A multi-band fusion extrapolation method based on multi-dictionary-fast sparse bayesian algorithm

Abstract

The application relates to a multi-band radar data fusion extrapolation method for multi-band radar data, in particular to a multi-band fusion extrapolation method based on a multi-dictionary-fast sparse Bayesian algorithm, which is suitable for fusing and extrapolating a missing frequency band after phase completion of multi-band radar signals and belongs to the technical field of multi-band radar super-resolution imaging. The method firstly models multi-band data; after phase registration, the FSBL-MD algorithm is used to extrapolate full-band data, and multi-band extrapolation is completed. The application can effectively realize high-precision multi-band fusion extrapolation and obtain a high-resolution target range image.

Description

Technical Field

[0001] This invention relates to a multi-band radar data fusion extrapolation method for multi-band radar data, and particularly to a multi-band fusion extrapolation method based on a multi-dictionary-fast sparse Bayesian algorithm. It is applicable to the fusion extrapolation of missing frequency bands after phase completion of multi-band radar signals, and belongs to the field of multi-band radar super-resolution imaging technology. Background Technology

[0002] Radar, with its all-weather and all-day operation, is widely used in numerous monitoring fields. High-resolution one-dimensional imaging of targets using radar effectively captures detailed features such as the shape and structure of targets or clusters, aiding in target identification. However, radar resolution is limited by the bandwidth of the transmitted signal. Traditional broadband radar requires transmitter bandwidths of several GHz to achieve fine one-dimensional imaging of small targets, posing significant challenges in manufacturing processes and cost. Multi-band radar bandwidth fusion extrapolation is an effective method to broaden radar signal bandwidth, achieving high resolution at a lower cost. This is of great significance for the detection and identification of large-scale unmanned aerial vehicle (UAV) clusters. This technology, starting from the algorithm level, coherently processes multi-band radar measurement signals and then estimates the scattering centers of the multi-band radar signals based on scattering center theory. This directly yields a full-band radar signal model of the target, thus obtaining a broadband radar signal at a lower cost and achieving high range resolution. The advantages of low cost and ease of implementation make multi-band radar signal extrapolation technology a promising field for application.

[0003] In traditional multi-band extrapolation methods, bandwidth extrapolation (BWE), represented by spectral estimation algorithms, uses attenuation exponents and models to model and solve for radar signals. These algorithms suffer from low model accuracy and are sensitive to noise during the solution process, affecting the quality of the fusion extrapolation. Therefore, high-precision GTD models are commonly used to improve model accuracy.

[0004] Sparse Bayes Learning (SBL) is a high-precision sparse representation algorithm commonly used in signal processing. However, in solving sparse equations, the large dimension of the dictionary matrix leads to high computational complexity for SBL algorithms, necessitating a reduction in computational load while improving accuracy. Therefore, it is necessary to research a fast, high-precision multi-band radar signal fusion and extrapolation algorithm suitable for engineering applications. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of existing technologies and propose a multi-band fusion extrapolation method based on a multi-dictionary-fast sparse Bayesian algorithm. This method can solve the problem of slow iteration in traditional Fast Sparsity Bayes Learning (FSBL) algorithms, and is an efficient and high-precision multi-band fusion extrapolation method. To address the slow iteration problem of traditional FSBL methods, a multi-dictionary switching approach is adopted. First, a coarse dictionary is used for fast estimation, and then a locally complete dictionary is used for fine estimation, thereby quickly and accurately solving for parameters and achieving fusion extrapolation. The proposed method aims to provide a fast and high-precision multi-band radar signal fusion extrapolation method that can be applied to the field of multi-band radar super-resolution imaging technology.

[0006] The technical solution of this invention is:

[0007] A high-precision multi-band fusion extrapolation method based on Fast Sparse Bayes Learning-Multi-Dictionary (FSBL-MD), where the multi-band includes two or more frequency bands;

[0008] A multi-band fusion extrapolation method based on a multi-dictionary-fast sparse Bayesian algorithm, the steps of which include:

[0009] Step 1: Perform phase coherent registration on the multi-band radar signals;

[0010] Step 2: Perform broadband modeling on the multi-band radar signal after coherent registration in Step 1 to obtain the broadband scattering center GTD model of the multi-band radar signal.

[0011] Step 3: Use the FSBL-MD algorithm to solve the broadband scattering center GTD model of the multi-band radar signal constructed in Step 2, and complete the fusion of multi-band radar signals.

[0012] In step one, the method for coherent registration of multi-band radar signals is as follows:

[0013] Suppose that the multi-band radar signal includes low-frequency band 1 and high-frequency band 2. Using low-frequency band 1 as the reference signal, high-frequency band 2 is phase-compensated to low-frequency band 1, and the compensated high-frequency band is marked as high-frequency band 2'.

[0014] First, establish the GTD model E1(f) of the scattering center in low frequency band 1. k′ ) and the GTD model E2(f) of the scattering center in high frequency band 2 q );

[0015] Among them, the scattering center GTD model E1(f in low frequency band 1) k′ )for:

[0016]

[0017] Among them, f k′ =f0 + k′Δf, k′ = 0, ..., N1-1; f0 is the starting frequency; N1 is the starting point of the spectrum sequence in low-frequency band 1; Q represents the ending point of the sequence bandwidth; Δf represents the frequency interval; M represents the number of scattering centers; σ m The r represents the target complex amplitude corresponding to the m-th scattering center, m = 1, 2, ..., M. m Let m be the relative distance from the m-th scattering center to the radar; The term is a factor that depends on both amplitude and frequency, α m =-1,-0.5,0,0.5,1;

[0018] The GTD model of the scattering center in high-frequency band 2, E2(f) q )for:

[0019]

[0020] Among them, f k″ =f0+k″Δf,k″=N2,...,Q-1; f0 is the starting frequency; N2 is the starting point of the spectral sequence in high-frequency band 2; Q represents the ending point of the sequence bandwidth; Δf represents the frequency interval; M represents the number of scattering centers; σ m The r represents the target complex amplitude corresponding to the m-th scattering center, m = 1, 2, ..., M. m Let m be the relative distance from the m-th scattering center to the radar; The term is a factor that depends on both amplitude and frequency. -1, -0.5, 0, 0.5, 1; s represents the phase error term present in high-frequency band 2;

[0021] After phase error compensation, the scattering center E of the high-frequency band 2' is obtained from the GTD model. 2′ (f k )for:

[0022]

[0023] Among them, f k″ =f0+k″Δf,k″=N2,...,Q-1; f0 is the starting frequency; N2 is the starting point of the spectral sequence in high-frequency band 2; Q represents the ending point of the sequence bandwidth; Δf represents the frequency interval; M represents the number of scattering centers; σ m The r represents the target complex amplitude corresponding to the m-th scattering center, m = 1, 2, ..., M. m Let m be the relative distance from the m-th scattering center to the radar; The term is a factor that depends on both amplitude and frequency, α m=-1,-0.5,0,0.5,1;

[0024] In step two, the broadband scattering center GTD model E(f) of the multi-band radar signal is established. k )for:

[0025]

[0026] Among them, f k = f0 + kΔf, k = 0, 1, ..., Q-1; Δf represents the frequency interval; Q represents the number of broadband signal frequency points; M represents the number of scattering centers; σ m The r represents the target complex amplitude corresponding to the m-th scattering center, m = 1, 2, ..., M. m Let be the relative distance from the m-th scattering center to the radar; where, The term is a factor that depends on both amplitude and frequency, α m =-1,-0.5,0,0.5,1;

[0027] In step three, the broadband scattering center GTD model E(f) of the multi-band radar signal described in step two is solved. k The method is as follows: First, use a Fourier dictionary to coarsely solve for the target amplitude vector; then, based on the coarsely solved amplitude vector value, select a local Fourier dictionary and use a GTD dictionary to refine the selected Fourier dictionary, thereby improving the dictionary's fineness, and solve for the amplitude vector value again; finally, further improve the dictionary's fineness to obtain the final solution for the amplitude vector, thus completing multi-band fusion.

[0028] The specific steps of this method include:

[0029] The first step is to construct the sparse vector form equation of the broadband scattering center GTD model as follows:

[0030] E=Φσ

[0031] Multi-band data E is

[0032] E = [E1(0),...,E1(N1-1),E 2′ (N2),...,E 2′ (Q-1)] T

[0033] The magnitude vector s is denoted as:

[0034] σ=[σ(0),...,σ(D-1)] T

[0035] D is the length of the sparse vector, and Φ is the dictionary matrix;

[0036] The second step is to construct the first-level dictionary: using a Fourier dictionary, the dictionary matrix Φ is constructed as follows:

[0037] Φ=[a0,a1,...,a D-1 ]

[0038] Where the d-th column vector (also called an atom) of the dictionary matrix Φ is a d Recorded as:

[0039]

[0040] In the formula, d = 0, 1, ..., D-1.

[0041] The SBL method is used to solve the sparse representation vector form equation in the first step to obtain the magnitude vector σ.

[0042] The third step is to construct the second-level dictionary to solve for the magnitude vector σ:

[0043] Find the non-zero elements in the magnitude vector σ obtained in the second step, and denote their sequence as D1 with length L1. Construct a Fourier dictionary matrix Φ1 using the corresponding dictionary matrix column vectors. The d1-th column vector (also called an atom) of dictionary matrix Φ1 is... Recorded as:

[0044]

[0045] In the formula, d1 = D1(1),...,D1(L1).

[0046] By increasing the dictionary precision by 10 times and expanding the number of atoms in the dictionary, we obtain the Fourier dictionary matrix Φ2, whose d2-th column vector... Recorded as:

[0047]

[0048] d2=10*D1(1)±3,10*D1(1)±2,10*D1(1)±1,10*D1(1),...,10*D1(L1)±3,10*D1(L1)±2,10*D1(L1)±1,10*D1(L1)

[0049] Switch the dictionary, using the frequency dependence factor m, and transform each atom in the Fourier dictionary matrix Φ2 into a GTD atom g. m as follows:

[0050]

[0051] Where m = -1, -0.5, 0, 0.5, 1.

[0052] GTD atoms with all m values ​​g mReconstruct the dictionary matrix Φ.

[0053] The SBL algorithm is used to solve the sparse representation vector form equation in the first step to obtain the magnitude vector σ.

[0054] Fourth step: Construct the third-level dictionary to solve for the magnitude vector σ:

[0055] Find the non-zero elements in the magnitude vector σ obtained in the second step, and reconstruct the local dictionary Φ1′ based on their positions in the dictionary matrix Φ.

[0056] The dictionary precision is increased by 10 times again, and the dictionary is expanded using neighboring values ​​based on the position values ​​of non-zero elements to obtain a new dictionary matrix Φ.

[0057] The SBL algorithm is used to solve the sparse representation vector form equation in the first step to obtain the magnitude vector σ.

[0058] Fifth, extend each atom in Φ to the full frequency range, denoted as Ψ. Then, the multi-band fusion extrapolated spectrum vector based on optimal dictionary selection orthogonal matching pursuit is:

[0059]

[0060] The broadband scattering center GTD model of multi-band radar signals has been solved, and multi-band fusion has been completed.

[0061] Beneficial effects

[0062] To address the challenge of multi-band fusion extrapolation, this paper proposes a multi-band fusion extrapolation method based on a multi-dictionary-fast sparse Bayesian algorithm. For multi-band data, this method first models the multi-band data; then, it uses the proposed FSBL-MD algorithm to extrapolate the full-band data, completing the multi-band extrapolation. This invention is expected to effectively achieve high-precision multi-band fusion extrapolation and obtain high-resolution target range profiles. Attached Figure Description

[0063] Figure 1 This is a schematic diagram comparing the broadband scattering center GTD model obtained by the method of the present invention with its theoretical value.

[0064] Figure 2 This is a schematic diagram comparing the range image of the model after processing by the method of the present invention with the range image of frequency band 1;

[0065] Figure 3 This is a graph showing the computation time versus signal-to-noise ratio variation between the method of this invention and the traditional algorithm;

[0066] Figure 4 The graph shows the root mean square error versus signal-to-noise ratio variation of the broadband scattering center GTD model, as presented in this invention, compared to traditional algorithms. Detailed Implementation

[0067] The implementation method of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0068] Example

[0069] The algorithm was validated using simulated signals. The simulated signals were constructed using the GTD model.

[0070] The parameters for low-frequency band 1 are as follows:

[0071] The number of scattering centers is M = 3.

[0072] The initial frequency f0 is 9*10 9

[0073] The length of the spectral sequence in low-frequency band 1 is N1 = 51;

[0074] The Δf of low frequency band 1 is 20*10 6 ;

[0075] sequence f k′ =f0+k′Δf,k′=0,...,N1-1

[0076] The complex amplitude σ1 of the first scattering center in low frequency band 1 is 4;

[0077] The first scattering center of low frequency band 1 for

[0078] The α1 of the first scattering center in low-frequency band 1 is -1;

[0079] The complex amplitude σ2 of the second scattering center in low-frequency band 1 is 1;

[0080] The second scattering center of low frequency band 1 for

[0081] The α2 of the second scattering center in low-frequency band 1 is 0;

[0082] The complex amplitude σ3 of the third scattering center in low-frequency band 1 is 1;

[0083] The third scattering center in low frequency band 1 for

[0084] The α3 of the third scattering center in low-frequency band 1 is 1;

[0085] The parameters for high-frequency band 2 are as follows:

[0086] The number of scattering centers is M = 3.

[0087] The initial frequency f0 is 9*10 9

[0088] The initial N2 = 101 of the spectral sequence for high-frequency band 2;

[0089] The sequence terminates at point Q = 151;

[0090] The Δf of high-frequency band 2 is 20*10 6 ;

[0091] sequence f k″ =f0+k″Δf,k″=N2,...,Q-1

[0092] The complex amplitude σ1 of the first scattering center in high-frequency band 2 is 4;

[0093] The first scattering center of high frequency band 2 for

[0094] The α1 of the first scattering center in high-frequency band 2 is -1;

[0095] The complex amplitude σ2 of the second scattering center in high-frequency band 2 is 1;

[0096] The second scattering center of high frequency band 2 for

[0097] The α2 of the third scattering center in high-frequency band 2 is 0;

[0098] The complex amplitude σ3 of the third scattering center in high-frequency band 2 is 1;

[0099] The third scattering center of high frequency band 2 for

[0100] The α3 of the third scattering center in high-frequency band 2 is 1;

[0101] Phase error s is e -j .

[0102] Using the simulated low-frequency band 1 signal and high-frequency band 2 radar signal, firstly, according to the requirements of step one, coherent registration of the multi-band radar signals is performed; then, according to the requirements of step two, broadband modeling of the multi-band radar signals is performed to obtain the broadband scattering center GTD model of the multi-band radar signals; finally, according to the process proposed in step three, the broadband scattering center model of the multi-band radar signals constructed in step two is solved using the FSBL-MD method to complete the multi-band fusion.

[0103] Figure 1The broadband scattering center model (red solid line) of the multi-band radar signal recovered by the method in this paper was compared with the theoretical value (blue solid line) of the broadband scattering center model of the multi-band radar signal. The selected low-frequency band 1 and high-frequency band 2 are represented by the blue scatter points in the figure. It can be seen that, under simulation conditions, the broadband scattering center model results of the multi-band radar signal are basically consistent with the theoretical values, and the fusion effect is good.

[0104] Figure 2 The range profile (red solid line) corresponding to the broadband scattering center model of the multi-band radar signal obtained by the method in this paper is compared with the range profile of low-frequency band 1 (blue solid line). It can be seen that for multiple targets that cannot be resolved in low-frequency band 1, the range profile obtained by the method in this paper can resolve three targets, and the result is basically consistent with the theoretical value.

[0105] Using the Monte Carlo method, 300 Monte Carlo experiments were conducted to compare the root mean square error (RMSE) of the broadband scattering center model estimation of multi-band radar signals between the proposed FSBL-MD method and the traditional FSBL method under noisy conditions. Figure 3 The computation time of the traditional method and the proposed method was compared with the signal-to-noise ratio (SNR): when the SNR range was 5-30dB, the computation time of the proposed FSBL-MD algorithm (black solid line) was better than that of the traditional algorithm (blue solid line).

[0106] Figure 4 The RMSE of the traditional algorithm and the proposed method were compared with the signal-to-noise ratio (SNR): when the SNR range was 5-30dB, the RMSE error of the proposed FSBL-MD algorithm (black solid line) was better than that of the traditional FSBL algorithm (blue solid line).

[0107] Simulation results show that the proposed FSBL-MD algorithm has better multi-band phase error estimation accuracy than the traditional FSBL algorithm.

[0108] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0109] The foregoing description illustrates and describes several preferred embodiments of the present invention. However, as previously stated, it should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the inventive concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

[0110] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-band fusion extrapolation method based on a multi-dictionary-fast sparse Bayesian algorithm, characterized in that... The steps of this method include: Step 1: Perform phase coherent registration on the multi-band radar signals; Step 2: Perform broadband modeling on the multi-band radar signal after coherent registration in Step 1 to obtain the broadband scattering center GTD model of the multi-band radar signal. Step 3: Use the FSBL-MD algorithm to solve the broadband scattering center GTD model of the multi-band radar signal constructed in Step 2, and complete the fusion of multi-band radar signals. In step one, the method for coherent registration of multi-band radar signals is as follows: Suppose that the multi-band radar signal includes low-frequency band 1 and high-frequency band 2. Using low-frequency band 1 as the reference signal, high-frequency band 2 is phase-compensated to low-frequency band 1, and the compensated high-frequency band is marked as high-frequency band 2'. First, establish the GTD model of the scattering center in low-frequency band 1. And the GTD model of the scattering center in high frequency band 2 ; Among them, the scattering center GTD model of low frequency band 1 for: in, ; The starting frequency; This is the starting point of the spectrum sequence for low-frequency band 1; Represents the end point of the sequence bandwidth; Represents frequency interval; M Represents the number of scattering centers; Representing the m The target complex amplitude corresponding to each scattering center m =1,2,…, M , For the first m The relative distance from each scattering center to the radar; The term is a factor that depends on both amplitude and frequency. = -1, -0.5, 0, 0.5, 1; GTD model of scattering center in high frequency band 2 for: in, ; The starting frequency; This is the starting point of the spectral sequence for high-frequency band 2; Represents the end point of the sequence bandwidth; Represents frequency interval; M Represents the number of scattering centers; Representing the m The target complex amplitude corresponding to each scattering center m =1,2,…, M , For the first m The relative distance from each scattering center to the radar; The term is a factor that depends on both amplitude and frequency. = -1, -0.5, 0, 0.5, 1; This refers to the phase error term present in high-frequency band 2; After phase error compensation, the GTD model of the scattering center in the high-frequency band 2' for: in, ; The starting frequency; This is the starting point of the spectral sequence for high-frequency band 2; Represents the end point of the sequence bandwidth; Represents frequency interval; M Represents the number of scattering centers; Representing the m The target complex amplitude corresponding to each scattering center m =1,2,…, M , For the first m The relative distance from each scattering center to the radar; The term is a factor that depends on both amplitude and frequency. = -1, -0.5, 0, 0.5, 1; In step three, the broadband scattering center GTD model of the multi-band radar signal described in step two is solved. The specific method is as follows: The first step is to construct the sparse vector form equation of the broadband scattering center GTD model as follows: Multi-band data for Magnitude vector Recorded as: The length of the sparse vector. dictionary matrix; The second step is to construct the first-level dictionary: using a Fourier dictionary, the dictionary matrix is... The construction is as follows: Where the dictionary matrix The d-th column vector Recorded as: In the formula, ; The SBL method is used to solve the sparse representation vector form equation in the first step to obtain the magnitude vector. ; The third step is to construct a second-level dictionary to solve for the magnitude vector. : Find the magnitude vector required in the second step. Non-zero elements are denoted by their sequence number as follows: Its length is Construct a Fourier dictionary matrix using its corresponding dictionary matrix column vectors. dictionary matrix The column vector Recorded as: In the formula, ; By increasing the dictionary's precision by 10 times and expanding the number of atoms in the dictionary, a Fourier dictionary matrix is ​​obtained. , its first column vector Recorded as: Switch dictionaries to use frequency-dependent factors Fourier dictionary matrix Each atom in the mixture is transformed into a GTD atom. as follows: in, = -1, -0.5, 0, 0.5, 1; all The value of the GTD atom Reconstruct the dictionary matrix ; The SBL algorithm is used to solve the sparse representation vector form equation in the first step to obtain the magnitude vector. ; The fourth step is to construct the third-level dictionary and solve for the magnitude vector. : Find the magnitude vector required in the second step. Non-zero elements are determined based on their position in the dictionary matrix. Location reconstruction yields a local dictionary ; The dictionary precision is increased by 10 times again, and the dictionary is expanded using neighboring values ​​based on the position values ​​of non-zero elements to obtain a new dictionary matrix. ; The SBL algorithm is used to solve the sparse representation vector form equation in the first step to obtain the magnitude vector. ; Fifth step, The atoms in the middle are extended to the full frequency range, denoted as Then, the multi-band fusion extrapolated spectrum vector selected based on the optimal dictionary for orthogonal matching pursuit is: ; The broadband scattering center GTD model of multi-band radar signals has been solved, and multi-band fusion has been completed.

2. The multi-band fusion extrapolation method based on multi-dictionary-fast sparse Bayesian algorithm according to claim 1, characterized in that: In step two, the broadband scattering center GTD model of the multi-band radar signal is established. for: in, ; Represents frequency interval; Represents the number of broadband signal frequency points; M Represents the number of scattering centers; Representing the m The target complex amplitude corresponding to each scattering center m =1,2,…, M , For the first m The relative distance from each scattering center to the radar; where, The term is a factor that depends on both amplitude and frequency. = -1,-0.5,0,0.5,1.

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