:24:01signal no real signals you were there any
0:24:05my book is devoted to
0:24:07G is base it up to model will F i a few or not clock models
0:24:12i'm do and not this position and but to the beast actually time
0:24:17for that actually times if few of them was designed to exactly and so and it a of it "'cause"
0:24:22it your exits their structure "'cause" a more change of big patient so
0:24:25is is so and so was a Q if you are exact in the gps S
0:24:29and and you get gain in a significant gain when you like this filter of four
0:24:33to one G S signals
0:24:35no yeah for for gps signal sequence but for all time incident last but time
0:24:39think my time was not position in
0:24:41and you get any gain for that
0:24:44significant gain over L
0:24:46yeah where
0:24:47what yes yes
0:24:50originally we used to the common few form but as the problem is a common use the use problem
0:24:56if you don't know noise correctly if it meet the arrows in the noise covariance matrix but the factor of
0:25:03tools for
0:25:04or or any ah a factor if you must fix a a a it's back for
0:25:09a yeah
0:25:10and i had just rows and how experiment are we
0:25:13uh investigations of these applications would G P S so finally has started to find some new result and the
0:25:19oh i that's is it
0:25:22anymore more questions
0:25:27so unfortunately the become the third presentation is missing
0:25:30oh you are here are we just checked in and okay