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

Abstract

The invention 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: modeling chest displacement signals extracted from radar echoes into the sum of sine waves with integral multiple frequencies of basic respiration and heart rate, and generating corresponding single-channel analysis signals through Hilbert transform; single-channel analysis signals are converted into multi-channel data through a signal rearrangement method, a chest wall signal model is equivalent to a uniform linear array multi-snapshot receiving signal model, and a one-to-one correspondence relation is established between the vital sign frequency and the signal source arrival direction; processing receiving data of the multi-snapshot receiving signal model through an alternating direction multiplier method framework, and solving a denoised signal matrix; and carrying out rooting on the denoised signal matrix by using a rootMUSIC algorithm, and carrying out frequency estimation. The signal model is converted, so that the frequency estimation range is equivalent to the angle estimation range, and the frequency estimation precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of biological signal processing, and specifically to a frequency estimation method, storage medium and device based on rootMUSIC and signal dimension conversion. Background Art

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

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

[0004] The MUSIC algorithm is a typical spatial spectrum estimation method based on feature analysis, which can effectively distinguish signals from multiple approaching directions. Its direction finding principle is based on the eigendecomposition of the matrix. Specifically, the MUSIC algorithm first constructs a covariance matrix for the signal data received by the array antenna, and performs eigendecomposition on it to separate the signal into a noise subspace G and a signal subspace S. On this basis, the orthogonality between the noise subspace G and the column vector of the array direction matrix A (i.e., the assumed signal direction) is used to construct the spatial spectrum estimation function P(ω), and the value of P(ω) in different wave arrival directions is calculated. The direction with the largest signal energy is the wave arrival direction. The core of the MUSIC algorithm lies in the subspace separation of signals and noise and their orthogonality. This spatial spectrum estimation principle based on eigendecomposition 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 regarded as the superposition of the respiratory signal, heartbeat signal, various harmonic signals of the respiratory signal and noise. That is, the chest wall displacement signal obtained by analysis contains effective components and noise, and the subspace of the effective component is orthogonal to the noise subspace. Therefore, a spatial spectrum function can be constructed and a spectrum peak search can be performed. The frequency corresponding to the peak angle is used as the frequency of the target signal, thereby realizing the spectrum estimation of the signal.

[0006] However, the MUSIC algorithm requires spectrum peak search to be implemented, which requires huge computation and makes it difficult to achieve real-time frequency estimation. In order to reduce the amount of computation, the search is only performed on limited discrete points, which will result in off-grid errors. That is, during the discretization search process, the actual wave direction or frequency of the signal may not fall exactly on the preset discrete grid points, resulting in errors between the estimated result and the true value. The larger the discretization step size of the grid, the larger the off-grid error may be.

[0007] In addition, in the existing methods, when using the MUSIC algorithm to estimate the frequency of vital sign signals, the problem that the range of respiratory frequency and heart rate does not match the original DOA estimation range is not considered. In the existing MUSIC spectrum estimation method, the spatial incident angle is replaced by the frequency and the frequency spectrum is directly estimated, that is, the direction matrix changes from A(θ) to A(ω):

[0008]

[0009] In the formula, ω i is the normalized frequency, which is different from the true frequency f i Satisfy i =2πf i T s =2πf i / f s The relationship between T s is the sampling interval, f s is the sampling rate; when replacing, replace the angle in A(θ) with the frequency, i.e. πsinθ i =ω i , 1≤i≤M; then divide [0,2π] into N equal intervals w A grid search is performed to estimate the frequency.

[0010] However, general methods do not take into account the frequency estimation of vital sign signals. i The normal breathing rate of an adult is between 10 and 30 times per minute, and the heart rate is between 48 and 120 times per minute. b ∈[0.17,0.5]Hz, f h ∈[0.8,2]Hz, and the sampling rate f s It is usually much larger than the highest frequency of the vital sign signal, assuming it is f s =200Hz, then ω i =2πf i / f s ∈[0,0.01]Hz, and πsinθ i∈[-π,π], the frequency estimation range is equivalent to the angle estimation range, which is much smaller than the angle estimation range when the MUSIC algorithm is used for DOA estimation. This makes the grid search range extremely redundant and reduces the frequency estimation accuracy. In order to improve the accuracy of the MUSIC algorithm in estimating the respiratory and heartbeat frequency in the vital signs monitoring scenario, the conventional operation is to further increase the density of the grid division, which will further increase the computational complexity. Summary of the invention

[0011] In order to solve the problems existing in the prior art, the present invention proposes a frequency estimation method, system, storage medium and device based on rootMUSIC and signal dimension conversion, adopts the rootMUSIC algorithm, replaces the spectrum peak search with polynomial root finding, reduces the amount of calculation, and converts the signal model so that the frequency estimation range is equivalent to the angle estimation range, improves the frequency estimation accuracy, and further reduces the amount of calculation.

[0012] In a first aspect, an embodiment of the present invention provides 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 basic breathing and heart rate, and the corresponding single-channel analytical signal is generated through Hilbert transform; the single-channel analytical signal is converted into multi-channel data through the signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array multi-snapshot receiving signal model, so that a one-to-one correspondence is established between the vital sign frequency and the arrival direction of the signal source;

[0014] S2, processing the received data of the multi-snap received signal model through the framework of the alternating direction multiplier method to solve the denoised signal matrix;

[0015] S3. Use the rootMUSIC algorithm to find the roots of the denoised signal matrix and perform frequency estimation; wherein the rootMUSIC algorithm is a polynomial root search form of the MUSIC algorithm based on the Pisarenko decomposition idea.

[0016] In a second aspect, based on the same inventive concept, an embodiment of the present invention provides a frequency estimation system based on rootMUSIC and signal dimension conversion, which is implemented by the above-mentioned frequency estimation method. The frequency estimation system includes the following modules:

[0017] The model conversion module is used to model the chest displacement signal extracted from the radar echo as the sum of sine waves with integer multiple frequencies of basic breathing and heart rate, and generate the corresponding single-channel analytical signal through Hilbert transform; the single-channel analytical signal is converted into multi-channel data through the signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array multi-snap shot receiving signal model, so that a one-to-one correspondence is established between the vital sign frequency and the arrival direction of the signal source;

[0018] The signal matrix solving module processes the received data of the multi-snap received signal model through the framework of the alternating direction multiplier method to solve the denoised signal matrix;

[0019] The frequency estimation module is used to find the roots of the denoised signal matrix using the rootMUSIC algorithm to perform frequency estimation; wherein the rootMUSIC algorithm is a polynomial root search form MUSIC algorithm based on the Pisarenko decomposition idea.

[0020] In a third aspect, an embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a computer, the computer executes the above-mentioned frequency estimation method.

[0021] In a fourth aspect, an embodiment of the present invention further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the above-mentioned frequency estimation method is implemented.

[0022] Compared with the prior art, the technical effects achieved by the present invention include:

[0023] 1. The present invention rearranges one-dimensional signal data into two-dimensional data, that is, converts single-channel data into multi-channel data, and combines the high-resolution spectrum estimation method rootMUSIC algorithm to improve the accuracy of frequency estimation, and uses polynomial root finding instead of spectrum peak search to reduce computational complexity; the signal model is converted so that the frequency estimation range is equivalent to the angle estimation range; it can be applied to vital sign monitoring scenarios in radar signal processing, as well as other application scenarios that require high-precision frequency estimation.

[0024] 2. The present invention uses off-grid MUSIC methods based on sparse representation. These algorithms directly estimate continuous parameters rather than parameters on discrete grid points through model adjustment and parameter optimization, thereby effectively reducing off-grid errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a flow chart of a frequency estimation method in an embodiment of the present invention;

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

[0027] The technical solution of the present invention is further described in detail below in conjunction with embodiments and drawings, but the implementation manner of the present invention is not limited thereto.

[0028] Example

[0029] This embodiment provides a frequency estimation method based on rootMUSIC and signal dimension conversion. First, the chest displacement signal extracted from the radar echo is modeled as the sum of sine waves with integer multiple frequencies of basic breathing and heart rate, and the corresponding analytical signal is generated by Hilbert transform. On this basis, the single-channel data is converted into multi-channel data through signal rearrangement method to facilitate subsequent frequency estimation. On the basis of signal rearrangement, the alternating direction method of multipliers (ADMM) framework is used to solve the denoised signal matrix, and then the rootMUSIC algorithm is used to find the root of the denoised signal matrix to solve the frequency to be estimated. The processing flow is as follows: Figure 1 As shown, the specific steps include:

[0030] 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 basic breathing and heart rate, and the corresponding single-channel analytical signal is generated through Hilbert transform. The single-channel analytical signal is converted into multi-channel data through the signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array (ULA) multi-snap receiving signal model, so that a one-to-one correspondence is established between the vital sign frequency and the direction of arrival (DOA) of the signal source.

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

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

[0033]

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

[0035] S12, generating an analytical signal, and generating a corresponding single-channel analytical signal through Hilbert transform for subsequent processing.

[0036] For the simplicity of the following derivation, only P is considered. b =P h =1, that is:

[0037]

[0038] definition is the Hilbert transform of the sine wave combination r(t), then As shown below:

[0039]

[0040] Then the expression of the analytical signal R(t) is as follows:

[0041]

[0042] where a b is the amplitude of the respiratory component, is the initial phase of the breathing component, a h is the amplitude of the heartbeat component, is the initial phase of the heartbeat component, Represents the complex amplitude.

[0043] S13. Convert the single-channel analytical signal into multi-channel data through a signal rearrangement method, thereby converting the chest wall signal model into a uniform linear array multi-snapshot receiving signal model, so that a one-to-one correspondence is established between the vital sign frequency and the arrival direction of the signal source.

[0044] Sample the continuous signal R(t), assuming its duration is T and 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 sampled discrete signal R(n) is M l ,in 0≤n≤M l -1, we get:

[0045]

[0046] Use f i Indicates the frequency of vital signs signal, replacing the previous f b and f h and use A i Instead of the previous complex amplitude A b and A h, and i = 1, 2. Write the sampled discrete signal R(n) in matrix form R:

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

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

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

[0050] R=A(τ)S A (7)

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

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

[0053] x(n)=A(θ)s(n)+z(n) (8)

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

[0055] Comparing formula (7) with signal model (8), we can see that the exponential term and the term in A(θ) Very similar. 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-related parameters and angles are in one-to-one correspondence, that is, the frequency estimation signal model is associated with the angle estimation signal model.

[0056] It should be noted that f s Usually much higher than f i For example, when f s =200Hz and maximum f i When the frequency does not exceed 2 Hz, the estimated parameter τ i =f i / f s The range of is limited to between 0 and 0.01. Since the wavelength ratio d / λ corresponding to the array element spacing is usually equal to 1 / 2, considering the DOA angle θ i The range is -90°~90°, then -dsinθ i / λ ranges from -0.5 to 0.5. Compared with the angle estimation range, τ i The range of τ is obviously narrower. Therefore, to improve the estimation accuracy and frequency resolution, it is necessary to expand τ i =f i / f s The range of -dsinθ is i / λ range.

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

[0058]

[0059] Define the M×L matrix obtained after rearrangement as X, and let the i-th row of X be X i ; The first row X1 of the matrix X is decomposed into:

[0060]

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

[0062]

[0063] Similarly, the Mth row of matrix X, i.e. the last row X M is broken down into:

[0064]

[0065]

[0066] Observe the rearranged M×L matrix X. Each row of the matrix can be decomposed in turn. Each 1×L row vector X from X i Can be decomposed into A i S, that is, X i =A i S, according to the matrix block multiplication, can be obtained

[0067]

[0068] in:

[0069]

[0070] Therefore, the discrete signal R(n) is rearranged into an M×L matrix form X with L new sampling points, which is similar to the far-field ULA receiving signal model with M elements, two signal sources and L snapshots (i.e., in the previous far-field receiving signal model, L s =L). In this far-field ULA receiving signal model, it is originally defined as -dsinθ i The parameter τ / λ i 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, Lτ i The range corresponds approximately to -dsinθ i / λ, thus solving the problem due to τ i The problem of insufficient estimation accuracy due to the limited original range.

[0071] Thus, this embodiment successfully converts the unique chest wall signal model r(t) 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 a 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. The received data of the multi-snap received signal model is processed through the alternating direction method of multipliers (ADMM) framework to solve the denoised signal matrix.

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

[0074] S21. Considering the harmonic influence of breathing and heartbeat signals, the fundamental frequency and harmonics of the vital sign signal are taken into account. In order to correspond to the array signal model with P signal sources in the previous text, let 2≤i≤P, that is, the number of harmonics to be considered is P.

[0075] According to the modeling in step S1, after converting the single-channel data into multi-channel data, taking into account the observation noise, the received data of the ULA multi-snap received signal model can be expressed as:

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

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

[0078] S22. Define the atomic set corresponding to the received data Y Specifically:

[0079]

[0080] Where A(f,φ) represents the set of atoms An atom in 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 a primitive of a potential component in the signal, which is used for gridless sparse signal recovery and DOA estimation; φ H represents the conjugate transpose of the complex vector φ (same as the Hermitian transpose); φ represents a normalized complex vector, satisfying ||φ||2=1, representing the phase and amplitude information of the signal; a(f) represents the steering vector, defined as shown in formula (16), representing the array response of the signal at the normalized frequency f. The atomic set defined in the constraint norm is the 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, we can define the atomic norm l0 to describe Y, that is, Y is an atomic set The linear combination of P atoms in :

[0082]

[0083] Among them, xp represents a non-negative weight coefficient, indicating the contribution intensity of the pth atom; f p The normalized frequency corresponding to the pth atom, φ p represents the normalized complex vector corresponding to the pth atom, and ||φ p ||2=1.

[0084] The goal is to find the sparsest representation of the received data Y, and the goal is equivalent to an atomic norm minimization problem. This embodiment considers the following atomic norm l0 minimization problem:

[0085]

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

[0087] S23. Convert the atomic norm minimization problem into a convex optimization problem.

[0088] The rank constraint of the above atomic norm minimization problem is non-convex, so it cannot be solved using convex optimization methods. Secondly, if the measurement results are interfered by noise, there will be no optimal low rank. To solve this problem, the following will be transformed into a convex optimization problem, and the atomic norm of Y is defined as follows:

[0089]

[0090] S24. Due to the atomic collection Containing countless atoms, the transformed convex optimization problem is a semi-infinite problem, and equation (20) still cannot be solved. However, it can be further transformed into an SDP problem through the Vandermonde decomposition theory. Convert equation (20) into an equivalent SDP definition:

[0091]

[0092] in 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 solved directly using the CVX toolbox, but the convergence speed of this method is very slow. In order to speed up the convergence speed and protect the accuracy of the reconstructed signal, this embodiment solves the SDP problem using the alternating direction method of multipliers (ADMM) algorithm to obtain the reconstructed denoised estimate After that, as long as The DOA estimate can be obtained by solving the problem.

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

[0095] The rootMUSIC algorithm is a polynomial root search MUSIC algorithm based on the Pisarenko decomposition concept. In this patent, the following steps are included:

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

[0097]

[0098] by For example,

[0099] S32, perform singular value decomposition on the covariance matrix C to obtain the left singular vectors, right singular vectors 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 is The descending diagonal matrix of singular values ​​∑=diag(σ1,…,σ M ), and the right singular vectors σ1 represents the maximum singular value, corresponding to the principal component of the signal subspace, σ M Represents the smallest singular value, usually corresponding to the noise subspace.

[0102] S33. According to the previous text, the number of harmonics to be considered is also P. Then, the column vectors corresponding to the first P larger singular values ​​in the left singular vector U are taken to form the signal subspace E. 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, constructing a spatial spectrum of the MUSIC algorithm according to the steering vector and the noise subspace, converting the peak value of the spatial spectrum into the root of the inverse of the spatial spectrum, thereby obtaining the frequency to be estimated.

[0107] The spatial spectrum formula of the MUSIC algorithm in this embodiment is:

[0108]

[0109] where a H (θ) represents the conjugate transpose of the steering vector a(θ), Denotes 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 inverse of the spatial spectrum P -1 (θ) root:

[0110]

[0111] Let ω=-j2πdsinθ / λ, z=e jω , Where G is a 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] P -1 (z) is expanded to:

[0115]

[0116] According to the expansion results, it is easy to get that P -1 (z) is a 2M-2 degree polynomial with 2M-1 terms and has only 2M-2 roots. Where G[m,n] is the element in the mth row and nth column of the matrix G, z -p The coefficient of the term a p represents the sum of the p-th diagonal of the matrix G, that is,

[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 an effective root z with a modulus close to 1 i , i = 1, ..., K, and exclude the mirror root, that is, the root outside the unit circle; in order to obtain z i Then, according to z = e jω and ω=2πτL we get:

[0118]

[0119] S35, according to τ i = -dsinθ i / λ and Lτ i =Lf i / f s , the required frequency is:

[0120]

[0121] That is, the frequency f to be estimated is obtained through the rootMUSIC algorithm i .

[0122] Based on the same inventive concept, this embodiment also provides a frequency estimation system based on rootMUSIC and signal dimension conversion, which is implemented by the above-mentioned frequency estimation method. The frequency estimation system includes the following modules:

[0123] The model conversion module is used to model the chest displacement signal extracted from the radar echo as the sum of sine waves with integer multiple frequencies of basic breathing and heart rate, and generate the corresponding single-channel analytical signal through Hilbert transform; the single-channel analytical signal is converted into multi-channel data through the signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array multi-snap shot receiving signal model, so that a one-to-one correspondence is established between the vital sign frequency and the arrival direction of the signal source;

[0124] The signal matrix solving module processes the received data of the multi-snap received signal model through the framework of the alternating direction multiplier method to solve the denoised signal matrix;

[0125] The frequency estimation module is used to find the roots of the denoised signal matrix using the rootMUSIC algorithm to perform frequency estimation; wherein the rootMUSIC algorithm is a polynomial root search form MUSIC algorithm based on the Pisarenko decomposition idea.

[0126] The above modules are used to implement steps S1-S3 respectively, and the detailed implementation process thereof can be found in the above steps.

[0127] In addition, this embodiment further provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a computer, the computer executes the above-mentioned frequency estimation method.

[0128] Furthermore, this embodiment also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the above-mentioned frequency estimation method is implemented.

[0129] The above embodiment is one of the implementation modes of the present invention, and the implementation modes of the present invention are not limited to the above embodiment. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and shall be included in the protection scope of the present invention.

Claims

1. A frequency estimation method based on rootMUSIC and signal dimension conversion, characterized in that: The following steps are involved: 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 basic breathing and heart rate, and the corresponding single-channel analytical signal is generated through Hilbert transform; the single-channel analytical signal is converted into multi-channel data through the signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array multi-snapshot receiving signal model, so that a one-to-one correspondence is established between the vital sign frequency and the arrival direction of the signal source; S2, processing the received data of the multi-snap received signal model through the framework of the alternating direction multiplier method to solve the denoised signal matrix; S3. Use the rootMUSIC algorithm to find the roots of the denoised signal matrix and perform frequency estimation; wherein the rootMUSIC algorithm is a polynomial root search form of the MUSIC algorithm based on the Pisarenko decomposition idea.

2. The frequency estimation method according to claim 1, characterized in that: In step S1, the received signal model has L snapshots, and the one-to-one correspondence between the vital sign frequency and the signal source arrival direction is established as follows: Lf i / f s =-d sinθ i / l; where θ i is the azimuth angle of the i-th signal source, λ is the wavelength, d is the array element spacing of the far-field receiving uniform linear array, and f s is the sampling frequency, f i Indicates the frequency of vital sign signals.

3. The frequency estimation method according to claim 1, characterized in that: Step S2 includes: S21. Considering the P harmonics of the vital sign signal, the received data of the multi-snapshot received signal model is represented as Y=A(f)S+Z, where 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 arrival direction of the p-th source, S represents the transmitted signals of the P sources at the new sampling point, and Z is an additive white Gaussian noise matrix; S22. Define the atomic set corresponding to the received data Y Considering the signal sparsity, the atomic norm l0 is defined to describe the received data Y. The goal is to find the sparsest representation of the received data Y, which is equivalent to an atomic norm l0 minimization problem. S23, transform the atomic norm l0 minimization problem into a convex optimization problem; S24. Through the Vandermonde decomposition theory, the convex optimization problem is transformed into the SDP problem, and then the SDP problem is solved by the alternating direction multiplier method algorithm to obtain the reconstructed denoised signal matrix 4. The frequency estimation method according to claim 3, characterized in that: Step S21: receiving data L represents the number of snapshots, which is equivalent to the number of new sampling points in the data matrix, and M is the number of array elements; the steering matrix Each column corresponds to the antenna response vector corresponding to the arrival direction of the pth source, where is the steering vector; f i Indicates the frequency of vital sign signals; Represents the transmitted signals of P sources at L new sampling points; The atomic set in step S22 is A(f,φ) represents the set of atoms An atom in is composed of the outer product of the normalized frequency f and the normalized complex vector φ; φ H represents the conjugate transpose of the complex vector φ; a(f) represents the steering vector, which represents the array response of the signal at the normalized frequency f; The atomic norm l0 is defined as: where x p represents a non-negative weight coefficient, indicating the contribution intensity of the pth atom; f p The normalized frequency corresponding to the pth atom, φ p represents the normalized complex vector corresponding to the pth atom, and ||φ p ||2=1; The atomic norm l0 minimization problem is: Where η is the constraint parameter; In the convex optimization problem transformed in step S23, the atomic norm of Y is defined as follows: The SDP problem converted in step S24 is: Where Q 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.

5. The frequency estimation method according to claim 1, characterized in that: Step S3 includes: S31, calculating the covariance matrix of the denoised signal matrix; S32, perform singular value decomposition on the covariance matrix to obtain a descending diagonal matrix of left singular vectors, right singular vectors and singular values ​​of the covariance matrix; the descending diagonal matrix is ​​∑=diag(σ1,…,σ M ), where the maximum singular value σ1 corresponds to the principal component of the signal subspace, and the minimum singular value σ M Corresponding to the noise subspace; S33, considering the P harmonics of the vital sign signal, taking the column vectors corresponding to the first P larger singular values ​​from the left singular vector to form a signal subspace, and the remaining MP column vectors to form a noise subspace; S34, constructing a spatial spectrum of the MUSIC algorithm according to the steering vector and the noise subspace, converting the peak value of the spatial spectrum into the root of the inverse of the spatial spectrum, thereby obtaining the frequency to be estimated; S35. Calculate the frequency of the vital sign signal through the relationship between phase and frequency.

6. The frequency estimation method according to claim 5, characterized in that: The spatial spectrum formula of the MUSIC algorithm in step S34 is: where a H (θ) represents the conjugate transpose of the steering vector a(θ), Denotes the noise subspace matrix E n The conjugate transpose of the spatial spectrum P(θ) is equivalent to the inverse of the spatial spectrum P -1 (θ) Find the root:

7. A frequency estimation system based on rootMUSIC and signal dimension conversion, characterized in that: The frequency estimation method according to any one of claims 1 to 6 is used to implement the frequency estimation system, wherein the frequency estimation system comprises the following modules: The model conversion module is used to model the chest displacement signal extracted from the radar echo as the sum of sine waves with integer multiple frequencies of basic breathing and heart rate, and generate the corresponding single-channel analytical signal through Hilbert transform; the single-channel analytical signal is converted into multi-channel data through the signal rearrangement method, so that the chest wall signal model is equivalent to a uniform linear array multi-snap shot receiving signal model, so that a one-to-one correspondence is established between the vital sign frequency and the arrival direction of the signal source; The signal matrix solving module processes the received data of the multi-snap received signal model through the framework of the alternating direction multiplier method to solve the denoised signal matrix; The frequency estimation module is used to find the roots of the denoised signal matrix using the rootMUSIC algorithm to perform frequency estimation; wherein the rootMUSIC algorithm is a polynomial root search form MUSIC algorithm based on the Pisarenko decomposition idea.

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

9. A computer device comprising a memory, a processor, and a computer program stored in 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 to 6 is implemented.

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