Robust time delay estimation method based on signal cyclostationary characteristic

Abstract

The invention discloses a robust time delay estimation method based on a signal cyclostationary characteristic, which belongs to the technical field of positioning, and comprises the following steps of: firstly, preprocessing a signal by adopting beam forming to suppress same-frequency interference, and secondly, carrying out hyperbolic tangent transformation and related operation based on Taylor expansion on the signal by utilizing the stationary characteristic of the signal to obtain a robust time delay estimation result. Therefore, time delay estimation is carried out on signals with co-frequency interference, target signals and interference signals are separated on a cyclic frequency domain, the problem that an existing time delay estimation method is low in time delay estimation accuracy under the conditions of low signal-to-noise ratio and co-frequency interference can be effectively solved, and the robustness of time delay estimation is improved.

Description

Technical Field

[0001] The invention belongs to the field of positioning technology, and in particular relates to a robust delay estimation method based on signal cyclostationary characteristics. Background Art

[0002] In the multi-station passive positioning system, according to the dependent measurement parameters, it can be further divided into direction finding cross positioning technology, arrival time difference passive positioning technology, arrival frequency difference passive positioning technology and combined positioning methods covering the above parameters. As a core branch of multi-station passive positioning, arrival time difference passive positioning technology has been widely studied by many scholars due to its high positioning accuracy and long range. Its basic principle is to estimate the time difference between the target radiation source signal arriving at multiple receiving stations and solve the location information of the target radiation source. The accuracy of time difference positioning is affected by multiple factors, among which the estimation accuracy of arrival time difference is one of the primary factors affecting positioning accuracy. Therefore, in-depth research and development of high-precision time difference estimation methods are crucial to improving the accuracy of passive time difference positioning technology. High-precision time difference positioning technology can not only enhance electronic warfare combat capabilities in the military field, but also has great potential and wide practicality in the civilian field.

[0003] Signal delay estimation is the most critical step in TDOA positioning. The generalized cross-correlation method (GCC) is one of the most widely used methods for delay estimation. Its basic principle is to perform weighting in the power spectrum of the signal, thereby suppressing noise interference in the time domain and sharpening the related signals. In addition, some researchers have proposed delay estimation methods based on high-order cumulants and delay estimation methods based on fractional low-order statistics. The delay estimation method based on high-order cumulants uses the property that the cumulants of the Gaussian process higher than the second order are equal to zero to achieve the effect of suppressing noise that obeys the Gaussian distribution. Furthermore, the delay estimation method based on fractional low-order statistics can suppress the influence of co-frequency interference signals while suppressing noise, thereby improving the signal's anti-interference ability. These existing algorithms are all based on the Gaussian noise model and are suitable for situations with high signal-to-noise ratio or sufficient prior knowledge conditions, which has certain defects in practical applications.

[0004] In the current complex electromagnetic environment, there will be a lot of pulse noise and co-band interference coexisting, resulting in the peak of the correlation function of the existing time difference estimation method not being sharp enough, and the appearance of pseudo peaks, resulting in a significant decrease in the time difference estimation performance. Therefore, it is necessary to optimize the existing algorithm and improve the accuracy of delay estimation under low signal-to-noise ratio. Summary of the invention

[0005] In view of the problem that the performance of existing delay estimation methods is significantly degraded due to the coexistence of impulse noise and co-band interference, the present invention provides a robust delay estimation method based on the cyclostationary characteristics of the signal. First, beamforming is used to preprocess the signal to suppress the co-channel interference. Secondly, the stationary characteristics of the signal are used to perform a hyperbolic tangent transformation and related operations based on Taylor expansion on the signal, so as to estimate the delay of the signal with co-channel interference, and separate the target signal from the interference signal in the cyclic frequency domain. This can effectively solve the problem that the delay estimation accuracy of the existing delay estimation method is low under the conditions of low signal-to-noise ratio and co-channel interference, and improve the robustness of the delay estimation.

[0006] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is: first, beamforming is used to pre-process the signal to suppress co-channel interference; secondly, the stationary characteristics of the signal are utilized to perform a hyperbolic tangent transform and related operations based on Taylor expansion on the signal, thereby performing delay estimation on the signal with co-channel interference, and separating the target signal and the interference signal in the cyclic frequency domain. This can effectively solve the problem of low delay estimation accuracy of existing delay estimation methods under low signal-to-noise ratio and co-channel interference conditions, and improve the robustness of delay estimation.

[0007] Specifically, the following steps are included:

[0008] 1) Receive the radiation source signals collected by multiple receivers and sample them to obtain the signal represented by X i The signal samples;

[0009] 2) Sample the signal X i Preprocessing is performed by constructing a noise power minimization problem under the constraint of interference-to-noise ratio, and using beamforming technology to extract useful signals and suppress co-channel interference;

[0010] 3) Based on the preprocessing, iteratively update the estimated value of the target radiation source signal Until convergence;

[0011] 4) Using the signal estimate obtained in step 3 Decompose the parameter matrix R1(k) and construct the optimization problem P2;

[0012] 5) Based on the optimization problem P2, fix Solve to obtain the beamforming vector w;

[0013] 6) Update the Lagrangian vector λ according to the beamforming vector w g and λ h , to optimize the beamforming process;

[0014] 7) Determine whether the iterative process has reached the predetermined maximum number of cycles. If not, return to step 3 to continue iterating until the iteration end condition is met;

[0015] 8) Using the beamforming vector w obtained in step 5, i Perform beamforming processing to obtain y i =w H X i ;

[0016] 9) Performing a hyperbolic tangent transform based on Taylor expansion on the beamformed signal yi to extract the cyclostationary characteristics of the signal;

[0017] 10) Based on the signal transformation result obtained in step 9, estimate the signal delay and complete the delay estimation.

[0018] Furthermore, the specific steps are as follows:

[0019] Step 1: Different receivers receive the signal sent by the radiation source and sample the received signal, which is expressed as

[0020]

[0021] X i represents the signal received by the i-th receiver, s0=[s0(T s ),…,s0(kT s ),…,s0(NT s )] T represents the sampling signal of the target radiation source, represents the sampling rate, N represents the length of the sampled signal, α0 represents the complex gain, and N is the Gaussian noise matrix;

[0022] Step 2: Preprocess the signal to extract useful signals and suppress co-channel interference. First, construct the noise power minimization problem under the following interference-to-noise ratio constraint:

[0023]

[0024] in, represents the estimated value of the target radiation source signal s0, w represents the beamforming vector, The threshold of the interference-to-noise ratio, I N Represents the N×N identity matrix.

[0025] Step 3: First iteratively update the parameters At the kth iteration of the outer layer, Update according to the following formula:

[0026]

[0027] Step 4: Decompose the parameter matrix R1(k) and introduce auxiliary variables g=w H Uk and h = w, construct the optimization problem P2:

[0028]

[0029]

[0030] Among them, λ g and λ h is the introduced Lagrangian vector, and ρ is the custom penalty parameter

[0031] Step 5: Fix Solve for w. At the tth iteration of the inner layer, update the following parameters:

[0032]

[0033]

[0034]

[0035]

[0036] in, and It is a customized intermediate parameter.

[0037] Step 6: Update the Lagrangian vector λ g and λ h :

[0038] λ g (t) = λ g (t-1)+ρ(g(t)-w H (t)U k ) (8)

[0039] λ h (t) = λ h (t-1)+ρ(h(t)-w(t)) (9)

[0040] Step 7: Determine whether the inner loop has reached the maximum number of loops N t , if t<N t , then return to step 7, otherwise, output w(N t );

[0041] Step 8: Determine whether the outer loop has reached the maximum number of loops N k , if t<N k , then return to step 3, otherwise, output w * =w(N t )and

[0042] Step 9: Signal X i Beamforming is performed, that is, y i =w H X i =[y i (1),y i (2),…,y i (N)];

[0043] Step 10: Perform a hyperbolic tangent transform on the signal based on Taylor expansion, expressed as

[0044]

[0045]

[0046] Where y1(n) represents the signal sample after beamforming, ε represents the cycle frequency, and D represents the delayed sampling point during the correlation operation. is the Taylor expansion order, B 2n is the Bernoulli coefficient, and H is the signal threshold.

[0047] Step 11: Estimate the signal delay based on the correlation values ​​of signal transformations (10) and (11), such as:

[0048]

[0049] Among them, R(ε,e i ) represents the correlation function of the signal, T s is the sampling period, M represents the delay range of the search, is the estimated delay.

[0050] The beneficial effects of the present invention are as follows:

[0051] 1. The present invention effectively suppresses co-channel interference and noise through beamforming preprocessing, and pays more attention to the target radiation signal.

[0052] 2. Based on the stability of the signal, the present invention designs a robust delay estimation method, which can effectively suppress impulse noise and co-band interference, and improve the anti-interference performance of the algorithm.

[0053] 3. Compared with other methods, the present invention significantly reduces the delay estimation error in a low signal-to-noise ratio environment, can significantly improve the estimation success rate, and shows good accuracy and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The beam pattern of the present invention is shown.

[0055] Figure 2 This is a graph showing how the mean square error varies with the kernel length σ.

[0056] Figure 3 This is a delay estimation diagram of the present invention.

[0057] Figure 4 This is the delay estimation diagram of the CSD algorithm.

[0058] Figure 5 This is the delay estimation diagram of the FLOCC algorithm.

[0059] Figure 6 This is the delay estimation diagram of the MCCAPA algorithm.

[0060] Figure 7 This is a graph showing how the delay estimation accuracy changes with the pulse noise characteristic index α.

[0061] Figure 8 This is a graph showing how the delay estimation accuracy changes with the signal-to-noise ratio. DETAILED DESCRIPTION

[0062] In order to enable those skilled in the art to better understand the technical solution, the present invention is described in detail below in conjunction with embodiments. The description in this section is only exemplary and explanatory and should not have any limiting effect on the scope of protection of the present invention.

[0063] like Figure 1-Figure 8 As shown, the basic steps of the technical solution of the present invention are as follows: first, beamforming is used to preprocess the signal to suppress co-channel interference. Secondly, the signal's stationary characteristics are utilized to perform a hyperbolic tangent transform and related operations based on Taylor expansion on the signal, thereby performing delay estimation on the signal with co-channel interference, and separating the target signal from the interference signal in the cyclic frequency domain. This can effectively solve the problem of low delay estimation accuracy of existing delay estimation methods under low signal-to-noise ratio and co-channel interference conditions, and improve the robustness of delay estimation.

[0064] The specific steps include:

[0065] 1) Receive the radiation source signals collected by multiple receivers and sample them to obtain the signal represented by X i The signal samples;

[0066] 2) Sample the signal X i Preprocessing is performed by constructing a noise power minimization problem under the constraint of interference-to-noise ratio, and using beamforming technology to extract useful signals and suppress co-channel interference;

[0067] 3) Based on the preprocessing, iteratively update the estimated value of the target radiation source signal Until convergence;

[0068] 4) Using the signal estimate obtained in step 3 Decompose the parameter matrix R1(k) and construct the optimization problem P2;

[0069] 5) Based on the optimization problem P2, fix Solve to obtain the beamforming vector w;

[0070] 6) Update the Lagrangian vector λ according to the beamforming vector w g and λ h , to optimize the beamforming process;

[0071] 7) Determine whether the iterative process has reached the predetermined maximum number of cycles. If not, return to step 3 to continue iterating until the iteration end condition is met;

[0072] 8) Using the beamforming vector w obtained in step 5, i Perform beamforming processing to obtain y i =w H X i ;

[0073] 9) Performing a hyperbolic tangent transform based on Taylor expansion on the beamformed signal yi to extract the cyclostationary characteristics of the signal;

[0074] 10) Based on the signal transformation result obtained in step 9, estimate the signal delay and complete the delay estimation.

[0075] The following provides a detailed description of the specific embodiments:

[0076] s0(t) is the target signal source, s1(t) is the co-band interference signal, α0 and α1 are the corresponding complex channel gains, τ1 and τ2 are the time when the target signal arrives at receiver 1 and receiver 2, τ1′ and τ2′ are the time when the interference signal arrives at receiver 1 and receiver 2, θ0 and θ1 are the wave directions of the target signal and interference signal arriving at receiver 1, θ0′ and θ1′ are the wave directions of the target signal and interference signal arriving at receiver 2, and n1(t) and n2(t) are the independent Gaussian additive noise signals corresponding to receiver 1 and receiver 2.

[0077] The detailed implementation steps are as follows:

[0078] Step 1: Different receivers receive the signal sent by the radiation source and sample the received signal, which is expressed as

[0079]

[0080] X i represents the signal received by the i-th receiver, s0=[s0(T s ),…,s0(kT s ),…,s0(NT s )]T represents the sampling signal of the target radiation source, represents the sampling rate, N represents the length of the sampled signal, α0 represents the complex gain, and N is the Gaussian noise matrix;

[0081] Two receivers are used to receive the signal and sample the signal with a sampling frequency of f. s , the sampling length is N, respectively expressed as

[0082]

[0083]

[0084] Where, s0=[s0(T s -τ1),…,s0(NT s -τ1)] T , s1=[s1(T s -τ2),…,s1(NT s -τ2)] T , N1=[n1(T s ),…,n1(NT s )] T , N2=[n2(T s ),…,n2(NT s )] T .

[0085] Step 2: Preprocess the signal to extract useful signals and suppress co-channel interference. First, construct the noise power minimization problem under the following interference-to-noise ratio constraint:

[0086]

[0087] in, represents the estimated value of the target radiation source signal s0, w represents the beamforming vector, The threshold of the interference-to-noise ratio, I N Represents the N×N identity matrix.

[0088] In this embodiment, we construct optimization problem P1 for X1 and X2 respectively;

[0089] Step 3: First iteratively update the parameters At the kth iteration of the outer layer, Update according to the following formula:

[0090]

[0091] In this embodiment, we perform an outer loop according to formula (2) to estimate the target radiation source signal at receiver 1 and receiver 2 respectively. and Perform iterative updates.

[0092] Step 4: Decompose the parameter matrix R1(k) and introduce auxiliary variables g=w H U k and h = w, construct the optimization problem P2:

[0093]

[0094]

[0095] Among them, λ g and λ h is the introduced Lagrangian vector, and ρ is a custom penalty parameter.

[0096] In this embodiment, we decompose the parameter matrix R1(k) at receiver 1 and receiver 2 according to formula (3).

[0097] Step 5: Fix Solve for w. At the tth iteration of the inner layer, update the following parameters:

[0098]

[0099]

[0100]

[0101]

[0102] in, and It is a customized intermediate parameter.

[0103] In this embodiment, we fix and According to formulas (4)-(7), perform the inner loop and update w1(t) and w2(t);

[0104] Step 6: Update the Lagrangian vector λ g and λ h :

[0105] λ g (t) = λ g (t-1)+ρ(g(t)-w H (t)U k ) (8)

[0106] λ h(t) = λ h (t-1)+ρ(h(t)-w(t)) (9)

[0107] In this embodiment, according to formulas (8) and (9), the Lagrangian variables corresponding to receiver 1 are updated: and And the Lagrangian variable corresponding to receiver 2 and

[0108] Step 7: Determine whether the inner loop has reached the maximum number of loops N t , if t<N t , then return to step 7, otherwise, output w(N t );

[0109] In this embodiment, it is determined whether the inner loop is finished. If finished, w1(N t ) and w2(N t ), otherwise, go to step 5;

[0110] Step 8: Determine whether the outer loop has reached the maximum number of loops N k , if t<N k , then return to step 3, otherwise, output w * =w(N t )and

[0111] In this embodiment, it is determined whether the outer loop is finished. If finished, w1(N t ), w2(N t ), and Otherwise, go to step 3;

[0112] Step 9: Signal X i Beamforming is performed, that is, y i =w H X i =[y i (1),y i (2),…,y i (N)];

[0113] In this embodiment, beamforming processing is performed on X1 and X2 respectively. and

[0114] Step 10: Perform a hyperbolic tangent transform on the signal based on Taylor expansion, expressed as

[0115]

[0116]

[0117] Where y1(n) represents the signal sample after beamforming, ε represents the cycle frequency, and D represents the delayed sampling point during the correlation operation. is the Taylor expansion order, B 2n is the Bernoulli coefficient, and H is the signal threshold.

[0118] In this embodiment, y1 is selected as the reference signal, and the hyperbolic tangent transform of y1 is calculated according to formula (10): Calculate the hyperbolic tangent transform according to formula (11):

[0119] Step 11: Estimate the signal delay based on the correlation values ​​of signal transformations (10) and (11), such as:

[0120]

[0121] Among them, R(ε,e i ) represents the correlation function of the signal, T s is the sampling period, M represents the delay range of the search, is the estimated delay.

[0122] In this embodiment, according to formula (12) and The cross-correlation of and peak detection are performed to obtain the estimated delay, which is expressed as

[0123] The experimental conditions are set as follows: the target signal and the same-band interference are both BPSK signals, the target signal carrier frequency is f1 = 1000 Hz, the interference signal carrier frequency is f2 = 950 Hz, and the symbol rate, i.e., the cycle frequency, is ε s =ε h = 200 Hz, the time delays of the target signal and the interference signal reaching receiver 1 and receiver 2 are set to τ1 = τ′1 = 0, τ2 = 20 / f respectively. s ,τ′2=40 / f s . The arrival directions of the target and interference signals to receiver 1 and receiver 2 are θ0=θ′0=0° and θ0=θ′0=70°, respectively. The following figure compares the performance of the present invention (denoted as CCE) and the existing delay estimation algorithms, wherein the existing delay estimation algorithms include spectral coherence delay estimation based on second-order cyclic statistics (denoted as CSD), delay estimation based on fractional low-order cyclic statistics with prior knowledge (denoted as FLOCC_Good), delay estimation based on fractional low-order cyclic statistics without prior knowledge (denoted as FLOCC_Bad), and delay estimation based on the maximum correlation entropy criterion (denoted as MCCAPA).

[0124] Figure 1This is the beam diagram after preprocessing of the present invention. It can be seen that the beam gain in the target radiation direction is 0dB, while the beam gain in the interference direction is -200dB, which has a large attenuation, indicating that the present invention can effectively suppress co-channel interference.

[0125] Figure 2 The mean square error of the delay estimation of the present invention changes with the core length σ of the Gaussian kernel. The core length σ is an important parameter for suppressing noise interference in the Gaussian kernel. It can be observed that when σ changes from 0 to 2, the mean square error will first decrease and then increase. When σ = 0.8, the mean square error reaches the minimum value. Therefore, it can be determined that the optimal core length σ is 0.8.

[0126] Figure 3-Figure 6 The single delay estimation results of the present invention and the existing delay estimation algorithm. As can be seen from the figure, the present invention, the CSD algorithm and the FLOOC algorithm all use the different cyclic frequencies of the target signal and the interference signal to suppress the influence of the same-band interference and obtain the correct delay estimation of the target signal. However, the MCCAPA algorithm ignores the cyclic characteristics of the signal and only performs an adaptive filter, resulting in its delay estimation being seriously affected by the interference signal and unable to obtain a correct delay estimation.

[0127] Figure 7 The delay estimation performance of the present invention and the existing delay estimation algorithm under pulse noise of different intensities. When the signal-to-noise ratio is -3dB, the accuracy of the present invention and the existing delay estimation algorithm will increase with the increase of the noise characteristic index, that is, it will increase with the weakening of the pulse noise. Under noise of the same pulse intensity, the present invention is better than the existing delay estimation algorithm. When the characteristic index is 1.3, the delay estimation accuracy of the present invention is 93%, which is slightly higher than the FLOCC_Good algorithm, 18% better than the FLOCC_Bad algorithm, 88% better than the CSD algorithm, and 53% better than the MCCAPA algorithm.

[0128] Figure 8 The delay estimation performance comparison chart of the present invention and the existing delay estimation algorithm under different signal-to-noise ratios. When the noise characteristic index is 1.4, the performance of the present invention and the existing delay estimation algorithm will improve with the increase of the signal-to-noise ratio, and the delay estimation accuracy of the present invention is better than that of several other algorithms. Although the delay estimation accuracy achieved by the FLOCC algorithm is close to that of the present invention, it needs to obtain information such as prior knowledge of noise before processing the signal, and the selection of algorithm parameters will also affect the accuracy of the delay estimation. Therefore, the FLOCC algorithm has certain difficulties in actual use. The present invention does not require information such as prior knowledge, and can obtain a higher delay estimation accuracy in strong pulse noise and low signal-to-noise ratio environments, and is practical.

[0129] It should be noted that, in this article, the terms: include, contain and any other variants are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. Specific examples are used in this article to illustrate the principle and implementation of the technical solution of the present invention. The above examples are only used to help understand the method of the present invention and its core idea. The above is only a preferred implementation of the present invention. It should be pointed out that due to the limitations of textual expression and the objective existence of infinite specific structures, for ordinary technicians in this technical field, without departing from the principle of the present invention, several improvements, modifications or changes can be made, and the above technical features can also be combined in an appropriate manner; these improvements, modifications, changes or combinations, or the direct application of the concept and technical solution of the present invention to other occasions without improvement, should be regarded as the protection scope of the present invention.

Claims

1. A robust delay estimation method based on signal cyclostationary characteristics, characterized in that: The following steps are involved: 1) Receive the radiation source signals collected by multiple receivers and sample them to obtain the signal represented by X i The signal samples; 2) Sample the signal X i Preprocessing is performed by constructing a noise power minimization problem under the constraint of interference-to-noise ratio, and using beamforming technology to extract useful signals and suppress co-channel interference; 3) Based on the preprocessing, iteratively update the estimated value of the target radiation source signal Until convergence; 4) Using the signal estimate obtained in step 3 Decompose the parameter matrix R1(k) and construct the optimization problem P2; 5) Based on the optimization problem P2, fix Solve to obtain the beamforming vector w; 6) Update the Lagrangian vector λ according to the beamforming vector w g and λ h , to optimize the beamforming process; 7) Determine whether the iterative process has reached the predetermined maximum number of cycles. If not, return to step 3 to continue iterating until the iteration end condition is met; 8) Using the beamforming vector w obtained in step 5, i Perform beamforming processing to obtain y i =w H X i ; 9) For the beamformed signal y i Perform hyperbolic tangent transform based on Taylor expansion to extract the cyclostationary characteristics of the signal; 10) Based on the signal transformation result obtained in step 9, estimate the signal delay and complete the delay estimation.

2. The method according to claim 1, characterized in that In step 1, different receivers receive the signal sent by the radiation source and sample the received signal, which is expressed as X i represents the signal received by the i-th receiver, s0=[s0(T s ),…,s0(kT s ),…,s0(NT s )] T represents the sampling signal of the target radiation source, represents the sampling rate, N represents the length of the sampled signal, α0 represents the complex gain, and N is the Gaussian noise matrix.

3. The method according to claim 1, characterized in that In step 2, preprocessing includes constructing the optimization problem P1, where P1 is: in, represents the estimated value of the target radiation source signal s0, w represents the beamforming vector, The threshold of the interference-to-noise ratio, I N represents the N×N unit matrix, a(θ0) represents the direction vector of the target signal, and θ0 represents the incoming direction of the target signal.

4. The method according to claim 1, characterized in that In step 3, iterative update Follow the following formula: Where X represents the received signal matrix and w(k-1) represents the beamforming vector of the k-1th iteration.

5. The method according to claim 1, characterized in that In step 4, the decomposition of the parameter matrix R1(k) and the construction of the optimization problem P2 are as follows: Among them, U k is the decomposed matrix, X represents the received signal matrix, represents the target signal estimation value of the kth iteration; λ g and λ h is the introduced Lagrangian vector, and ρ is the penalty parameter.

6. The method according to claim 1, characterized in that In step 5, the process of solving for w involves the following update formula: Among them, I M represents the M×M identity matrix, ρ is a custom penalty parameter, U k is the matrix obtained by decomposition, r is the intermediate calculation parameter, γ is the intermediate calculation parameter in the iterative process, and a(θ0) represents the direction vector of the target signal.

7. The method according to claim 1, characterized in that In step 6, the Lagrangian vector λ g and λ h The update formula is as follows: l g (t)=λ g (t-1)+ρ(g(t)-w H (t)U k ) (8) l h (t)=λ h (t-1)+ρ(h(t)-w(t)) (9) Among them, λ g and λ h is the Lagrangian vector, ρ is the penalty parameter, g(t) and h(t) are auxiliary variables in the optimization problem, and w(t) is the beamforming vector at the tth iteration.

8. The method according to claim 1, characterized in that In step 8, after beamforming, signal X i Convert to y i =w H X i , where w is the beamforming vector, X i is the signal received by the i-th receiver.

9. The method according to claim 1, characterized in that: In step 9, the hyperbolic tangent transformation based on Taylor expansion is specifically: Where y1(n) represents the signal sample after beamforming, ε represents the cycle frequency, and D represents the delayed sampling point during the correlation operation. is the Taylor expansion order, B 2n is the Bernoulli coefficient, and H is the signal threshold.

10. The method according to claim 1, characterized in that In step 10, the specific method of signal delay estimation is: Among them, R(ε,e i ) represents the correlation function of the signal, T s is the sampling period, M represents the delay range of the search, is the estimated delay.

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