0:00:18rubber that there's particle filtering for
0:00:21we will have a description of a
0:00:23what the competition
0:00:25the main problem which is the
0:00:27a news
0:00:30and then
0:00:31well let's part
0:00:32and is used to be for problem
0:00:35you have any fists right
0:00:36is how for white
0:00:38i at all
0:00:39at then
0:00:42em and or am decomposition is i up and they said a method for finalising on a station
0:00:48and nonlinear signals
0:00:51that can be a that can be used for analysing on a station and nonlinear a signals such as easy
0:00:56so he can be decomposed as a mixtures not to and number of was selected waveforms forms called intrinsic mode
0:01:03functions or i
0:01:05so if you have like emd to a mixture signal on we we can have a a number of i
0:01:09M F source of by the highest frequency to the low
0:01:12to the look that's frequency
0:01:14most times if if you first generated i S are noisy
0:01:17because they contain the highest frequencies in the mixture signal
0:01:22and because yeah an add up to
0:01:24is that is that they that that might what we can use the sum of generated i M S in
0:01:28order to construct the
0:01:30and them it's just not
0:01:35so yeah
0:01:36if we can see that the i M F as the real part
0:01:39it's you the transform at the complex part we can form an analytic signal using is on a takes signal
0:01:45we can estimate the instantaneous amplitude and is thing instantaneous frequent this phase of the
0:01:50i yeah
0:01:52and because the mixture signal can be reconstructed using the sum of i F these i S are the real
0:01:57part of these complex plot
0:02:00so have uh the main problem the
0:02:02uh the main problem is to estimate or tracked the east instantaneous phase
0:02:07of all sedation or or or of and i am
0:02:10so we can uh because the i'm if is noise scene if we consider these uh a question if the
0:02:15i'm if is noisy these instantaneous amplitude and these
0:02:18instantaneous phase is not the exact nine
0:02:22so the E the the object to used to estimate the actual east an instantaneous amplitude and he's then you
0:02:28a for me noisy i M it because if the i'm is a noisy these
0:02:32parameters on not the exact i
0:02:34here we try to use their of a lose the particle filtering you in order to
0:02:39uh track the instantaneous phase and amplitude of and i i i M
0:02:44uh the the idea is to extract these
0:02:46in some as amplitude and phase and formulated in the is that the space of the part get field day
0:02:51uh we we need to define the a state transition function and the observation function the vision function is simple
0:02:58because we can their the mixture signal the observation and those the vision function
0:03:02can be of using this formulation
0:03:05because this is the sum of i on the sum of i S can be a using these a question
0:03:10these value of errors are for in the S it this space the main problem is to
0:03:14that term mean or are obtained the it's state transition function which is not
0:03:18and easy
0:03:22we can the like less part to get free in order to reform form that the problem them to use
0:03:27the size of the it's data space
0:03:29row but i colours particle filtering are extension of part to get thing that can be applied to
0:03:34conditionally linear
0:03:36a state value of a so if we partition a state is into linear part and nonlinear part we can
0:03:41estimate the
0:03:42you linear one using the con feeding and we can estimate the nonlinear for using particle filtering so you we
0:03:48like all but part to get free any
0:03:51we the rate use number of particles are required in order to estimate the
0:03:56a state of the system because the linear parties taken out an estimated by common fig
0:04:01so here we really is are proper them this is the observation and this is the observation function
0:04:08we can take the um to use instantaneous amplitudes uh uh out and form a big or
0:04:13this vector has a linear relation to to the mixture signal so these signal can be estimated by on free
0:04:19and then this is the vector or of the them
0:04:22yeah of these there and the nonlinear linear S by are instantaneous phase
0:04:27so it is in san then it's phase are the non linear uh part of the problem so we need
0:04:32to use part to give any in order to estimate these value bits can i'm filter use used to estimate
0:04:37this of bits
0:04:38so the
0:04:40that's state this space size is a rate used to estimate this
0:04:44again the main problem used to define the state transition function
0:04:48so because um the main as state by a bizarre in then use phase
0:04:52we need to define a a a a state transition
0:04:57a a transition
0:04:58this is not that use the yeah this this can what
0:05:01we obtain easy because and the phase transition function
0:05:05it is a complex function in it cannot be you know model for example using a simple first-order order be
0:05:11an for example for
0:05:13instantaneous amplitude you
0:05:15we can use a first-order markov be amp says and then uh we can track the instantaneous amplitude but for
0:05:20instantaneous phase as you be seen lay later the slide
0:05:24the instantaneous phase actress different time points sees and
0:05:27for example is an increasing from minus pi to paul i and then this
0:05:31face face then change
0:05:33so these channel changing the face sign
0:05:36makes is
0:05:38phase transition function very complex we can not have a simple function in order to
0:05:43tear and the phase transition function
0:05:45so we formulate the problem of tracking instantaneous amplitude and phase using i M F and E M Ds
0:05:52we formulate a everything but that should used to determine the
0:05:56phase transition
0:05:57function which is a no
0:05:59it's very calm
0:06:04we can uh
0:06:05if we have a
0:06:06access to that in to the estimated
0:06:09a face we and
0:06:10obtain the in the frequencies the frequencies can be of ten using the differentiation of the face so the instantaneous
0:06:17frequency can be obtained by differentiation of in as fate
0:06:22for a and scenes and i M if he's and all still a form in M narrowband frequency range
0:06:29instantaneous frequency
0:06:31i close uh different time points are a small for example
0:06:35i because i i am of
0:06:36belongs to a a a a specific narrowband frequency range
0:06:40so we expect that the instantaneous frequency
0:06:43is a teen a a specific narrowband frequency range as that
0:06:47so we can use these information of the instantaneous frequency and try to include the information of instantaneous frequency in
0:06:55that the into the related particle filter
0:06:58so but using these team formation
0:07:01but using the information of the frequencies we can try to estimate the instantaneous fig
0:07:07so the objective is to
0:07:09uh track the instantaneous phase while at the same time try to a what the frequency traces
0:07:15because when and i am if is noisy and we estimate the instantaneous
0:07:18and the frequency we can see that the
0:07:21instantaneous frequency frequency's not to in a specific
0:07:24frequency band for example there is a sudden change in the in N as frequency at it goes on the
0:07:29frequency range
0:07:30so we can use this information these this assumption that for an oscillation or for and
0:07:35oh yeah may have the in and it's frequency should be a small
0:07:39median in a specific narrowband frequency range
0:07:42so we use the additional information of instantaneous frequency try to
0:07:47include these at the on information in to the out into their out formulated a but i as particle filtering
0:07:53and try to estimate the instantaneous phase
0:07:56in the
0:07:58now in in this work we first try to use only one on them if they or later can be
0:08:03extended for different number of uh a i for for example
0:08:07in face tracking of all of the i M F at the same time but uh for this work we
0:08:13one you see consider one T one i if the observation is only one i F which is a noisy
0:08:17this is the observation noise
0:08:19this is the observation function is simply
0:08:22and it can be a ten using these them considering the instantaneous amplitude and instantaneous phase using the hilbert transform
0:08:29and then this is the yeah a state transition function this very bizarre amplitude and phase of one i you
0:08:36may have one noisy i'm
0:08:38is in something as amplitude is estimated using con um filtering and this should be
0:08:42estimated using part if we can but as far as we don't have access to the
0:08:47instantaneous phase transition function we need to use the information of in and it's frequency in order to
0:08:54you how we can estimate the instantaneous
0:08:59this is there uh sort do code of the uh
0:09:02in some as face tracking uh the main objective is to
0:09:06first first in this for used to estimate the in and frequency the K S
0:09:10is to
0:09:11uh estimate the phase actress different time points but we also estimate the um
0:09:16but for amplitudes we only use
0:09:18first the markovian process in order to
0:09:21yeah in order to to find a a state transition what for phase as i said in the previous the
0:09:27slide is a complex function we cannot
0:09:29simply really use the more cold first order of you know for some but the face on a you change
0:09:35so there are some but part to get initialisation in this that's the
0:09:39and then uh
0:09:41a a for example when we want to estimate the it's state the phase
0:09:45is that it's phase at each time point
0:09:48we generate two faces
0:09:49one he's are ten by the positive of the phase in the previous time point plus a the of motion
0:09:56one is up from the negative
0:09:58of the phase in the previous part time point process a
0:10:02a coach and white noise
0:10:04so we generated two face in order to select between these two of phase
0:10:09we need to estimate the instantaneous frequency and try to see that each one of these phase
0:10:16tries to S smooth the instantaneous frequency meeting and narrowband frequency range
0:10:22we also have one very but as the frequency
0:10:25and then we estimate this value but
0:10:28and we used use this a frequency by but comparing and and then we compare these uh a value but
0:10:33that's is a from the estimated frequency the previous time
0:10:36we compared to the frequency that it all that is a by each of considering in each of these phase
0:10:42and then we try to
0:10:43yeah i use these information of the frequency
0:10:47and then include it as the weight as some of uh as a B
0:10:51in order to all the weight of the particle filtering
0:10:54but the
0:10:55um when we try to use them
0:10:57but we implemented the at what that is
0:11:00this to look what was not uh working in and was not working in initial
0:11:05there is the situation for example the phase transition is around zero
0:11:09but the face transition is around zero so then T
0:11:13and because we use the hilbert transform diff in some as frequency becomes negative it becomes part the positive and
0:11:19backs to the
0:11:20a a a a a specific frequency range that the i M F B don't
0:11:24so because is
0:11:26uh these estimated frequency becomes negative is that because of the noise is because the phase transition is around zero
0:11:33is a special case
0:11:34in ours
0:11:35i'll go it we try to detect take this situation
0:11:38but the estimated instantaneous frequency is
0:11:41out of the frequency range but is not to to the noise or because of wrong estimation of the face
0:11:48from the positive or negative is because of phase transition around zero
0:11:51we detect take these situation so we use
0:11:54to to you as in order to update the weight of the particle
0:11:58and then at the if we have a uh some embedded part gets for example if the estimated phase is
0:12:02bigger than a i or less and minus by
0:12:05we set the weight of the invalid part can to zero in order not to have any contribution
0:12:10for the estimation of a state of the since
0:12:12or if they it it's an estimated in estimated as frequency
0:12:16is um
0:12:18large and then the maximum
0:12:19frequency of a a a specific
0:12:22but and that there are i M F don't
0:12:24we set the way to zero or if they estimate the once is a lower than the minimum frequency
0:12:30but the i mess and we as
0:12:31and we said the eight
0:12:33to weight of the part "'cause" to zero
0:12:35so we remove that you body part because
0:12:37so the important issue in in in this
0:12:40yeah in this to the so look what is that and because we can not seem really
0:12:45uh i have a
0:12:46function for phase transition we need to generate two phases one is from
0:12:51positive for face in then they get in the previous type point one is from negative of the in the
0:12:55previous i'm one
0:12:56then using the information of frequency
0:12:59we try to select between
0:13:01these two face also because
0:13:03we try to a mode the frequency traces actress different time points
0:13:08we we somehow hall
0:13:09a can the and really we somehow try to do noise the that it because for a noisy i'm F
0:13:14to estimated instantaneous frequency P on the frequency
0:13:18and also the for the is the a situation when the phase transition is a around zero we try to
0:13:24change are value
0:13:26we apply the at to set
0:13:28a two sets of simulated data or we generated for amplitude and frequency modulated sine wave we added a quotient
0:13:34wave not white noise
0:13:36the signals resolution is calculated using this formulation nation
0:13:40we can see that two snr levels tree and seven
0:13:44we estimate the instantaneous frequency using our proposed metal it also use the hilbert but transform of the noisy the
0:13:50i'm if and it is clear that in both the set of it are method
0:13:54uh oh or out forms the
0:13:56in then is frequent
0:13:57it the hilbert trance
0:13:59so this is one
0:14:01uh illustration for estimation of instantaneous phase
0:14:04the actual in something that's phase is that the act one
0:14:07and the for the noise is there red one the results of the tracking is a dot line
0:14:13and you can see that uh for tracking we have a better estimation
0:14:16and you can see here for example the face signed so then change
0:14:19are i'll quickly takes these situation and here
0:14:22the phase transition is around zero
0:14:25so the estimated instantaneous frequency in these part should be negative but this is not to to the not because
0:14:30of these transition
0:14:31and then a are it can and attracting sent in both snr level is better than the you but
0:14:38this is the result of tracking instantaneous um P pretty to you
0:14:42and the this is in some then news freak estimate these i in set is frequency the phase transition around
0:14:47zero or this is the
0:14:49but i one is the actual one
0:14:50becomes negative but is is that because of noise because of the phase transition on zero
0:14:55it's still our method can it's what the frequency traces the noisy i am F
0:14:59is the rest one this and
0:15:04we try to keep the instantaneous frequency in and narrow frequency band range
0:15:10and then
0:15:10a we applied the all into the real eight are we can see there's a reach an and
0:15:15and then we estimate the incense and phase um pretty two
0:15:21and the this is the uh a smoothing results in frequency domain
0:15:26so the
0:15:27does line is the in sentence
0:15:29a a frequency tracking or is sporting using a rubber close but can fit the noisy i M F
0:15:34frequencies this
0:15:36so we propose a new face tracking system that uses both em the N L but i close but get
0:15:41printing the idea is to this what frequency traces
0:15:45and uh also use some if then has rules be at that some concern to the rubber like this party
0:15:50of fitting formulation
0:15:52we try to do you know is that i am if at the same time
0:15:55attracting tracking the nist face
0:15:57and uh a here later the problem and the method can be a you can be extended more in order
0:16:01to solve them all what makes mixing problem of the em this should be a exploited in another is there's
0:16:07and the metal has application to and
0:16:10speech and has been also for
0:16:12phase a
0:16:15basic synchronization of each just signal in different frequency band M on different region the method can be
0:16:49initial if we use only part to give we the number of
0:16:51a a a a a state
0:16:53a value as is high yeah but we partition the to very busy
0:16:56a linear non not being about
0:16:58uh so if we use a a use number of a state value as
0:17:03so that required number of part to get it should be low but
0:17:07for one i am F because the S state only contains one phase
0:17:12so i i can see that at ten a on ten thousand part get
0:17:16yes because uh uh is because we use some a con constraint in that all but i close party think
0:17:21we need to
0:17:22have a number of a higher number of party in order to be like the the
0:17:25estimate the
0:17:26a a
0:17:27but if use several i am and
0:17:29so and and you have several and nonlinear possible of all phases
0:17:33we need to decrease the increase the number of a part
0:17:36it is a the some some minor problems with the part you're thinking is that
0:17:40a the number of for to gets
0:17:42in some cases should be high
0:17:44you know it have it like that
0:17:59propose a i used a pair you that's T
0:18:04so are used for a period then as the proposal density so
0:18:07uh the the rate can be up billy really using their weights
0:18:11in the previous time point multiplied by the likelihood function