Speech Transcript - DESTINATION-AWARE TARGET TRACKING VIA SYNTACTIC SIGNAL PROCESSING.

0:00:14	so my name is the current crush them more the and i'm presenting the top michael orders uh
0:00:19	my graduate student was stuff a and also line white to in the audience you lying is from the you
0:00:24	is your badly
0:00:26	uh so just to kind of give you a pictorial
0:00:29	description of what the problem is it's kind of nice to start with something artistic so uh
0:00:34	this is a main idea
0:00:36	we are looking at
0:00:38	eight basic scenario where you're trying to track a moving target so
0:00:54	signal processing that B
0:00:56	the silly in papers where what you do is you do some sort of bayesian estimate of the state of
0:01:01	the top given noisy measurements
0:01:03	uh and of kind of written that abstractly
0:01:16	once you have those track estimates
0:01:18	typically you have some he wouldn't being looking at a
0:01:21	television screen and saying okay this it
0:01:24	is doing something interesting
0:01:26	well this start it is not doing something interest
0:01:29	what we wanna do is all to mate that high level
0:01:32	that's why we call this metalevel tracking so
0:01:34	in other words
0:01:46	no i i had to have a project a a a a a thing
0:01:49	the red button you
0:01:50	so the idea is given these dot
0:01:54	how do you joint the essential
0:01:57	can you tell from these dots what sort trajectory the talk it's gonna do
0:02:01	and
0:02:02	do this in a page and sense to some sort of non than you filter
0:02:05	estimate the trajectory
0:02:07	so this is to automate
0:02:09	several possible toss which are of interest
0:02:11	for example you might have a target
0:02:14	which you interested in which goes to a check point of fills up fuel goes to another point and then
0:02:19	a final this
0:02:21	um are only interested in targets which go to this trajectory go to those but specific point
0:02:27	how can i we construct
0:02:28	an estimate of such a project
0:02:30	you know patience and
0:02:32	so this kind of bills on a a legacy tracker
0:02:36	and a goal is to see how could be construct good models to this
0:02:40	and once you do construct a good model how can you actually can L
0:02:45	so uh just to give you a further example of this this is a typical example which kind of motivated
0:02:50	by we did some of this research
0:02:52	so this could be maybe somewhere in a city where a
0:02:57	typically traffic
0:02:59	road traffic goes like this
0:03:00	donna role
0:03:02	and then some day
0:03:04	do you to maybe the local people knowing that i have something was deployed in the role maybe and i
0:03:08	i D use something
0:03:10	you see a lot of traffic
0:03:12	by pass a particle part of the road
0:03:15	so probably a track see all the dots done with people by past the that
0:03:19	so previous so you're going the straight line
0:03:21	now you kind of died reading and then going back
0:03:25	how could you actually construct some like to classify for that
0:03:29	given given the do
0:03:32	so all an obvious way of more like this would be that
0:03:35	in some sense i'm deviating
0:03:37	some amount
0:03:38	X
0:03:38	from the road
0:03:40	and then a coming back but a same amount
0:03:42	now that a more X could be variable a baby got all the way here are then going back
0:03:46	so we need a model which is scale invariant
0:03:48	which allows you to go in a particular dimension probably a random number of step
0:03:53	and then you need to remember that that a number of steps to come back and we model construct a
0:03:57	model which does that
0:03:59	it's kind of obvious that a standard finite state markov chain cannot do that
0:04:03	is a markov chain cannot embed them E which is
0:04:06	variable in it
0:04:07	i mean of course you can construct a state space which is a maximal possible size
0:04:11	that's ridiculous because a of possible that's very here
0:04:13	so it sort of possible use
0:04:15	station
0:04:15	so we need something smarter than a markov chain
0:04:18	so uh the that's that's basically the idea of what we gonna talk about
0:04:21	so you can think from an abstract point of view this is a special case of a trajectory which we
0:04:26	call it a
0:04:27	where you deviation away from it is equal to the deviation to words that
0:04:31	and this D V A should could be around random
0:04:33	what to do
0:04:34	so could be anything
0:04:35	another example could be top which just circling the building so for example a to be something suspicious build themselves
0:04:41	up or whatever
0:04:42	so
0:04:43	can you tell from a bunch of don't
0:04:45	isolate only those trajectories
0:04:48	where talk it's something a building
0:04:49	for example going a rectangle
0:04:52	uh a or for example maybe be power just going straight fine to be known
0:04:55	so how do you isolate different trajectories you using some sort of nonlinear filtering operation um
0:05:04	okay so i just just a kind of again reinforce the idea that
0:05:08	in conventional talk tracking which i guess to lots of papers and signal processing it's so one
0:05:12	the main idea you construct a steak space model for the trajectory of the top
0:05:17	that's fantastic if you're doing very short ranges over time because you can approximate things by random walks
0:05:24	but over long periods of time the drivers not a random block
0:05:27	he has a well defined destination
0:05:29	and they typically going through for example
0:05:32	a street man
0:05:33	a digital that for example which you could we construct google
0:05:36	or whatever
0:05:37	so how do you construct
0:05:39	an efficient model which can do that and then the questions how can you estimate that
0:05:43	so the main idea the talk is we we dealing with a particular class of models which are called stochastic
0:05:48	context free grammars
0:05:49	and maybe is useful to start with this picture the border
0:05:52	so if you if you did a elementary course and radical computer science
0:05:55	you would see that a markov chain
0:05:58	or for like to go to state space models
0:06:00	are
0:06:00	regular grammars
0:06:02	they assume that what happens now depends probabilistic lee
0:06:06	on what happened at the previous time point
0:06:09	it's not true would most complicated trajectories because if you're gonna go in a square
0:06:14	you have a long range dependency because you're starting and ending point of the simple
0:06:18	that's not my
0:06:19	so
0:06:20	in in computer science there is this more general model call eight context free grammar
0:06:25	which is a level of abstraction we gonna talk about today
0:06:28	where
0:06:29	you can actually construct
0:06:31	several very interesting
0:06:33	trajectories
0:06:34	which are non that of you
0:06:35	such as rectangles all since a
0:06:38	a but size which but you can prove
0:06:40	a markov chain cannot
0:06:42	we can write and talk about the
0:06:45	now of course there are even more general language
0:06:47	such as context-sensitive grammars
0:06:49	but there are no use to was because they do not have all real time out
0:06:53	some things not all of the you know it's not
0:06:56	from an engineering point of view
0:06:57	useful and that there are restricted was just like one i'm talking about
0:07:01	it's kind of a while english so speak
0:07:03	so typically regular is
0:07:06	mark or V a know the sort of stuff everybody does
0:07:08	what we're trying to do here something a slight generalisation of the context free
0:07:12	me
0:07:14	so this is called a chomsky hierarchy a formal language that and our goal is to see can one constructs
0:07:19	the equivalent filters such as a kalman filter or the hidden markov model filter so one
0:07:24	in this domain where you have long range dependence
0:07:27	okay not a can be a little bit more insight
0:07:30	now you might say why is this of any use and i want give you some more insight as to
0:07:34	why this is of use
0:07:36	for starts this is a very convenient model for human operators
0:07:40	you can imagine that
0:07:42	in ideally only what happens is off to the tracker operates and as a should in the first slide we
0:07:47	trying to build something on top of that
0:07:49	which helps to human
0:07:51	automate to the process of detecting if something doing
0:07:54	something interest
0:07:55	now it's pretty hard to teach the average soldier probability theory and detection it's so on and make them understand
0:08:01	how to construct a bayesian estimate
0:08:03	if you can automate that process by allowing the average soldier just to estimate
0:08:08	to put in
0:08:09	uh_huh
0:08:10	metalevel is that if a target is doing something it's a species
0:08:13	if is not doing something not speech
0:08:15	so essentially actually you can quantify these rules
0:08:19	in two
0:08:19	fairly interesting types
0:08:21	of of production rules what you call be size
0:08:24	and you can check the consistency of those by a compiler which which are long describe here but it's pretty
0:08:28	easy to do
0:08:29	second point is once you do that
0:08:32	just like a regular grammars in the context free grammar domain main you have
0:08:36	polynomial out
0:08:38	a estimation
0:08:39	a lot of this work is really been motivated by recent research should by all informatics
0:08:44	where you also have long range dependencies
0:08:46	and i want to give you some insight as to what i mean
0:08:48	so this is a typical buyer informatics type example this is
0:08:51	a protein which coils
0:08:54	or a given thing D N A which is a you can declare nuclear tag sequence which also close like
0:08:58	this now the dependencies you're a spatial so this guy here depends a lot of disk Q even though it's
0:09:03	pretty far we you will always call
0:09:06	rather than have a linear depends
0:09:08	okay so mark of in type processes can not more the sort of dependency with this guy
0:09:12	is spatially very close to you
0:09:14	long
0:09:16	another example
0:09:17	think of a computer language
0:09:18	this is a a complete or experiment it's not it's not a actual useful thing but it's it's a nice
0:09:22	thought experiment
0:09:23	suppose to take
0:09:24	something like a computer language like C your back to that
0:09:28	have a big in if
0:09:30	and then i have a lot of stuff and then at the end
0:09:32	if a computer language was marked for the and then at have a a and if
0:09:35	with a high probability you be B up for beginners
0:09:38	although an actual computer language you have a lot of stuff
0:09:41	so now you can think of the core experiment
0:09:42	suppose i think this computer language
0:09:45	this code and a corrupted by noise
0:09:47	how that we can
0:09:48	now i can't use a markov chain because this is not
0:09:52	representation
0:09:53	so that's another example
0:09:55	i
0:09:56	so the ball is how can you construct a useful things here
0:09:59	and the point is
0:10:00	they should be scale invariant you C
0:10:02	all of these are the structure it scale in it's i have a big in if i can have a
0:10:06	lot of junk could between and nine is but me and
0:10:08	so the size of how much stuff is in between
0:10:11	should not matter for the context of the a
0:10:14	so that's that's something which we want as well
0:10:16	now it turns out that
0:10:17	for such that the models people are shown i'm not to give you any right studies here
0:10:22	that
0:10:22	in terms of entropy
0:10:24	these context free grammars
0:10:26	do fantastic stick that is
0:10:28	for a equal size parameterization of a model
0:10:32	if we look at the
0:10:33	predicted entropy
0:10:35	these are extremely efficient models when you have to sort of scale and
0:10:39	okay so let's not jump in
0:10:41	the actual types of trajectories we want talk about
0:10:44	so this is the first trajectory a random walk which is simply
0:10:48	a good role of chain which you do was state space
0:10:51	this is a widely used
0:10:53	it target tracking but as i said it's pretty useless because no drivers a drunk or simply flips a point
0:10:57	it is that's but gonna drive
0:10:59	they got go in a directed we from a to B
0:11:01	a much more sophisticated model which michael a line white is that's a pretty cool work alone
0:11:05	is very you know the beginning and you don't the and
0:11:09	and you want an so it's called the reciprocal process are a lot of you bridge which is a generalisation
0:11:13	of a brownian bridge so you clap the two and but you start this
0:11:18	definition as random pass
0:11:19	and then you construct
0:11:21	a dependency but each point now depends so the next point at the previous one
0:11:24	to this is a one dimensional model round fee
0:11:27	and that's called them up with you
0:11:29	now you can think of a much more generalisation of that we is a stochastic context free grammar
0:11:33	so rather than have
0:11:35	i start from a a
0:11:36	and i'm restrict to reach time be at a fixed future time
0:11:41	i now want to go through particular weight points these could be for example a ones
0:11:45	so i one like topic to go from a to C to be
0:11:49	and in between to you i'll i'll a we project
0:11:53	how can a now if uh
0:11:55	given this sort of model
0:11:56	construct from noisy estimates
0:11:58	the actual trajectory that would be a question once
0:12:01	so here are examples of cases where you can not fit simple markov change
0:12:06	so i the said one of them is an out
0:12:08	so if i goal in this direction a four and point
0:12:12	and then and and the tree number of points to this direction B
0:12:15	and then come back
0:12:16	see for and points
0:12:18	you can prove
0:12:19	by something colour pumping level like computer signs that
0:12:21	such a string
0:12:23	when you have and As
0:12:25	a bunch of bees and then and sees were and is a battery
0:12:28	can not exclusive we generated by a markov process it's a possible you can do that you can actually she
0:12:33	for like four
0:12:34	so a rectangle
0:12:36	so suppose i when equal number of points year then here than equal number of points and the backward
0:12:41	such a close trajectory can not be generate by
0:12:44	the intuition is that a markov chain cannot store memory in
0:12:47	it's got a markov chain is simply a regular automata
0:12:50	to store memory you need something called push down stack you have to store stuff and you put that out
0:12:55	of the stack
0:12:56	and that's a lot of
0:12:58	so anyway so these are kind of
0:13:00	but a things i don't just one a very quickly give you a a uh some inside
0:13:05	as to how this differs from a standard construction of a
0:13:08	hidden markov model which is
0:13:10	what you typically do
0:13:12	when you deal that are tracked
0:13:13	a little
0:13:15	so most if you would know what a hidden markov model or a probabilistic model of them are uh functional
0:13:19	markov chain
0:13:21	we start with the transition matrix so this is an underlying markov chain
0:13:25	which of evolves over time
0:13:27	and we observe the markov chain
0:13:29	it also to alphabet you a and B
0:13:31	well these are the probabilities of the observation a given state one
0:13:35	these are the probabilities of the observation a given state doing so so this is you parameterize it to do
0:13:41	um now
0:13:42	you can as right this in in the type of rules we wanted to do to express a context free
0:13:46	grammar and the next page
0:13:47	by simply saying that we have a bunch of terminals which uh what you'll to
0:13:52	and a bunch of non terminals which are state
0:13:55	okay
0:13:55	and essentially actually you can qualify all these in to rules that if i scott
0:13:59	from some starting state S one
0:14:01	then i generate
0:14:02	a a and remain S one it probably point five for and that's pretty clear is the i-th eight point
0:14:06	nine mike transition matrix of boy from S one to S one
0:14:09	and not blah but the probably a generate eight point nine ten point six point five and i can do
0:14:13	this for all possibilities and this is be the production rules
0:14:16	the drama which can generate any string which is mark of view
0:14:20	this is how a re
0:14:22	and then i simply start for example a S one
0:14:25	i use a real i S one piece me a S two with some probably point to just my simulation
0:14:29	i keep generating and what you see here is the markov chain grows
0:14:33	on a bayesian network from left to right
0:14:36	dependencies is just
0:14:37	one
0:14:38	this is trivial this is well known
0:14:40	now we let me give you some insight to the stochastic to three gram
0:14:43	so here are the same rules as what we and the previous page
0:14:46	the only difference
0:14:48	is this last rule
0:14:49	what you see here is that we have
0:14:52	a not want term at
0:14:53	a state if you like
0:14:55	which maps
0:14:56	not just to another stadium but
0:14:58	a bunch of state
0:15:00	and this is the key difference you see when you have a context free grammar the chomsky
0:15:05	sort of hierarchy of languages tells you that
0:15:07	any time you map from a nonterminal on one side
0:15:10	to a terminal and
0:15:12	multiple non terminals
0:15:14	such as a language the string can not be model by a markov G
0:15:19	now this is
0:15:20	oh wait so this ground or would generate and we compute a language you know such as C
0:15:25	for of whatever the all examples
0:15:27	of things we set for the strong
0:15:29	of course this is a probabilistic version because we log probabilities but things
0:15:33	the big a generalisation of course which we want consider here is context sensitive
0:15:37	in context sensitive you have a
0:15:39	eight
0:15:40	terminal followed by a non little which maps of the right and say that would be the context
0:15:44	this don't to
0:15:46	anyway so this is how you would generate
0:15:48	using these rules uh a stochastic context free grammars string
0:15:51	and what you know here is
0:15:53	the recursive embedding it doesn't just left to right but it grows inside out
0:15:57	so it other words
0:15:58	you see this a and this at
0:16:01	get further and further away and yet they depend on each other
0:16:04	C is long range dependence
0:16:06	which which can a picture
0:16:09	this is
0:16:09	in very simple terms
0:16:11	how you generate a stochastic context free grammar
0:16:13	now to some mathematics
0:16:14	so everything here so far been pictorial next one X three
0:16:17	so
0:16:18	how would you that he model this in terms of and
0:16:20	or stochastic process well these are actually special types of branching process
0:16:25	that multi type gal and what's and branching process
0:16:28	where the order of the caff the bottom process better
0:16:32	so you can view this is saying roughly speaking that each realise a should is a
0:16:36	three
0:16:37	or a patient at
0:16:38	so each realise asian is a patient
0:16:40	so every time we realise it
0:16:42	you have different patient
0:16:44	just like for
0:16:45	state space models you have a realisation T this case the call chomsky don't forms and so one
0:16:50	and to prove that i have a string and it does not belong to a particular language
0:16:55	there are well defined rooms which are called pumping that
0:16:58	which can like to show that
0:17:00	okay now i i guess wanna give you some more insight as a how you can process these sort of
0:17:04	strings
0:17:04	so i have a spring i have a bunch of observations which are noisy i want it's a is this
0:17:09	target gotta go has gone in a straight line has to go on and then all has gone in a
0:17:13	circle
0:17:15	these a context free grammar type things which cannot be recognized by a markov chain
0:17:18	what sort of out sums of it'll
0:17:20	well you know the are or in case
0:17:22	there are standard filters like a hidden markov model filter which is analogous to a kalman filter
0:17:27	if we want to do so a poster sequence estimate the the viterbi out
0:17:31	it's so
0:17:32	i you want to estimate the parameters that things like the so like to estimation by the expectation maximization
0:17:38	it turns out
0:17:38	all these things generalized to the stochastic context free grammar to me
0:17:42	so just like you have a forward-backward filter
0:17:44	in a stochastic context free grammar because you of on a parse tree
0:17:48	you have something called the inside outside help with
0:17:52	just like you have the viterbi algorithm in the stochastic context free grammar case you have you do the cook
0:17:57	younger "'cause" sound out the model only two parts
0:18:00	which which do
0:18:02	so
0:18:02	essentially what you have done is you of generalized the role or the evolution of a random process
0:18:08	on a straight line
0:18:10	to something which of balls on a tree now and that's that's basically that the i Q where eventually the
0:18:15	tree has long which dependencies because it start from a common
0:18:18	okay so that's uh
0:18:20	get get so this is a then your hmm the the
0:18:23	pitch a network
0:18:24	and
0:18:25	this is
0:18:26	for example stochastic comes to grab but this is called the parse tree
0:18:30	okay K and has that all these algorithms have polynomial only complexity what you lose is
0:18:34	typically for a
0:18:36	hmm or any type of mark of via process when you do
0:18:40	filtering
0:18:41	the complexity
0:18:43	of going through T points of data is then you're T
0:18:47	a common filter of your processing a million points requires a million
0:18:50	time to state space
0:18:51	in this case for a stochastic on is free grammars actually cubic peak the like the day but it still
0:18:55	or no
0:18:56	it's Q
0:18:58	okay
0:18:58	so uh here is a example of of some rules which are just distorted you bit more be killed the
0:19:03	paper give the out with them simulations and so on
0:19:05	so here is a sort of
0:19:07	flow of traffic in normal life
0:19:10	at this is actually a fight of the google that what of the things you can do very nice use
0:19:13	you can actually qualify
0:19:15	different maps digital maps in constraints in used to go
0:19:21	so you you have talk at just go in a straight line or a bunch of targets maybe be today
0:19:25	and then to you notice that
0:19:26	some that like this people are deviating from
0:19:29	how would you all to make that how you come up the bayesian inference that
0:19:32	something funny was going on you the people of changes
0:19:35	so you would qualify
0:19:36	the rule that people have on
0:19:38	equal amounts away and come back to the rule by equal
0:19:42	which is at a
0:19:43	and this sum the go by is a random amount
0:19:46	so you a fixed but you have a memory which is variable
0:19:49	and that cannot be and coded is
0:19:51	markov of G
0:19:52	and of course you measuring these a noise was of a noisy sensor
0:19:55	you can construct a grammatical and so this fairly easily terms of production rules
0:19:59	once you do that
0:20:00	you can construct an optimal filter
0:20:02	which gives it the optimal estimate of what's what's going on
0:20:06	so
0:20:07	i in the time available of course that can the find to how you derive still does but they given
0:20:11	in the paper and also the reference here
0:20:13	so i just one a kind of conclude with some some of the main points
0:20:16	what i want say here
0:20:18	so the first point is that these syntactic models which are constructed
0:20:22	context free grammar model
0:20:23	a a to really look at a complex
0:20:26	trajectories of targets
0:20:28	which can not be dealt with it the markovian work
0:20:31	there are several classes of trajectories which you can prove
0:20:35	can not be generated by a markov process
0:20:37	and
0:20:38	so i in some sense this allows us to go into a slightly more general class
0:20:43	these are meant to replace the human operator who sits and looks at track lit
0:20:48	coming out of a track or you wanna automate that for
0:20:51	the second point is that these algorithms of polynomial complexity so the practical
0:20:56	just like in
0:20:57	for a state space model you call that filtering she you would call that a parsing out
0:21:01	because you really constructing a parse S
0:21:05	uh in many cases you can view this is a human sensor interface because there's been a lot of work
0:21:09	done in the actual sense signal processing
0:21:13	how can i or to made the process of using that
0:21:15	estimate from the sensor level
0:21:17	to something which helps if you mean
0:21:20	determine a something's happen
0:21:21	that's really what we're talking about you
0:21:23	is the human sensor interface also known as middle where
0:21:27	there's a very interesting system you ready issues which i haven't even mentioned you
0:21:30	okay so the first thing is if we have a parse tree which keeps generating these non terminal to eventually
0:21:35	stops
0:21:36	of course you need the eventual length of you string to be fine i
0:21:40	so how do you and sure that's the case
0:21:42	those that stability issues he's a course some pretty cool than what's of processes
0:21:46	and essentially you need to spectral norm a particular matrix vol be the probabilities to be less and one
0:21:51	there are also constraint
0:21:54	if you know that a the target gonna and up at some particular location
0:21:57	how do you constrain the probabilities in your mobile so that
0:22:02	so that you model actually ends up there
0:22:04	piece so those are also pretty interesting problem
0:22:07	fine are several unresolved issues and this problem as i said much of the detail as been developed in the
0:22:12	by informatics that are only the last ten fifteen years
0:22:15	and
0:22:17	things like how sensitive is your beige an estimator to prior
0:22:22	does it for get you initialization geometrically fast which just to for example the kalman filter so
0:22:26	these are unresolved issues
0:22:29	so in time sort of that picture there's been a lot of work done research in this area are just
0:22:33	given you a couple of
0:22:34	references here
0:22:35	uh and we also use this quite a bit not only to model trajectories but also to model
0:22:41	for example radars
0:22:42	complex sensors are not markovian because they
0:22:46	they have feedback structure with the them and and really you can you
0:22:50	the
0:22:51	oh put of a complex sequence of sensors as a grammatical more
0:22:55	and so essentially the idea is
0:22:58	by doing that you can apply
0:23:00	patient signal processing to come up with
0:23:03	so that's really all the one C thank you
0:23:09	five questions to me
0:23:11	that
0:23:12	you're all we should really be asking questions
0:23:17	um can you go back to your original picture at the beginning where you had the
0:23:22	the uh
0:23:22	legacy tracker and
0:23:31	oh
0:23:32	yeah uh yeah right so
0:23:34	you have here
0:23:35	um the
0:23:37	try what's coming into the middle level of and you have a portable and saying feedback
0:23:42	uh
0:23:43	can you call in a or
0:23:45	so one additional point did mention is now suppose you can infer that talk it is actually gonna in a
0:23:50	rectangle
0:23:51	you can use that information to help you track at the lower that
0:23:54	which you low level tracker does on know that you low level tracker simply assuming a top it's sit down
0:23:58	target
0:23:59	flipping a point deciding where it's still
0:24:01	a if you had this high level infers that you know what's gonna make a right to
0:24:04	or if you look at the global maps and you figure out the constraint that the role only you can
0:24:08	go left or right any can't go right out of the role
0:24:11	you can of course utilise information to
0:24:13	to improve you estimates and and that's that's really good
0:24:16	that
0:24:16	i did mention that you're so of course as a feedback structure where you can use that to
0:24:20	proof proof you
0:24:25	yeah
0:24:31	uh could you please one tell the differences between a stochastic context free grammar and the mark of tree as
0:24:37	a small doing and in is can a good point
0:24:40	okay so the idea here is
0:24:43	we're looking at a actually a a a probably go to that little picture which are
0:24:49	okay so
0:24:51	this would be a standard finite state markov chain which is kind of a
0:24:55	this is our parse tree which is really and count and what's and branching process so i start with
0:25:01	a bunch of parents they have children they actually not children and so on and it keeps scrolling
0:25:05	but the point is the order of the chill the name of the children matters in a standard multi think
0:25:09	type gas the what's process you only K they have three kids of for kids
0:25:13	here the name of the matter because they can wait different trajectories
0:25:16	eventually
0:25:18	all these children stop and that's your all of that the the thing you read and you meet a from
0:25:22	that to right and that's for example that all or some sort of straw
0:25:26	so that's the multi type gas and what's some process we considering here
0:25:29	so it's really a a realisation of for tree whose size
0:25:34	is not a you know
0:25:36	you could only
0:25:37	more the expectation of that
0:25:38	you to come up with the as of that and and so
0:25:49	okay well are out of time thank very much we go to the next speaker or no

DESTINATION-AWARE TARGET TRACKING VIA SYNTACTIC SIGNAL PROCESSING.

Classification and Pattern Recognition

Presented by: Vikram Krishnamurthy, Author(s): Mustafa Fanaswala, Vikram Krishnamurthy, University of British Columbia, Canada; Langford White, The University of Adelaide, Australia