Frequency estimation method based on rootMUSIC and signal dimension conversion, storage medium and equipment

Abstract

The present application relates to the field of biological signal processing, in particular to a frequency estimation method based on rootMUSIC and signal dimension conversion, a storage medium and equipment. The method comprises the following steps: chest displacement signals extracted from radar echoes are modeled as the sum of sine waves with integer multiple frequencies of basic respiration and heart rate, and corresponding single-channel analytic signals are generated through Hilbert transform; the single-channel analytic signals are converted into multi-channel data through a signal rearrangement method, the chest wall signal model is equivalent to a uniform linear array multi-shot receiving signal model, so that the vital sign frequency and the signal source direction of arrival establish a one-to-one correspondence; the received data of the multi-shot receiving signal model is processed through an alternating direction multiplier method framework, and a denoised signal matrix is solved; the rootMUSIC algorithm is used for the denoised signal matrix to solve the frequency estimation. The present application converts the signal model, makes the frequency estimation range equivalent to the angle estimation range, and improves the frequency estimation accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of biological signal processing, in particular to a frequency estimation method based on rootMUSIC and signal dimension conversion, a storage medium and an equipment. BACKGROUND

[0002] In the field of signal processing, especially in biomedical signal monitoring and radar signal processing applications, accurate estimation of the frequency components of a signal is crucial.

[0003] In the prior art, the Multiple Signal Classification (MUSIC) algorithm is generally used to estimate the frequency of the respiratory and heartbeat signals in the chest wall displacement signal. The MUSIC algorithm is a high-resolution algorithm for estimating the direction of arrival of signals, and can also effectively distinguish multiple signals with similar frequencies. However, the frequency spectrum search of the MUSIC algorithm relies on grid search, which poses a significant computational challenge and makes it difficult to achieve real-time frequency estimation.

[0004] The MUSIC algorithm is a typical spatial spectrum estimation method based on eigenvalue analysis, which can effectively distinguish multiple signals with similar directions. Its direction finding principle is based on eigenvalue decomposition of a matrix. Specifically, the MUSIC algorithm first constructs a covariance matrix from the signal data received by the array antenna, and performs eigenvalue decomposition on it to separate the signal into a noise subspace G and a signal subspace S. On this basis, a spatial spectrum estimation function P(ω) is constructed using the orthogonality between the noise subspace G and the column vectors of the array direction matrix A (i.e. the assumed signal direction), and the values of P(ω) at different directions of arrival are calculated. The direction with the highest signal energy is the direction of arrival. The core of the MUSIC algorithm lies in the subspace separation and orthogonality of the signal and noise, and this spatial spectrum estimation principle based on eigenvalue decomposition is universal, so the algorithm can also be used for frequency estimation.

[0005] The chest wall displacement signal obtained from the radar echo can be considered as the superposition of respiratory signals, heartbeat signals, high-order harmonic signals of respiratory signals, and noise. That is, the chest wall displacement signal obtained by analysis contains both effective components and noise, and the subspace of the effective components is orthogonal to the noise subspace. Therefore, a spatial spectrum function can be constructed, and a spectral peak search can be performed to obtain the frequency corresponding to the peak angle as the frequency of the target signal, thereby achieving frequency spectrum estimation of the signal.

[0006] However, the MUSIC algorithm requires spectral peak search, which is computationally intensive and difficult to implement in real-time frequency estimation. In order to reduce the computational load, the search is performed only on a limited number of discrete points, which will result in off-grid error. That is, during the discretization search process, the actual direction of arrival or frequency of the signal may not fall exactly on the preset discrete grid points, resulting in an error between the estimated result and the true value. Moreover, the larger the discretization step size of the grid, the greater the off-grid error may be.

[0007] Furthermore, existing methods using the MUSIC algorithm to estimate vital sign signal frequencies do not consider the mismatch between the ranges of respiratory and heart rate and the original DOA estimation range. Current MUSIC spectrum estimation methods directly estimate the frequency spectrum after replacing the spatial incident angle with frequency, i.e., the direction matrix changes from A(θ) to A(ω):

[0008]

[0009] ω in the formula i For the normalized frequency, compared with the true frequency f i Satisfy ω i =2πf i T s =2πf i / f s The relationship between T s f is the sampling interval. s The sampling rate is used; during the replacement, the angular quantities in A(θ) are replaced with frequency quantities, i.e., πsinθ. i =ω i , 1≤i≤M; then divide [0,2π] into N equal intervals. w The frequency is estimated by performing a grid search.

[0010] However, conventional methods do not consider the ω value in the context of vital sign signal frequency estimation. i The range of ranges. A normal adult's respiratory rate is 10 to 30 breaths per minute, and their heart rate is 48 to 120 beats per minute. Therefore, f... b ∈[0.17,0.5]Hz, f h ∈[0.8,2]Hz, while the sampling rate f s It is usually much higher than the highest frequency of vital signs, let's say f. s =200Hz, then ω i =2πf i / f s ∈[0,0.01]Hz, while πsinθ iThe frequency estimation range is equivalent to an angle estimation range which is much smaller than the angle estimation range of the MUSIC algorithm used in a DOA estimation problem, which makes the grid search range greatly redundant and reduces the frequency estimation accuracy. In order to improve the accuracy of the MUSIC algorithm in estimating the breathing and heartbeat frequencies in the vital sign monitoring scene, the conventional operation is to further improve the density of the grid division, which will further increase the computational complexity. SUMMARY

[0011] In order to solve the problems existing in the prior art, the present application provides a frequency estimation method and system based on rootMUSIC and signal dimension conversion, a storage medium and equipment, which adopts the rootMUSIC algorithm, replaces the spectrum peak search with polynomial root finding, reduces the computational complexity, converts the signal model, makes the frequency estimation range equivalent to the angle estimation range, improves the frequency estimation accuracy, and further reduces the computational complexity.

[0012] In a first aspect, the embodiments of the present application provide a frequency estimation method based on rootMUSIC and signal dimension conversion, comprising the following steps:

[0013] S1, signal model conversion, the chest displacement signal extracted from the radar echo is modeled as the sum of sine waves with integer multiple frequencies of the basic breathing and heart rate, and the corresponding single-channel analytic signal is generated by Hilbert transform; the single-channel analytic signal is converted into multi-channel data by a signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array multi-shot receiving signal model, and a one-to-one correspondence is established between the vital sign frequency and the signal source direction of arrival;

[0014] S2, the received data of the multi-shot receiving signal model is processed by an alternating direction multiplier method framework to solve the denoised signal matrix;

[0015] S3, the rootMUSIC algorithm is used to find the root of the denoised signal matrix for frequency estimation; wherein the rootMUSIC algorithm is a polynomial root finding form of the MUSIC algorithm based on the Pisarenko decomposition idea.

[0016] In a second aspect, based on the same inventive concept, the embodiments of the present application provide a frequency estimation system based on rootMUSIC and signal dimension conversion, which is realized by using the above frequency estimation method, and comprises the following modules:

[0017] A model conversion module is configured to model the chest displacement signal extracted from the radar echo as a sum of sinusoidal waves with fundamental breathing and integer multiple frequency of heart rate, and generate a corresponding single-channel analytic signal through Hilbert transform; convert the single-channel analytic signal into multi-channel data through a signal rearrangement method, so as to equivalently convert the chest wall signal model into a uniform linear array multi-shot receiving signal model, and establish a one-to-one correspondence between the vital sign frequency and the signal source direction of arrival;

[0018] A signal matrix solving module is configured to process the received data of the multi-shot receiving signal model through an alternating direction multiplier method framework, and solve a denoised signal matrix.

[0019] A frequency estimation module is configured to use a rootMUSIC algorithm to perform frequency estimation on the denoised signal matrix; the rootMUSIC algorithm is a polynomial root searching form of the MUSIC algorithm based on the Pisarenko decomposition idea.

[0020] In a third aspect, the embodiments of the present application further provide a computer readable storage medium having a computer program stored thereon, and when the computer program is run by a computer, the computer is caused to execute the frequency estimation method.

[0021] In a fourth aspect, the embodiments of the present application further provide a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable by the processor, and when the processor executes the computer program, the frequency estimation method is implemented.

[0022] Compared with the prior art, the present application has the following technical effects:

[0023] 1. The present application rearranges one-dimensional signal data into two-dimensional data, i.e., converts single-channel data into multi-channel data, and combines the high-resolution spectral estimation method rootMUSIC algorithm to improve the accuracy of frequency estimation, uses polynomial root finding instead of spectral peak searching to reduce the computational complexity, converts the signal model, and equivalently converts the frequency estimation range to the angle estimation range; the present application can be applied to the vital sign monitoring scene in radar signal processing and other application scenarios requiring high-precision frequency estimation.

[0024] 2. The present application uses the off-grid MUSIC method based on sparse representation, which directly estimates continuous parameters instead of discrete grid points through model adjustment and parameter optimization, thereby effectively reducing the off-grid error. DETAILED DESCRIPTION

[0025] Figure 1 is a flowchart of the frequency estimation method in the embodiments of the present application;

[0026] Figure 2is a distribution diagram of roots in a complex plane calculated by a rootMUSIC algorithm in an embodiment of the present application. DETAILED DESCRIPTION

[0027] The technical solutions of the present application will be further described in detail below in combination with embodiments and drawings, but the embodiments of the present application are not limited thereto.

[0028] EMBODIMENT

[0029] The embodiment provides a frequency estimation method based on rootMUSIC and signal dimension conversion. First, chest displacement signals extracted from radar echoes are modeled as a sum of sinusoidal waves with basic breathing and integer multiple frequency of heart rate, and corresponding analytical signals are generated by Hilbert transform; on this basis, single-channel data is converted into multi-channel data by a signal rearrangement method to facilitate subsequent frequency estimation; on the basis of signal rearrangement, an alternating direction multiplier method (ADMM) framework is used to solve the denoised signal matrix, and then the rootMUSIC algorithm is used to solve the roots of the denoised signal matrix to solve the frequency to be estimated. The processing flow is as shown in Figure 1 , and specifically includes the following steps:

[0030] S1, signal model conversion, chest displacement signals extracted from radar echoes are modeled as a sum of sinusoidal waves with basic breathing and integer multiple frequency of heart rate, and corresponding single-channel analytical signals are generated by Hilbert transform; the single-channel analytical signals are converted into multi-channel data by a signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array (ULA) multi-shot receiving signal model, so that the vital sign frequency and the signal source direction of arrival (DOA) establish a one-to-one correspondence.

[0031] In the embodiment, the signal model conversion specifically includes the following steps:

[0032] S11, signal modeling, the chest displacement signals are modeled as a combination of sinusoidal waves of breathing and heart rate, which contains multiple harmonic components. The expression of the combination of sinusoidal waves is:

[0033]

[0034] where f b is the breathing frequency, f h is the heart rate, P b is the considered breathing harmonic order, P h is the considered heart harmonic order, a bi , are the amplitude and initial phase of the i-th breathing component, respectively, and a hj , are the amplitude and initial phase of the j-th heartbeat component, respectively.

[0035] S12, generating an analytic signal, generating a corresponding single-channel analytic signal by Hilbert transform, so as to carry out subsequent processing.

[0036] For the following derivation is simple, only consider P b = P h = 1 case, namely:

[0037]

[0038] Definition The Hilbert transform of the sinusoidal combination r(t) is: As follows:

[0039]

[0040] The expression of the analytic signal R(t) is as follows:

[0041]

[0042] Where a b is the amplitude of the respiratory component, is the initial phase of the respiratory component, a h is the amplitude of the heartbeat component, is the initial phase of the heartbeat component, represents the complex amplitude.

[0043] S13, converting the single-channel analytic signal into multi-channel data by a signal rearrangement method, so as to equivalently convert the chest wall signal model into a uniform linear array multi-snapshot receiving signal model, so that the vital sign frequency and the signal source direction of arrival establish a one-to-one correspondence.

[0044] The continuous signal R(t) is sampled, assuming that its duration is T, the sampling frequency is f s , the sampling interval is T s = 1 / f s . Let t = nT s , then the number of points of the discrete signal R(n) obtained by sampling is M l , wherein 0≤n≤M l -1, we get:

[0045]

[0046] Use f i to represent the vital sign signal frequency, instead of the previous f b and f h , and use A i to replace the previous complex amplitude A b and A hand i = 1,2. The sampled discrete signal R(n) can be written in matrix form R:

[0047] R = A(f)S A (6)

[0048] where represents a steering matrix related to the frequency of vital sign signals, and represents a steering vector in the steering matrix A(f); S A = [A1, A2] T represents a complex amplitude matrix.

[0049] Let τ i = f i T s = f i T s , then Therefore, the sampled discrete signal matrix R = A(f)S A can be rewritten in the following matrix form:

[0050] R = A(τ)S A (7)

[0051] where represents a steering matrix related to the frequency of vital sign signals and the sampling rate; and represents a steering vector in the steering matrix A(τ);

[0052] In the case of a commonly used far-field receiving uniform linear array (ULA), the signal model is expressed as follows:

[0053] x(n) = A(θ) s(n) + z(n) (8)

[0054] where represents a steering matrix, and θ i is the azimuth angle of the i-th source, λ is the wavelength, and d is the inter-element distance of the far-field receiving uniform linear array; represents a signal source vector; represents a white noise vector; M is the number of array elements, L s is the number of snapshots, and P is the number of signal sources. When L s = 1, it represents the ULA single snapshot model.

[0055] Comparing formula (7) with the signal model (8), it can be seen that the exponential term is very similar to the term in A(θ). By defining τ i = f i T s= - dsinθ i / λ, the discrete signal matrix R corresponding to the chest wall motion can be converted into a single snapshot model of the ULA received signal (i.e. L s = 1). In this single snapshot model, the frequency dependent parameter and the angle are one-to-one corresponding, i.e. the frequency estimation signal model is corresponding to the angle estimation signal model.

[0056] It is noted that f s is usually much higher than f i . For example, when f s = 200 Hz and the maximum f i is no more than 2 Hz, the range of the estimated parameter τ i = f i / f s is limited between 0 and 0.01. Since the wavelength corresponding to the array element spacing is usually equal to d / λ = 1 / 2, and considering the DOA angle θ i ranging from -90° to 90°, then -dsinθ i / λ ranges from -0.5 to 0.5. Compared with the range of the angle estimation, the range of τ i is obviously narrower. Therefore, to improve the estimation accuracy and the frequency resolution, it is necessary to extend the range of τ i = f i / f s to match the range of -dsinθ i / λ.

[0057] Assuming the signal length is denoted as M l , where M l = M x L, the matrix R is rearranged from the M l x 1 vector to the M x L matrix. This process effectively converts the single channel model to the multi-channel format. Subsequently, a simplified model containing only two frequencies will be introduced to analyze the rearranged matrix representation:

[0058]

[0059] Let the M x L matrix obtained after the rearrangement be denoted as X, and let the i-th row of X be denoted as X i ; the first row X1 of the matrix X is decomposed as:

[0060]

[0061] The second row X2 of the matrix X is decomposed as:

[0062]

[0063] Similarly, the M-th row, i.e. the last row X M of the matrix X is decomposed as:

[0064]

[0065]

[0066] The obtained M x L matrix X is observed, and each row of the matrix can be decomposed in turn. Each 1 x L row vector X i from X can be decomposed as A i S, that is, X i = A i S, and according to matrix block multiplication, it can be obtained that

[0067]

[0068] wherein:

[0069]

[0070] Therefore, the discrete signal R(n) is rearranged into an M x L matrix form X, with L new sampling points, and the structure is similar to a far-field ULA received signal model with M elements, two signal sources and L snapshots (that is, in the previous far-field received signal model, L s =L). In this far-field ULA received signal model, the parameter τ i originally defined as -dsinθ i / λ is replaced by Lτ i . By setting L=50 and f s =200Hz, the new parameter becomes Lτ i =Lf i / f s ∈(0,0.5), that is, the range of Lτ i corresponds to -dsinθ i / λ approximately, thereby solving the problem of insufficient estimation accuracy due to the limited original range of τ i .

[0071] Thus, the unique chest wall signal model r(t) is successfully converted into a ULA multi-snapshot received signal model with the original length. In this converted model, there is a one-to-one correspondence between the vital sign frequency and the direction of arrival (DOA) of the signal source, specifically Converting the single-channel model into a multi-channel model not only improves the accuracy of parameter estimation, but also simplifies subsequent signal processing and analysis.

[0072] S2, by an alternating direction multiplier method (ADMM) framework, the received data of the multi-snapshot received signal model is processed to solve a signal matrix after denoising.

[0073] In this embodiment, the following steps are specifically included:

[0074] S21, considering the harmonic effect of the respiration and heartbeat signals, the frequency fundamental wave and the harmonics of the vital sign signal are considered, in order to correspond to the array signal model with P sources in the foregoing, 2≤i≤P, that is, the number of harmonics to be considered is P.

[0075] According to the modeling of step S1, after converting the single-channel data into multi-channel data, considering the observation noise, the received data of the ULA multi-snapshot receiving signal model can be represented as:

[0076] Y = A(f)S + Z (16)

[0077] wherein, L represents the number of snapshots, which is equivalent to the number of new sampling points of the data matrix, and M is the number of array elements; represents a steering matrix related to the vital sign signal frequency and the sampling rate, each column of which corresponds to the antenna response vector of the DOA of the pth source, wherein is a steering vector, f i represents the vital sign signal frequency; represents the transmission signal of the P sources at the L new sampling points; Z is an additive white Gaussian noise matrix.

[0078] S22, define an atom set corresponding to the received data Y Specifically,

[0079]

[0080] wherein A(f, φ) represents an atom in the atom set , which is composed of the outer product of the steering vector a(f) of the normalized frequency f and the normalized complex vector φ; its physical meaning is to describe the base element of a potential component in the signal, which is used for meshless sparse signal recovery and DOA estimation; φ H represents the conjugate transpose of the complex vector φ (same as Hermitian transpose); φ represents the normalized complex vector, which satisfies ||φ||2=1, representing the phase and amplitude information of the signal; a(f) represents the steering vector, which is defined in formula (16), representing the array response of the signal at the normalized frequency f. The atom set defined in the constraint norm is a set of all matrices with a constraint norm of 1, which can be created by the array steering vector and any measurement value.

[0081] Considering the sparsity of the signal, the atom norm l0 can be defined to describe Y, that is, Y is a linear combination of P atoms in the atom set

[0082]

[0083] wherein, x​p denotes the contribution strength of the p-th atom; f p denotes the normalized frequency of the p-th atom, φ p denotes the normalized complex vector corresponding to the p-th atom, and ||φ p ||2=1.

[0084] The sparsest representation of the received data Y is sought, and the goal is equivalent to a minimization problem of an atomic norm. The embodiment considers the following atomic norm l0minimization problem:

[0085]

[0086] where η is a constraint parameter, and denotes the maximum allowed value of the model error or residual, which is used to define the upper limit of the error.

[0087] S23, the atomic norm minimization problem is converted into a convex optimization problem,

[0088] The rank constraint of the above atomic norm minimization problem is non-convex, and therefore cannot be solved using a convex optimization method. Secondly, if the measurement result is disturbed by noise, there will be no optimal low rank. To solve this problem, the following is converted into a convex optimization problem, and the atomic norm of Y is defined as follows:

[0089]

[0090] S24, since the atomic set contains an infinite number of atoms, the converted convex optimization problem is a semi-infinite problem, and formula (20) cannot be solved. However, it can be further converted into an SDP problem through the Vandermonde decomposition theory. Formula (20) is converted into an equivalent SDP definition:

[0091]

[0092] where is a free variable and a conjugate symmetric matrix, is a Hermitian Toeplitz matrix with u as the first column and rank K≤M, Tr(T(u)) is the trace of T(u), and Tr(Q) is the trace of Q.

[0093] The SDP problem can be directly solved using the CVX toolbox, but this method converges very slowly. In order to speed up the convergence speed while protecting the accuracy of the reconstructed signal, the embodiment solves the SDP problem through the alternating direction multiplier method (ADMM) algorithm, and obtains the reconstructed denoising estimate After that, as long as the solution of is obtained, the DOA estimate value can be obtained.

[0094] S3. Frequency estimation based on the rootMUSIC algorithm.

[0095] The rootMUSIC algorithm is a polynomial root-finding MUSIC algorithm based on the Pisarenko decomposition idea. This patent includes the following steps:

[0096] S31. First, process the denoised signal matrix obtained using the ADMM method. Find the covariance matrix C:

[0097]

[0098] by For example, then

[0099] S32. Perform singular value decomposition on the covariance matrix C to obtain the left singular vector, right singular vector, and descending diagonal matrix of singular values ​​of the covariance matrix:

[0100] C=U∑V T (twenty three)

[0101] Among them, the left singular vector of the covariance matrix C A descending diagonal matrix of singular values ​​∑=diag(σ1,…,σ M ), and the right singular vector σ1 represents the maximum singular value, corresponding to the principal component of the signal subspace, σ M This represents the minimum singular value, which typically corresponds to the noise subspace.

[0102] S33. Based on the preceding text, the harmonic number to be considered is also P. Then, the signal subspace E is formed by taking the column vectors corresponding to the first P larger singular values ​​from the left singular vector U. s ,Right now:

[0103] E s = U(:,1:P) (24)

[0104] The remaining MP column vectors constitute the noise subspace E n :

[0105] E n = U(:,P+1:M) (25)

[0106] S34. Construct the spatial spectrum of the MUSIC algorithm based on the steering vector and noise subspace, and convert the peak value of the spatial spectrum into the root of the reciprocal of the spatial spectrum, thereby obtaining the frequency to be estimated.

[0107] In this embodiment, the spatial spectrum formula for the MUSIC algorithm is:

[0108]

[0109] Where a H (θ) represents the conjugate transpose of the guiding vector a(θ). Represents the noise subspace matrix E n The conjugate transpose of; a(θ) = [1, e -j2πdsinθ / λ ,…,e -j2π(M-1)dsinθ / λ ] T Finding the peak value of the spatial spectrum P(θ) is equivalent to finding the reciprocal of the spatial spectrum P. -1 (θ) Find the root:

[0110]

[0111] Let ω=-j2πdsinθ / λ, z=e jω , Where G is the Hermitian matrix, we get:

[0112] a(z) = [1, z, z] 2 ,…,z M-1 ] T =a(θ) (28)

[0113] P -1 (z)=a H (z)Ga(z)=P -1 (θ) (29)

[0114] For P -1 (z) expands to:

[0115]

[0116] Based on the expansion results, it is easy to see that P -1 (z) is a univariate polynomial of degree 2M-1 terms with exactly 2M-2 roots. Here, G[m,n] is the element in the m-th row and n-th column of matrix G, and z... -p The coefficient a of the term p This represents the summation of the p-th diagonal of matrix G, i.e.

[0117] P -1 The 2M-2 roots of (z) form mirror pairs with respect to the unit circle, such as Figure 2 As shown. Select the effective root z whose modulus is close to 1. i ,i=1,…,K, and exclude mirror roots, i.e., roots located outside the unit circle; in obtaining z i Then, according to z = e jω And from ω=2πτL, we get:

[0118]

[0119] S35、According to the i = -d sin θ i / λ and L τ i = L f i / f s The frequency to be estimated is obtained by the rootMUSIC algorithm, that is, f = 2πf

[0120]

[0121] The frequency to be estimated is obtained by the rootMUSIC algorithm, that is, f = 2πf i .

[0122] Based on the same inventive concept, the embodiment also provides a frequency estimation system based on rootMUSIC and signal dimension conversion, which is implemented by using the frequency estimation method, and comprises the following modules:

[0123] The model conversion module is configured to model the chest displacement signal extracted from the radar echo as a sum of sinusoidal waves with integer multiple frequencies of the basic respiration and heart rate, and generate a corresponding single-channel analytic signal through Hilbert transform; and convert the single-channel analytic signal into multi-channel data through a signal rearrangement method, so as to equivalently convert the chest wall signal model into a uniform linear array multi-snapshot receiving signal model, so that the vital sign frequency and the signal source direction of arrival establish a one-to-one correspondence.

[0124] The signal matrix solving module is configured to process the received data of the multi-snapshot receiving signal model through an alternating direction multiplier method framework, and solve a denoised signal matrix.

[0125] The frequency estimation module is configured to use the rootMUSIC algorithm to solve the root of the denoised signal matrix, and perform frequency estimation; wherein the rootMUSIC algorithm is a polynomial root searching form of the MUSIC algorithm based on the Pisarenko decomposition idea.

[0126] The above modules are respectively used to implement steps S1-S3, and the detailed implementation process is described above.

[0127] In addition, the embodiment also provides a computer readable storage medium, which stores a computer program, and when the computer program is run by a computer, the computer executes the frequency estimation method.

[0128] Further, the embodiment also provides a computer device, which comprises a memory, a processor and a computer program stored in the memory and executable by the processor, and when the processor executes the computer program, the frequency estimation method is implemented.

[0129] The above embodiment is one of the embodiments of the present application, and the embodiments of the present application are not limited to the above embodiment, and any change, modification, replacement, combination, simplification, which is not deviated from the spirit and principle of the present application, should be equivalent replacement mode, and all are included in the protection scope of the present application.

Claims

1. A frequency estimation method based on rootMUSIC and signal dimension conversion, characterized in that, The method comprises the following steps: S1, signal model conversion, the chest displacement signal extracted from the radar echo is modeled as the sum of sine waves with integer multiple frequencies of the basic respiration and heart rate, and a corresponding single-channel analytic signal is generated by Hilbert transform; the single-channel analytic signal is converted into multi-channel data by a signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array multi-shot receiving signal model, and a one-to-one correspondence between the vital sign frequency and the signal source direction of arrival is established; S2, the received data of the multi-shot receiving signal model is processed by an alternating direction multiplier method framework to solve a denoised signal matrix; S3, rootMUSIC algorithm is used to solve the denoised signal matrix for frequency estimation; wherein the rootMUSIC algorithm is a polynomial root searching form of MUSIC algorithm based on the Pisarenko decomposition idea; The one-to-one correspondence between the vital sign frequency and the signal source direction of arrival established in step S1 has L shots, and is as follows: Lf i / f s = -d sin θ i / λ; where θ i is the azimuth angle of the ith source, λ is the wavelength, d is the inter-element spacing of the uniform linear array in the far field, f s is the sampling frequency, f i represents the vital sign signal frequency; Step S2 comprises: S21, considering P harmonics of the vital sign signal, the received data of the multi-shot receiving signal model is expressed as Y=A(f)S+Z, wherein A(f) represents a steering matrix related to the vital sign signal frequency and the sampling rate, each column of the steering matrix corresponds to the antenna response vector corresponding to the direction of arrival of the pth source, S represents the transmission signal of the P sources at the new sampling point, Z is an additive white Gaussian noise matrix; f represents the normalized frequency; S22, an atom set G corresponding to the received data Y is defined; considering the signal sparsity, an atom norm l0 is defined to describe the received data Y, and finding the sparsest representation of the received data Y is taken as the goal, and it is equivalent to a l0 norm minimization problem; S23, the l0 norm minimization problem is converted into a convex optimization problem; S24, by Van der Monde decomposition theory, the convex optimization problem is converted into SDP problem, and the SDP problem is solved by the alternating direction multiplier method algorithm to obtain the reconstructed denoised signal matrix 2. The frequency estimation method of claim 1, wherein, Data received in step S21 L represents the number of snapshots, which is equivalent to the number of newly sampled points of the data matrix, and M is the number of array elements; the steering matrix Each column thereof corresponds to an antenna response vector corresponding to the direction of arrival of the pth source, wherein is a steering vector; f i represents the frequency of the vital sign signal; represents the transmission signal of the P sources at the L newly sampled points; The atom set in step S22 is A(f,Φ) denotes an atom in the atom set G, consisting of the outer product of a steering vector a(f) of a normalized frequency f and a normalized complex vector Φ H denotes the conjugate transpose of the complex vector Φ; a(f) denotes a steering vector representing the array response of the signal at a normalized frequency f; The atomic norm l0is defined as: where x p represents a non-negative weight coefficient, and represents the contribution intensity of the pth atom; f p corresponds to the normalized frequency of the pth atom, and Ф p represents the normalized complex vector corresponding to the pth atom, and ||Ф p ||2=1; The atomic norm l0minimization problem is: where η is a constraint parameter; In the convex optimization problem converted in step S23, the atom norm of Y is defined as follows: The transformed SDP problem in step S24 is: where Q is a free variable and is a Hermitian positive semidefinite matrix; is a Hermitian Toeplitz matrix with the first column being u and rank K < M; Tr(T(u)) is the trace of T(u) and Tr(Q) is the trace of Q.

3. The frequency estimation method of claim 1, wherein, Step S3 comprises: S31, the covariance matrix of the denoised signal matrix is solved; S32, singular value decomposition is performed on the covariance matrix to obtain left singular vectors, right singular vectors and a descending order diagonal matrix of singular values of the covariance matrix; the descending order diagonal matrix is Σ = diag(σ1, …, σ M ), wherein the largest singular value σ1 corresponds to the principal component of the signal subspace, and the smallest singular value σ m corresponds to the noise subspace; S33, considering P harmonics of the vital sign signal, the column vectors corresponding to the first P largest singular values in the left singular vector are taken to form a signal subspace, and the remaining M-P column vectors form a noise subspace; S34, the spatial spectrum of the MUSIC algorithm is constructed according to the steering vector and the noise subspace, and the peak value of the spatial spectrum is converted into the root of the reciprocal of the spatial spectrum, so as to solve the frequency to be estimated; S35, the vital sign signal frequency is solved by the relationship between the phase and the frequency.

4. The frequency estimation method of claim 3, wherein, The spatial spectrum formula of the MUSIC algorithm in step S34 is as follows: where a H (0) denotes the conjugate transpose of the steering vector a(0), denotes the noise subspace matrix E n the conjugate transpose; peaking the spatial spectrum P(0) is equivalent to finding the roots of the reciprocal of the spatial spectrum P -1 (0):

5. A frequency estimation system based on rootMUSIC with signal dimension conversion, characterized in that, The frequency estimation method of any one of claims 1-4 is adopted to realize the frequency estimation system, and the frequency estimation system comprises the following modules: The model conversion module is configured to model the chest displacement signal extracted from the radar echo as a sum of sinusoidal waves with fundamental respiratory and integer multiple of heart rate frequencies, and generate a corresponding single-channel analytic signal by Hilbert transform; convert the single-channel analytic signal into multi-channel data by a signal rearrangement method, so as to equivalently model the chest wall signal as a uniform linear array multi-shot receiving signal model, and establish a one-to-one correspondence between the vital sign frequency and the signal source direction of arrival; The signal matrix solving module is configured to process the received data of the multi-shot receiving signal model by an alternating direction multiplier method framework, and solve a denoised signal matrix. The frequency estimation module is configured to use a rootMUSIC algorithm to solve the denoised signal matrix, and perform frequency estimation; the rootMUSIC algorithm is a polynomial root searching form of the MUSIC algorithm based on the Pisarenko decomposition idea.

6. A computer-readable storage medium having stored thereon a computer program, characterized in that, When the computer program is run by the computer, the computer is caused to execute the frequency estimation method according to any one of claims 1-4.

7. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor runs the computer program, the frequency estimation method according to any one of claims 1-4 is implemented.

Images