A cyclic iteration echo reconstruction solution distance ambiguity method based on compressed sensing

Abstract

The application discloses a method based on compressed sensing and cyclic iteration to suppress folding clutter and solve range ambiguity. In the PD radar system of transmitting a variable waveform, a range-Doppler sensing matrix model under a range ambiguity scene is constructed, and the feasibility of echo reconstruction by compressed sensing is analyzed. An optimized sparse degree adaptive matching pursuit (OSAMP) algorithm is proposed to realize non-ambiguous information estimation of scattering points and echo reconstruction. The OSAMP algorithm is embedded into a cyclic iteration framework to form a CI-OSAMP algorithm, the influence of ambiguous energy is gradually reduced, and the reconstruction accuracy and ambiguity suppression performance are improved. The CI-OSAMP algorithm can be applied to compressed samples, and the limitation between the radar signal bandwidth and the sampling rate is broken through.

Description

Technical Field

[0001] This invention relates to the field of pulse Doppler radar with orthogonal agile waveforms, and specifically to a method for suppressing folded clutter and resolving range ambiguity based on compressed sensing and cyclic iteration. Background Technology

[0002] Pulse-Doppler (PD) radar can detect targets in complex environments and obtain accurate information on target range and velocity. PD radar transmits periodic coherent pulse sequences, inevitably introducing ambiguity in range and velocity measurements, leading to significant deviations in target detection and tracking, and consequently, decreased accuracy. Poor ambiguity suppression can result in severe missed detections or false alarms. Since the requirements for pulse repetition frequency to eliminate range and velocity ambiguity are mutually exclusive, the ambiguity problem in PD radar varies depending on the operating mode. To enhance the radar's ability to detect high-speed targets and increase its transmit power, a medium-to-high repetition rate operating mode is typically employed to obtain a wider unambiguous velocity measurement range, thereby effectively distinguishing clutter from targets in the Doppler dimension. Therefore, implementing a high-precision range ambiguity suppression algorithm is crucial.

[0003] A typical method for resolving range ambiguity in radar systems is to transmit multiple pulse train signals with staggered pulse repetition frequencies (PRFs) and then use the Chinese remainder theorem to resolve the ambiguity. However, this does not improve range and velocity resolution and leads to a longer coherent processing cycle. Therefore, research on resolving range ambiguity under single-pulse repetition frequency conditions is increasingly being conducted.

[0004] Another commonly used method for resolving range ambiguity is to use agile waveforms with different modulations between radar transmitted pulses. This method requires low cross-correlation between waveforms to effectively distinguish echoes from different range segments. Although studies on orthogonal waveforms have effectively optimized the cross-correlation characteristics between signals, most of the aforementioned studies have not considered the impact of Doppler frequency shift on the cross-correlation characteristics. Furthermore, due to the different modulations between pulses, the sidelobe structures of the matched filtering results for each pulse are also different. This phenomenon is called Range Sidelobe Modulation (RSM), which causes a rise in the floor of the range-Doppler imaging plane during PD processing, severely affecting the radar's target detection performance. Moreover, when the energy of strong clutter in the near-range segment is high, the isolation between agile waveforms alone cannot achieve effective ambiguity suppression; targets at long range will still be obscured by the scattered energy in the near-range segment.

[0005] Compressed sensing (CS) theory breaks through the limitations of the traditional Nyquist sampling law. By solving a nonlinear optimization problem, it can achieve accurate signal reconstruction with a measurement signal using fewer Nyquist sampling points. It has been extensively studied in radar detection, estimation, and imaging. Radar imaging utilizes target echoes to obtain the spatial distribution of the target's backscattering coefficients. Therefore, radar imaging is essentially a process of reconstructing target representations using echoes. While existing sparse reconstruction algorithms achieve range ambiguity suppression, they do not consider the impact of ambiguity energy on the accuracy of the reconstruction algorithm, which can cause a certain degree of distortion and ambiguity residue in the target representation.

[0006] Therefore, based on the PD radar system that transmits orthogonal phase-coded signals, a method based on compressed sensing and cyclic iteration is developed to effectively suppress folded clutter and improve the accuracy of range ambiguity suppression, thereby enabling the target to be effectively detected. This has important practical significance and application value. Summary of the Invention

[0007] This invention proposes a method based on compressed sensing and cyclic iteration to suppress folded clutter and resolve range ambiguity in a PD radar system transmitting orthogonal phase-coded signals. First, a range-Doppler sensing matrix model is built for range-ambiguous scenarios. Based on this, the rationale for using compressed sensing for echo reconstruction is analyzed. Then, the optimized sparsity adaptive matching pursuit (OSAMP) algorithm for ambiguity-free information estimation of scattering points and echo reconstruction is described in detail, effectively reducing reconstruction errors. Finally, the OSAMP algorithm is combined with the cyclic iterative (CI) method to form a complete echo reconstruction and range ambiguity resolution CI-OSAMP algorithm, which suppresses ambiguity energy outside the current range segment, reduces reconstruction errors, and improves reconstruction accuracy and ambiguity suppression performance. Furthermore, the reconstruction algorithm can be directly applied to compressed samples, breaking the correlation between radar signal bandwidth and sampling rate. The reconstruction accuracy under different compression rates and signal-to-noise ratios is analyzed. This method utilizes compressed sensing and cyclic iteration to ensure echo reconstruction accuracy and ambiguity suppression performance. Simulation experiments and measured data processing show that the proposed method can effectively suppress folded clutter while improving the reconstruction effect, and achieve echo decorrelation at different distance segments.

[0008] The distance ambiguity resolution method based on compressed sensing for cyclic iterative echo reconstruction described in this invention is achieved through the following technical solution:

[0009] Step S1: Convert the baseband echo obtained by downconverting the radar echo to obtain a linear echo model suitable for compressed sensing algorithm.

[0010] Step S2: Based on the linear echo model obtained in Step S1 in the distance-free ambiguity scene, construct the distance-Doppler sensing matrix model in the distance-free ambiguity scene.

[0011] Step S3: Based on the echo data and range-Doppler sensing matrix model from step S2, the OSAMP reconstruction algorithm is proposed to achieve information estimation of scattering points and echo reconstruction.

[0012] Step S4: Construct a distance-Doppler perception matrix model for distance-ambiguous scenarios, and consider the impulse truncation effect in practice;

[0013] Step S5: Based on the range-Doppler sensing matrix and echo data in the range-ambiguous scene in Step S4, and combining the OSAMP reconstruction algorithm in Step S3 with the iterative framework, the CI-OSAMP algorithm is formed. This gradually reduces the reconstruction error, decreases distortion, improves echo reconstruction accuracy and ambiguity suppression performance, and proposes three radar imaging methods.

[0014] Step S1 includes the following steps:

[0015] Step S11: Down-convert the radar echo to obtain the baseband echo;

[0016] Step S12: Convert the baseband echo to obtain a linear echo model suitable for compressed sensing algorithm.

[0017] Step S2 includes the following steps:

[0018] Step S21, the target scattering coefficient σ on the time-delay-Doppler two-dimensional plane (τ,v) (τ,v) Discretize to obtain the discrete echo scattering coefficient matrix Λ of the scene;

[0019] Step S22: Vectorize the discrete echo scattering coefficient matrix Λ in step S21, and discretize the received signal of the nth PRT of the baseband echo after downconversion in step S12.

[0020] Step S23, define the l-th steering vector ψ of the n-th echo signal. n,l and in step S22 r n It can be written in matrix form: r n =Ψ n σ;

[0021] Step S24: Based on the echo matrix representation of a single PRT from step S23, expand it to an echo matrix representation within CPI: r = Ψσ. Then, compress the original echo data r using the measurement matrix Φ to obtain subsampled echo data y: y = Φr = ΦΨσ = ​​Aσ, where A is called the range-Doppler sensing matrix.

[0022] Step S3 includes the following steps:

[0023] Step S31: Based on the input data obtained in step S2, perform parameter initialization;

[0024] Step S32: Using the OSAMP reconstruction algorithm, obtain the sparse vector estimate of the scattering coefficients. The reconstructed signal can be obtained by using the transformation matrix.

[0025] Step S4 includes the following steps:

[0026] Step S41: Construct a distance-Doppler perception matrix model in a distance-ambiguous scene;

[0027] Step S42: Considering the pulse truncation effect, the measurement matrix is ​​equivalent to the truncation matrix.

[0028] Step S5 includes the following steps:

[0029] Step S51: Based on the echo data and range-Doppler sensing matrix model in the distance-ambiguous scene obtained in step S4, complete the OSAMP echo reconstruction deambiguation without iterative loops.

[0030] Step S52 proposes the CI-OSAMP algorithm, which gradually reduces the influence of ambiguity energy outside the current range segment through iterative iteration, thereby achieving iterative echo reconstruction and deambiguation.

[0031] In step S53, based on the output of the algorithm after convergence in S52, three radar imaging methods for different application scenarios are proposed.

[0032] Beneficial effects:

[0033] This invention proposes a method based on compressed sensing and iterative iteration to suppress folded clutter and resolve range ambiguity in a PD radar system with orthogonal agile waveforms. Compared to traditional multi-pulse train staggered repetition frequency deambiguation methods, this method requires only one pulse train, shortening the coherent processing cycle. First, an underdetermined range-Doppler recovery problem is established for range-ambiguous scenarios. Based on this, the OSAMP algorithm is used to estimate the unambiguous information of the scattering point and reconstruct the echo. Finally, the OSAMP and iterative methods are combined to form the CI-OSAMP algorithm, reducing reconstruction errors. This invention improves echo reconstruction accuracy and ambiguity suppression performance by utilizing compressed sensing and iterative iteration, achieving effective suppression of folded clutter. Attached Figure Description

[0034] Figure 1 A graphical summary of the invention described herein;

[0035] Figure 2A schematic diagram of pulse Doppler results based on constant pulses and agile pulses;

[0036] Figure 3 Flowchart of echo reconstruction and range ambiguity suppression based on CI-OSAMP algorithm;

[0037] Figure 4 (a) PD processing results of the first three distance segments before blur suppression (3D view);

[0038] Figure 4 (b) PD processing results for the first three distance segments before blur suppression (distance-velocity projection map);

[0039] Figure 4 (c) PD processing results of the first three distance segments after blur suppression (3D view);

[0040] Figure 4 (d) PD processing results of the first three distance segments after blur suppression (distance-velocity projection map);

[0041] Figure 5 Echo reconstruction residuals in the third range segment;

[0042] Figure 6 Unambiguous range-velocity estimation results for scattering points in the first three range segments;

[0043] Figure 7 Reconstruction power at different compression ratios and signal-to-noise ratios;

[0044] Figure 8 (a) PD stitching results of measured fuzzy echoes at various distance segments before CI-OSAMP processing (3D view);

[0045] Figure 8 (b) PD stitching results of measured fuzzy echoes at various distance segments before CI-OSAMP processing (distance-velocity projection diagram);

[0046] Figure 8 (c) Reconstructed sub-echo joint mismatch filtering imaging after CI-OSAMP processing (3D view);

[0047] Figure 8 (d) Reconstructed sub-echo joint mismatch filtering imaging after CI-OSAMP processing (range-velocity projection map);

[0048] Figure 8 (e) Imaging of the difference between the total echo after CI-OSAMP processing and the reconstructed sub-echo from other range segments using a joint mismatch filter (3D view);

[0049] Figure 8(f) Image of the difference between the total echo after CI-OSAMP processing and the reconstructed sub-echoes outside the range segment, combined with mismatch filtering (range-velocity projection map);

[0050] Figure 9 Unambiguous range-velocity estimation results for scattering points in the first 11 range segments. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. A graphical summary of the objectives and solutions of this invention is also provided, such as... Figure 1 As shown. The specific steps of a distance ambiguity suppression method based on a joint reversible mismatch filter and nonlinear processing are as follows:

[0052] Step S1 involves converting the baseband echo obtained by down-converting the radar echo to obtain a linear echo model suitable for compressed sensing algorithms, including the following steps:

[0053] Step S11: Down-convert the radar echo to obtain the baseband echo.

[0054] Assuming the radar's transmitted signal is an orthogonal phase-coded signal, and there are different pulse sequences within one CPI, each pulse signal is modulated by a different M-phase code, the time domain of the nth transmitted pulse signal can be expressed as:

[0055]

[0056]

[0057] In the formula For the m-th phase encoding within the n-th pulse, φ n (m) is the phase modulation function, taking any value in [0, 2π), and T c T is the symbol width. r This is the pulse repetition interval.

[0058] The received signal consists of attenuation of the transmitted signal and time-shifted / frequency-biased copies. The scattered points are sparsely distributed in the range-velocity dimension; therefore, a sparse vector of scattered point information can be obtained by constructing a suitable dictionary and reconstructing the algorithm. Assume there are K targets within the nth PRT, and the kth target has a time delay: τ k =2R k / c, frequency shift: υ k =2f c v k / c, where 1≤k≤K, R k v k Let f be the distance and velocity from the k-th target to the radar, respectively. cLet c be the transmission carrier frequency and c be the speed of light. Ignoring echo broadening and compression, the received signal in the nth PRT after down-conversion to baseband can be expressed as:

[0059]

[0060] Where σ k It is the complex reflectance of the k-th target.

[0061] Step S12: Convert the baseband echo to obtain a linear echo model suitable for compressed sensing algorithm.

[0062] The change of Doppler frequency shift within the pulse duration can be ignored, i.e., using the stop-and-go model, equation (3) can be expressed as:

[0063]

[0064] Define the time delay operator T τ [·], delaying the signal time τ:

[0065] T τ [u n [(t)]=u n (t-τ k (5)

[0066] Define the frequency offset operator Add a frequency offset phase to the signal:

[0067]

[0068] The time delay-frequency shift operator for the signal is defined as follows:

[0069]

[0070] Equation (4) can be simplified to:

[0071]

[0072] Step S2, based on the linear echo model obtained in Step S1 under the unambiguous distance scenario, constructs the distance-Doppler sensing matrix model under the unambiguous distance scenario, including the following steps:

[0073] Step S21, the target scattering coefficient σ on the time-delay-Doppler two-dimensional plane (τ,v) (τ,v) Discretize to obtain the discrete echo scattering coefficient matrix Λ of the scene.

[0074] The signal ultimately received by the radar can be viewed as a linear superposition of target echoes with different velocities, distances, and scattering coefficients within the observation scene, i.e., (8) extended as:

[0075]

[0076] Where Ω represents the set of all possible values ​​for the target's high-resolution range and velocity, and σ (τ,v) Let σ be the scattering coefficient of the target at (τ,v) with range and velocity corresponding to τ. The main task of compressed sensing processing is to reconstruct the target scene and estimate the target scattering coefficient σ on the time-delay-Doppler two-dimensional plane (τ,v). (τ,v) .

[0077] The two-dimensional plane [τ] is usually considered begin ,τ end ]×[v begin ,v end Discretization: The distance dimension and velocity dimension are discretized into P and Q grid points, respectively, i.e., τ0, τ1, ... τ. P-1 v0, v1, ... v P-1 The grid values ​​should cover all distance-velocity cells of interest.

[0078] After discretization, the echo scattering coefficients σ(τ,v) of the scene can be represented by a two-dimensional P×Q complex matrix.

[0079]

[0080] In this matrix, the p-th row and q-th column indicate that there exists an RCS value in the p-th distance cell and the q-th Doppler cell. The target point.

[0081] Step S22: Vectorize the discrete echo scattering coefficient matrix Λ in step S21, and discretize the received signal of the nth PRT of the baseband echo after downconversion in step S12.

[0082] Vectorize Λ to form a vector.

[0083]

[0084] in, Let the l-th element in vector σ be denoted as

[0085] Where 0≤p≤P-1, 0≤q≤Q-1, l=q+pQ, 0≤l≤PQ-1, equation (8) can be rewritten as:

[0086]

[0087] For the discrete echo data of the nth PRT receiving interval, N s =f s T r f sU is the sampling frequency. n =[u n,0 ,u n,1 ,…u n,L-1 ] T The discretized representation of the nth transmitted signal has a length of L = f s T p T p =MT c This represents the pulse width.

[0088] Step S23, define the l-th steering vector ψ of the n-th echo signal. n,l and in step S22 r n It can be written in matrix form: r n =Ψ n σ.

[0089] Define the l-th steering vector ψ of its n-th echo signal. n,l It can also be called an atom:

[0090]

[0091] Indicates the transmitted signal u n If the signal copy after time delay and frequency shift is obtained, then equation (12) can be written in matrix form:

[0092] r n =Ψ n σ (14)

[0093] in, This is called the transformation matrix, and can be specifically represented as:

[0094]

[0095] Indicates signal U n The time delay matrix satisfies N s =P+L-1,U n Represented as:

[0096]

[0097] Step S24: Based on the echo matrix representation of a single PRT from step S23, expand it to an echo matrix representation within the CPI: r = Ψσ. Then, compress the original echo data r using the measurement matrix Φ to obtain subsampled echo data y: y = Φr = ΦΨσ = ​​Aσ. A is called the range-Doppler sensing matrix.

[0098] Echo within a CPI Represented as:

[0099]

[0100] The transformation matrix corresponding to r is

[0101]

[0102] The radar observation equations within CPI can then be written in matrix form as follows:

[0103] r=Ψσ (19)

[0104] The original echo data r can also be compressed using the measurement matrix Φ to obtain the subsampled echo data y:

[0105] y=Φr=ΦΨσ=Aσ (20)

[0106] A is called the perception matrix, and Φ is the identity matrix if subsampling is not performed. The reconstruction of the radar observation scene can be modeled by solving for the vector σ from equation (19) or (20). σ must satisfy that most of its elements are zero, which means that there is no significant scattering target in the corresponding range-velocity unit, i.e., σ is a sparse vector. Based on the non-zero elements in σ, the estimated values ​​of the range, velocity, and scattering coefficient of the corresponding target can be inferred.

[0107] Step S3: Based on the echo data and range-Doppler sensing matrix model from step S2, the OSAMP reconstruction algorithm is proposed to achieve information estimation of scattering points and echo reconstruction, including the following steps:

[0108] Step S31: Based on the input data obtained in step S2, perform parameter initialization.

[0109] The input is an M×N perception matrix A = ΦΨ, N = N s N prt Let y be the echo length within the uncompressed CPI, and y be the M×1 dimensional compressed echo. Initialization: residual r0 = y, support set... The initial sparsity is L = K0, the number of iterations is t = 1, and the step index is n = 1.

[0110] Step S32: Using the OSAMP reconstruction algorithm, obtain the sparse vector estimate of the scattering coefficients. The reconstructed signal can be obtained by using the transformation matrix.

[0111] Equation (20) is an underdetermined equation with infinitely many solutions. The focus is on finding the sparsest solution, i.e., minimizing the l0 norm of the σ vector while satisfying the constraints. CS theory has proven that, under certain constraints on the sensing matrix A, the solutions to the l1 norm minimization problem and the l0 norm minimization problem are equivalent, successfully transforming the CS signal recovery problem from a non-convex optimization problem into a convex optimization problem.

[0112]

[0113] Considering the influence of noise, the optimization problem of equation (21) is changed to:

[0114]

[0115] Here, ||||1 and ||||2 represent the 1-norm and 2-norm of the orientation vector, respectively, and ∈≥o is a parameter determined by the additive noise intensity. The OSAMP algorithm proposed below is used to solve the above problem of minimizing the 1-norm. It is a greedy algorithm that approximates the signal vector by selecting appropriate atoms and using a series of incremental steps.

[0116] The OSAMP algorithm is primarily derived from the subspace pursuit (SP) algorithm, but determining the optimal step size and the number of scattering points is difficult. Given unknown sparsity, this algorithm makes the following improvements: 1) By using dynamic programming (PD) to estimate the number of scattering points in the environment and employing a non-linear step size to gradually adjust the step size to approximate the actual number of scattering points, the algorithm can quickly approach the true sparsity and improve convergence speed; 2) A sparsity judgment subprocess is set up. By setting a threshold, sparsity judgment is performed to reduce the influence of noise, obtain the final sparse solution, and improve the accuracy of sparse vector reconstruction. The specific algorithm flow is shown below:

[0117]

[0118] Where, r t The residual is represented by t, and the iteration number is represented by t. Represents the empty set, Λ t Let L represent the set of atomic position indices (column numbers) of the support set in the t-th iteration (with L being the step size for each iteration). The symbol ∪ represents the set union operation, and abs[·] represents the absolute value.

[0119] The OSAMP algorithm does not require precise knowledge of sparsity. Given unknown sparsity, it approximates the original signal sparsity K piecewise using an initial sparsity estimate K0 and a nonlinear step size set S. A suitable threshold is used to obtain the sparsity estimate K. The atoms that best match the signal are selected from the observation matrix, and the signal residual is calculated. This process is repeated iteratively, selecting atoms that best match the signal residual. Each iteration satisfies regularization constraints to ensure that each loop result is the optimal solution. The final signal can be represented by the linear sum of these atoms plus the final residual value, i.e., using the transformation matrix and scattering coefficient vector estimate. The reconstructed signal can be obtained

[0120] Step S4: Construct a distance-Doppler sensing matrix model for distance-ambiguous scenes, taking into account the impulse truncation effect in practice, including the following steps:

[0121] Step S41: Construct a distance-Doppler perception matrix model in a distance-ambiguous scene.

[0122] When the target distance exceeds the length of one PRT interval, range ambiguity occurs, and the measured distance obtained by the radar from the pulse time interval between adjacent transmitted and echoed waves cannot be determined as the actual distance. When using a constant waveform, it is impossible to distinguish which range segment the target originates from, resulting in a significant reduction in imaging and detection performance. Furthermore, weak targets at long ranges are easily obscured by the energy dispersion of strong targets at close ranges. When using agile waveforms, range gating characteristics are obtained through the isolation between pulses, distinguishing echoes from different range segments in the waveform domain, as illustrated in the diagram below. Figure 2 As shown.

[0123] When distance ambiguity exists, the received echo in equation (17) is updated as follows:

[0124]

[0125] Where, r i Represents the echo of the i-th distance segment:

[0126] r i =Ψ i σ i (twenty four)

[0127] Where σ i Ψ represents the scattering coefficient vector for the i-th range segment. i The transformation matrix for the i-th distance segment is:

[0128]

[0129] Ψ i That is, the transformation matrix of the first distance segment. Shift downwards along the row for i-1 pulse repetition cycles.

[0130] Similarly, subsampled fuzzy echo data y can be obtained by compressing the original fuzzy echo data r using the measurement matrix Φ:

[0131]

[0132] Step S42: Considering the pulse truncation effect, the measurement matrix is ​​equivalent to the truncation matrix.

[0133] In practice, considering the pulse truncation effect, the measurement matrix can be a truncated matrix. N J The sampling length of the actual echo data y when there is a blind zone can be expressed as:

[0134]

[0135] Where diag[·] is used to construct a diagonal matrix, J j Represented as:

[0136]

[0137] During processing, due to the large matrix dimension, it is necessary to comprehensively consider the velocity range and velocity resolution of the scattering points in the actual scene. Parallel processing is performed by dividing the data into blocks according to Doppler unit channels and by segmenting the data into PRT intervals for parallel processing, in order to reduce the computational burden and improve the processing speed.

[0138] Step S5, based on the range-Doppler sensing matrix and echo data in the range-ambiguous scene from Step S4, and combining the OSAMP reconstruction algorithm from Step S3 with a cyclic iterative framework, forms the CI-OSAMP algorithm. This gradually reduces reconstruction error, decreases distortion, improves echo reconstruction accuracy and blur suppression performance, and proposes three radar imaging methods. The steps include:

[0139] Step S51: Based on the echo data and range-Doppler sensing matrix model obtained in step S4 under the distance ambiguity scene, complete the OSAMP echo reconstruction deambiguity without iterative loops.

[0140] As can be seen from the radar range equation, the magnitude of the backscattering coefficient is inversely proportional to the range. Therefore, we first solve for the scattering coefficient vector of the first range segment, and equation (26) can be expressed as:

[0141]

[0142] The estimated value of the scattering coefficient vector for the first range segment is obtained using the OSAMP algorithm. and reconstructed sub-echo Then, subtracting the reconstructed sub-echo of the first range segment from the total echo yields the echo data after blur suppression in the first range segment:

[0143]

[0144] The estimated value of the scattering coefficient vector for the second range segment is obtained by using (30) and the OSAMP reconstruction algorithm. and reconstructed sub-echo This process continues until all I fuzzy range segment echoes have been reconstructed.

[0145] Step S52 proposes the CI-OSAMP algorithm, which gradually reduces the influence of ambiguity energy outside the current range segment through iterative iteration, thereby achieving iterative echo reconstruction and deambiguation.

[0146] As can be seen from the second term of (30), the fuzzy components will inevitably affect the reconstruction effect. Therefore, a single reconstruction cannot avoid the influence of fuzzy energy in the non-local distance segment, resulting in reconstruction errors and affecting the fuzz suppression effect. Therefore, it is necessary to gradually reduce the influence of fuzzy energy in the non-local distance segment through iterative iteration to improve the reconstruction accuracy. The algorithm iteration process is as follows: Figure 3 As shown.

[0147] For the i-th range segment, the input to the reconstruction submodule is the total echo minus the reconstructed sub-echoes of other range segments excluding the i-th range segment. The OSAMP reconstruction submodule is used to obtain the estimated backscattering coefficient vector of the i-th range segment and the reconstructed sub-echoes. The value of i is incremented by 1; when i = 1, one iteration of reconstruction is completed. Then, i is reset to 1, and the reconstruction of sub-echoes for each range segment is repeated until the difference between two adjacent iterations is less than a preset threshold.

[0148] In step S53, based on the output of the algorithm after convergence in S52, three radar imaging methods for different application scenarios are proposed.

[0149] Based on the converged output of the algorithm in S52, the backscattering coefficient vector and reconstructed sub-echoes for each range segment are finally obtained, and three radar imaging methods with different applicable scenarios are proposed.

[0150] Method 1): When the signal-to-noise ratio is high and the backscattering coefficient vector estimation is relatively accurate, the reconstructed one-dimensional backscattering coefficient vector is matrixed according to the range and velocity interval division rules of the sensing matrix to obtain two-dimensional range-Doppler scattering point information, without the sidelobe effect of PD processing.

[0151] Method 2): The reconstruction echo error is relatively small. It is necessary to improve the signal-to-noise ratio. When achieving two-dimensional accumulation, the reconstructed sub-echoes of each range segment are jointly mismatched and filtered to improve the range sidelobe modulation effect caused by the change in inter-pulse modulation form and obtain the pulse Doppler result.

[0152] Method 3): When the reconstructed sub-echoes may have significant losses and require two-dimensional accumulation, the reconstructed sub-echoes of the current range segment are obtained by subtracting the reconstructed sub-echoes of non-current range segments from the total echoes. Then, joint mismatch filtering is performed to obtain the pulse Doppler result.

[0153] The present invention provides the following embodiments to illustrate the method:

[0154] The effectiveness of the CI-OSAMP algorithm is verified using point target simulation experiments and real-world scenario experiments, employing inter-pulse phase-coded signals. The algorithm's reconstruction performance and ambiguity suppression capability are analyzed, and the noise robustness of the reconstruction algorithm under different compression rates is analyzed through Monte Carlo simulation. The specific parameters of the radar and the scenario are listed in the table below.

[0155]

[0156]

[0157] First, the reconstruction and fuzziness suppression performance of the CI-OSAMP algorithm proposed in this invention is verified and analyzed. Clutter is distributed in the first two range segments, with four point targets in the second and third range segments. First, conventional range segment PD processing is performed on the fuzzy echoes, and the results are as follows: Figure 4 As shown in a and 4b, the second and third long-range segments are blocked by the scattered energy of strong clutter in the first short-range segment. This is because the receiving filter bank is mismatched with the echoes of other range segments, and the energy of the folded clutter will be scattered across the entire imaging plane, which seriously affects the radar target detection and imaging performance.

[0158] The CI-OSAMP algorithm is used to progressively reduce the reconstruction error of echoes at each range segment. Using imaging mode 2 in step S53, the unambiguous reconstructed echoes at each range segment are subjected to joint mismatch filtering to obtain the PD results as shown below. Figure 4 As shown in c and 4d, the RSM problem is solved, avoiding the Doppler dispersion of sidelobe energy caused by the different sidelobe structures due to waveform diversity, which prevents coherent accumulation in the slow time dimension. It also achieves ambiguity suppression, enabling imaging and detection of targets at long ranges, and effectively overcoming the clutter folding problem in traditional PD radar.

[0159] To quantitatively analyze the blur suppression effect of the algorithm, this paper uses the residual energy between the reconstructed signal and the true signal in the i-th distance segment as the evaluation criterion:

[0160]

[0161] The reconstruction residual results of the third distance segment are as follows: Figure 5As shown, the distance ambiguity suppression performance gradually increases as the iteration decreases. In the 12th iteration, the convergence condition is met, the echo reconstruction residual is almost 0, the computational load is small and the complexity is low, and the ambiguity-free echoes of each distance segment are recovered from the ambiguity echoes.

[0162] In addition to reconstructing the echo data, the CI-OSAMP algorithm also outputs scattering coefficient vectors for each range segment. Using imaging mode 1 in step S53, these vectors are matrixed to obtain two-dimensional range-velocity information of the scattering points. The stitched result of the scattering point information for the three range segments is as follows: Figure 6 As shown in the image, the four targets marked with red circles are clearly visible.

[0163] First, the noise robustness of the reconstruction algorithm proposed in this invention is analyzed. Five point targets are randomly selected, and the signal-to-noise ratio (SNR) after accumulating fast and slow times is increased from -10dB to 35dB in 1dB increments. The uncompressed echo is obtained using the Nyquist sampling rate, and then the echo is compressed using random Gaussian matrices at compression ratios of 50%, 25%, 10%, and 5% to obtain sub-Nyquist echo data. One hundred Monte Carlo simulations are performed under different compression ratios and SNRs. If the distance-velocity estimation of the point targets is correct and the complex amplitude estimation error is less than a certain threshold in each iteration, the reconstruction is considered successful. The reconstruction power curve is shown below. Figure 7 As shown.

[0164] The Nyquist sampling mode was found to outperform the sub-Nyquist sampling mode in terms of recovery performance, with the latter's performance decreasing as the compression ratio decreased. This is because sub-Nyquist sampling leads to sample reduction and SNR loss. Nevertheless, the sub-Nyquist sampling mode still ensures successful recovery of the target parameters at high signal-to-noise ratios.

[0165] Finally, to further verify the effectiveness of the algorithm presented in this paper, actual measurement data from a ground-based radar was used for verification and analysis. The transmitted waveform was an inter-pulse phase-coded signal. In the measured echo data, clutter and target echoes were folded into the same ambiguous range segment, resulting in severe range ambiguity. Figure 8 a and Figure 8 As shown in b, the scattering energy of strong clutter in the near-range segment severely affects the imaging results in the far-range segment.

[0166] After processing using the CI-OSAMP method, clutter echoes from different range segments can be effectively reconstructed, achieving effective suppression of folded clutter and thus enabling effective target detection. During processing, echo data is not compressed; the pulse truncation effect of the actual echo data is considered, i.e., the measurement matrix is ​​a truncated matrix. Based on the PD results before ambiguity suppression, the velocity range of the scattering points is preliminarily analyzed. Doppler cell channels within the range are processed in blocks to avoid invalid velocity grid redundancy values, thereby reducing computational burden and improving processing speed.

[0167] Using imaging mode 2 in step S53, the reconstructed echoes of each range segment are directly processed by range segment PD, and the results are as follows. Figure 8 c and Figure 8 As shown in d, because there is no subtraction operation in imaging mode 3, there is no noise or residual components from other range segments, resulting in better imaging performance. However, this processing relies on the accuracy of the algorithm reconstruction. If imaging mode 3 in step S53 is used, for each range segment, the reconstructed non-range segment clutter is subtracted from the total echo to suppress folded clutter, obtaining the reconstructed echo after blur suppression for each range segment. Then, range segment PD processing is performed, and the result is as follows. Figure 8 e and Figure 8 As shown in f, this method effectively suppresses folded clutter, enabling effective target detection. It offers advantages such as low computational cost and complexity, no need for prior clutter statistics, and good robustness. The target was detected in the 11th range segment, with a range of 117.48 km and a velocity of 99.4463 m / s.

[0168] Similarly, using imaging method 1 in step S53, the scattering coefficient vector matrix of each range segment is converted to obtain the two-dimensional range-velocity information of the scattering points. The stitching result of the scattering point information of the 11 range segments is as follows: Figure 9 As shown in the image, the target marked in red was measured, achieving unambiguous ranging and velocity measurement.

[0169] This invention proposes a novel method for suppressing folded clutter and resolving range ambiguity based on compressed sensing and iterative iteration in a PD radar system employing a single PRF and orthogonal phase-coded signals. First, a compressed sensing model for underdetermined range-Doppler recovery in range-ambiguity-free scenarios is derived and extended to range-ambiguity scenarios. Then, the OSAMP algorithm is proposed to estimate the unambiguous information of the scatterer and reconstruct the corresponding echo. Finally, the OSAMP and iterative methods are combined to form the CI-OSAMP algorithm, reducing reconstruction errors and improving echo reconstruction accuracy and ambiguity suppression performance. Furthermore, this paper proposes three radar imaging methods suitable for different scenario requirements. Simulation analysis and experimental data processing confirm the effectiveness of the proposed method, and the reconstruction accuracy of the algorithm under different compression ratios and signal-to-noise ratios is analyzed, providing a basis for parameter selection.

[0170] 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 method for resolving distance ambiguity through cyclic iterative echo reconstruction based on compressed sensing, characterized in that... The steps of this method include: Step S1: Convert the baseband echo obtained by downconverting the radar echo to obtain a linear echo model suitable for compressed sensing algorithm. Step S2: Based on the linear echo model obtained in Step S1 in the distance-free ambiguity scene, construct the distance-Doppler sensing matrix model in the distance-free ambiguity scene. Step S3: Based on the echo data and range-Doppler sensing matrix model from step S2, the OSAMP reconstruction algorithm is proposed to achieve information estimation of scattering points and echo reconstruction. Step S4: Construct a distance-Doppler perception matrix model for distance-ambiguous scenarios, and consider the impulse truncation effect in practice; Step S5: Based on the range-Doppler sensing matrix and echo data in the range-ambiguous scene in Step S4, and combining the OSAMP reconstruction algorithm in Step S3 with the iterative framework, the CI-OSAMP algorithm is formed to gradually reduce the reconstruction error, reduce distortion, improve the echo reconstruction accuracy and blur suppression performance, and propose three radar imaging methods. Step S1 includes the following steps: Step S11: Down-convert the radar echo to obtain the baseband echo; Step S12: Convert the baseband echo to obtain a linear echo model suitable for compressed sensing algorithm; Step S2 includes the following steps: Step S21, for the time-delay-Doppler two-dimensional plane Target scattering coefficient Discretization yields the discrete echo scattering coefficient matrix of the scene. ; Step S22, the discrete echo scattering coefficient matrix in step S21 is... Vectorized representation as And the received signal of the nth pulse repetition period PRT of the baseband echo after downconversion in step S12 is discretized; Step S23, define the nth echo signal's... l Guiding vectors And the discrete echo data of the nth PRT receiving interval in step S22 Written in matrix form: ; Step S24, based on the echo matrix representation of a single PRT from step S23, expand it to an echo matrix representation within CPI: And using the measurement matrix Compress raw echo data Subsampled echo data were obtained. : , This is called the range-Doppler sensing matrix; Step S3 includes the following steps: Step S31: Based on the input data obtained in step S2, perform parameter initialization; Step S32: Using the OSAMP reconstruction algorithm, obtain the sparse vector estimate of the scattering coefficients. The reconstructed signal can be obtained using the transformation matrix; Step S4 includes the following steps: Step S41: Construct a distance-Doppler perception matrix model in a distance-ambiguous scene; Step S42: Considering the pulse truncation effect, the measurement matrix is ​​equivalent to the truncation matrix; Step S5 includes the following steps: Step S51: Based on the echo data and range-Doppler sensing matrix model in the distance-ambiguous scene obtained in step S4, complete the OSAMP echo reconstruction deambiguation without iterative loops. Step S52 proposes the CI-OSAMP algorithm, which gradually reduces the influence of ambiguity energy outside the current range segment through iterative iteration, thereby achieving iterative echo reconstruction and deambiguation. In step S53, based on the output of the algorithm after convergence in S52, three radar imaging methods for different application scenarios are proposed.

2. The method for resolving distance ambiguity based on compressed sensing and iterative echo reconstruction according to claim 1, characterized in that: In step S11, it is assumed that the radar's transmitted signal is an orthogonal phase-coded signal, and within one CPI there are Each of the three transmitted pulse signals is modulated by a different phase code. n The time-domain representation of a single transmitted pulse signal is as follows: ; In the formula For the first n The first pulse within the [number] pulses m Each phase code, For the phase modulation function, in Take any value, The width of the symbol. The pulse repetition interval is , and the received signal consists of the attenuation of the transmitted signal and time-shifted frequency offset copies. The scattering points are sparsely distributed in the range-velocity dimension. Therefore, a sparse vector of scattering point information can be obtained by constructing a suitable dictionary and reconstruction algorithm. No. n PRT assumptions K The first goal, the... k Each target has a time delay: Frequency shift: ,in, , , The first k The distance and speed of the target from the radar. For transmitting signal carrier frequency, For the speed of light; ignoring echo broadening and compression, the first frequency after down-conversion to baseband... n The received signal within a PRT is represented as follows: ; in It is the first k Complex reflectance of an object.

3. The method for resolving distance ambiguity based on compressed sensing and iterative echo reconstruction according to claim 1, characterized in that: In step S12, the change of Doppler frequency shift within the pulse width is ignored, that is, the echo model adopts the stop-and-go model, which is expressed by equation (3): ; Define the delay operator Signal delay : ; Define the frequency offset operator This adds a frequency offset phase to the signal: ; The time delay-frequency shift operator for the signal is defined as follows: ； Equation (4) simplifies to: (8)。 4. The method for resolving distance ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S21, the signal finally received by the radar is regarded as a linear superposition of target echoes with different velocities, distances, and scattering coefficients within the observation scene, that is, (8) is extended as follows: ； Where Ω represents the set of all possible values ​​for the target's high-resolution range and velocity. For distance and speed corresponding to The scattering coefficient of the target; the main task of compressed sensing processing is to reconstruct the target scene and estimate the time-delay-Doppler two-dimensional plane. Target scattering coefficient ; Two-dimensional plane Discretization, the distance dimension and velocity dimension are discretized into... P and Q Grid points, i.e. , The grid values ​​should cover all range-velocity cells of interest. After discretization, the echo scattering coefficient of the scene Represented by a two-dimensional P × Q complex matrix ； Among them, the first in the matrix p line, number q Column represents the first p The distance unit, the first q There exists an RCS value in each Doppler element. The target point.

5. The method for resolving distance ambiguity based on compressed sensing and iterative echo reconstruction according to claim 1, characterized in that: In step S22, the discrete echo scattering coefficient matrix from step S21 is... Vectorization representation, and the baseband echo after down-conversion in step S12 n Discretized representation of the received signal of each PRT; Will Vectorization, forming vectors , ； in, , will vector The first in l The elements are denoted as ,in , , , Equation (8) can be rewritten as: ； For the first n Discrete echo data of each PRT receiving interval , Sampling frequency, For the first n The discretized representation of each transmitted signal, with a length of , This represents the pulse width.

6. The method for resolving distance ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S23, the first... n The first echo signal l Guiding vectors and in step S22 Written in matrix form: ; Define its first n The first echo signal l Guiding vectors These are called atoms: ； Indicates the transmitted signal If the signal copy after time delay and frequency shift is obtained, then equation (12) can be written in matrix form: ； in, This is called the transformation matrix, and can be specifically represented as: ； Indicates signal The time delay matrix satisfies , Represented as: （16）。 7. The method for resolving distance ambiguity based on compressed sensing and iterative echo reconstruction according to claim 1, characterized in that: In step S24, the echo matrix representation based on the single PRT in step S23 is expanded to an echo matrix representation within CPI: And using the measurement matrix Compress raw echo data Subsampled echo data was obtained. : ; This is called the range-Doppler sensing matrix; Echo within a CPI Represented as: ； and The corresponding transformation matrix is : ； The radar observation equations within CPI can then be written in the following matrix form: ； It can also be done through the measurement matrix Compress raw echo data Subsampled echo data was obtained. : ； in This is called the perceptual matrix. If subsampling is not performed, then... The identity matrix is ​​used; the reconstruction model of the radar observation scene is to solve for the vector from equation (19) or (20). , It is necessary that most of the elements are zero, indicating that there is no significant scattering target in the corresponding range-velocity unit, i.e. It is a sparse vector; according to By using non-zero elements, we can infer the estimated values ​​of the target's distance, velocity, and scattering coefficient.

8. The method for resolving distance ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S31, the input is: M × N Perception matrix , The echo length within the uncompressed CPI. M ×1D compressed echo ; Initialize: Residual Support set initial sparsity L = K 0, number of iterations t =1, step index n =1.

9. The method for resolving range ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S32, the OSAMP reconstruction algorithm obtains the sparse vector estimate of the scattering coefficients. The reconstructed signal can be obtained using the transformation matrix; Equation (20) is an underdetermined equation with infinitely many solutions. What is of interest is finding the sparsest solution, that is, a solution that satisfies the constraints while making the following: vector Norm minimization; CS theory has proven its application in the perceptron matrix. Under certain constraints, Norm minimization problem and The solutions to the norm minimization problem are equivalent, successfully transforming the CS signal recovery problem from a non-convex optimization problem into a convex optimization problem. ； Considering the influence of noise, the optimization problem of equation (21) is changed to: ； in, and These represent the 0-norm and 2-norm of the orientation quantity, respectively. It is a parameter determined by the intensity of additive noise.

10. The method for resolving distance ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S41, when distance ambiguity exists, the received echo in equation (17) is updated as follows: ； in, Indicates the first i Echoes for each distance segment: ； in Indicates the first i The scattering coefficient vector for each distance segment, The transformation matrix for the i-th distance segment is: ； That is, the transformation matrix of the first distance segment. Circular shift down the row One pulse repetition cycle; Similarly, this can also be achieved through the measurement matrix. Compressing raw fuzzy echo data Subsampled fuzzy echo data were obtained. : ； in, for I Concatenation of the transformation matrices of each distance segment for I The splicing of scattering coefficient vectors.

11. The method for resolving distance ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S42, considering the pulse truncation effect, the measurement matrix is ​​equivalent to the truncation matrix. In practice, considering the pulse truncation effect, the measurement matrix can be a truncated matrix. , Actual echo data when blind zones exist The sampling length can be expressed as: ； in Used to construct diagonal matrices Represented as: 。 12. The method for resolving distance ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S51, it is known from the radar range equation that the magnitude of the backscattering coefficient is inversely proportional to the range. Therefore, the scattering coefficient vector of the first range segment is first solved, and equation (26) can be expressed as: ； The estimated value of the scattering coefficient vector for the first range segment is obtained using the OSAMP algorithm. and reconstructed sub-echo Then, subtracting the reconstructed sub-echo of the first range segment from the total echo yields the echo data after blur suppression for the first range segment: ； The estimated value of the scattering coefficient vector for the second range segment is obtained by using (30) and the OSAMP reconstruction algorithm. and reconstructed sub-echo And so on, until there is ambiguity. I Each range segment echo is reconstructed once.

13. The method for resolving range ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S52, the algorithm iteration process is as follows: for the first... i For the distance segment, the input to the reconstruction submodule is: total echo minus the value of the first segment. i Reconstructed sub-echoes of other range segments; using the OSAMP reconstruction submodule to obtain the first... i The estimated value of the backscattering coefficient vector for the range segment and the reconstructed sub-echo; i Increment by 1, when i = I At that time, complete one iteration of reconstruction; and reset. i =1, repeat the reconstruction of the echoes of each distance segment until the difference between two adjacent iterations is less than the preset threshold.

14. The method for resolving range ambiguity based on compressed sensing cyclic iterative echo reconstruction according to claim 1, characterized in that: In step S53, based on the output of the algorithm after convergence in S52, the backscattering coefficient vector and reconstructed sub-echo of each range segment are finally obtained, and three radar imaging methods with different applicable scenarios are proposed. Method 1: When the signal-to-noise ratio is high and the backscattering coefficient vector estimation is relatively accurate, the reconstructed one-dimensional backscattering coefficient vector is matrixed according to the range and velocity interval division rules of the sensing matrix to obtain two-dimensional range-Doppler scattering point information, without the sidelobe effect of PD processing. Method 2: The reconstruction echo error is relatively small. It is necessary to improve the signal-to-noise ratio. When achieving two-dimensional accumulation, the reconstructed sub-echoes of each range segment are jointly mismatched and filtered to improve the range sidelobe modulation effect caused by the change in inter-pulse modulation form and obtain pulse Doppler results. Method 3: When the reconstructed sub-echoes may have significant losses and require two-dimensional accumulation, the reconstructed sub-echoes of the current range segment are obtained by subtracting the reconstructed sub-echoes of non-current range segments from the total echoes. Then, joint mismatch filtering is performed to obtain the pulse Doppler result.

Images