right

i

yeah

rubber that there's particle filtering for

we will have a description of a

what the competition

the main problem which is the

a news

a

for

part

and then

well let's part

and is used to be for problem

you have any fists right

is how for white

i at all

at then

em and or am decomposition is i up and they said a method for finalising on a station

and nonlinear signals

uh

that can be a that can be used for analysing on a station and nonlinear a signals such as easy

signal

so he can be decomposed as a mixtures not to and number of was selected waveforms forms called intrinsic mode

functions or i

so if you have like emd to a mixture signal on we we can have a a number of i

M F source of by the highest frequency to the low

to the look that's frequency

most times if if you first generated i S are noisy

because they contain the highest frequencies in the mixture signal

and because yeah an add up to

is that is that they that that might what we can use the sum of generated i M S in

order to construct the

and them it's just not

so yeah

if we can see that the i M F as the real part

it's you the transform at the complex part we can form an analytic signal using is on a takes signal

we can estimate the instantaneous amplitude and is thing instantaneous frequent this phase of the

i yeah

and because the mixture signal can be reconstructed using the sum of i F these i S are the real

part of these complex plot

so have uh the main problem the

uh the main problem is to estimate or tracked the east instantaneous phase

of all sedation or or or of and i am

so we can uh because the i'm if is noise scene if we consider these uh a question if the

i'm if is noisy these instantaneous amplitude and these

instantaneous phase is not the exact nine

so the E the the object to used to estimate the actual east an instantaneous amplitude and he's then you

a for me noisy i M it because if the i'm is a noisy these

parameters on not the exact i

here we try to use their of a lose the particle filtering you in order to

uh track the instantaneous phase and amplitude of and i i i M

uh the the idea is to extract these

in some as amplitude and phase and formulated in the is that the space of the part get field day

uh we we need to define the a state transition function and the observation function the vision function is simple

because we can their the mixture signal the observation and those the vision function

can be of using this formulation

because this is the sum of i on the sum of i S can be a using these a question

and

these value of errors are for in the S it this space the main problem is to

that term mean or are obtained the it's state transition function which is not

and easy

problem

pro

we can the like less part to get free in order to reform form that the problem them to use

the size of the it's data space

row but i colours particle filtering are extension of part to get thing that can be applied to

conditionally linear

a state value of a so if we partition a state is into linear part and nonlinear part we can

estimate the

you linear one using the con feeding and we can estimate the nonlinear for using particle filtering so you we

like all but part to get free any

we the rate use number of particles are required in order to estimate the

a state of the system because the linear parties taken out an estimated by common fig

so here we really is are proper them this is the observation and this is the observation function

we can take the um to use instantaneous amplitudes uh uh out and form a big or

this vector has a linear relation to to the mixture signal so these signal can be estimated by on free

data

and then this is the vector or of the them

yeah of these there and the nonlinear linear S by are instantaneous phase

so it is in san then it's phase are the non linear uh part of the problem so we need

to use part to give any in order to estimate these value bits can i'm filter use used to estimate

this of bits

so the

that's state this space size is a rate used to estimate this

again the main problem used to define the state transition function

so because um the main as state by a bizarre in then use phase

we need to define a a a a state transition

phase

a a transition

this is not that use the yeah this this can what

we obtain easy because and the phase transition function

it is a complex function in it cannot be you know model for example using a simple first-order order be

an for example for

instantaneous amplitude you

we can use a first-order markov be amp says and then uh we can track the instantaneous amplitude but for

instantaneous phase as you be seen lay later the slide

the instantaneous phase actress different time points sees and

for example is an increasing from minus pi to paul i and then this

face face then change

so these channel changing the face sign

makes is

phase transition function very complex we can not have a simple function in order to

tear and the phase transition function

so we formulate the problem of tracking instantaneous amplitude and phase using i M F and E M Ds

we formulate a everything but that should used to determine the

phase transition

function which is a no

it's very calm

combine

and

we can uh

if we have a

a face we and

obtain the in the frequencies the frequencies can be of ten using the differentiation of the face so the instantaneous

frequency can be obtained by differentiation of in as fate

for a and scenes and i M if he's and all still a form in M narrowband frequency range

the

instantaneous frequency

i close uh different time points are a small for example

i because i i am of

belongs to a a a a specific narrowband frequency range

so we expect that the instantaneous frequency

is a teen a a specific narrowband frequency range as that

so we can use these information of the instantaneous frequency and try to include the information of instantaneous frequency in

that the into the related particle filter

so but using these team formation

but using the information of the frequencies we can try to estimate the instantaneous fig

so the objective is to

uh track the instantaneous phase while at the same time try to a what the frequency traces

because when and i am if is noisy and we estimate the instantaneous

and the frequency we can see that the

instantaneous frequency frequency's not to in a specific

frequency band for example there is a sudden change in the in N as frequency at it goes on the

frequency range

so we can use this information these this assumption that for an oscillation or for and

oh yeah may have the in and it's frequency should be a small

median in a specific narrowband frequency range

so we use the additional information of instantaneous frequency try to

include these at the on information in to the out into their out formulated a but i as particle filtering

and try to estimate the instantaneous phase

in the

now in in this work we first try to use only one on them if they or later can be

extended for different number of uh a i for for example

in face tracking of all of the i M F at the same time but uh for this work we

one you see consider one T one i if the observation is only one i F which is a noisy

this is the observation noise

this is the observation function is simply

and it can be a ten using these them considering the instantaneous amplitude and instantaneous phase using the hilbert transform

and then this is the yeah a state transition function this very bizarre amplitude and phase of one i you

may have one noisy i'm

is in something as amplitude is estimated using con um filtering and this should be

estimated using part if we can but as far as we don't have access to the

instantaneous phase transition function we need to use the information of in and it's frequency in order to

you how we can estimate the instantaneous

this is there uh sort do code of the uh

in some as face tracking uh the main objective is to

first first in this for used to estimate the in and frequency the K S

is to

uh estimate the phase actress different time points but we also estimate the um

but for amplitudes we only use

first the markovian process in order to

yeah in order to to find a a state transition what for phase as i said in the previous the

slide is a complex function we cannot

simply really use the more cold first order of you know for some but the face on a you change

so there are some but part to get initialisation in this that's the

and then uh

a a for example when we want to estimate the it's state the phase

is that it's phase at each time point

we generate two faces

one he's are ten by the positive of the phase in the previous time point plus a the of motion

noise

one is up from the negative

of the phase in the previous part time point process a

a coach and white noise

so we generated two face in order to select between these two of phase

we need to estimate the instantaneous frequency and try to see that each one of these phase

tries to S smooth the instantaneous frequency meeting and narrowband frequency range

so

we also have one very but as the frequency

and then we estimate this value but

and we used use this a frequency by but comparing and and then we compare these uh a value but

that's is a from the estimated frequency the previous time

we compared to the frequency that it all that is a by each of considering in each of these phase

and then we try to

yeah i use these information of the frequency

and then include it as the weight as some of uh as a B

in order to all the weight of the particle filtering

but the

um when we try to use them

but we implemented the at what that is

this to look what was not uh working in and was not working in initial

because

there is the situation for example the phase transition is around zero

but the face transition is around zero so then T

and because we use the hilbert transform diff in some as frequency becomes negative it becomes part the positive and

backs to the

a a a a a specific frequency range that the i M F B don't

so because is

and

uh these estimated frequency becomes negative is that because of the noise is because the phase transition is around zero

is a special case

in ours

i'll go it we try to detect take this situation

but the estimated instantaneous frequency is

out of the frequency range but is not to to the noise or because of wrong estimation of the face

from the positive or negative is because of phase transition around zero

we detect take these situation so we use

to to you as in order to update the weight of the particle

and then at the if we have a uh some embedded part gets for example if the estimated phase is

bigger than a i or less and minus by

we set the weight of the invalid part can to zero in order not to have any contribution

for the estimation of a state of the since

or if they it it's an estimated in estimated as frequency

is um

large and then the maximum

frequency of a a a specific

but and that there are i M F don't

we set the way to zero or if they estimate the once is a lower than the minimum frequency

but the i mess and we as

and we said the eight

to weight of the part "'cause" to zero

so we remove that you body part because

so the important issue in in in this

yeah in this to the so look what is that and because we can not seem really

uh i have a

function for phase transition we need to generate two phases one is from

positive for face in then they get in the previous type point one is from negative of the in the

previous i'm one

then using the information of frequency

we try to select between

these two face also because

we try to a mode the frequency traces actress different time points

we we somehow hall

a can the and really we somehow try to do noise the that it because for a noisy i'm F

to estimated instantaneous frequency P on the frequency

and also the for the is the a situation when the phase transition is a around zero we try to

change are value

we apply the at to set

a two sets of simulated data or we generated for amplitude and frequency modulated sine wave we added a quotient

wave not white noise

the signals resolution is calculated using this formulation nation

we can see that two snr levels tree and seven

we estimate the instantaneous frequency using our proposed metal it also use the hilbert but transform of the noisy the

i'm if and it is clear that in both the set of it are method

uh oh or out forms the

in then is frequent

it the hilbert trance

so this is one

uh illustration for estimation of instantaneous phase

the actual in something that's phase is that the act one

and the for the noise is there red one the results of the tracking is a dot line

so

and you can see that uh for tracking we have a better estimation

and you can see here for example the face signed so then change

are i'll quickly takes these situation and here

the phase transition is around zero

so the estimated instantaneous frequency in these part should be negative but this is not to to the not because

of these transition

and then a are it can and attracting sent in both snr level is better than the you but

this is the result of tracking instantaneous um P pretty to you

and the this is in some then news freak estimate these i in set is frequency the phase transition around

zero or this is the

but i one is the actual one

becomes negative but is is that because of noise because of the phase transition on zero

it's still our method can it's what the frequency traces the noisy i am F

is the rest one this and

frequency

so

we try to keep the instantaneous frequency in and narrow frequency band range

and then

a we applied the all into the real eight are we can see there's a reach an and

and then we estimate the incense and phase um pretty two

and the this is the uh a smoothing results in frequency domain

so the

does line is the in sentence

a a frequency tracking or is sporting using a rubber close but can fit the noisy i M F

frequencies this

so we propose a new face tracking system that uses both em the N L but i close but get

printing the idea is to this what frequency traces

and uh also use some if then has rules be at that some concern to the rubber like this party

of fitting formulation

we try to do you know is that i am if at the same time

attracting tracking the nist face

and uh a here later the problem and the method can be a you can be extended more in order

to solve them all what makes mixing problem of the em this should be a exploited in another is there's

and

and the metal has application to and

speech and has been also for

phase a

for

basic synchronization of each just signal in different frequency band M on different region the method can be

initial if we use only part to give we the number of

a a a a a state

a value as is high yeah but we partition the to very busy

a linear non not being about

uh so if we use a a use number of a state value as

so that required number of part to get it should be low but

but

for one i am F because the S state only contains one phase

so i i can see that at ten a on ten thousand part get

yes because uh uh is because we use some a con constraint in that all but i close party think

we need to

have a number of a higher number of party in order to be like the the

estimate the

a a

but if use several i am and

so and and you have several and nonlinear possible of all phases

we need to decrease the increase the number of a part

it is a the some some minor problems with the part you're thinking is that

a the number of for to gets

in some cases should be high

you know it have it like that

propose a i used a pair you that's T

so are used for a period then as the proposal density so

uh the the rate can be up billy really using their weights

in the previous time point multiplied by the likelihood function