Sub-band coherent registration method based on signal sparse reconstruction and local grid refinement

Abstract

The application belongs to the field of radar signal processing, and particularly relates to a sub-band coherent registration method based on signal sparse reconstruction and local grid refinement. The application is aimed at high-speed moving targets, and a sub-band mismatch condition is modeled in detail under a complex background of system errors, and a mismatch factor is solved through a joint method of signal sparse reconstruction and local grid subdivision. The method does not depend on frequency band extrapolation data or pole solving results, and effectively improves the solving accuracy and noise resistance of the mismatch factor.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of radar signal processing, and particularly relates to a sub-band coherent registration method based on signal sparse reconstruction and local grid refinement. BACKGROUND

[0002] It can be known from a definition expression of the range resolution of a radar that the range resolution of the radar is inversely proportional to the bandwidth of a transmitted signal, that is, the greater the bandwidth of the transmitted signal, the higher the range resolution of the radar. However, in an actual production process, the bandwidth of the radar cannot be infinitely increased due to the limitation of a radar waveform generator and other hardware, and obtaining a large bandwidth signal also increases the design cost of a radar system, therefore, a multi-band fusion technology emerges as the times require. The multi-band fusion refers to that two or more radars at different positions in space transmit LFM signals with different frequency bands at a transmitting end, and the echo signals of high and low frequency bands are coherently registered at a receiving end, after the correlation between sub-band echo signals is recovered, the missing band signals can be estimated by interpolation, so that a complete virtual ultra-wideband signal is obtained, and the range resolution is improved to a level equivalent to that of an ideal full-band signal. However, before the band fusion, due to the high-speed motion of a target and the system error existing in the system, the correlation between two sub-band echoes is poor, if the sub-band correlation is not recovered, the full-band data after the fusion will be inevitably disordered, therefore, the non-correlation between sub-bands needs to be compensated first, and then the band fusion is performed. SUMMARY

[0003] The application provides a method for coherently registering mismatched sub-bands based on signal sparse reconstruction and local grid refinement under the condition that the target moves at a high speed and the system error exists in the system.

[0004] The technical scheme of the present application is: firstly, considering the high-speed motion of the target and the system error between systems, velocity estimation and compensation are performed on the echo to eliminate the influence of high-speed motion of the target, at this time, velocity compensation residual and system error will exist between sub-band echoes. Then, the GTD model parameters of the echo are solved to obtain the related parameters of the target scattering center, such as the model order, the relative position of the scattering center, the scattering intensity, the geometric type and the like. Secondly, after resampling of the sub-band, a sub-band echo mismatch model is established to describe the mismatch condition between the sub-bands, at this time, the non-correlation quantity between the sub-bands is mainly linear phase difference, fixed phase difference and amplitude difference. Then, based on the sparsity of the sub-band, the linear phase factor is preliminarily estimated through a sparse reconstruction algorithm, and then the best linear phase value is searched in the vicinity of the preliminarily estimated linear phase factor, as the final linear phase estimation structure. Then, the phase correlation coefficient (PCC) is taken as the target function, and the best fixed phase is solved in the fixed phase interval. Finally, the amplitude correlation coefficient (ACC) is taken as the target function, and the best amplitude difference is solved in the amplitude difference interval. After the mismatch factors between the sub-bands are obtained, the correlation compensation is performed on the mismatched sub-bands to restore the correlation of the sub-bands.

[0005] The technical scheme of the present application is:

[0006] The sub-band coherent registration method based on signal sparse reconstruction and local grid refinement comprises the following steps:

[0007] Step 1: after the echoes of the target are received by the two radars, velocity estimation and compensation are performed on the echoes;

[0008] Step 2: the GTD model parameters of the sub-band echo are solved to obtain the related parameters of the target scattering center, and the related parameters include the GTD model order, the scattering intensity, the relative position and the geometric type of the scattering center;

[0009] Step 3: the GTD model of the echo signal is established by using the obtained GTD model parameters, and after the resampling and discretization processing of the echoes of the two radars, the mismatch model between the sub-bands is obtained, including the linear phase difference, the fixed phase difference and the amplitude difference;

[0010] Step 4: according to the GTD model order solved in step 2, the sparse representation of each sub-band is solved through a sparse reconstruction algorithm;

[0011] Step 5: the preliminary linear phase factor estimation value is calculated by using the grid position relationship of the joint one-dimensional range profile image between the multiple sub-bands;

[0012] Step 6: a search interval is set in the vicinity of the obtained linear phase estimation value, and the grid is subdivided, and the best matching linear phase factor is solved by taking the joint HRRP image entropy of the high and low frequency bands as the target function in the search interval;

[0013] Step 7: Using the obtained optimal linear phase factor, perform linear phase compensation on the mismatched subband, and solve for the optimal fixed phase factor in the interval [-π,π] with PCC as the objective function;

[0014] Step 8: Using the obtained optimal linear phase factor and optimal fixed phase factor, perform linear phase compensation and fixed phase compensation on the mismatched sub-bands, and use ACC as the objective function to solve for the optimal amplitude difference between sub-bands;

[0015] Step 9: Use the obtained optimal linear phase factor, optimal fixed phase factor, and optimal amplitude difference to compensate for the mismatched subbands and restore their correlation.

[0016] The beneficial effects of this invention are as follows: For high-speed moving targets, this invention provides a detailed model of subband mismatch under the complex background of system errors, and solves for the mismatch factor through a joint method of sparse signal reconstruction and local mesh subdivision. This method does not rely on frequency band extrapolation data or pole solution results, effectively improving the accuracy of the mismatch factor solution and its noise resistance. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the subband resampling model involved in the present invention.

[0018] Figure 2 This is a flowchart of the algorithm proposed in this invention. Detailed Implementation

[0019] The specific technical solution of the present invention will be described below with reference to the accompanying drawings.

[0020] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings:

[0021] like Figure 1 As shown, it is assumed that the transmitted signal of radar 1 is in the 3-3.5 GHz frequency band, and the transmitted signal of radar 2 is in the 6-6.5 GHz frequency band.

[0022] like Figure 2 The diagram shows the process of this invention, which specifically includes:

[0023] Step 1: Perform velocity compensation on the sub-band echo signals. Assume the radar transmits an LFM signal, and the target's velocity is v, y i (f), where i = 1, 2 are the echo signals of the i-th radar, then the phase compensation required for modeling moving target echoes is:

[0024]

[0025] Where K i Let f be the frequency modulation slope of the i-th radar. ciThe carrier frequency of the i-th radar, f is frequency, c is the speed of light, The estimated velocity of the target. Next, it is further explained how to estimate the target velocity by the image minimum entropy algorithm based on binary search.

[0026] The HRRP after velocity compensation is denoted as h i (k) = IFFT[y(f i )], k = 1, 2, … N, IFFT is the inverse Fourier transform, and N is the number of sampling points of the signal. The image entropy of HRRP can be expressed as a function of where p i is the amplitude distribution of HRRP, and its expression is

[0027]

[0028] The target velocity can be estimated by . Where v min and v max are the lower bound and upper bound of the target velocity, respectively.

[0029] The specific steps are as follows:

[0030] 1. Initialization: Determine the search lower bound v min , the search upper bound v max , the search step v step ; Initialize the vector v = [v0, v1, v2…v n-1 ], n = (v max -v min ) / △v+1; Determine the left pointer l = 0, the right pointer r = n-1.

[0031] 2. Iteration: If l≥r, stop the algorithm, output

[0032] 3. Calculate the middle pointer

[0033] 4. Calculate H(v m ), H(v m-1 ), H(v m+1 );

[0034] 5. If H(v m )<H(v m-1 ) and H(v m )<H(v m+1 ), output the algorithm ends;

[0035] 6. If H(v m-1 )<H(v​m ) <H(v m+1 ), r = m - 1, return to 2;

[0036] 7. If H(v) m-1 )>H(v m )>H(v m+1 ), l = m + 1, return to 2;

[0037] Step 2: After velocity compensation, estimate the parameters of the sub-band GTD model. The model order M can be estimated using the AIC criterion. The relative position r of the m-th scattering center m The poles of the echo can be estimated by: r m =-arg(z m )c / 4π△f, where z m Let α be the pole of the m-th scattering center, and Δf be the frequency sampling interval. The geometric type α of the m-th scattering center is... m It can be estimated using the MUSIC algorithm, that is... Where p(k,r) m () represents the projection of an element in the signal subspace onto the noise subspace. The scattering intensity at the m-th scattering center. It can be estimated by solving the least squares solution of the echo signal.

[0038] Step 3: Due to the limited accuracy of the velocity compensation algorithm, a velocity compensation residual Δv will still exist after processing. Furthermore, there are time synchronization errors t0 and initial phase differences in the transmitted signals between radar systems. After estimating the GTD parameters of the echo signal, a GTD model can be established for the echo signal, i.e.

[0039]

[0040]

[0041] Where t0 is the time synchronization error between the two radars. Let λ be the initial phase difference between the transmitted signals of the two radars, and λ be the velocity compensation residual factor.

[0042] After resampling and discretizing the echoes from the two radars, the mismatch models for the two sub-band echo signals can be established as follows:

[0043]

[0044]

[0045] where n = 1, 2, …, N is the sampling frequency point, A is the joint amplitude of the target scattering center, p is the amplitude difference between subbands, y is the linear phase difference between subbands, and η is the fixed phase difference between subbands.

[0046] Step 4: Construct an overcomplete dictionary for subband 1 and subband 2 to obtain the sparse representation of the subband echo. The overcomplete dictionary is

[0047]

[0048] where ω n,p = exp(-j2πnp / P), P is the number of Fourier transform points, and P » N.

[0049] Further, the sparse representation of the subband can be solved in the following flow. In the following flow, y1 represents the N-dimensional subband 1 echo, y2 represents the N-dimensional subband 2 echo, t represents the iteration number, r it represents the residual of y i after the tth iteration, represents an empty set, λ it represents the atom index (column number of the matrix Ω) located by the tth iteration of y i , Λ it represents the atom index set found by the tth iteration of y i , ω j represents the jth column of the matrix Ω, Ω it represents the column set of Ω selected by Λ it , and x represents the sparse representation coefficient of y i after the tth iteration, represents the final sparse representation coefficient of y i .

[0050] 1. Initialize r i0 = 0, t = 1;

[0051] 2. Find the index λ it such that

[0052] 3. Let Λ it = Λ it-1 ∪ {λ it}, Ω it = Ω it-1 ∪ {ω λit};

[0053] 4. Solve the least square solution of y i = Ω it x it , that is,

[0054] 5. Update residual

[0055] 6. t = t + 1, if t > M, let Stop iteration, otherwise go back to 2;

[0056] Step 5: Solve the preliminary linear phase estimate using the grid relationship Find the index I of the maximum i , and the preliminary linear phase estimate γ' = 2π(I1-I2) / P.

[0057] Step 6: Refine the grid to find the optimal linear phase factor. The detailed procedure is as follows

[0058] 1. Determine the search lower bound and lower bound γ L = γ' - 2π△I / P, search upper bound γ U = γ' + 2π△I / P, search step size γ step = 2π / (KP). Where△I is the number of grids to be subdivided;

[0059] 2. Initialize k = 1, γ1= γ L , hrrp i = IFFT(y i ), H min = H(hrrp1+hrrp2);

[0060] 3. Let γ k = [exp(jγ k ), exp(j2γ k ), …, exp(j2γ k N)] T , hrrp2 = IFFT[y2⊙(-γ k )];

[0061] 4. k = k + 1, γ k = γ k-1 + γ step , if γ k ≤ γ U , go back to 3, otherwise output

[0062] Step 7: Estimate the fixed phase, and perform linear phase compensation on y1(n) to get Define the phase correlation coefficient PCC, whose expression is

[0063]

[0064] ​η can be searched in the range of [-π, π] with △η as the step, and

[0065] Step 8: Estimate the amplitude difference, and linear phase compensation is performed on y1(n) with to obtain Define the amplitude correlation coefficient ACC, and its expression is

[0066]

[0067] Make

[0068] Step 9: Perform amplitude difference and phase compensation on y1(n) to restore the correlation of y1(n) and y2(n).

Claims

1. A sub-band coherent registration method based on signal sparse reconstruction and local grid refinement, characterized in that, The method comprises the following steps: Step 1: after two radars receive echoes of a target, velocity estimation and compensation are performed on the echoes; Step 2: GTD model parameters are solved for sub-band echoes to obtain relevant parameters of a target scattering center, and the relevant parameters include GTD model order, scattering intensity, relative position and geometric type of the scattering center; Step 3: a GTD model of echo signals is established by using the obtained GTD model parameters, after resampling and discretization processing of echoes of the two radars, a mismatch model between sub-bands is obtained, including linear phase difference, fixed phase difference and amplitude difference; Step 4: according to the GTD model order solved in step 2, a sparse representation of each sub-band is solved by a sparse reconstruction algorithm; Step 5: a preliminary linear phase factor estimation value is calculated by using a grid position relationship of joint one-dimensional range profiles between multiple sub-bands; Step 6: a search interval is set near the obtained linear phase estimation value, and grid subdivision is performed, and a best matching linear phase factor is solved by taking joint HRRP image entropy of high and low frequency bands as an objective function in the search interval; Step 7: the obtained optimal linear phase factor is used to compensate for linear phase of mismatched sub-bands, and an optimal fixed phase factor is solved in the interval [-π, π] by taking PCC as an objective function; Step 8: the obtained optimal linear phase factor and optimal fixed phase factor are used to compensate for linear phase and fixed phase of mismatched sub-bands, and an optimal amplitude difference between sub-bands is solved by taking ACC as an objective function; Step 9: the obtained optimal linear phase factor, optimal fixed phase factor and optimal amplitude difference are used to compensate for mismatched sub-bands to restore the correlation of the sub-bands.

2. The sub-band coherent registration method based on signal sparse reconstruction and local grid refinement of claim 1, wherein, The radar transmits LFM signals in step 1, the target's moving speed is v, y i (f), i = 1, 2 is the echo signal of the i-th part of the radar, and the phase to be compensated according to the moving target echo modeling is: where K i is the frequency modulation slope of the ith radar, f ci is the carrier frequency of the ith radar, f is the frequency, and c is the speed of light, is the estimated velocity of the target; An image minimum entropy algorithm based on binary search is used to estimate the target velocity, and specifically: The HRRP after velocity compensation is defined as h i (k) = IFFT[y(f i )], k = 1, 2, … N, IFFT is inverse Fourier transform, N is the number of sampling points of the signal, and the image entropy of the HRRP is a function of where p ik is the amplitude distribution of the HRRP. The target speed is given by It is estimated that v min and v max are lower and upper bounds of the target speed, respectively; In step 2, the order M of the GTD model is estimated by the AIC criterion: Relative position r of the mth scattering center m By solving the echo pole estimation: r m = -arg(z m ) c / 4π△f, where z m is the pole of the mth scattering center, and △f is the frequency sampling interval Geometric type of the mth scattering center a m is estimated by the MUSIC algorithm, i.e. where p(k, r m ) is the projection of the elements in the signal subspace on the noise subspace. the scattering intensity of the mth scattering center is estimated by solving a least square solution of the echo signals.

3. The sub-band coherent registration method based on signal sparse reconstruction and local grid refinement of claim 2, wherein, In step 3, a GTD model is established for echo signals as follows: where t0 is the time synchronization error between the two radars, is the initial phase difference between the two radars transmitting signals, and λ is the velocity compensation residual error factor, After resampling and discretization processing of echoes of the two radars, a mismatch model of two sub-band echo signals is established as follows: Wherein n = 1, 2, …, N is a sampling frequency point, A is a joint amplitude of a target scattering center, r is an amplitude difference between sub-bands, γ is a linear phase difference between sub-bands, and η is a fixed phase difference between sub-bands.

4. The sub-band coherent registration method based on signal sparse reconstruction and local grid refinement of claim 3, wherein, In step 4, a sparse representation of a sub-band is obtained by constructing an overcomplete dictionary for the sub-band, and then sparse representation coefficients of the sub-band are solved, and the overcomplete dictionary is as follows: where ω n,p = exp(-j2πnp / P), P is the number of Fourier transform points, P » N; Set y i The echo representation of subband i, i = 1, 2, is obtained as y i The final sparse representation coefficients are In step 5, the resulting linear phase estimate is γ' = 2π(I1- I2) / P, I i is the index of the maximum. In step 6, the search interval is set as: search lower bound γ L = γ'-2π△I / P, search upper bound γ U = γ'+2π△I / P, search step γ step = 2π / (KP), where △I is the number of grids to be subdivided; the joint HRRP image entropy of the high and low frequency bands is taken as the objective function in the search interval, and the best matching linear phase factor obtained is defined as In step 7, y1(n) is linear phase compensated to obtain The phase correlation coefficient PCC is defined as​ Let η search in the range [-π, π] with step size △η, so that In step 8, y1(n) is linear phase compensated to obtain The amplitude correlation coefficient ACC is defined as​ causing

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