CN114343675A - Extraction method of electroencephalogram components - Google Patents
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Abstract
The invention provides an electroencephalogram component extraction method, which comprises the following steps: acquiring an original electroencephalogram signal, and acquiring a resting electroencephalogram signal and an excitation electroencephalogram signal from the original electroencephalogram signal; performing parameter estimation of a Kalman filtering model by taking the resting electroencephalogram signal as a value basis to obtain a state prediction parameter; and performing Kalman filtering on the excitation electroencephalogram signal according to the state prediction parameters to obtain the filtered electroencephalogram signal. Because the resting electroencephalogram signal and the excitation electroencephalogram signal are parts of the original electroencephalogram signal, the noise composition components in the resting electroencephalogram signal and the excitation electroencephalogram signal are similar. In addition, the resting electroencephalogram signals reflect electroencephalogram signals of the brain in an unstimulated state, the signal fluctuation is stable, and the method is suitable for being used as a value basis for extracting state prediction parameters. The resting electroencephalogram signals are used as the value basis for parameter estimation, and high-quality state prediction parameters can be provided for the filtering process of the excitation electroencephalogram signals, so that the accuracy of extraction of electroencephalogram components is further improved.
Description
Technical Field
The invention relates to the field of computer information processing, in particular to an electroencephalogram component extraction method.
Background
The current research on the brain function cognition is mainly completed by extracting relevant components from brain electrical signals. Because the electroencephalogram signal is a complex non-stationary random signal, the data acquisition process is easily interfered by the external environment and the physiological conditions of the testee. Therefore, the signals need to be filtered to eliminate the influence of interference, and the required cognitive components are acquired as much as possible.
In the related art, kalman filtering is often applied to the extraction of cognitive components of electroencephalogram signals, but the development of the theory is still not mature enough. The Kalman filtering is applied to the extraction of cognitive components of the electroencephalogram signals, a Jacobi (Jacobi) matrix needs to be calculated, and the complex calculation of the Jacobi matrix has a certain limiting effect on the actual application. Therefore, in order to improve the calculation efficiency of kalman filtering and improve the numerical stability of the algorithm in the estimation of the electroencephalogram component, an electroencephalogram component extraction method capable of estimating the electroencephalogram noise more accurately is urgently needed.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the electroencephalogram component extraction method can be used for estimating the electroencephalogram noise more accurately.
The electroencephalogram component extraction method according to the embodiment of the invention comprises the following steps:
acquiring original electroencephalogram signals, and acquiring resting electroencephalogram signals and excitation electroencephalogram signals from the original electroencephalogram signals, wherein the resting electroencephalogram signals reflect electroencephalogram signals with the brain in an unstimulated state, and the excitation electroencephalogram signals reflect electroencephalogram signals with the brain in a stimulated state;
performing parameter estimation of a Kalman filtering model by taking the resting electroencephalogram signal as a value basis to obtain a state prediction parameter;
and performing Kalman filtering on the excitation electroencephalogram signal according to the state prediction parameters to obtain a filtered electroencephalogram signal.
The method for extracting the electroencephalogram components has the following beneficial effects:
the electroencephalogram component extraction method firstly acquires original electroencephalogram signals, and then acquires resting electroencephalogram signals and excitation electroencephalogram signals from the original electroencephalogram signals. Further, Kalman filtering parameter estimation is carried out by taking the resting electroencephalogram signal as a value basis to obtain a state prediction parameter, Kalman filtering is carried out on the excitation electroencephalogram signal according to the state prediction parameter, and finally the filtered electroencephalogram signal is obtained. Because the resting electroencephalogram signal and the excitation electroencephalogram signal are parts of the original electroencephalogram signal, the noise composition components in the resting electroencephalogram signal and the excitation electroencephalogram signal are similar. In addition, the resting electroencephalogram signals reflect electroencephalogram signals of the brain in an unstimulated state, the signal fluctuation is stable, and the method is suitable for being used as a value basis for extracting state prediction parameters. Based on the reasons, the resting electroencephalogram signals are used as the value basis for parameter estimation, and higher-quality state prediction parameters can be provided for the filtering process of the excitation electroencephalogram signals, so that the accuracy of electroencephalogram component extraction can be further improved.
Optionally, according to some embodiments of the present invention, the performing parameter estimation of the kalman filter model based on the resting electroencephalogram signal to obtain a state prediction parameter includes:
analyzing the resting electroencephalogram signal to obtain an autoregressive model coefficient;
substituting the autoregressive model coefficient into a state equation and an observation equation, and estimating to obtain a state transition matrix and a measurement matrix in the state prediction parameters;
and obtaining an observation noise covariance matrix and a process noise covariance matrix in the state prediction parameters according to the autoregressive model coefficient, the state equation and the observation equation.
Optionally, according to some embodiments of the invention, the method further comprises:
establishing a P-order autoregressive model
Wherein a is1，a2，...，apIs the coefficient of an autoregressive model of order P, zsRepresenting said resting brain electrical signal, v, free of noisesK represents the time when the observation data is acquired in order to observe noise;
when x isp(k)＝[zs(k-p),zs(k-p+1),…zs(k-1),zs(k)]TObtaining the state equation of Kalman filtering through the autoregressive model:
Optionally, according to some embodiments of the present invention, substituting the autoregressive model coefficient into a state equation and an observation equation, and estimating to obtain a state transition matrix and a measurement matrix in the state prediction parameters includes:
extracting P-order autoregressive model coefficient a from the resting electroencephalogram signal1，a2，...，apSubstituting the state equation and the observation equation to estimate a Kalman filtering state transition matrix in the state prediction parameters
Measurement matrix H of kalman filter [0 … 01 ═]。
Optionally, according to some embodiments of the present invention, the deriving an observation noise covariance matrix and a process noise covariance matrix in the state prediction parameters includes:
(iv) measuring the observed noise vsA multivariate normal distribution (0, R) expressed as a mean of 0 and a covariance matrix of R;
measuring the observation noise v by taking the resting electroencephalogram signal as an observation basissAnd obtaining the observation noise covariance matrix R;
noise the process
A multivariate normal distribution (0, Q) expressed as mean 0 and covariance matrix Q;
according to the P-order autoregressive model coefficient a1，a2，...，apWith the observation noise vsAnd obtaining the process noise covariance matrix Q.
Optionally, according to some embodiments of the present invention, the performing kalman filtering on the excitation electroencephalogram signal according to the state prediction parameter includes:
according to the excitation electroencephalogram signal J (t-1) detected at the last moment t-1 and the state prediction parameters, calculating a prior state vector of the current moment t from the last moment t-1 to the current moment t
Covariance matrix with prior error
According to the prior state vector of the current time t
Covariance matrix with prior error
Obtaining a Kalman gain;
the excitation electroencephalogram signal J (t), the Kalman gain and the prior state vector which are detected according to the current time t
Covariance matrix of the prior error
Calculating to obtain a posterior state vector x of the current time ttCovariance matrix P with a posteriori errort；
According to the xtAnd said PtAnd generating an output value of the filtered electroencephalogram signal at the current time t.
Optionally, according to some embodiments of the invention, the method further comprises:
the x is measuredtAs the prior state vector at time t +1, let P betCalculating and updating the Kalman gain and updating the state prediction parameters as a prior error covariance matrix at the moment of t + 1;
calculating to obtain a posterior state vector x of the next moment t +1 according to the excitation electroencephalogram signal J (t +1) detected at the next moment t +1, the Kalman gain in the updating state and the state prediction parameters in the updating statet+1Covariance matrix P with a posteriori errort+1；
According to the xt+1And said Pt+1And generating an output value of the filtered electroencephalogram signal at the next moment t + 1.
Optionally, according to one of the inventionIn some embodiments, the prior state vector of the current time t is derived from the last time t-1 to the current time t
Covariance matrix with prior error
The method comprises the following steps:
substituting the state transition matrix A and the process noise covariance matrix Q in the state prediction parameters into a state variable update equation
Update equation with error covariance
To obtain the
And the above-mentioned
Wherein xt-1Is the state variable at the last time t-1, Pt-1Is the error covariance matrix at the last time t-1.
Optionally, according to some embodiments of the invention, the a priori state vector according to the current time t
Covariance matrix with prior error
Deriving a Kalman gain comprising:
the measurement matrix H, the observation noise covariance matrix R and the prior state vector of the current moment t
Covariance matrix with prior error
Substitution formula
And obtaining a Kalman gain K.
Optionally, according to some embodiments of the invention, the calculating derives a posterior state vector x of the current time ttCovariance matrix P with a posteriori errortThe method comprises the following steps:
the measurement matrix H, the Kalman gain K, the excitation electroencephalogram signal J (t) detected at the current moment t, and the prior state vector at the current moment t
Substitution formula
Obtaining the posterior state vector x of the current time tt；
The measurement matrix H, the Kalman gain K and the prior error covariance matrix of the current time t
Substitution formula
Obtaining a posterior error covariance matrix P of the current time tt。
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
fig. 1 is a schematic flow chart of an electroencephalogram component extraction method according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of another method for extracting brain electrical components according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart of another method for extracting brain electrical components according to an embodiment of the present invention;
FIG. 4 is a schematic flow chart of another method for extracting brain electrical components according to an embodiment of the present invention;
FIG. 5 is a schematic flow chart of another method for extracting brain electrical components according to an embodiment of the present invention;
FIG. 6 is a schematic flow chart of another method for extracting brain electrical components according to an embodiment of the present invention;
FIG. 7 is a schematic flow chart of another method for extracting brain electrical components according to an embodiment of the present invention;
FIG. 8 is a schematic flow chart of another method for extracting brain electrical components according to an embodiment of the present invention;
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the present invention, the meaning of a plurality of means is one or more, the meaning of a plurality of means is two or more, and larger, smaller, larger, etc. are understood as excluding the number, and larger, smaller, inner, etc. are understood as including the number. If the first and second are described for the purpose of distinguishing technical features, they are not to be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present invention, it should be understood that the orientation or positional relationship referred to in the description of the orientation, such as the upper, lower, left, right, front, rear, etc., is based on the orientation or positional relationship shown in the drawings, and is only for convenience of description and simplification of description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
In the description of the present invention, it should be noted that unless otherwise explicitly defined, terms such as arrangement, installation, connection and the like should be broadly understood, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific contents of the technical solutions.
The current research on the brain function cognition is mainly completed by extracting relevant components from brain electrical signals. Because the electroencephalogram signal is a complex non-stationary random signal, the data acquisition process is easily interfered by the external environment and the physiological conditions of the testee. Therefore, the signals need to be filtered to eliminate the influence of interference, and the required cognitive components are acquired as much as possible.
In the related art, kalman filtering is often applied to the extraction of cognitive components of electroencephalogram signals, but the development of the theory is still not mature enough. The Kalman filtering is applied to the extraction of cognitive components of the electroencephalogram signals, a Jacobi (Jacobi) matrix needs to be calculated, and the complex calculation of the Jacobi matrix has a certain limiting effect on the actual application. Therefore, in order to improve the calculation efficiency of kalman filtering and improve the numerical stability of the algorithm in the estimation of the electroencephalogram component, an electroencephalogram component extraction method capable of estimating the electroencephalogram noise more accurately is urgently needed.
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the electroencephalogram component extraction method can be used for estimating the electroencephalogram noise more accurately.
The following is further explained based on the attached drawings.
Referring to fig. 1, the electroencephalogram component extraction method according to the embodiment of the invention comprises the following steps:
step S101, collecting original electroencephalogram signals, and acquiring resting electroencephalogram signals and excitation electroencephalogram signals from the original electroencephalogram signals, wherein the resting electroencephalogram signals reflect electroencephalogram signals with the brain in an unstimulated state, and the excitation electroencephalogram signals reflect electroencephalogram signals with the brain in a stimulated state;
in some embodiments of the invention, the acquired original electroencephalogram signals include resting electroencephalogram signals reflecting that the brain is in an unstimulated state, and also include excitation electroencephalogram signals reflecting that the brain is in a stimulated state. The whole original brain electrical signal records the change process and the continuous process of the brain from the non-stimulated state to the stimulated state.
S102, taking the resting electroencephalogram signal as a value basis to carry out parameter estimation of a Kalman filtering model to obtain a state prediction parameter;
it should be noted that both the resting electroencephalogram signal and the excitation electroencephalogram signal are part of the original electroencephalogram signal, so that the noise components in the resting electroencephalogram signal and the excitation electroencephalogram signal are similar. In addition, the resting electroencephalogram signals reflect the electroencephalogram signals of the brain in an unstimulated state, and the signal fluctuation is stable. Therefore, the resting electroencephalogram signals are suitable for being used as a value basis for extracting the state prediction parameters, and the extracted state prediction parameters are used for performing Kalman filtering on the excitation electroencephalogram signals subsequently so as to extract the filtered electroencephalogram signals.
And S103, performing Kalman filtering on the excitation electroencephalogram signal according to the state prediction parameters to obtain the filtered electroencephalogram signal.
It should be noted that the theoretical basis of kalman filtering is an estimation problem, i.e., filtering noise from a noisy observation signal, and recovering the target signal itself or approaching the target signal. The input of the filter is the observed quantity of the system, the evaluated value is the output of the filter by using the statistical characteristics of the system noise and the observation noise, the input and the output of the filter are connected by the time updating equation and the observation updating equation, and all the signals needing to be processed are evaluated according to the two equations. The Kalman filtering design method is simple and easy to implement and wide in application range, but the theoretical development of the Kalman filtering design method is not mature. Firstly, a Jacobi (Jacobi) matrix needs to be calculated, and the complex calculation of the Jacobi matrix has a certain limit effect on practical application; in addition, the assumption that the probability distribution function has a gaussian characteristic makes it impossible to use it for a random system of nonlinear non-gaussian. Therefore, the state prediction parameters obtained by taking the resting electroencephalogram signals as the value basis can improve the numerical stability of the algorithm on the electroencephalogram component estimation.
The electroencephalogram component extraction method firstly acquires original electroencephalogram signals, and then acquires resting electroencephalogram signals and excitation electroencephalogram signals from the original electroencephalogram signals. Further, Kalman filtering parameter estimation is carried out by taking the resting electroencephalogram signal as a value basis to obtain a state prediction parameter, Kalman filtering is carried out on the excitation electroencephalogram signal according to the state prediction parameter, and finally the filtered electroencephalogram signal is obtained. Because the resting electroencephalogram signal and the excitation electroencephalogram signal are parts of the original electroencephalogram signal, the noise composition components in the resting electroencephalogram signal and the excitation electroencephalogram signal are similar. In addition, the resting electroencephalogram signals reflect electroencephalogram signals of the brain in an unstimulated state, the signal fluctuation is stable, and the method is suitable for being used as a value basis for extracting state prediction parameters. Based on the reasons, the resting electroencephalogram signals are used as the value basis for parameter estimation, and higher-quality state prediction parameters can be provided for the filtering process of the excitation electroencephalogram signals, so that the accuracy of electroencephalogram component extraction can be further improved.
Referring to fig. 2, according to some embodiments of the present invention, in step S102, performing parameter estimation of the kalman filter model based on the resting electroencephalogram signal to obtain a state prediction parameter includes:
step S201, analyzing the resting electroencephalogram signal to obtain an autoregressive model coefficient;
step S202, substituting the autoregressive model coefficient into a state equation and an observation equation, and estimating to obtain a state transition matrix and a measurement matrix in the state prediction parameters;
step S203, according to the autoregressive model coefficient, the state equation and the observation equation, an observation noise covariance matrix and a process noise covariance matrix in the state prediction parameters are obtained.
It should be noted that the state prediction parameters include a state transition matrix, a measurement matrix, an observation noise covariance matrix, and a process noise covariance matrix. In some embodiments of the invention, the state transition matrix, the measurement matrix, the observation noise covariance matrix and the process noise covariance matrix obtained on the basis of the resting electroencephalogram signal as a value are used for constructing prior estimation for a subsequent Kalman filtering process of the excitation electroencephalogram signal.
Referring to fig. 3, according to some embodiments of the invention, the state equations of kalman filtering and the observation equations of kalman filtering are obtained by:
step S301, establishing a P-order autoregressive model
Wherein a is1，a2，...，apIs the coefficient of an autoregressive model of order P, zsRepresenting a noise-free resting electroencephalogram signal, vsK represents the time when the observation data is acquired in order to observe noise;
it should be noted that the Autoregressive model (AR model) is a statistical method for processing time series, and uses previous stages of the same variable to predict the performance of the present stage, and assumes a linear relationship. This is called autoregression, since it is developed from linear regression in regression analysis, and the current-stage performance of the variable itself is predicted by using the variables of the previous stages.
And S302, when the state variable takes values from the resting electroencephalogram signals, obtaining a state equation and an observation equation of Kalman filtering through an autoregressive model.
When x isp(k)＝[zs(k-p),zs(k-p+1),…zs(k-1),zs(k)]TAnd obtaining a state equation of Kalman filtering through an autoregressive model:
Referring to fig. 4, according to some embodiments of the present invention, substituting the autoregressive model coefficients into the state equation and the observation equation and estimating the state transition matrix and the measurement matrix in the state prediction parameters in step S202 includes:
step S401, extracting P-order autoregressive model coefficient a from resting electroencephalogram signals1，a2，...，apSubstituting the state equation and the observation equation;
step S402, estimating and obtaining a Kalman filtering state transition matrix in the state prediction parameters
Measurement matrix H of kalman filter [0 … 01 ═]。
Referring to fig. 5, the deriving of the observed noise covariance matrix and the process noise covariance matrix in the state prediction parameters in step S203 according to some embodiments of the invention includes:
step S501, observing the noise vsExpressed as a multivariate normal distribution (0, R) with a mean of 0 and a covariance matrix of R, the process noise
A multivariate normal distribution (0, Q) expressed as mean 0 and covariance matrix Q;
step S502, measuring observation noise v by taking the resting electroencephalogram signal as an observation basissAnd obtaining an observation noise covariance matrix R;
step S503, according to the P-order autoregressive model coefficient a1，a2，...，apAnd observation noise vsAnd obtaining a process noise covariance matrix Q.
Referring to fig. 6, according to some embodiments of the present invention, step S103 performs kalman filtering on the excitation electroencephalogram signal according to the state prediction parameters, including:
step S601, according to the excitation electroencephalogram signal J (t-1) detected at the last time t-1 and the state prediction parameters, calculating from the last time t-1 to the current time t to obtain the prior state vector of the current time t
Covariance matrix with prior error
According to some embodiments provided by the invention, if the current time t is the starting time of the excitation electroencephalogram signal, the excitation electroencephalogram signal does not exist at the last time t-1, and at the moment, the prior state vector of the current time t is carried out according to the state prediction parameter acquired by taking the resting electroencephalogram signal as a value basis
Covariance matrix with prior error
It should be understood that the case where the current time t is the starting time of the excitation electroencephalogram signal is included in the literal meaning of step S601.
Step S602, according to the prior state vector of the current time t
Covariance matrix with prior error
Obtaining a Kalman gain;
step S603, according to the excitation EEG signal J (t), Kalman gain and prior state vector detected at the current time t
Covariance matrix with prior error
Calculating to obtain a posterior state vector x of the current time ttCovariance matrix P with a posteriori errort；
It should be noted that, the excitation electroencephalogram signal j (t) detected at the current time t, the kalman gain estimation, and the prior state vector are used to estimate the current time t
Covariance matrix with prior error
Obtaining the posterior state vector x of the current time ttCovariance matrix P with a posteriori errortAiming at reducing the prior state vector at the current time t
Covariance matrix with prior error
Error from the actual value, thereby obtaining the posterior state vector x closer to the actual valuetCovariance matrix P with a posteriori errort。
Step S604, according to xtAnd PtAnd generating an output value of the filtered electroencephalogram signal at the current time t.
It should be noted that the vector x is based on the posterior statetCovariance matrix P with a posteriori errortThe generated output value is the value of the generated filtered electroencephalogram signal at the current time t. In general, the observed values of the excitation EEG signals at all the moments are processed to obtain the posterior state vectors and the posterior error covariance matrixes at all the moments, so that the output values at all the moments are obtained, and finally the output values at all the moments are combined to form the filtered afterbrain telecommunicationThe waveform of the sign.
Referring to fig. 7, according to some embodiments of the present invention, the step S103 performs kalman filtering on the excitation electroencephalogram signal according to the state prediction parameter, and further includes:
step S701, x istAs the prior state vector at time t +1, let P betCalculating and updating Kalman gain and updating state prediction parameters as a prior error covariance matrix at the moment of t + 1;
in some embodiments of the present invention, updating the state prediction parameter mainly refers to updating the process noise covariance Q. Specifically, by Qt+1＝K1Qt+K2K (J (t +1) -HX) to update the process noise covariance Q, where K1，K2Are all weighting coefficients, and 0<K1<1,0<K2<1, K is Kalman filtering gain, J (t +1) is an excitation EEG signal detected at the next moment t +1, H is a measurement matrix of Kalman filtering, and X is a state variable matrix consisting of state variables. Along with the updating of the Kalman gain according to the state prediction parameters in each cycle, the Kalman filtering process can generate self-adaptive adjustment along with the change of the excitation electroencephalogram signal, so that the accuracy of the electroencephalogram component extraction method is further improved.
Step S702, calculating to obtain a posterior state vector x of the next time t +1 according to the excitation electroencephalogram signal J (t +1) detected at the next time t +1, the Kalman gain of the updating state and the state prediction parameters of the updating statet+1Covariance matrix P with a posteriori errort+1；
Step S703, according to xt+1And Pt+1And generating an output value of the filtered electroencephalogram signal at the next moment t + 1.
It should be noted that, in this embodiment, steps S701 to S703 form a cycle of a kalman filtering process, a kalman gain and a state prediction parameter can be updated once after each cycle, and an output value of the filtered electroencephalogram signal is obtained until the excitation electroencephalogram signal is completely processed by the kalman filtering, and the filtered electroencephalogram signal is generated all at random. Because the output of each cycle is obtained by the posterior state vector and the posterior error covariance matrix corresponding to the cycle, the output value close to the actual value can be obtained in each cycle, and the accuracy of the finally formed filtered electroencephalogram signal is correspondingly improved.
Referring to fig. 8, according to some embodiments of the present invention, step S601 derives the prior state vector of the current time t from the previous time t-1 to the current time t
Covariance matrix with prior error
The method comprises the following steps:
step S801, substituting a state transition matrix A and a process noise covariance matrix Q in the state prediction parameters into a state variable updating equation
Update equation with error covariance
Wherein xt-1Is the state variable at the last time t-1, Pt-1The error covariance matrix at the last moment t-1;
step S802, obtaining prior state vector of current time t
Covariance matrix with prior error
According to some embodiments of the invention, step S602 is based on a prior state vector at the current time t
Covariance matrix with prior error
Deriving a Kalman gain comprising:
measuring matrix H, observation noise covariance matrix R and prior state vector of current time t
Covariance matrix with prior error
Substitution formula
And obtaining a Kalman gain K.
According to some embodiments of the invention, the a posteriori state vector x at the current time t is derived in step S603tCovariance matrix P with a posteriori errortThe method comprises the following steps:
measuring matrix H, Kalman gain K, excitation electroencephalogram signals J (t) detected at current time t, and prior state vector of current time t
Substitution formula
Obtaining the posterior state vector x of the current time tt；
Measuring matrix H, Kalman gain K and prior error covariance matrix of current time t
Substitution formula
Obtaining a posterior error covariance matrix P of the current time tt。
It should be appreciated that the various implementations provided by the embodiments of the present invention can be combined arbitrarily to achieve different technical effects.
While the preferred embodiments of the present invention have been described in detail, it will be understood by those skilled in the art that the foregoing and various other changes, omissions and deviations in the form and detail thereof may be made without departing from the scope of this invention.
Claims (10)
1. An electroencephalogram component extraction method is characterized by comprising the following steps:
acquiring original electroencephalogram signals, and acquiring resting electroencephalogram signals and excitation electroencephalogram signals from the original electroencephalogram signals, wherein the resting electroencephalogram signals reflect electroencephalogram signals with the brain in an unstimulated state, and the excitation electroencephalogram signals reflect electroencephalogram signals with the brain in a stimulated state;
performing parameter estimation of a Kalman filtering model by taking the resting electroencephalogram signal as a value basis to obtain a state prediction parameter;
and performing Kalman filtering on the excitation electroencephalogram signal according to the state prediction parameters to obtain a filtered electroencephalogram signal.
2. The method of claim 1, wherein the performing the parameter estimation of the kalman filter model based on the resting electroencephalogram signal to obtain the state prediction parameters comprises:
analyzing the resting electroencephalogram signal to obtain an autoregressive model coefficient;
substituting the autoregressive model coefficient into a state equation and an observation equation, and estimating to obtain a state transition matrix and a measurement matrix in the state prediction parameters;
and obtaining an observation noise covariance matrix and a process noise covariance matrix in the state prediction parameters according to the autoregressive model coefficient, the state equation and the observation equation.
3. The method of claim 2, further comprising:
establishing a P-order autoregressive model
Wherein a is1，a2，...，apIs the coefficient of an autoregressive model of order P, zsRepresenting said resting brain electrical signal, v, free of noisesK represents the time when the observation data is acquired in order to observe noise;
when x isp(k)＝[zs(k-p),zs(k-p+1),…zs(k-1),zs(k)]TObtaining the state equation of Kalman filtering through the autoregressive model:
obtaining the observation equation of Kalman filtering through the autoregressive model:
wherein x is a state variable, said Ip-1Is an identity matrix of order P-1,
z represents a noisy resting brain electrical signal, being process noise.
4. The method of claim 3, wherein substituting the autoregressive model coefficients into a state equation and an observation equation and estimating a state transition matrix and a measurement matrix in the state prediction parameters comprises:
extracting P-order autoregressive model coefficient a from the resting electroencephalogram signal1，a2，...，apSubstituting the state equation and the observation equation to estimate a Kalman filtering state transition matrix in the state prediction parameters
Measurement matrix H of kalman filter [0 … 01 ═]。
5. The method of claim 4, wherein said deriving an observed noise covariance matrix and a process noise covariance matrix in the state prediction parameters comprises:
(iv) measuring the observed noise vsA multivariate normal distribution (0, R) expressed as a mean of 0 and a covariance matrix of R;
measuring the observation noise v by taking the resting electroencephalogram signal as an observation basissAnd obtaining the observation noise covariance matrix R;
noise the process
A multivariate normal distribution (0, Q) expressed as mean 0 and covariance matrix Q;
according to the P-order autoregressive model coefficient a1，a2，...，apWith the observation noise vsAnd obtaining the process noise covariance matrix Q.
6. The method of claim 5, wherein said Kalman filtering of said excitation electroencephalogram signal according to said state prediction parameters comprises:
according to the excitation electroencephalogram signal J (t-1) detected at the last moment t-1 and the state prediction parameters, calculating a prior state vector of the current moment t from the last moment t-1 to the current moment t
Covariance matrix with prior error
According to the prior state vector of the current time t
Covariance matrix with prior error
Obtaining a Kalman gain;
the excitation electroencephalogram signal J (t), the Kalman gain and the prior state vector which are detected according to the current time t
Covariance matrix of the prior error
Calculating to obtain a posterior state vector x of the current time ttCovariance matrix P with a posteriori errort；
According to the xtAnd said PtAnd generating an output value of the filtered electroencephalogram signal at the current time t.
7. The method of claim 6, wherein said Kalman filtering the excited brain electrical signal according to the state prediction parameters, further comprising:
the x is measuredtAs the prior state vector at time t +1, let P betCalculating and updating the Kalman gain and updating the state prediction parameters as a prior error covariance matrix at the moment of t + 1;
calculating to obtain a posterior state vector x of the next moment t +1 according to the excitation electroencephalogram signal J (t +1) detected at the next moment t +1, the Kalman gain in the updating state and the state prediction parameters in the updating statet+1Covariance matrix P with a posteriori errort+1；
According to the xt+1And said Pt+1And generating an output value of the filtered electroencephalogram signal at the next moment t + 1.
8. The method according to claim 6, wherein the a priori state vector of the current time t is derived by estimating from the last time t-1 to the current time t
Covariance matrix with prior error
The method comprises the following steps:
substituting the state transition matrix A and the process noise covariance matrix Q in the state prediction parameters into a state variable update equation
Update equation with error covariance
To obtain the
And the above-mentioned
Wherein xt-1Is the state variable at the last time t-1, Pt-1Is the error covariance matrix at the last time t-1.
9. Method according to claim 8, characterized in that said a priori state vector according to said current time t
Covariance matrix with prior error
Deriving a Kalman gain comprising:
the measurement matrix H, the observation noise covariance matrix R and the prior state vector of the current moment t
Covariance matrix with prior error
Substitution formula
And obtaining a Kalman gain K.
10. The method according to claim 9, wherein said estimating derives a posterior state vector x for a current time ttCovariance matrix P with a posteriori errortThe method comprises the following steps:
the measurement matrix H, the Kalman gain K, the excitation electroencephalogram signal J (t) detected at the current moment t, and the prior state vector at the current moment t
Substitution formula
Obtaining the posterior state vector x of the current time tt；
The measurement matrix H, the Kalman gain K and the prior error covariance matrix of the current time t
Substitution formula
Obtaining a posterior error covariance matrix P of the current time tt。
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