A radar target high-resolution estimation and range ambiguity suppression method based on MUSIC-AP

Abstract

The application discloses a radar target high-resolution estimation and distance ambiguity suppression method based on MUSIC-AP. Firstly, echoes of different distance sections in a CPI are preprocessed to obtain multiple single-shot data, an imaging function is formed, and local maximum values of the imaging function are identified as a distance frequency set and converted into distance information of scattering points; then, complex amplitude information of the scattering points is obtained by combining a least square method to reconstruct echoes of different distance sections; by using an alternating projection (AP) algorithm, ambiguous echo energy and noise energy of non-target distance sections are gradually suppressed, and echo reconstruction precision and de-ambiguity performance are further improved; and complex amplitude information of different pulses of different distance sections after convergence is used again to obtain a velocity frequency set by using a MUSIC high-resolution algorithm, and the velocity frequency set is converted into velocity information of the scattering points.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and particularly relates to a radar target high-resolution estimation and range ambiguity suppression method based on MUSIC-AP. BACKGROUND

[0002] Pulse Doppler (PD) processing enables target echoes to be in-phase accumulated in each frequency sampling unit, effectively improving the signal-to-noise ratio of the target. In a coherent processing interval (CPI), a traditional PD radar transmits an in-phase pulse sequence with constant pulse width and pulse repetition frequency (PRF), and realizes in-phase accumulation of echo energy through PD processing of the received echo. However, constant modulation parameters will cause periodic echoes along the range dimension and the velocity dimension, i.e., cause range ambiguity and velocity ambiguity problems to affect the detection of the target. In general, a medium-high frequency working mode is adopted to obtain a larger velocity non-ambiguous range, but there is a serious range ambiguity problem.

[0003] The first classic method for deblurring is to transmit multiple sets of coherent signals with different PRFs and use the Chinese remainder theorem to deblur and obtain the true distance of the target. However, it cannot effectively utilize echo energy and may produce ghosting or false targets when there are multiple targets. The second effective solution is to utilize the range gating characteristic of Waveform Diversity (WD). Different modulated pulses are transmitted within a single CPI, and deambiguity is achieved by constructing receiving filter banks for different range segments. Common waveform diversity methods include: inter-pulse initial phase agility, which destroys the phase coherence of the slow-time dimension ambiguous signal, causing the ambiguous echo power to expand in the Doppler spectrum. However, this method relies on phase changes, which are highly sensitive to noise, and it also raises the overall Doppler sidelobes; inter-pulse frequency agility, which modulates different carrier frequencies for each pulse, preventing coherent accumulation of the ambiguous signal in the fast time dimension and enabling broadband synthesis, but requires multi-frame joint processing, reducing the speed-unambiguous range; and inter-pulse code agility, which modulates different coding sequences for different pulses with the same carrier frequency, providing a larger speed-unambiguous range compared to inter-pulse frequency agility signals. However, due to the different sidelobe distributions of different pulses, the sidelobe energy is dispersed along the Doppler dimension. Traditional pulse Doppler processing methods, when applied to waveform diversity systems, achieve range gating, but the ambiguity energy is not removed. Instead, it is distributed as scattered energy in the range-Doppler plane, which can severely affect target detection when the ambiguity target energy is large. The third method is unambiguous range-Doppler estimation of waveform diversity signals based on compressed sensing. This method requires high scene sparsity, with the observation matrix dimension proportional to the atom length and pulse repetition period, resulting in relatively high computational complexity. Furthermore, it suffers from grid mismatch, affecting estimation performance and leading to traversal loss and imaging distortion. Reducing the spacing of the discretized grid is typically necessary to lower the estimation error, but the ideal grid spacing is difficult to determine, and refining the grid dramatically increases computational complexity and atom correlation.

[0004] Therefore, based on waveform diversity technology, solving the grid mismatch problem, achieving accurate estimation of scattering point information at different ranges, and then reconstructing the echoes at different ranges to achieve de-ambiguity, thus improving the target detection performance of radar, has important practical significance and application value. Summary of the Invention

[0005] Based on waveform diversity technology, the target range-velocity estimation problem is transformed into a spectral estimation problem, modeled as a superposition of multiple complex sinusoidal signals. Echoes from different range segments within a single CPI are preprocessed to obtain multiple single-shot data, which are then converted into Hankel matrices in parallel. The MUSIC (Multiple Signal Classification) high-resolution algorithm is then used to perform Singular Value Decomposition (SVD) on the Hankel matrices to find the noise null space associated with the Hankel matrix, forming an imaging function. The local maxima of the imaging function are identified as range frequency sets, which are then converted into range information for the scattering points. The least squares method is then used to obtain the complex amplitude information of the scattering points, reconstructing the echoes from different range segments. The Alternating Projection (AP) algorithm is used to progressively suppress the blurred echo energy and noise energy from outside the current range segment, further improving the echo reconstruction accuracy and deblurring performance. Finally, the complex amplitude information of different pulses from different range segments after convergence is again processed using the MUSIC high-resolution algorithm to obtain a velocity frequency set, which is then converted into velocity information for the scattering points.

[0006] The MUSIC-AP algorithm has low computational complexity, can overcome the limitations of traditional radar resolution, effectively avoids the basis mismatch problem, improves the reconstruction effect, and also improves the range and velocity resolution and reduces the range and velocity measurement error, thus achieving high-resolution estimation of radar target information and range ambiguity suppression.

[0007] The high-resolution radar target estimation and range ambiguity suppression method based on MUSIC-AP described in this invention is achieved through the following technical solution:

[0008] Step S1: Construct a line spectrum estimation model for a scene without distance ambiguity;

[0009] Step S2: Using the line spectrum estimation model obtained in step S1, the MUSIC high-resolution spectrum estimation algorithm is used to obtain the distance estimate of the scattering point. The time-domain or frequency-domain echo model is combined with the linear least squares method to obtain the complex amplitude information of the scattering point. The MUSIC high-resolution algorithm is used again to obtain the velocity estimate of the scattering point, thereby realizing the two-dimensional high-resolution estimation of the scattering point information in the unambiguous scene.

[0010] Step S3: Construct a line spectrum estimation model for distance-ambiguous scenarios;

[0011] Step S4: Based on the MUSIC high-resolution spectrum estimation algorithm and the line spectrum estimation model in the distance ambiguity scene, and using the AP algorithm to construct the MUSIC-AP processing method, the distance-velocity two-dimensional information of the scattering points and the echo spectrum matrix of different distance segments are obtained.

[0012] The step S1 comprises the following steps:

[0013] Step S11, constructing a phase-coded signal time-frequency domain echo model with code length M and pulse number N in a non-range ambiguous scene; prt

[0014] Step S12, obtaining an echo power spectrum matrix based on the weighted matched filtering of the echo spectrum matrix obtained in S11, and performing coherent accumulation in the slow time dimension to obtain a line spectrum estimation model;

[0015] The step S2 comprises the following steps:

[0016] Step S21, constructing a Hankel matrix from the line spectrum estimation model obtained in step S1;

[0017] Step S22, obtaining a noise subspace by SVD of the Hankel matrix, forming an imaging function to obtain a range-frequency set, and converting it into a scatter point range estimation value;

[0018] Step S23, obtaining scatter point complex amplitude information (including Doppler phase factor) based on the time domain or frequency domain echo model combined with the linear least square method, and again using the MUSIC high resolution algorithm to obtain a Doppler frequency set, and converting it into a scatter point velocity estimation value;

[0019] The step S3 comprises the following steps:

[0020] Step S31, constructing an echo spectrum matrix in a range ambiguous scene;

[0021] Step S32, constructing a set of weighted matched filters for different distance segments, obtaining echo power spectrum matrices for different distance segments, and a line spectrum estimation model after coherent accumulation in the slow time dimension;

[0022] The step S4 comprises the following steps:

[0023] Step S41, constructing a Hankel matrix based on the line spectrum estimation model for different distance segments, obtaining a noise subspace by SVD, forming an imaging function to obtain a range-frequency set, and converting it into a scatter point range estimation value;

[0024] Step S42, obtaining scatter point complex amplitude information based on the time domain or frequency domain echo model combined with the linear least square method, and reconstructing the echo spectrum matrix for different distance segments;

[0025] Step S43, gradually reducing the echo spectrum residual by combining the MUSIC and AP algorithms to obtain more accurate echo spectrum matrices for different distance segments, and again using the MUSIC high resolution algorithm to obtain a velocity-frequency set from the converged complex amplitude information of different pulses for different distance segments, and converting it into a scatter point velocity estimation value;

[0026] ​Beneficial effects:

[0027] The application provides a radar target high-resolution estimation and distance ambiguity suppression method based on MUSIC-AP. Waveform diversity technology is adopted to obtain distance gating; a radar target distance-speed estimation problem is converted into a spectrum estimation problem, high-resolution distance-speed estimation values are obtained by using a MUSIC algorithm, the limitation of traditional radar resolution is broken, a base mismatch problem is solved, and echo reconstruction accuracy of different distance sections is improved; and AP algorithm is used to gradually suppress the energy of ambiguous echoes and noise energy of non-target distance sections, and echo reconstruction accuracy and ambiguity resolution performance are further improved; the MUSIC-AP algorithm has low calculation complexity, and realizes high-resolution estimation of radar target information and distance ambiguity suppression. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 A distance gating schematic diagram based on waveform diversity and different distance section receiving filter groups;

[0029] Figure 2 A flowchart of the radar target high-resolution estimation and distance ambiguity suppression method based on MUSIC-AP;

[0030] Figure 3 (a1) first distance section PD processing result (three-dimensional view);

[0031] Figure 3 (a2) first distance section PD processing result (distance-amplitude side view);

[0032] Figure 3 (b1) second distance section PD processing result (three-dimensional view);

[0033] Figure 3 (b2) second distance section PD processing result (distance-amplitude side view);

[0034] Figure 4 (a) alternating projection residual before and after echo spectrum reconstruction of the first distance section;

[0035] Figure 4 (b) alternating projection residual before and after echo spectrum reconstruction of the second distance section;

[0036] Figure 5 (a) comparison between real target information and reconstructed target information of the first distance section after MUSIC-AP processing;

[0037] Figure 5 (b) comparison between real target information and reconstructed target information of the second distance section after MUSIC-AP processing;

[0038] Figure 6(a) The reconstructed echo PD result of the first distance segment after the MUSIC-AP processing (three-dimensional view);

[0039] Figure 6 (b) The reconstructed echo PD result of the second distance segment after the MUSIC-AP processing (three-dimensional view);

[0040] Figure 7 (a) The alternating projection residual of the first distance segment before and after the echo spectrum reconstruction when the target minimum interval is the theoretical resolution;

[0041] Figure 7 (b) The alternating projection residual of the second distance segment before and after the echo spectrum reconstruction when the target minimum interval is the theoretical resolution;

[0042] Figure 8 The comparison between the real target information and the reconstructed target information of the first and second distance segments after the MUSIC-AP processing when the target minimum interval is the theoretical resolution;

[0043] Figure 9 The reconstruction accuracy rate under different target intervals and different signal-to-noise ratios;

[0044] Figure 10 (a) The alternating projection residual of the first distance segment before and after the echo spectrum reconstruction in the noise scenario;

[0045] Figure 10 (b) The alternating projection residual of the second distance segment before and after the echo spectrum reconstruction in the noise scenario;

[0046] Figure 11 (a) The ambiguous echo PD result of the first and second distance segments in the noise scenario before the MUSIC-AP processing;

[0047] Figure 11 (b) The reconstructed echo PD result of the first and second distance segments in the noise scenario after the MUSIC-AP processing;

[0048] Figure 11 (c) The echo PD result of the first and second distance segments in the ideal scenario without noise and ambiguity; DETAILED DESCRIPTION

[0049] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. The specific steps of a distance ambiguity suppression method based on a joint reversible mismatch filter and nonlinear processing are as follows:

[0050] Step S1, constructing a line spectrum estimation model in a scenario without distance ambiguity, including the following steps:

[0051] Step S11, construct the phase-coded signal time-frequency domain echo model with code length M and pulse number N prt in non-fuzzy scene.

[0052] Assume that the radar transmit signal is a phase modulation diversity signal, there are N prt different pulse sequences in a CPI, and each pulse signal u n (n=0…N prt -1) is modulated by different M phase codes. The time domain of the nth transmit pulse signal can be expressed as:

[0053]

[0054] In the formula, is the mth phase code in the nth pulse, φ n (m) is a phase modulation function, which takes any value in [0, 2π), t represents fast time, T c is the symbol width, and T r is the pulse repetition interval.

[0055] The frequency domain of the nth transmit pulse signal can be expressed as:

[0056]

[0057] Where f represents the fast time frequency. Under the scattering center model, the radar echo can be approximately expressed as the superposition of sub-echoes generated by multiple strong scattering centers. Assuming K targets, the time delay frequency shift of the kth target in the nth PRI is ignored. The nth received signal after baseband down-conversion can be expressed as:

[0058]

[0059] Where σ k is the complex reflectivity of the kth target (assuming constant within the CPI), and f0 is the carrier frequency. At this time, the traditional PD processing is to match filter the echo within the PRT, and to perform slow-time FFT on the delay-aligned match filter output to realize two-dimensional coherent accumulation of echo energy. However, the method proposed in this paper first converts the echo data into a line spectrum model for subsequent processing.

[0060] Assuming that the change of Doppler shift within the pulse width can be ignored, i.e. using the stop-and-go model, the received signal in the nth (0≤n≤N prt -1) pulse interval can be expressed as:

[0061]

[0062] Where represents the time delay of the kth target in the nth pulse echo, the Fourier transform of equation (5) is:

[0063]

[0064] v < c, then The above equation is simplified as:

[0065]

[0066] The above equation is discretized as:

[0067]

[0068] where, f = lΔf, Δf = f s / N spectrum is the frequency interval of two frequency points, f s is the sampling rate, N spe is the number of frequency points, then the CPI unambiguous echo spectrum matrix can be expressed as:

[0069]

[0070] The above equation is a 2D-line spectrum estimation model, is a linear combination of K 2-D complex sinusoids, which can be expressed as:

[0071]

[0072] where, are respectively:

[0073]

[0074]

[0075]

[0076] where, T, H and ⊙ represent transpose, conjugate transpose and Hadamard product respectively, and the flow matrix is defined as:

[0077]

[0078]

[0079] Note that some targets may have overlapping frequencies in one dimension but not in the other, i.e., if τ m = τ n , m≠n, then υ m ≠ υ n must be satisfied.

[0080] Then, equation (10) can be rewritten as:

[0081]

[0082] where, The diag() function is used to construct a diagonal matrix, and based on the frequency-domain echo model of equation (16), subsequent research is carried out.

[0083] In step S12, the echo power spectrum matrix is obtained based on the echo spectrum matrix obtained in S11 by weighted matched filtering, and the line spectrum estimation model is obtained by coherent accumulation in the slow time dimension.

[0084] Based on the echo spectrum matrix obtained in equation (16), a corresponding weighted matched filter bank is constructed:

[0085] H(f) = U(f) * ⊙[|U(f)| 2 ] -1 (17)

[0086] where [·] -1 represents taking the reciprocal of each element, or constructing a joint mismatch filter bank to ensure that the spectrum in the slow time dimension is coherent, and then the echo power spectrum matrix can be obtained as:

[0087]

[0088] where t r = nT r represents the slow time, and the element in the lth row and nth column is:

[0089]

[0090] The nth column is the weighted matched filtering power spectrum of the nth received echo:

[0091]

[0092] The lth row is the phase change of the lth frequency unit in the slow time dimension:

[0093]

[0094] In order to reduce the influence of noise and improve the estimation accuracy, the FFT coherent accumulation is performed on Y(f, t r ) in the slow time dimension t r , and a weighted window function can be used to reduce the frequency spectrum leakage caused by FFT when processing in the slow time dimension. In order to facilitate analysis, no windowing and no time domain zero padding are added here, and the slow time dimension FFT result can be obtained as:

[0095]

[0096] where FFT{x l (t r )} is:

[0097]

[0098] where δ(·) is the Dirac function, thus when υ = υ k , it reaches the maximum value:

[0099]

[0100] where represents the number of targets with Doppler frequency υ k , the conjugate and discretization of the above formula can be expressed as:

[0101]

[0102] It can be seen that formula (25) is the superposition of multiple complex sinusoidal signals, so the estimation problem of scattering centers can be converted into the problem of line spectrum estimation, where the frequency components satisfy:

[0103]

[0104] f k ∈[0,1], thus the construction of the line spectrum estimation model is completed.

[0105] Step S2, using the line spectrum estimation model obtained from step S1, the MUSIC high-resolution algorithm is used to obtain the scattering point distance estimation value, the time domain or frequency domain echo model is combined with the linear least square method to obtain the complex amplitude information of the scattering point, and the MUSIC high-resolution algorithm is used again to obtain the scattering point velocity estimation value, realizing the two-dimensional high-resolution estimation of the scattering point information in the non-ambiguous scene, including the following steps:

[0106] Step S21, the Hankel matrix is constructed based on the line spectrum estimation model obtained from step S1.

[0107] The data of formula (25) can be equivalently expressed as:

[0108]

[0109] Based on the signal y, the Hankel matrix H(y) can be constructed:

[0110]

[0111] In the formula, m+n=N+1, H(y) can be expressed as:

[0112]

[0113] H(y) = Φ m S(Φn ) T , S = diag(s1,..., sn) (30) K ) (30)

[0114] where Φ m is the Vandermonde matrix:

[0115]

[0116] If K ≤ min(m, n), rank(H(y)) = K, Φ m is the signal subspace, so we need to find the orthogonal complement of the signal subspace, i.e. the noise subspace, to get the estimate of f k .

[0117] Step S22, the noise subspace is obtained by SVD of the Hankel matrix, the imaging function is formed to obtain the distance frequency set, and is converted into the distance estimate of the scattering point.

[0118] SVD of H(y) matrix is:

[0119]

[0120] where U1 corresponds to the signal subspace, and U2 corresponds to the noise subspace. The second order statistic of eigenvalues (SORTE) method is used to determine the frequency number K in the present patent, so as to determine the noise subspace by finding the eigenvectors corresponding to the last N-K small eigenvalues.

[0121] Φ m is the signal subspace, and U2 is the orthogonal complement of the noise subspace U2, so the frequency can be identified as the zero set of the orthogonal projection of the imaging vector φ m (f), so the frequency can be identified as the zero point of the noise space correlation function:

[0122]

[0123] or the peak value of the imaging function:

[0124]

[0125] The frequency interval of φ m (f) can be refined to achieve the purpose of improving the resolution, and all frequencies can be accurately recovered by finding the local maximum of J(f). In the case of no noise, as long as the number of measured data is at least twice the number of different frequencies to be recovered, the accurate reconstruction of any arbitrary frequency set can be guaranteed, and in the case of noise, the robustness is analyzed by the embodiments.

[0126] Step S23, based on the time domain or frequency domain echo model combined with linear least squares to get the scattering point complex amplitude information (including Doppler phase factor), and again using the MUSIC high resolution algorithm to get the Doppler frequency set, and convert to scattering point velocity estimate value;

[0127] Based on the distance frequency of step S22 Then, the time delay estimate value can be obtained from formula (26) From formula (14), the reconstruction can be obtained And then, formula (18) combined with least squares can be reconstructed to obtain:

[0128]

[0129] Where, pinv(·) is the pseudo-inverse operator, The reconstruction echo spectrum can be obtained by the linear superposition of the Doppler frequency complex sine signal:

[0130]

[0131] Again using the MUSIC high resolution algorithm described in steps S21 and S22 to get the Doppler frequency estimate value From formula (15), the reconstruction can be obtained And then, formula (35) can be obtained

[0132]

[0133] So far, we have realized the two-dimensional high-resolution estimation of scattering point information and the reconstruction of frequency domain echo in the non-ambiguous scene.

[0134] Considering the pulse truncation effect, the above frequency domain echo model is invalid, so we reconstruct it based on the time domain echo model. Assuming that the echo truncation interval is the pulse width, the truncated echo expression is:

[0135]

[0136] Where, J(t) is the truncation function:

[0137]

[0138] First, the time delay estimate value The nth time domain pulse echo of the kth target is constructed as:

[0139]

[0140] The time domain echo matrix constructed by K targets is:

[0141]

[0142] The discretization of the echo is N r = T r f s is the number of time-domain sampling points in the fast time dimension, and the truncated matrix is constructed

[0143]

[0144] where N p = T p f s is the number of time-domain truncation points, and the nth truncated reconstructed echo is expressed as where contains the Doppler frequency modulation and the target complex amplitude information, and the least square method is used to obtain

[0145]

[0146] where is the nth discrete real echo vector, and the nth reconstructed truncated echo is:

[0147]

[0148] The complex amplitude matrix is constructed The MUSIC high-resolution algorithm is used again to obtain the Doppler frequency estimation value The two-dimensional high-resolution estimation of the scattering point information and the time-domain echo reconstruction in the non-ambiguous pulse truncated scene are realized.

[0149] Step S3, constructing a line spectrum estimation model in the range ambiguity scene, comprising the following steps:

[0150] Step S31, constructing an echo spectrum matrix in the range ambiguity scene.

[0151] When there are different distance segment echo foldovers, the imaging and detection performance is greatly reduced, and the far distance weak target is easily blocked by the energy dispersion of the near distance strong target. The echo spectrum matrix of formula (16) is updated as:

[0152]

[0153] where R p (f) is the pth distance segment echo spectrum matrix, which is defined in the same way as formula (16), P is the maximum number of ambiguity segments, and U p (f) is the pth distance segment transmit signal spectrum matrix, that is, the first distance segment transmit signal spectrum matrix U1(f) is cyclically shifted to the right by p-1 pulse repetition periods along the column direction, and is defined as follows:

[0154]

[0155] Step S32, construct the weighted matched filter bank of different distance segments, and obtain the echo power spectrum matrix of different distance segments and the line spectrum estimation model after coherent accumulation in the slow time dimension.

[0156] The echo power spectrum matrix of the pth distance segment is obtained by constructing the weighted matched filter bank of different distance segments respectively:

[0157]

[0158] The first term in formula (47) is:

[0159]

[0160] The definition in formula (18) is the same, so the first term Y1 can be coherent accumulated in the slow time dimension.

[0161] The second term in formula (47) is:

[0162]

[0163] The slow time dimension in the second term Y2 is due to U n (f)⊙U p (f) (n≠p) cannot be coherent accumulated, and the energy is dispersed in the range-Doppler plane. The slow time FFT is performed on formula (47), and when the peak value of the Doppler dimension υ appears, that is, υ=υ k , a model similar to formula (25) is obtained:

[0164]

[0165] Where f p,k and s p,k respectively represent the range frequency and complex amplitude of the kth scattering point in the pth distance segment when υ=υ k , s p,k contains the Doppler shift phase, E p represents the dispersed energy of the non-local distance segment. According to the radar equation, the closer the distance, the greater the energy, so it is processed from near to far, that is, p increases from 1 to P. The peak value data of the Doppler dimension obtained from (50) is used for subsequent processing.

[0166] Step S4, based on the MUSIC high-resolution spectrum estimation algorithm and the line spectrum estimation model under the range ambiguity scene, and using the AP algorithm to form the MUSIC-AP processing method, the range-velocity two-dimensional information of the scattering point and the echo spectrum matrix of different distance segments are obtained.

[0167] The influence of the rest of the distance segment spread energy in the second term of equation (47) on the estimation and reconstruction accuracy of the two-dimensional information of the current distance segment cannot be avoided by single echo reconstruction. Then, the AP algorithm is used to reconstruct the spectral matrix of different distance segments, and the influence of the non-current distance segment spread energy is gradually reduced. The echo spectral residual of each iteration is defined as:

[0168]

[0169] wherein is the reconstruction result of the echo spectral matrix of the pth distance segment in the ith iteration, R p is the real echo spectral matrix of the pth distance segment. When there is noise, equation (45) is updated as:

[0170]

[0171] wherein, is a noise term, and the MUSIC-AP algorithm flow is as shown in Figure 2 and Table 1 below:

[0172] Table 1

[0173]

[0174] The present application gives the following examples to illustrate the method of the application:

[0175] First, in the ideal case of a point target without noise, the effectiveness of the target parameter high-resolution estimation and distance ambiguity suppression of the algorithm is verified. The radar waveform parameters and target parameters are as shown in Table 2 and Table 3, wherein the target distance value of the second distance segment is the ambiguous distance value.

[0176] Table 2 Radar waveform parameters

[0177]

[0178] Table 3 Radar target parameters

[0179]

[0180] The frequency interval of φ m (f) in equation (34) is refined to achieve the purpose of improving the resolution. Here, the fine sampling distance unit set by the algorithm is 1.2288 m, and the fine sampling speed unit is 0.0064103 m / s, which is greatly improved compared with the coarse sampling distance / speed unit of the traditional PD processing in Table 2.

[0181] The results of the traditional distance-segment PD processing of the first and second distance segments are as shown in Figure 3As shown, the targets in non-own distance bins have higher energy spread due to the mismatch of the receive filter bank to the echoes of other distance bins. When the targets in non-own distance bins have larger energy, the energy will spread in the whole imaging plane, which seriously affects the radar target detection performance. Moreover, due to the limitations of the coarse sampling unit, bandwidth and CPI, targets smaller than the range and velocity resolution cannot be distinguished, such as target 2 and target 4 in the first distance bin, and target loss phenomenon exists.

[0182] In order to realize high-resolution estimation of radar targets and distance ambiguity suppression, the MUSIC-AP algorithm in Table 1 is used, the spectral residual error of each AP, and the spectral residual error curve before and after the reconstruction of the MUSIC are as follows Figure 4 As shown, through the MUSIC-AP algorithm, the reconstruction residual decreases with iteration, the reconstruction accuracy gradually rises, and the estimation accuracy of the two-dimensional information of the target gradually rises, that is, the high-resolution estimation performance and distance ambiguity suppression performance of the radar target gradually rise. At the 9th iteration, the convergence condition is met, and the spectral reconstruction residual of the echoes of each distance bin is almost 0, which has the advantages of small calculation amount and low complexity.

[0183] The two-dimensional information of the scattering points in the first and second distance bins after convergence is as follows Figure 5 As shown, the resolution limit of the traditional radar imaging is broken, the distortion problem caused by the grid mismatch is overcome, the high-resolution accurate estimation of the scattering point information is realized, and there is no target loss phenomenon. The reconstructed echoes of the first and second distance bins after convergence are processed by the traditional distance bin PD, and the result is as follows Figure 6 As shown, compared with Figure 3 It can be seen that the ambiguous energy in non-own distance bins is almost completely suppressed, and the blind reconstruction of echoes between different distance bins is realized.

[0184] Then, the minimum distance / velocity interval of the target is set as the theoretical resolution of the algorithm, that is, twice the fine sampling distance / velocity unit, to verify the effectiveness of the algorithm in improving the resolution, and the radar target parameters are as shown in Table 4.

[0185] Table 4 Radar target parameters

[0186]

[0187] After the MUSIC-AP algorithm processing, the spectral residual error curve is as follows Figure 7 As shown, at the 12th iteration, the convergence condition is met, and the spectral reconstruction residual of the echoes of each distance bin is almost 0. The ambiguous energy in non-own distance bins is almost completely suppressed. Similarly, the two-dimensional information of the scattering points in the first and second distance bins after convergence is spliced to obtain Figure 8 As a result, the two-dimensional information of the targets in different distance bins is accurately estimated, the range / velocity resolution reaches the theoretical resolution of the algorithm, and the length of the imaging vector can be set according to the resolution requirement.

[0188] Then, 100 times of Monte Carlo simulation are performed to verify the reconstruction accuracy of different target intervals under different SNRs without range ambiguity. When the range and velocity estimation bias are less than a certain threshold, the reconstruction is determined to be successful, and the Monte Carlo simulation results are shown in Figure 9 When there is no noise, as long as the number of measurement data is at least twice the number of different frequencies to be recovered, the accurate estimation of any frequency can be guaranteed. However, in the presence of noise, the disturbance of noise spatial correlation is proportional to the noise energy, and as the SNR decreases, the reconstruction accuracy and resolution will be affected accordingly. Figure 9 The numerical simulation experiment of the MUSIC algorithm shows that the MUSIC algorithm still has strong stability and low computational complexity for frequency estimation accuracy and resolution. Note that the AP algorithm is not used here, and only the noise robustness of the MUSIC algorithm is analyzed.

[0189] However, in actual situations, when the noise is large, it will have a non-negligible impact on the reconstruction performance of the algorithm. Therefore, in the alternating projection reconstruction process, a noise reconstruction sub-process is added to reduce the impact of noise on reconstruction accuracy. The radar target parameter

[0190] Table 4, but a Gaussian white noise is added to the target, and the SNRs of the 6 targets are 15, 20, 25, 30, 20, and 25, respectively. The minimum target distance interval is appropriately relaxed to 2 times the theoretical distance resolution, and the distances of target 4 and target 6 are changed to 24580.9152 m. The minimum target velocity interval is still the theoretical velocity resolution, verifying the effectiveness of the MUSIC-AP algorithm in reducing noise, and the effectiveness of high-resolution estimation and range ambiguity suppression of target parameters in the presence of noise.

[0191] The spectrum residual curve is shown in Figure 10 At the 4th iteration, the convergence condition is met, and the reconstructed echo spectrum residual of each distance segment is about -60 dB, which includes the residual amount of ambiguous echo spectrum and noise spectrum outside the current distance segment. The reconstructed echo of the first and second distance segments after convergence is obtained by traditional distance segment PD splicing processing Figure 11 (b), compared with Figure 11 (a) and Figure 11 (c), it can be seen that the ambiguous components are almost completely suppressed, and the noise is greatly eliminated. However, the noise cannot be completely eliminated, and the resolution will be affected. The distance / velocity dimension resolution cannot simultaneously reach the theoretical resolution of the algorithm, but it is still better than the Rayleigh resolution of the traditional method. The specific resolution that can be achieved is related to the noise residual amount, and the Monte Carlo simulation experiment results in Figure 9 can be referred to.

[0192] Finally, the sparsity requirement of the algorithm is analyzed. The theoretical analysis shows that, in the case of no noise, as long as the number of measurement data is at least twice the number of different frequencies to be recovered, the accurate estimation of any frequency can be guaranteed. According to Table 1, the number of sampling points in the distance dimension in a PRT interval is 2600, and the maximum number of targets is not more than 1300. Therefore, on the same velocity unit, different numbers of scattering points are set along the distance dimension, and the sparsity requirement is simulated and analyzed, and the following results are obtained

[0193] The results in Table 5.

[0194] Table 5

[0195]

[0196] When the number of targets increases to a certain value, the target loss and estimation error increase, and the reconstructed echo spectrum residual decreases. Therefore, when using the algorithm, attention should be paid to the sparsity requirement.

[0197] From the above results, it can be seen that the present application solves the problem of grid mismatch, converts the target distance-velocity estimation problem into a spectrum estimation problem, and realizes accurate estimation of scattering point information in different distance segments as the starting point, so that the echo reconstruction accuracy of different distance segments is improved. The alternating projection algorithm is used to gradually suppress the blurred echo energy and noise energy of non-distance segments, further improving the echo reconstruction accuracy. The MUSIC-AP method of the present application realizes high-resolution estimation and distance ambiguity suppression of radar targets.

[0198] In summary, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A radar target high resolution estimation and range ambiguity suppression method based on MUSIC-AP, characterized in that, The method comprises: Step S1, constructing a line spectrum estimation model in a non-range ambiguous scene; Step S2, using the line spectrum estimation model obtained in step S1, using a MUSIC high resolution spectrum estimation algorithm to obtain a scattering point distance estimation value, using a time domain or frequency domain echo model combined with a linear least square method to obtain scattering point complex amplitude information, and using the MUSIC high resolution algorithm again to obtain a scattering point speed estimation value, to realize two-dimensional high resolution estimation of scattering point information in a non-ambiguous scene; Step S3, constructing a line spectrum estimation model in a range ambiguous scene; Step S4, based on the MUSIC high resolution spectrum estimation algorithm and the line spectrum estimation model in the range ambiguous scene, and using an AP algorithm to form a MUSIC-AP processing method, to obtain scattering point distance-speed two-dimensional information and an echo spectrum matrix in different distance segments; The step S1 comprises the following steps: Step S11, construct the phase encoding signal time-frequency domain echo model under the non-blurred scene with code length M and pulse number N prt ; Step S12, based on the echo spectrum matrix obtained in S11, using weighted matched filtering to obtain an echo power spectrum matrix, and using slow time dimension phase correlation accumulation to obtain a line spectrum estimation model; The step S2 comprises the following steps: Step S21, constructing a Hankel matrix based on the line spectrum estimation model obtained in step S1; Step S22, using SVD of the Hankel matrix to obtain a noise subspace, forming an imaging function to obtain a distance frequency set, and converting into a scattering point distance estimation value; Step S23, based on a time domain or frequency domain echo model combined with a linear least square method to obtain scattering point complex amplitude information, and using the MUSIC high resolution algorithm again to obtain a Doppler frequency set, and converting into a scattering point speed estimation value; The step S3 comprises the following steps: Step S31, constructing an echo spectrum matrix in a range ambiguous scene; Step S32, constructing a weighted matched filter set in different distance segments, obtaining an echo power spectrum matrix in different distance segments, and a line spectrum estimation model after slow time dimension phase correlation accumulation; The step S4 comprises the following steps: Step S41, based on the line spectrum estimation model in different distance segments, constructing a Hankel matrix, using SVD to obtain a noise subspace, forming an imaging function to obtain a distance frequency set, and converting into a scattering point distance estimation value; Step S42, based on a time domain or frequency domain echo model combined with a linear least square method to obtain scattering point complex amplitude information, reconstructing an echo spectrum matrix in different distance segments; Step S43, combining MUSIC and AP algorithms to gradually reduce echo spectrum residuals, obtaining more accurate echo spectrum matrices in different distance segments, and using the converged complex amplitude information of different pulses in different distance segments again using the MUSIC high resolution algorithm to obtain a speed frequency set, and converting into a scattering point speed estimation value.

2. The MUSIC-AP based radar target high resolution estimation and range ambiguity suppression method according to claim 1, characterized in that, The step S11 constructs the phase encoding signal time-frequency domain echo model under the non-fuzzy scene with code length M and pulse number N prt ; assuming that the radar transmitting signal is a phase modulation diversity signal, there are N prt different pulse sequences in a CPI, and each pulse signal u n (n=0…N prt -1) is modulated by different M phase encodings, and the nth transmitting pulse signal time domain is represented as: wherein is the mth phase encoding within the nth pulse, φ n (m) is a phase modulation function, arbitrarily valued in [0, 2π), t represents fast time, T c is the symbol width, T r is the pulse repetition interval; The frequency domain expression of the nth transmitting pulse signal is: where f represents fast time frequency; under the scattering center model, the radar echo is approximately expressed as the superposition of the echo generated by multiple strong scattering centers; assuming K targets, the time delay of the kth target in the nth PRI frequency shift Ignoring echo expansion / compression and time delay phase constant, the nth received signal after baseband down-conversion is expressed as: where σ k is the complex reflectivity of the kth target, assuming constant within CPI, and f0is the carrier frequency; at this time, the traditional PD processing is matched filtering to the echoes within PRT, and slow-time FFT on the delay-aligned matched filter outputs, to realize two-dimensional coherent accumulation of echo energy; It is assumed that the variation of Doppler shift within the pulse duration is negligible, i.e. a walk-stop model is adopted, the nth(0≤n≤N prt -1) pulse interval is expressed as: wherein denotes the time delay of the kth target in the nth pulse echo, the Fourier transform of equation (5) is: v « c, then The above equation simplifies to: The discrete expression of the above formula is: where f = lΔf, Δf = f s / N spectrum is the frequency interval between two frequency points, f s is the sampling rate, N spe is the number of spectral points, then the CPI unambiguous echo spectrum matrix is given by The above equation is a 2D-line spectrum estimation model, is a linear combination of K 2-D complex sinusoids, represented as: wherein respectively. Wherein, T, H and are respectively transpose, conjugate transpose and Hadamard product, and the definition flow matrix is: Some targets can have overlapping frequencies in one dimension but not in another, i.e. if τ m = τ n , m≠n, then must satisfy υ m ≠ υ n ; Then, the formula (10) is rewritten as: wherein The function diag() constructs a diagonal matrix.

3. The MUSIC-AP based radar target high resolution estimation and range ambiguity suppression method according to claim 2, characterized in that, In the step S12, based on the echo spectrum matrix obtained in S11, using weighted matched filtering to obtain an echo power spectrum matrix, and using slow time dimension phase correlation accumulation to obtain a line spectrum estimation model; Based on the echo spectrum matrix obtained in formula (16), a corresponding weighted matched filter set is constructed: H(f) = U(f) * ⊙[|U(f)| 2 ] -1 (17) where [·] -1 denotes taking the reciprocal of each element, or constructing a joint mismatch filter bank that guarantees the slow-time dimension spectrum to be coherent, then the echo power spectrum matrix is given by where t r = nT r denotes the slow time, and the element in the lth row and nth column is: The nth column is the weighted matched filter power spectrum of the nth received echo: The lth row is the phase change of the lth frequency unit in the slow time dimension: In order to reduce the influence of noise and improve the estimation accuracy, the Y(f, t r ) is phase-accumulated by FFT in the slow time dimension t r , and a weighting window function is used to reduce the spectrum leakage caused by FFT in the slow time dimension processing. The FFT result in the slow time dimension is obtained as where FFT{x l (t r )} is: where δ(·) is the Dirac function, thus taking a maximum value when υ = υ k max: where represents the number of targets with Doppler frequency k The conjugate and discretized representation of the above is given by Formula (25) is the superposition of multiple complex sinusoidal signals, so the estimation problem of the scattering center is converted into a line spectrum estimation problem, where the frequency components satisfy: where f k ∈ [0, 1].

4. The MUSIC-AP based radar target high resolution estimation and range ambiguity suppression method according to claim 3, characterized in that, In the step S21, the line spectrum estimation model obtained in the step S1 is used to construct a Hankel matrix; The data equivalent expression of formula (25) is: A Hankel matrix is constructed based on the signal y: In the formula, m+n=N+1, and H(y) represents: H(y) = Φ m S(Φ n ) T ,S = diag(s1,...s K ) (30) where Φ m is the Vandermonde matrix: If K≤min(m,n), then rank(H(y))=K, Φ m is the signal subspace, and the noise subspace is used to obtain an estimate of f k .

5. The MUSIC-AP based radar target high resolution estimation and range ambiguity suppression method according to claim 4, characterized in that, In the step S22, the noise subspace is obtained by SVD of the Hankel matrix, the distance-frequency set is formed by the imaging function, and the distance estimation value of the scattering point is converted; The SVD of the H(y) matrix is: Wherein, U1 corresponds to the signal subspace, U2 corresponds to the noise subspace, the number of frequencies K is determined by using the second-order statistics method of eigenvalues, so as to determine the noise subspace by finding the eigenvectors corresponding to the last N-K small eigenvalues; Φ m is the orthogonal complement of the noise subspace U2, then the frequencies are identified as imaging vectors φ m (f) the null set of the orthogonal projection of the noise subspace U2, then the frequencies are identified as the zeros of the noise space correlation function: Or the peak value of the imaging function:

6. The MUSIC-AP based radar target high resolution estimation and range ambiguity suppression method according to claim 5, characterized in that, In step S23, the distance frequency Then, the delay estimate is obtained from equation (26) Then, the delay estimate is obtained from equation (26) Then, the delay estimate is obtained from equation (26) where pinv(·) is the pseudo-inverse operator, is a linear superposition of complex sinusoids with Doppler frequencies, the reconstructed echo spectrum is given by The Doppler frequency estimation value is obtained using the MUSIC high resolution algorithm described in steps S21, S22 Reconstructing from equation (15) gives Again from equation (35) gives Thus, the two-dimensional high-resolution estimation of the scattering point information in the non-ambiguous scene and the frequency domain echo reconstruction are realized; Considering the pulse truncation effect, the above frequency domain echo model is invalid, so the reconstruction is performed based on the time domain echo model. Assuming that the echo truncation interval is the pulse width, the truncated echo expression is: Wherein, J(t) is a truncation function: First, a time delay estimate value Constructing the nth time domain pulse echo of the kth target: The time domain echo matrix constructed by the K targets is: discrete representation of N r = T r f s is the number of fast-time domain samples, and the truncated matrix is constructed as where N p = T p f s is the number of time domain truncation points, the nth truncated reconstructed echo is expressed as where contains the Doppler frequency modulation, the target complex amplitude information, then the least square method is used to obtain wherein, Let Rnbe the nth truncated real echo discretization vector, then the nth reconstructed truncated echo is: Constructing a complex amplitude matrix Doppler frequency estimates are obtained using the MUSIC high resolution algorithm again Two-dimensional high-resolution estimation of scatterer information and time-domain echo reconstruction are realized in the unambiguous pulse truncation scenario.

7. The MUSIC-AP based radar target high resolution estimation and range ambiguity suppression method according to claim 6, characterized in that, In the step S31, when there are different distance segment echo folds, the imaging and detection performance are greatly reduced, and the far distance weak target is easily blocked by the energy dispersion of the near distance strong target. The echo spectrum matrix of formula (16) is updated as: where R p (f) is the pth range bin echo spectrum matrix, defined as in equation (16), P is the maximum number of ambiguous bins, U p (f) is the pth range bin transmit signal spectrum matrix, which is a cyclic shift of the first range bin transmit signal spectrum matrix U1(f) by p-1 pulse repetition periods in the column direction, defined as 8. The MUSIC-AP based radar target high resolution estimation and range ambiguity suppression method according to claim 1, characterized in that, In the step S32, a weighted matched filter group of different distance segments is constructed, and the echo power spectrum matrix of different distance segments and the line spectrum estimation model after slow time dimension coherent accumulation are obtained. A weighted matched filter group of different distance segments is constructed respectively, and the echo power spectrum matrix of the pth distance segment is obtained as: The first term in formula (47) is: The definition is the same as that in formula (18), so the first term Υ1 is accumulated in the slow time dimension; The second term in formula (47) is: The second term Y2 has a slow time dimension due to U n (f)⊙U p (f) (n≠p) cannot be coherently integrated, the energy is spread in the range-Doppler plane, and the slow time FFT of equation (47) gives a model similar to equation (25) when the peak of the Doppler spectrum occurs at υ = υ k 0. where f p,k and s p,k denote the range frequency and complex amplitude of the kth scatterer in the pth range bin when u = u k p,k contains the Doppler shift phase, E p denotes the dispersive energy of the non-local range bin. According to the radar equation, the closer the distance, the greater the energy, so it is processed from near to far, that is, p increases from 1 to P; the peak value data of Doppler V is obtained from (50).​ 9. The MUSIC-AP based radar target high resolution estimation and range ambiguity suppression method according to claim 1, characterized in that, In the step S4, the MUSIC high-resolution spectrum estimation algorithm and the line spectrum estimation model in the distance ambiguous scene are used to form a MUSIC-AP processing method by using the AP algorithm, and the distance-speed two-dimensional information of the scattering point and the echo spectrum matrix of different distance segments are obtained. Only through single echo reconstruction, the influence of the energy dispersion of the remaining distance segments in the second term of formula (47) on the two-dimensional information estimation and reconstruction accuracy of the current distance segment cannot be avoided. Then, the AP algorithm is used to reconstruct the spectrum matrix of different distance segments, and the influence of the energy dispersion of the non-current distance segments is gradually reduced. The echo spectrum residual error of each iteration is defined as: wherein is the reconstructed result of the pth range segment echo spectrum matrix for the ith iteration, R p is the pth range segment real echo spectrum matrix; When there is noise, formula (45) is updated as: wherein is a noise term.

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