A multi-band fusion extrapolation method based on GTD dictionary orthogonal matching pursuit

Abstract

The application relates to a multi-frequency band fusion extrapolation method based on GTD dictionary orthogonal matching pursuit, and particularly relates to a multi-frequency band fusion extrapolation method based on geometrical theory of diffraction (GTD) orthogonal matching pursuit (OMP), which is suitable for fusing and extrapolating a missing frequency band after phase compensation of multi-frequency band radar signals and belongs to the technical field of multi-frequency band radar super-resolution imaging. For multi-frequency band data, the method firstly models the multi-frequency band data; after phase registration, the OMP-GTD algorithm is used to extrapolate full-frequency band data, and multi-frequency band extrapolation is completed. The application can effectively realize high-precision multi-frequency band fusion extrapolation and obtain a high-resolution target range image.

Description

Technical Field

[0001] This invention relates to a multi-band fusion extrapolation method based on GTD dictionary orthogonal matching pursuit. This method is designed for multi-band radar data fusion extrapolation, and particularly relates to a multi-band fusion extrapolation method based on Geometrical Theory of Diffraction (GTD) and Orthogonal Matching Pursuit (OMP). 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.

[0004] Orthogonal Matching Pursuit (OMP) is an efficient sparse representation algorithm commonly used in signal processing. However, its computation is limited by the orthogonality of the sparse dictionary, making it difficult to use high-precision non-orthogonal dictionaries. Using a low-precision Fourier orthogonal dictionary results in low model accuracy. Directly using a GTD dictionary is computationally intensive and slow. 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 orthogonal matching pursuit using a GTD dictionary. This method can solve the problem of insufficient accuracy in traditional OMP algorithm models and is an efficient and high-precision multi-band fusion extrapolation method. To address the accuracy issues of traditional OMP methods, an orthogonal matching pursuit (OMP-GTD) algorithm based on geometrical diffraction theory is adopted. First, a Fourier dictionary is used to coarsely solve the multi-band radar signal model; then, frequency dependence factor discrimination is performed based on the principle of minimum residual, thereby equivalently obtaining a high-precision radar signal GTD model and reducing the dimensionality of the actual computation matrix. The proposed method aims to provide a high-precision and fast 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 multi-band fusion extrapolation method based on GTD dictionary orthogonal matching pursuit, where the multi-band includes two or more bands, includes the following steps:

[0008] Step 1: Perform phase coherent registration on the multi-band radar signals;

[0009] 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.

[0010] Step 3: Use the OMP-GTD 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.

[0011] In step one, the method for coherent registration of multi-band radar signals is as follows:

[0012] 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'.

[0013] 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 );

[0014] Among them, the scattering center GTD model E1(f in low frequency band 1) k′ )for:

[0015]

[0016] 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;

[0017] The GTD model of the scattering center in high-frequency band 2, E2(f) q )for:

[0018]

[0019] 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; s represents the phase error term present in high-frequency band 2;

[0020] After phase error compensation, the scattering center E of the high-frequency band 2' is obtained from the GTD model. 2′ (f k )for:

[0021]

[0022] 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;

[0023] In step two, the broadband scattering center GTD model E(f) of the multi-band radar signal is established. k )for:

[0024]

[0025] 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;

[0026] 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:

[0027] The first step is to construct the sparse vector representation of the broadband scattering center GTD model:

[0028] E=Φσ

[0029] Multi-band data E is represented as

[0030] E = [E1(0),...,E1(N1-1),E 2′ (N2),...,E 2′ (Q-1)] T

[0031] The magnitude vector s is denoted as:

[0032] σ=[σ(0),...,σ(D-1)] T

[0033] D is the length of the sparse vector;

[0034] The dictionary matrix Φ is represented as:

[0035] Φ=[a0,a1,...,a D-1 ]

[0036] Where the d-th column vector (also called an atom) of the dictionary matrix Φ is a d Recorded as:

[0037]

[0038] In the formula, d = 0, 1, ..., D-1;

[0039] The second step is initialization: Define an index set L to store the valid atoms of the dictionary matrix, and initialize the index set. The residual vector R = E;

[0040] The third step is to select the optimal atom: take the inner product of the current residual and each atom in the dictionary matrix, and find the column d containing the atom with the largest inner product. max :

[0041]

[0042] Here, <> represents the inner product operation, and || represents the modulo operation. According to the OMP algorithm update criterion, the larger the inner product of the selected atoms, the smaller the 2-norm of the updated residual. The smaller the 2-norm of the residual, the more accurate the model estimation. The atom with the smallest updated 2-norm of the residual is called the optimal atom. Therefore, the column vector with the largest inner product... It is selected as the optimal Fourier atom in the current dictionary matrix.

[0043] Step 4, GTD Model Correction: Compared to the Fourier dictionary, the GTD dictionary provides a more accurate description of radar scattering echoes. The traditional model is corrected to a GTD model. Compared to the ideal Fourier model, the GTD model adds... Therefore, it is only necessary to solve for the frequency dependence factor α corresponding to the optimal Fourier atom. m This allows the optimal Fourier atom to be converted into the optimal GTD atom.

[0044] Step 5, GTD Atom Transformation: Transforming Fourier Atoms Transformed into GTD atoms g m as follows:

[0045]

[0046] Where, α m =-1,-0.5,0,0.5,1.

[0047] Step 6, Residual Update: Rearrange different α values... m The value of GTD atom g m Add them one by one to Λ, denoted as Λ m Calculate α m Residual R corresponding to different values m :

[0048] R m =E-Λ m (Λ m T Λ m ) -1 Λ m T E

[0049] Step 7, Minimum Residual Selection: Select the minimum value of the 2-norm of the residuals and assign its corresponding value m. best As the optimal frequency dependence factor for this atom, the optimal GTD atom is obtained. And add it to L.

[0050] Step 8: Determine the iteration termination condition: When the residual 2-norm is less than the set threshold, the iteration can be terminated and step 9 can be executed; otherwise, repeat steps 3 to 8.

[0051] The ninth step, after the iteration is complete, is to use the final calculated Λ to solve for the sparse vector.

[0052]

[0053] Step 10, finally, extend each atom in Λ 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:

[0054]

[0055] The broadband scattering center GTD model of multi-band radar signals has been solved, and multi-band fusion has been completed.

[0056] Beneficial effects

[0057] To address the challenge of multi-band fusion extrapolation, this paper proposes a high-precision multi-band fusion extrapolation method based on GTD dictionary orthogonal matching pursuit. For multi-band data, this method first models the multi-band data; then, it uses the proposed OMP-GTD 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 images. Attached Figure Description

[0058] 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;

[0059] Figure 2 This is a schematic diagram comparing the distance image and the theoretical value of the distance image of the model before and after processing by the method of the present invention.

[0060] 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;

[0061] 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

[0062] The implementation method of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0063] Example

[0064] The algorithm was validated using simulated signals. The simulated signals were constructed using the GTD model.

[0065] The parameters for low-frequency band 1 are as follows:

[0066] The number of scattering centers is M = 2.

[0067] The initial frequency f0 is 9*10 9

[0068] The length of the spectral sequence in low-frequency band 1 is N1 = 51;

[0069] The Δf of low frequency band 1 is 20*10 6 ;

[0070] sequence f k′ =f0+k′Δf,k′=0,...,N1-1

[0071] The complex amplitude σ1 of the first scattering center in low frequency band 1 is 4;

[0072] The first scattering center of low frequency band 1 for

[0073] The α1 of low frequency band 1 is -1;

[0074] The complex amplitude σ2 of the second scattering center in low-frequency band 1 is 1;

[0075] The second scattering center of low frequency band 1 for

[0076] In the low-frequency band 1, α2 is 1;

[0077] The parameters for high-frequency band 2 are as follows:

[0078] The number of scattering centers is M = 2.

[0079] The initial frequency f0 is 9*10 9

[0080] The initial N2 = 101 of the spectral sequence for high-frequency band 2;

[0081] The sequence terminates at point Q = 151;

[0082] The Δf of high-frequency band 2 is 20*10 6 ;

[0083] sequence fk″ =f0+k″Δf,k″=N2,...,Q-1

[0084] The complex amplitude σ1 of the first scattering center in high-frequency band 2 is 4;

[0085] The first scattering center of high frequency band 2 for

[0086] α1 in high-frequency band 2 is -1;

[0087] The complex amplitude σ2 of the second scattering center in high-frequency band 2 is 1;

[0088] The second scattering center of high frequency band 2 for

[0089] α2 in high-frequency band 2 is 1;

[0090] The error s is e -j .

[0091] 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 OMP-GTD method is used to solve the broadband scattering center model of the multi-band radar signals constructed in step two, thus completing the multi-band fusion.

[0092] Figure 1 The 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.

[0093] Figure 2 The range profile (red dashed line) corresponding to the broadband scattering center model of multi-band radar signals obtained by the method in this paper is compared with the theoretical range profile (black solid line) of the broadband scattering center model of multi-band radar signals. The range profile of low-frequency band 1 is represented by the blue solid line. It can be seen that for multiple targets that cannot be distinguished in low-frequency band 1, the range profile obtained by the method in this paper can distinguish two targets, and the result is basically consistent with the theoretical value.

[0094] Using the Monte Carlo method, 300 Monte Carlo experiments were conducted to compare the root mean square error (RMSE) of the proposed method in estimating the broadband scattering center model of multi-band radar signals with the traditional OMP method under noisy conditions.

[0095] Figure 3 The computation time of the traditional algorithm 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 algorithm (pink solid line) was better than that of the traditional OMP algorithm (gray solid line).

[0096] 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 algorithm (pink solid line) was better than that of the traditional OMP algorithm (gray solid line).

[0097] Simulation results show that the proposed algorithm has better multi-band phase error estimation accuracy than the traditional OMP algorithm.

[0098] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0099] 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.

[0100] 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 GTD dictionary orthogonal matching pursuit, 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 OMP-GTD 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 end point of the spectral sequence in 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 termination point of the spectral sequence in 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 step two, the broadband scattering center GTD model of the multi-band radar signal is established. for: in, ; The term is a factor that depends on both amplitude and frequency; In step three, the broadband scattering center GTD model of the multi-band radar signal described in step two is solved. The method is as follows: The first step is to construct the sparse vector representation of the broadband scattering center GTD model: Multi-band data Represented as Magnitude vector Recorded as: The length of the sparse vector; dictionary matrix Represented as: Where the dictionary matrix The d-th column vector (also called an atom) Recorded as: In the formula, The second step is initialization: defining the index set. Used to store valid atoms of the dictionary matrix and initialize the index set. residual vector The third step is to select the optimal atom: take the inner product of the current residual and each atom in the dictionary matrix, and find the column containing the atom with the largest inner product. : in, This represents the inner product operation. This represents the column vector with the largest inner product obtained by modulo operation. Selected as the optimal Fourier atom in the current dictionary matrix; Step 4, GTD model correction: convert the optimal Fourier atom into the optimal GTD atom; Step 5, GTD Atom Transformation: Transforming Fourier Atoms Transformed into GTD atoms as follows: Step 6, Residual Update: Replace different GTD atom value Add them one by one in turn In Chinese, it is written as calculate Residuals corresponding to different values : Step 7, Minimum Residual Selection: Select the value with the minimum 2-norm of the residuals and assign its corresponding value... As the optimal frequency dependence factor for this atom, the optimal GTD atom is obtained. and add to middle; Step 8: Determine the iteration termination condition: when the residual 2-norm is less than the set threshold, terminate the iteration and execute step 9; otherwise, repeat steps 3 to 8. Step 9: After the iteration is complete, use the final calculated result... Solving sparse vectors : Step 10, finally, will 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.

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