Method for measuring horizontal coherence length of underwater acoustic signal based on effective degree of freedom of eigenvalue difference
Patent Information
- Application Number
- CN202611468914.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-21
- Publication Date
- 2026-10-30
AI Technical Summary
[0006]综上所述，现有基于特征值分布的水平相干长度测量方法的主要技术缺陷在于：互谱密度矩阵的特征值分布在低信噪比条件下会受到噪声的显著干扰，导致相干测度的估计精度下降，从而影响水平相干长度的测量准确性
[0034]第一，本发明通过构造特征值差分，利用噪声能量在互谱密度矩阵特征值上近似均匀分布的特性，通过差分抵消噪声能量，抑制噪声功率对特征值分布的影响，从而提高了水平相干长度测量方法对噪声的稳健性。理论分析和实验验证均表明，在信噪比高于-10dB时，本发明的换算关系曲线与无噪声条件下的换算关系曲线几乎重合。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of horizontal coherence length measurement technology in underwater acoustic signal processing, specifically to a method for measuring the horizontal coherence length of underwater acoustic signals based on eigenvalue difference effective degrees of freedom, which can be used for spatial coherence assessment and array design of large-aperture underwater acoustic arrays. Background Technology
[0002] Large-aperture arrays can achieve significant signal gain by coherently superimposing received signals. However, as the array aperture increases, the spatial coherence of the signals received by each element gradually decreases with the element spacing, causing the array gain to tend towards a limit rather than increasing indefinitely. Therefore, spatial coherence significantly affects the array's processing performance. The horizontal coherence length provides the maximum length at which a signal can maintain significant coherence and can serve as a reference for designing the array aperture length in engineering, thereby balancing system cost and processing performance.
[0003] In existing technologies, a common method for measuring horizontal coherence length is to estimate the horizontal coherence length by using the array's measured spatial coherence function and estimating the element spacing when the function decreases to 1 / e. This method requires the array length to exceed the measured spatial coherence length, and because the measurement of the spatial coherence function is susceptible to noise interference, a high signal-to-noise ratio is also required. However, in actual marine environments, due to experimental limitations and the influence of marine environmental noise, these two conditions are often difficult to meet simultaneously. Therefore, the horizontal coherence length measurement method based on the spatial coherence function cannot meet the actual measurement accuracy requirements.
[0004] To address the challenge of measuring horizontal coherence length under conditions of low signal-to-noise ratio and limited array length, Carey established a quantitative conversion relationship between array beam output and horizontal coherence length by using array signal gain degradation (ASGD) as the original coherence measure (Carey W M. The determination of signal coherence length based on signal coherence and gain measurements in deep and shallow water[J]. The Journal of the Acoustical Society of America, 1998, 104(2): 831-837.). This method alleviates the dependence on array aperture length to some extent and improves the robustness of measurement results to noise interference. However, the beam output effect of this method depends on the matching degree of the signal model and the accuracy of the array element positions, and is therefore easily affected by model mismatch and array element position errors.
[0005] Heaney established a conversion relationship between the two coherence measures and coherence length using two eigenvalue distribution-based coherence measures: power factor and eigenvalue ratio (Heaney K D. Shallow water narrowband coherence measurements in the Florida Strait. The Journal of the Acoustical Society of America, 2011, 129(4): 2026-2041.). This type of method reduces the impact of signal model mismatch and element position errors, but because noise can change the eigenvalue distribution of the cross-spectral density matrix, this type of method is still sensitive to the signal-to-noise ratio.
[0006] In summary, the main technical drawback of existing horizontal coherence length measurement methods based on eigenvalue distribution is that the eigenvalue distribution of the cross-spectral density matrix is significantly affected by noise under low signal-to-noise ratio conditions, leading to a decrease in the estimation accuracy of coherence measure and thus affecting the measurement accuracy of horizontal coherence length. Summary of the Invention
[0007] Building upon the method of measuring horizontal coherence length based on eigenvalue distribution, this invention provides a method for measuring the horizontal coherence length of underwater acoustic signals based on eigenvalue difference effective degrees of freedom to further improve the noise robustness of such methods. This method constructs a new coherence measure—effective degrees of freedom—based on the eigenvalue difference results. Utilizing the characteristic that noise is approximately uniformly distributed across the eigenvalues of the cross-spectral density matrix, it suppresses the influence of noise on the eigenvalue distribution through the difference between adjacent eigenvalues, thereby improving the noise resistance of the eigenvalue distribution-based horizontal coherence length measurement method.
[0008] The technical solution of this invention is as follows:
[0009] A method for measuring the horizontal coherence length of underwater acoustic signals based on eigenvalue difference effective degrees of freedom includes the following steps:
[0010] Step 1: Divide the narrowband signal received by the array into time-domain snapshots, estimate the cross-spectral density matrix of each sub-signal, and perform eigenvalue decomposition on the cross-spectral density matrix to obtain the eigenvalues arranged in descending order.
[0011] Step 2: Perform forward difference analysis on adjacent feature values of the descendingly ordered feature values, and calculate the effective degrees of freedom (EDOF) using the difference results;
[0012]
[0013] in The number of array elements , The first in descending order One eigenvalue;
[0014] Step 3: Under the assumption that the spatial coherence function is of Gaussian form, construct the theoretical cross-spectral density matrix based on the spatial coherence function. The element expression; given the horizontal coherence length The theoretical cross-spectral density matrix at this horizontal coherence length is constructed using the aforementioned element expression. For the theoretical cross-spectral density matrix Perform eigenvalue decomposition to obtain eigenvalues in descending order, and calculate the effective degrees of freedom (EDOF) at this horizontal coherence length according to step 2; change the given horizontal coherence length value and repeat the above construction, eigenvalue decomposition, and calculation process to establish the relationship between the effective degrees of freedom (EDOF) and the horizontal coherence length. The monotonically decreasing conversion relationship between them; the effective degrees of freedom (EDOF) calculated based on measured data, and the horizontal coherence length estimated through the conversion relationship. The spatial coherence function is:
[0015]
[0016] The distance variable is the array element distance.
[0017] In a further preferred embodiment, in step 1, for A uniform linear array is used to divide the received signal into sub-signals by windowing and overlapping processing. The cross-spectral density matrix is represented as follows:
[0018]
[0019] in For the number of snapshots, This is time-domain snapshot data. Indicates conjugate transpose;
[0020] For the cross-spectral density matrix Perform eigenvalue decomposition:
[0021]
[0022] The number of eigenvalues is equal to the number of array elements. , Cross-spectral density matrix Eigenvalues sorted in descending order Eigenvalues The corresponding feature vector.
[0023] In a further preferred embodiment, in step 2, the forward difference between adjacent feature values is divided into:
[0024]
[0025] The effective degrees of freedom (EDOF) ranges from 1 to 10. The smaller the EDOF value, the stronger the spatial coherence.
[0026] In a further preferred embodiment, in step 3, the theoretical cross-spectral density matrix The elements are represented as:
[0027]
[0028] in For signal amplitude, The distance between adjacent array elements. For the first Each element and the first The spacing between array elements.
[0029] Furthermore, the present invention also proposes an electronic device and a computer-readable storage medium:
[0030] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described above.
[0031] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the above-described method.
[0032] Beneficial effects:
[0033] Compared with the prior art, the present invention has the following advantages:
[0034] First, this invention constructs an eigenvalue difference mechanism, utilizing the approximately uniform distribution of noise energy across the eigenvalues of the cross-spectral density matrix. This difference mechanism cancels out noise energy, suppressing the influence of noise power on the eigenvalue distribution, thereby improving the robustness of the horizontal coherence length measurement method to noise. Both theoretical analysis and experimental verification show that when the signal-to-noise ratio is higher than -10dB, the conversion curve of this invention almost coincides with the conversion curve under noise-free conditions.
[0035] Second, compared with measurement methods based on signal gain decay (ASGD), this invention reduces the impact of signal model mismatch and array element position errors, making the measurement of horizontal coherence length more accurate. Experimental data verification shows that the measurement results of the method of this invention are highly consistent with the ASGD method in terms of magnitude and variation trend, and the method of this invention has a stronger ability to suppress non-ideal factors.
[0036] Third, compared with existing measurement methods based on eigenvalue distribution (such as Heaney's power factor method and eigenvalue ratio method), this invention suppresses the influence of noise on eigenvalue distribution through differential processing, and further improves noise resistance while maintaining the advantage of insensitivity to pair element position error and model mismatch.
[0037] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0038] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:
[0039] Figure 1 Diagram of conventional beamforming results for receiving data;
[0040] Figure 2 The graph shows the change of effective degrees of freedom at each frequency over time.
[0041] Figure 3 A graph showing the conversion relationship between effective degrees of freedom and horizontal coherence length;
[0042] Figure 4 A comparison of the conversion relationship curves as a function of signal-to-noise ratio under Gaussian white noise conditions;
[0043] Figure 5 This is a comparison chart of the results of the effective degrees of freedom measurement method of the present invention and the ASGD measurement method. Detailed Implementation
[0044] This invention proposes a method for measuring the horizontal coherence length of underwater acoustic signals based on eigenvalue difference effective degrees of freedom. For narrowband signals received by an array, this method calculates the cross-spectral density matrix and solves for its eigenvalues. The eigenvalues are then sorted in descending order, and adjacent eigenvalues are subtracted. The effective degrees of freedom are then calculated using these eigenvalue differences. Assuming the spatial coherence function is of Gaussian form, a conversion relationship between effective degrees of freedom and horizontal coherence length is established through numerical simulation. Therefore, the horizontal coherence length can be measured by measuring the effective degrees of freedom.
[0045] Specifically, the following steps are included:
[0046] Step 1: For A uniform linear array is used to perform a Hilbert transform on the narrowband signal received by the array to obtain a time-domain snapshot. Then, windowing and overlapping processing are applied according to the actual situation to divide the received signal into several sub-signals. For each sub-signal, the cross-spectral density matrix of each sub-signal is estimated:
[0047]
[0048] in For the number of snapshots, This is time-domain snapshot data. This indicates the conjugate transpose.
[0049] For the cross-spectral density matrix Perform eigenvalue decomposition:
[0050]
[0051] The number of eigenvalues is equal to the number of array elements. , Cross-spectral density matrix Eigenvalues sorted in descending order Eigenvalues The corresponding feature vector.
[0052] Step 2: Perform forward difference operations on adjacent eigenvalues for the descendingly ordered eigenvalues:
[0053]
[0054] When the noise power does not vary significantly between adjacent eigenvalues (i.e., the noise eigenvalues are approximately uniformly distributed), noise energy can be canceled out through differentiation, thereby suppressing the influence of noise power on the eigenvalue distribution. The mathematical principle is as follows:
[0055] Construct the effective degrees of freedom (EDOF) using the difference results;
[0056]
[0057] From a mathematical perspective, the above formula can be equivalently understood as a difference sequence. A measure of energy concentration. If we denote the arithmetic mean of the difference sequences as:
[0058]
[0059] The mean square value is:
[0060]
[0061] The formula for effective degrees of freedom (EDOF) is equivalently transformed into:
[0062]
[0063] The closer this ratio is to 1, the more concentrated the energy of the difference sequence is in a few values. The stronger the corresponding spatial coherence, the closer the ratio is to... This indicates that the more the energy of the difference sequence is dispersed across each individual sequence, the better. The weaker the corresponding spatial coherence.
[0064] From a physical perspective, EDOF measures the eigenvalue from its highest point. Landing at the lowest point The "effective number of drops" experienced during the process: when the sound field is completely coherent, only And its ,at this time , Substituting into the EDOF formula, we get When the sound field is completely incoherent or the received signal is pure noise, the eigenvalues are approximately equal. Substituting into the EDOF formula, we get Therefore, the range of EDOF values is... The smaller the value, the stronger the spatial coherence; the larger the value, the weaker the spatial coherence.
[0065] The principle of differential processing to suppress the influence of noise power can be stated as follows: Under additive white Gaussian noise conditions, the eigenvalues of the noise covariance matrix are approximately equal (all equal to the noise power). Let the noise-inducing characteristic value be... (Under ideal conditions, the noise characteristic values are uniformly distributed), then:
[0066]
[0067] Therefore, the noise term The noise is completely canceled out during the differential process, and EDOF is insensitive to white noise power. For noise fields with approximately uniform eigenvalue distribution in real marine environments, differential processing can also effectively suppress the influence of noise energy. This is the core technological improvement of this invention in terms of noise resistance compared to existing measurement methods based on eigenvalue distribution.
[0068] Step 3: Under the assumptions of constant amplitude and random phase fluctuations following a Gaussian distribution, the spatial coherence function adopts a Gaussian form:
[0069]
[0070] in The horizontal coherence length, For the element distance variable. Combining the above spatial coherence function form, the theoretical cross-spectral density matrix... The elements can be represented as:
[0071]
[0072] in For signal amplitude, The distance between adjacent array elements. For the first Each element and the first The spacing between array elements;
[0073] The given horizontal coherence length can be obtained using the above formula. Theoretical cross-spectral density matrix Then, the theoretical cross-spectral density matrix Perform eigenvalue decomposition to obtain eigenvalues arranged in descending order, and calculate the effective degrees of freedom (EDOF) according to step 2; change the given horizontal coherence length value and repeat the above construction and calculation process, thereby establishing the relationship between the effective degrees of freedom (EDOF) and the horizontal coherence length. The conversion relationship is monotonically decreasing. In actual measurements, the effective degrees of freedom (EDOF) are calculated based on measured data, and the horizontal coherence length can be estimated using the above conversion relationship. .
[0074] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to illustrate the present invention and should not be regarded as limiting the scope of the present invention.
[0075] Example 1:
[0076] This embodiment uses measured data to verify the performance of the horizontal coherence length measurement method based on eigenvalue difference effective degrees of freedom proposed in this invention.
[0077] 1. Brief introduction of measured data and preprocessing of received signal
[0078] The measured data used in this embodiment comes from a deep-sea convergence zone acoustic propagation experiment conducted in a certain sea area. The transmitted signal consists of 9 sets of uncorrelated chaotic frequency-modulated sequences, each lasting 20 seconds, for a total duration of 180 seconds. The operating frequency is 100Hz-250Hz, the transmission depth is 105m (approximately 5400m deep), and the target bearing is approximately 144°. During signal transmission, the signal is paused for 30 seconds every 10 minutes to allow for differentiation between the target signal and interference. The towed array contains 192 elements, spaced 1.5m apart, with a total length of 317m. The straight-line distance between the two ships is approximately 56.4km. The received data from each element is filtered, digitized, and stored at a sampling rate of 12kHz.
[0079] To reduce the impact of ship self-noise and array distortion, data from array elements 20 to 192 were selected for processing. The received signal was passed through multiple bandpass filters to obtain a set of narrowband signals with center frequencies of 103Hz, 129Hz, 160Hz, 203Hz, and 250Hz. To suppress interference and noise from other directions, the selected array elements were divided into overlapping subarrays, and the beamout of each subarray at the target azimuth was used as the received signal of the first element in the subarray. A subarray length of 51 elements was chosen, with adjacent subarrays overlapping by 50 elements (i.e., elements 20-70 form the first subarray, elements 21-71 form the second subarray, and so on). After the above processing, received data from 123 array elements were obtained.
[0080] The received signal was divided into sub-signals of 10 seconds in length for processing, with an overlap rate of 50% and a sampling rate of 12 kHz. Since the radial motion between the transmitting and receiving ships was weak and the terrain did not change significantly, the received signal within 10 seconds could be considered stationary. The cross-spectral density matrix was estimated using the time-domain snapshot data within 10 seconds for subsequent processing.
[0081] like Figure 1 As shown, the conventional beamforming results of the received data processed by the subarray show that the azimuth is pointing in the positive transverse direction and there is no other obvious interference. This indicates that the dominant eigenvalues and eigenvectors of the cross-spectral density matrix of the received signal are only related to the target sound source, rather than other interference sources. Therefore, the horizontal coherence length can be measured using a measurement method based on eigenvalue distribution.
[0082] 2. Calculation of eigenvalue differences and effective degrees of freedom
[0083] For each sub-signal, the cross-spectral density matrix is decomposed according to step 1 to obtain eigenvalues. The eigenvalues are then sorted in descending order and forward differencing is performed according to step 2. The effective degrees of freedom (EDOF) are constructed using the difference results.
[0084] The effective degrees of freedom (EDOF) were calculated using the above method for a data segment with a total duration of approximately 42 minutes. Figure 2 The calculation results for five narrowband signals with center frequencies of 103Hz, 129Hz, 160Hz, 203Hz, and 250Hz are displayed, with the peak values representing the data gap caused by a 30-second pause. Different frequency signals have different interference structures and spatial distributions of signal intensity; therefore, the fluctuations in the effective degrees of freedom (EDOF) at different frequencies are asynchronous in time. During periods of lower beam output peak intensity, the coherence measurement results for each frequency fluctuate dramatically without significant frequency dependence. During periods of higher beam output peak intensity, the coherence measurement results show a trend of smaller values at lower frequencies (103Hz, 129Hz, 160Hz) and larger values at higher frequencies (203Hz, 250Hz).
[0085] 3. Conversion relationship between effective degrees of freedom and horizontal coherence length
[0086] Under the assumptions of stable amplitude and random phase fluctuations following a Gaussian distribution, the spatial coherence between array elements exhibits a Gaussian variation. Based on this spatial coherence function form, the conversion relationship between effective degrees of freedom and horizontal coherence length is established according to step 3.
[0087] Given horizontal coherence length Using the theoretical cross-spectral density matrix Element expression:
[0088]
[0089] Constructing a horizontal coherence length of Theoretical cross-spectral density matrix Then, the theoretical cross-spectral density matrix Perform eigenvalue decomposition to obtain eigenvalues arranged in descending order, and calculate the horizontal coherence length according to step 2. The effective degrees of freedom (EDOF) are calculated by iterating through different horizontal coherence length values and repeating the above construction and calculation process. This allows us to establish the conversion curve between effective degrees of freedom and horizontal coherence length, as shown below. Figure 3 As shown.
[0090] It is worth noting that, under ideal conditions, the theoretical cross-spectral density matrix In the calculation process, the time harmonic term They will cancel each other out, so the result no longer explicitly depends on frequency. From Figure 3 It can be seen that the effective degrees of freedom (EDOF) decreases monotonically with increasing horizontal coherence length. This is because the effective degrees of freedom (EDOF) measure the change in eigenvalues from their highest point. Landing at the lowest point The effective number of descents experienced during the process. When the horizontal coherence length is sufficiently large, all energy is concentrated at the first eigenvalue, and the eigenvalue exists only at... and A precipitous drop occurred between them, namely... It's huge, and the follow-up... to When the value is almost zero (with only minor noise fluctuations), the EDOF is approximately equal to 1, meaning there is only one effective decrease.
[0091] Under the influence of noise, the eigenvalue distribution of the cross-spectral density matrix will be disturbed. To verify the noise resistance of the effective degree-of-freedom measurement method of this invention, the theoretical cross-spectral density matrix is... Gaussian white noise is introduced during the calculation process, and the same processing flow is used to obtain the conversion relationship curve under noisy conditions, such as... Figure 4As shown in the figure, when the signal-to-noise ratio (SNR) is higher than -10 dB, the relationship curve almost coincides with the relationship curve under noise-free conditions; only when the SNR drops to -30 dB does the curve of effective degrees of freedom versus coherence length show a significant deterioration, indicating that the effective degrees of freedom measurement method of this invention has strong robustness to white noise. This is because eigenvalue differencing can effectively weaken the influence of noise energy: white noise in the theoretical cross-spectral density matrix... The eigenvalues in the signal are approximately uniformly distributed. Differential processing can suppress most of the equal-power noise components, thereby highlighting the eigenvalue changes caused by the coherent structure of the signal.
[0092] 4. Comparison of results between the method of this invention and the ASGD method
[0093] To verify the feasibility of the effective degree of freedom measurement method based on eigenvalue difference of the present invention, this embodiment introduces the method based on signal gain attenuation (ASGD) to calculate the spatial coherence length as a reference benchmark, and compares and analyzes the similarities and differences between the two coherence measures in terms of magnitude and trend of change.
[0094] Figure 5 The results of the two methods are compared under five narrowband signal conditions, with center frequencies of 103Hz, 129Hz, 160Hz, 203Hz, and 250Hz. The vertical axis represents the horizontal coherence length after wavelength normalization, expressed in wavelengths. Within the effective time series, the calculation results based on ASGD and those based on eigenvalue difference show a high correlation. The comparison results show that the two methods not only maintain consistency in magnitude but also almost overlap in their trends of fluctuation over time, demonstrating the effectiveness of the eigenvalue difference-based effective degrees of freedom measurement method in measuring the magnitude of spatial coherence.
[0095] Furthermore, the horizontal coherence length estimated by the ASGD method is slightly smaller than that obtained by the effective degrees of freedom method. This is because ASGD uses array gain decay as a measure of coherence, and the gain reduction caused by non-ideal factors such as model mismatch and element position errors is also equivalently included in the coherence loss. This indicates that the effective degrees of freedom method based on eigenvalue differences has a certain ability to suppress signal model mismatch and element position errors, thus improving the robustness of the horizontal coherence length measurement results.
[0096] The actual data processing results show that the effective degree-of-freedom measurement method based on eigenvalue difference proposed in this invention can improve the noise sensitivity of traditional measurement methods based on eigenvalue distribution. Furthermore, compared to methods based on ASGD, the effective degree-of-freedom method also has a certain ability to suppress signal model mismatch and array element position errors, thereby effectively improving the array's measurement performance for horizontal coherence length.
[0097] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.
Claims
1. A method for measuring the horizontal coherence length of underwater acoustic signals based on eigenvalue difference effective degrees of freedom, characterized in that: Includes the following steps: Step 1: Divide the narrowband signal received by the array into time-domain snapshots, estimate the cross-spectral density matrix of each sub-signal, and perform eigenvalue decomposition on the cross-spectral density matrix to obtain the eigenvalues arranged in descending order. Step 2: Perform forward difference analysis on adjacent feature values of the descendingly ordered feature values, and calculate the effective degrees of freedom (EDOF) using the difference results; in The number of array elements , The first in descending order One eigenvalue; Step 3: Under the assumption that the spatial coherence function is of Gaussian form, construct the theoretical cross-spectral density matrix based on the spatial coherence function. The element expression; given the horizontal coherence length The theoretical cross-spectral density matrix at this horizontal coherence length is constructed using the aforementioned element expression. For the theoretical cross-spectral density matrix Perform eigenvalue decomposition to obtain eigenvalues in descending order, and calculate the effective degrees of freedom (EDOF) at this horizontal coherence length according to step 2; change the given horizontal coherence length value and repeat the above construction, eigenvalue decomposition, and calculation process to establish the relationship between the effective degrees of freedom (EDOF) and the horizontal coherence length. The monotonically decreasing conversion relationship between them; the effective degrees of freedom (EDOF) calculated based on measured data, and the horizontal coherence length estimated through the conversion relationship. The spatial coherence function is: The distance variable is the array element distance.
2. The method according to claim 1, characterized in that: In step 1, for A uniform linear array is used to divide the received signal into sub-signals by windowing and overlapping processing. The cross-spectral density matrix is represented as follows: in For the number of snapshots, This is time-domain snapshot data. Indicates conjugate transpose; For the cross-spectral density matrix Perform eigenvalue decomposition: The number of eigenvalues is equal to the number of array elements. , Cross-spectral density matrix Eigenvalues sorted in descending order Eigenvalues The corresponding feature vector.
3. The method according to claim 1, characterized in that: In step 2, the forward difference between adjacent feature values is divided into: The effective degrees of freedom range is as follows: The smaller the effective degrees of freedom, the stronger the spatial coherence.
4. The method according to claim 1, characterized in that: In step 3, the theoretical cross-spectral density matrix The elements are represented as: in For signal amplitude, The distance between adjacent array elements. For the first Each element and the first The spacing between array elements.
5. An electronic 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 executes the program, it implements the method of any one of claims 1 to 4.
6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the method described in any one of claims 1 to 4.