Speech Transcript - A KALMAN-LIKE ALGORITHM WITH NO REQUIREMENTS FOR NOISE AND INITIAL CONDITIONS

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

A KALMAN-LIKE ALGORITHM WITH NO REQUIREMENTS FOR NOISE AND INITIAL CONDITIONS

Target Detection and Localisation

Presented by: Yuriy Shmaliy, Author(s): Yuriy Shmaliy, Guanajuato University, Mexico