0:00:13 | morning |
---|---|

0:00:15 | or or known is the probably one of the most all of the stuff but still |

0:00:20 | what the leaves |

0:00:21 | approach to the in track and the state estimation and control |

0:00:26 | and that is a problem to meet here use so she that to noise that can what was |

0:00:31 | be B goes on |

0:00:33 | it can have a all lives and industrial applications will become |

0:00:37 | a a tail |

0:00:38 | so that the colour field of |

0:00:40 | but it was lunch |

0:00:42 | it's this presentation i'm going to show that that was it not only two |

0:00:45 | oh |

0:00:45 | is based on the finite impulse |

0:00:47 | few |

0:00:48 | is if you for i'm going to the present a doesn't require a the knowledge about noise |

0:00:54 | and initial conditions |

0:00:55 | and a is it by uh |

0:00:58 | in control |

0:00:58 | a a car you know that |

0:01:00 | use that workers |

0:01:04 | you of the skulls as you |

0:01:06 | just a a a and a a a a a a a you give a finally several important but |

0:01:11 | most the scene |

0:01:12 | vacations for too few |

0:01:16 | so what can this so if you have to |

0:01:19 | you you know that she some data base of some points that in |

0:01:23 | well as and for the in if |

0:01:26 | initial one in a to the present point |

0:01:29 | we can apply the averaging procedure and the provide a few per use a you step |

0:01:35 | a a a a a a a P she is zero small so |

0:01:38 | P |

0:01:40 | a it you've |

0:01:49 | much |

0:01:52 | uh this you know get you've in V B is keep the T V can you to you to be |

0:01:56 | capable of the model |

0:01:58 | um and uh and the |

0:02:01 | it is a finite impulse response estimate or can be designed |

0:02:05 | is it is a H four |

0:02:06 | or in the iterative comma like form the day to can find |

0:02:10 | but |

0:02:11 | but to it by change in a a pretty will be can also solves the problems so pretty Q |

0:02:16 | i fight i you are and all smooth and i for a few |

0:02:20 | well |

0:02:21 | what is the difference between the the colour you are in the fight a few |

0:02:27 | if you need to extract some a of this uh uh uh the slide for example |

0:02:33 | a a and you know have or in are the initial conditions and noise exactly that's how much you for |

0:02:38 | starts to some initial points and the |

0:02:42 | do the step by step but also have produce and it |

0:02:45 | at each new step is that it's to that is very |

0:02:48 | close your related to the truck and before ones |

0:02:52 | because you know almost everything here |

0:02:55 | in control the F i i feel the that does |

0:02:58 | oh yeah it's on a are shown |

0:03:00 | that's that you in you voice and the initial conditions |

0:03:04 | it's not a |

0:03:04 | um the unknown points and the state by state |

0:03:09 | or the average and eyes and of an optimal point |

0:03:12 | go goes to that |

0:03:13 | last last point and and does also work the related to the actual value and uh |

0:03:19 | actually is a common estimate of that if i a estimates a of articles your |

0:03:25 | if you have of the Q sort of the column few buttons the T V O |

0:03:29 | i and that of the original work of calm on and column be C |

0:03:33 | the a field or |

0:03:34 | "'cause" test to or what |

0:03:36 | a are many midi if occasions related implications of the common field or two |

0:03:41 | to the problems use not gaussian white noise |

0:03:44 | we is the in set for systems |

0:03:46 | these is linearity as uh |

0:03:48 | for a large matrix is in many a a like quite problem solves that he finally |

0:03:53 | that it finds that |

0:03:55 | they come up to four as a part of the estimation as you not remote control |

0:04:00 | um |

0:04:00 | in the come like for we need only |

0:04:03 | i |

0:04:04 | this a result most most important results and that if i a area |

0:04:09 | uh a type of but come on a and B if used for and that |

0:04:13 | also the same or or or was a C parcels |

0:04:16 | really too |

0:04:17 | the modification of of the common structure to be a a fight a |

0:04:21 | and also is they just a an it the F if are that each right you've if like a a |

0:04:26 | you know a such as that is the construct structure for deterministic models and my are on but that |

0:04:32 | and |

0:04:34 | but start with the |

0:04:36 | model |

0:04:38 | you have the the this model in is usual for but |

0:04:42 | as as lead to |

0:04:43 | the real time problem not to the can problem |

0:04:47 | a a and the |

0:04:48 | all of the matrix is also the vectors that can be describe which a state space |

0:04:54 | uh a a correctly |

0:04:56 | uh a and a long of this model |

0:04:58 | or all |

0:05:00 | two vectors actors uh the vector of the system noise and the vector of that |

0:05:04 | at separation noise to get an you covariance matrix a so noise to have any distribution and the |

0:05:10 | "'cause" variance |

0:05:11 | send me |

0:05:12 | can |

0:05:13 | apply to the |

0:05:16 | the |

0:05:16 | the standard can um |

0:05:19 | which for two provides a a a what and and drive it's the final results also problem from the is |

0:05:24 | for |

0:05:25 | if have the model |

0:05:27 | you would like to design a a general P achieved |

0:05:30 | and people like |

0:05:31 | this uh is to make a would be a of the come like |

0:05:35 | for or if used to the to solve the problems so a few or be you're pretty should you are |

0:05:40 | that you one small and be a negative you |

0:05:42 | or discrete time |

0:05:43 | very state space models of this |

0:05:45 | no requirements for noise and initial conditions |

0:05:49 | but is the estimate a must be i by that that's exactly necessary to project |

0:05:54 | the that have or use the minimum shift |

0:06:00 | let's a back to the model |

0:06:02 | if you get this model that you'd |

0:06:04 | that yeah |

0:06:05 | translate or or a to pretty the became or from the in minus one point of one step back to |

0:06:11 | the present one |

0:06:12 | but if it lies a if i i approach is that we need |

0:06:16 | much more or since the model so we need to consider a the X |

0:06:20 | and it model start them from some last point to the present one so the this stays this model a |

0:06:26 | needs to be midi file two |

0:06:28 | somehow two |

0:06:30 | in in a all all the spy since yeah |

0:06:35 | that can be done if you can the that's it is the original model the uh use the for for |

0:06:40 | ten times solutions so if you can see that |

0:06:43 | step by step back a better down to the your or and all the equations and combined to the |

0:06:50 | a a a a to the expanded state is model |

0:06:53 | do find a like yeah right it is this |

0:06:55 | for four in which all of the |

0:06:57 | the back for some matrix is R |

0:06:59 | and determinant |

0:07:00 | now |

0:07:01 | so we have |

0:07:02 | the |

0:07:03 | uh a a state vector was that |

0:07:05 | in well |

0:07:06 | the a region of it them from that |

0:07:09 | initial point up to the present one the same for measurement and the same for |

0:07:14 | and they also have a or was that matters is inside describe it |

0:07:18 | or the average of her rise of off |

0:07:20 | and point |

0:07:22 | if you also introduce some it usual matrix is here |

0:07:26 | B |

0:07:27 | yeah can that |

0:07:28 | you can be in need to describe |

0:07:30 | i in a more correct way that |

0:07:32 | the only the matrix B and then use the |

0:07:35 | combinations of of of the matrix presentations to describe the model find then |

0:07:44 | in chi |

0:07:45 | or that and by to it as the |

0:07:48 | and by that if i estimator can but it if you is high now how sound |

0:07:53 | the |

0:07:54 | a |

0:07:55 | estimation matrix eight that actually is the gain matrix for all our measurement that wrote |

0:08:01 | all the cries and fall |

0:08:02 | a point and a to the present brilliant |

0:08:05 | and that uh it you know why it is it's this state space |

0:08:09 | a a representation |

0:08:11 | and then uh |

0:08:12 | a can see it is uh |

0:08:14 | it you should in each |

0:08:16 | X to this to do it was that the |

0:08:18 | estimate estimate and the parent and and plus P in which you be takes positive because a prediction this is |

0:08:25 | your it's a a a a a real time |

0:08:27 | or in and and uh is to negative it's small soon |

0:08:30 | and if it sounds uh it lies and by that this can you sense that this principle point here because |

0:08:36 | you would like as if you few to be and by it |

0:08:39 | so that if you it lies this condition |

0:08:42 | and the uh then the provides a a ever chance and it finally |

0:08:46 | oh i've uh the at the very simple relation |

0:08:50 | that means that the mean value of over is to make use |

0:08:54 | but is that cool to some image matrix |

0:08:57 | we see that |

0:08:59 | modified expanded matrix |

0:09:01 | the measurement equation and X |

0:09:04 | yeah represents the state in the initial points that places of a cost or in |

0:09:09 | uh and uh on the averaging horizon of the endpoint |

0:09:14 | yeah |

0:09:16 | we also need to describe the correctly with the ever issues that the |

0:09:22 | in case two |

0:09:24 | a she |

0:09:24 | used image relates to |

0:09:26 | a chance this for |

0:09:28 | where |

0:09:29 | yeah your presents the problem |

0:09:30 | for all of the |

0:09:32 | system and to them from the initial one up to the present one at the point and |

0:09:38 | and a if a a a a a way to to to a question |

0:09:41 | to results in accordance with the and by that this condition it finally arrive |

0:09:46 | and it is that is |

0:09:47 | relation |

0:09:48 | the it also gives us the and buys a gain in which case we have a |

0:09:54 | but |

0:09:54 | also also property is |

0:09:56 | or of the state space model it's that said to be a last |

0:10:00 | information about noise and the initial condition |

0:10:05 | now we are right at the fierce you |

0:10:07 | given uh |

0:10:08 | in a to put the cause and the second equation as that's it's model a zero-mean mutually uncorrelated and independent |

0:10:16 | and noise component |

0:10:17 | a a would distributions and known covariance functions |

0:10:21 | is if you are in is your P like small and be negative and P step prediction you you |

0:10:26 | can be probably a data and at and plus key use and data taken from |

0:10:30 | and |

0:10:31 | a a two and by the page if i a a and by the estimator as follows |

0:10:36 | so we have now the trust result |

0:10:39 | that time for |

0:10:40 | also information about of the that the state space model or but be a last noise and initial and you |

0:10:47 | but i |

0:10:48 | the yeah |

0:10:49 | it you can do this |

0:10:50 | because is there is a very important G phones in the harmonic here was that doesn't across a few |

0:10:56 | you have a a few of the trucks |

0:10:58 | on this very large number of the points |

0:11:01 | you know is that the white gaussian noise is reduced by the federal and the variance of the noise is |

0:11:07 | reduced by the factor of and |

0:11:09 | so if you're right |

0:11:10 | the advice if you are in a frame can be a dramatically in the F I F you reduce the |

0:11:16 | variance of the loss |

0:11:18 | but the is the problem is this |

0:11:20 | is the problem is this |

0:11:22 | a that to |

0:11:24 | so has |

0:11:25 | and how of matrix as |

0:11:28 | is that uh |

0:11:30 | a just let's it is the advantages and disadvantages that than about the problem |

0:11:35 | so a in the time varying of like estimator read with noise and initial conditions it have the form of |

0:11:41 | bit back just |

0:11:43 | it it slice |

0:11:44 | there is no no no no king jeez |

0:11:48 | but but at all |

0:11:49 | of course |

0:11:50 | "'cause" that of very strong engineering feature |

0:11:53 | a a a as a as a a hand when and and number of the points of yours to the |

0:11:57 | one 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 |

0:12:08 | but be do you is of a like to matter "'cause" of where two dimensions that we |

0:12:12 | in in color to the problem of |

0:12:15 | and |

0:12:15 | or computation |

0:12:17 | the is that the whole of this your and suggest just are right fusion colour like for presents |

0:12:23 | estimate |

0:12:24 | uh so uh |

0:12:26 | if you have that and by that the uh if you the re is uh the structure if fight a |

0:12:31 | then a F but that the kind of like for all of this estimator is the form of in |

0:12:36 | a representation |

0:12:37 | it is it i one you |

0:12:39 | actually |

0:12:40 | in H |

0:12:40 | this part represents presents a how about gain free of noise and the initial conditions |

0:12:46 | and that all of the just are described it |

0:12:49 | but is the only difference is used as a common that the the band can she if it the the |

0:12:54 | set yes us to use for G from male are useful future and |

0:12:57 | yeah prediction and small and in this case we have a unified |

0:13:02 | we can use it |

0:13:03 | but we just to select P problem |

0:13:07 | a in that case |

0:13:08 | we need to use calls the data base and how about that chief in case of the noise is the |

0:13:14 | nonstationary or |

0:13:16 | yeah |

0:13:19 | could |

0:13:19 | i noise is a stationary |

0:13:21 | then is can use |

0:13:22 | that that for for eyes and car yeah why it is that is |

0:13:26 | that that require uh the horizon rise in it |

0:13:29 | the works is as the point so it "'cause" much more attractive engineering feat feature |

0:13:36 | uh what's more important for all and F I i feel for we can also form in a very simple |

0:13:42 | way that |

0:13:43 | a bounds of shows |

0:13:45 | house if you for the |

0:13:47 | a a what is a an hour was if you of the time |

0:13:51 | uh and C so the bomb can be produce the crumbs enormous problem came and has a form of |

0:13:56 | the free C one noise bone |

0:14:01 | a is the speech of follows uh the can and so the optimal if i a few and we |

0:14:07 | the a wise upon souls that |

0:14:09 | one can see is that |

0:14:10 | when and if yours to be more than saudi so is almost no difference between to few or and that |

0:14:16 | i was position |

0:14:17 | to try a a a a noise an initial conditions of used to be a |

0:14:21 | car wreck for practical applications |

0:14:25 | now or let's consider several |

0:14:26 | the it's samples |

0:14:29 | uh |

0:14:29 | in insists is it to stay model uh a V is uh uncertainty certainty temporal and seventy you is channel |

0:14:36 | in inside |

0:14:37 | a junior is a process and probably lies a common standard kalman field and there |

0:14:42 | uh you introduce it to that if like a come by |

0:14:47 | but then this C |

0:14:49 | a was the became a a a time but the cable are all of the model of is and T |

0:14:54 | and to you know was demonstrated the |

0:14:57 | the G from the |

0:14:59 | uh a different be hit are in the |

0:15:02 | time invariant case |

0:15:03 | the most you want and G froze between the common and or and if we uh ones that |

0:15:08 | F F i a a a a two side like to it's conference so |

0:15:12 | the show the trends in |

0:15:13 | you controls the common few or "'cause" it for a discussion about larger trained |

0:15:18 | but the is the time you where in case both futile bottles |

0:15:22 | a a of the same project so as as the difference between two field of it's much more information |

0:15:28 | if is the same effect |

0:15:30 | it it |

0:15:30 | well i but sure the trains and and |

0:15:33 | and that if i a few or but the a filter "'cause" |

0:15:37 | it it's a to try in but for a extra |

0:15:41 | the same for the second stage |

0:15:45 | if you uh but the less now assume that we can describe a core right "'cause" a model of that |

0:15:51 | does it cheap people for vacations for example i don't know how to this type right "'cause" the noise in |

0:15:56 | the velocity of the moving object |

0:15:58 | or or in in the next orange |

0:16:00 | if it had miss some and house in that noise disk action for the common few or and for that |

0:16:06 | if i have few problems set so out to be a |

0:16:09 | like you and so does a very well reproduceable reproducible result |

0:16:14 | the common field are instantly demonstrate like to scarf |

0:16:18 | kind of instability in the you |

0:16:20 | or or is that if i if i a few |

0:16:23 | is your in sensitive to noise |

0:16:26 | i you do not can use |

0:16:28 | not descriptions of okay |

0:16:31 | and this is uh a for all the time for case |

0:16:36 | several of those of prediction |

0:16:38 | if you |

0:16:40 | do the same for all the model of that this type of a champ of and so to do and |

0:16:45 | some time in |

0:16:47 | and compared prior to know was that in town sounds it is a common few problems that |

0:16:51 | i i i a few |

0:16:53 | a produce almost was the same prediction is that |

0:16:56 | but a small difference is that i i few for has a big |

0:17:00 | uh a we have a yeah or it for was for the at comparison of the red and black |

0:17:05 | i else |

0:17:06 | but if it means some |

0:17:08 | and and you know that uh a and is the matrix connection |

0:17:13 | is the common field or part was much like yeah O |

0:17:16 | especially in this case the became a a a a is a it in contrast to the will be |

0:17:25 | let's in use now seven our planners |

0:17:28 | it was a a a a a a while but also house and it again in a plane to a |

0:17:33 | few hours |

0:17:34 | as and so the it does this is to fess use of i have set seven out sliders here |

0:17:39 | uh a for one side to a a a a to all as the same |

0:17:44 | at the same |

0:17:45 | a a will the |

0:17:47 | real behaviour or down to real became so that's of how to feel or |

0:17:52 | or or X to the out of players |

0:17:55 | because a noise it make it in the description of the for the common few hours of covariance matrix as |

0:18:01 | i a realise is that how one field or game but a better watch it's cars |

0:18:05 | it but also the common like one that has a a fixed extent |

0:18:11 | and it a second stage the as a results more impressive there was almost no sensitivity in that F a |

0:18:17 | few or to i'll by so that X that the but to as a cup few you forced to produce |

0:18:22 | large |

0:18:23 | stuff |

0:18:25 | so so to uh what can we say a of the source so |

0:18:28 | the don't known like and by it if i i estimator and noise noise and initial the is really and |

0:18:34 | ice |

0:18:34 | two for the optimal estimation and denotes listen |

0:18:38 | and if H just for trick can state estimation and uh |

0:18:41 | in a a a for the control problem |

0:18:43 | the estimator i can i'll be O forms a common field or if |

0:18:48 | noise and initial and uses and not a on exactly so if you do not know noise and it if |

0:18:54 | you have problems and more descriptions that's |

0:18:57 | try to use this you are your realise that it can |

0:19:00 | provide a better result and the output |

0:19:03 | a a it was this system and measurement noise components need to be if you |

0:19:07 | if per out |

0:19:08 | so are several problems that you need to few for power |

0:19:12 | but was lost components form that uh state this model in this case that i five a few times more |

0:19:18 | a |

0:19:19 | my and the match to the models i'm never it in the non about phone |

0:19:23 | a data or our for just our noise invited and insist case again |

0:19:29 | averaging procedure is more open for a |

0:19:33 | and that models have ten probably and so |

0:19:37 | that a month of about and times to computation time required by |

0:19:43 | the iteration procedure but no |

0:19:46 | do not be necessary if you designs the field or in are little computer for every new point you just |

0:19:52 | need to provide in part |

0:19:54 | but the computation of the next for the next step |

0:19:57 | so that this model computers because a not is a problem |

0:20:01 | so that's all sent |

0:20:09 | a for this become |

0:20:19 | yeah |

0:20:20 | now it's some quite you to that you are do not use a minimal by sec |

0:20:27 | minimum Y |

0:20:28 | sense so it "'cause" i i'm by |

0:20:30 | you |

0:20:36 | yes |

0:20:39 | yes is this your there |

0:20:41 | as this field or is not great converse |

0:20:43 | it is a a a to she you are so it does it have i a structure finite impulse response |

0:20:49 | in each case we can no feedback |

0:20:58 | L |

0:21:01 | i can not included this is a consist presentation because of limited time but seven as the sort and and |

0:21:06 | you are descriptions that was that L |

0:21:09 | equation to cook to is that the the final as a a a a a a a it's its output |

0:21:14 | for it's still it not small |

0:21:16 | you can use the is a a as as we see my sense and the |

0:21:20 | uh the is that yeah this to |

0:21:23 | so but is it a comparison is a common to for house that sake of almost the same performance in |

0:21:28 | that i do or it could be a case |

0:21:30 | you can all have or in the about |

0:21:32 | about the model |

0:21:33 | absolute absolute have as and the to few course provides or was the same result |

0:21:41 | i is uh |

0:21:49 | and standard standard and once we speaker |

0:21:51 | in in in the is like |

0:21:53 | so we are talking remote featuring problem |

0:21:57 | given that the whole last |

0:22:00 | all data from that |

0:22:01 | from the in finding blast test at meeting and we and variance estimate uh |

0:22:06 | so you you've can lean to but you are feature in you know way that |

0:22:09 | not the whole plus testifying to don't top last |

0:22:13 | L |

0:22:13 | it's that tool there actually use a finite impulse response so it works is a finite number of the points |

0:22:19 | and the past not use as a bus |

0:22:21 | yeah that in contrast to the common to those it those |

0:22:24 | the infinity in |

0:22:26 | that that's that's what i am trying to get that |

0:22:29 | we can interpret your three get as a a |

0:22:32 | up to feature a minimum variance feature |

0:22:36 | given a if i a blast |

0:22:38 | not that in fine but |

0:22:40 | well that |

0:22:42 | is this presentation of leads to the and buys a finite impulse response you come like um C |

0:22:48 | so was and that's of a a a a few it just a more as a minimum mean square error |

0:22:54 | sense so so that |

0:22:55 | it just and was the same like a |

0:22:57 | the common few uh in the minimum |

0:22:59 | the likelihood function so |

0:23:02 | it is the same but a is this presentation leads to and buys a field |

0:23:07 | i know what you're want to come now |

0:23:09 | you can find and might be a a a a a what it takes time |

0:23:14 | but can say in the case of that up to a few of we need to solve a take equation |

0:23:18 | as |

0:23:21 | but i and the averaging horizon out |

0:23:23 | much larger numbers of support |

0:23:27 | more questions |

0:23:32 | hi |

0:23:32 | the i think it can be easily extended to nonlinear ten so as like extend colour of yeah if i |

0:23:39 | was yes exactly S of course you just must apply the standard extended kalman filter |

0:23:45 | uh approach to use a that and apply to a nonlinear problems not problem |

0:23:49 | at all |

0:23:55 | and more question |

0:23:59 | oh have you applied this to G P S |

0:24:01 | signal no real signals you were there any |

0:24:04 | well |

0:24:05 | my book is devoted to |

0:24:07 | G is base it up to model will F i a few or not clock models |

0:24:12 | i'm do and not this position and but to the beast actually time |

0:24:17 | for that actually times if few of them was designed to exactly and so and it a of it "'cause" |

0:24:22 | it your exits their structure "'cause" a more change of big patient so |

0:24:25 | is is so and so was a Q if you are exact in the gps S |

0:24:29 | and and you get gain in a significant gain when you like this filter of four |

0:24:33 | to one G S signals |

0:24:35 | no yeah for for gps signal sequence but for all time incident last but time |

0:24:39 | think my time was not position in |

0:24:41 | and you get any gain for that |

0:24:44 | significant gain over L |

0:24:46 | yeah where |

0:24:47 | what yes yes |

0:24:49 | yeah |

0:24:50 | originally we used to the common few form but as the problem is a common use the use problem |

0:24:56 | if you don't know noise correctly if it meet the arrows in the noise covariance matrix but the factor of |

0:25:03 | tools for |

0:25:04 | or or any ah a factor if you must fix a a a it's back for |

0:25:09 | a yeah |

0:25:10 | and i had just rows and how experiment are we |

0:25:13 | uh investigations of these applications would G P S so finally has started to find some new result and the |

0:25:19 | oh i that's is it |

0:25:22 | anymore more questions |

0:25:27 | so unfortunately the become the third presentation is missing |

0:25:30 | oh you are here are we just checked in and okay |