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CN-116794625-B - Cyclic iteration echo reconstruction and distance ambiguity solving method based on compressed sensing

CN116794625BCN 116794625 BCN116794625 BCN 116794625BCN-116794625-B

Abstract

The invention discloses a method for suppressing folding clutter and resolving distance ambiguity based on compressed sensing and loop iteration. Under the PD radar system transmitting agile waveforms, a distance-Doppler perception matrix model under a distance fuzzy scene is constructed, feasibility of echo reconstruction by compressed perception is analyzed, an optimized sparsity self-adaptive matching pursuit (OSAMP) algorithm is provided for realizing non-fuzzy information estimation and echo reconstruction of scattering points, the OSAMP algorithm is embedded into a loop iteration frame to form a CI-OSAMP algorithm, influence of fuzzy energy is gradually reduced, reconstruction precision and fuzzy inhibition performance are improved, and the method can be applied to compressed samples, and limit between radar signal bandwidth and sampling rate is broken through.

Inventors

  • LI YUANSHUAI
  • SUN YUXIAN
  • CHANG SHAOQIANG
  • CHEN XINLIANG
  • FAN HUAYU
  • LIU QUANHUA

Assignees

  • 北京理工大学

Dates

Publication Date
20260512
Application Date
20230424

Claims (14)

  1. 1. A cyclic iteration echo reconstruction and distance ambiguity solving method based on compressed sensing is characterized by comprising the following steps: step S1, converting a baseband echo obtained by down-conversion of a radar echo to obtain a linear echo model suitable for a compressed sensing algorithm; S2, constructing a distance-Doppler sensing matrix model in the non-distance-blurred scene based on the linear echo model obtained in the non-distance-blurred scene in the step S1; Step S3, based on the echo data and the distance-Doppler sensing matrix model in the step S2, a OSAMP reconstruction algorithm is provided, and information estimation and echo reconstruction of scattering points are realized; S4, constructing a distance-Doppler sensing matrix model in a distance fuzzy scene, and considering the pulse cut-off effect in practice; Step S5, based on the distance-Doppler sensing matrix and echo data in the distance fuzzy scene in step S4, combining the OSAMP reconstruction algorithm in step S3 with a loop iteration frame to form a CI-OSAMP algorithm, gradually reducing reconstruction errors, reducing distortion, improving echo reconstruction precision and fuzzy inhibition performance, and providing three radar imaging methods; step S1 comprises the steps of: Step S11, performing down-conversion on the radar echo to obtain a baseband echo; Step S12, converting the baseband echo to obtain a linear echo model applicable to a compressed sensing algorithm; Step S2 includes the steps of: Step S21, time delay-Doppler two-dimensional plane Target scattering coefficient on Discretizing to obtain a discrete echo scattering coefficient matrix of the scene ; Step S22, the discrete echo scattering coefficient matrix in step S21 Vectorization is expressed as And discretizing the received signal of the nth pulse repetition period PRT of the down-converted baseband echo in step S12; step S23, defining the first steering vector of the nth echo signal And discrete echo data of the nth PRT receiving section in step S22 Written in matrix form: ; Step S24, based on the echo matrix representation of the single PRT of step S23, expanding into an echo matrix representation within the CPI: And utilize the measurement matrix Compressing raw echo data Obtaining subsampled echo data : , Known as a range-doppler sensing matrix; Step S3 includes the steps of: step S31, obtaining input data based on the step S2 and initializing parameters; step S32, obtaining scattering coefficient sparse vector estimation by utilizing OSAMP reconstruction algorithm And using the transformation matrix to obtain a reconstructed signal; step S4 includes the steps of: s41, constructing a distance-Doppler sensing matrix model in a distance fuzzy scene; step S42, considering the pulse truncation effect, and equating the measurement matrix as a truncation matrix; The step S5 includes the steps of: Step S51, based on the echo data and the distance-Doppler perception matrix model in the distance fuzzy scene obtained in step S4, performing OSAMP echo reconstruction and deblurring without loop iteration; Step S52, a CI-OSAMP algorithm is provided, and the influence of the fuzzy energy of the non-local distance segment is gradually reduced in a cyclic iteration mode, so that the cyclic iteration echo reconstruction solution ambiguity is realized; Step S53, three radar imaging methods of different application scenes are provided based on the output after the algorithm in S52 converges.
  2. 2. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S11, the radar transmitting signal is assumed to be a quadrature phase encoded signal, and a CPI is provided A different transmitted pulse signal, each pulse signal modulated by a different phase code, the nth transmitted pulse signal time domain represented as: ; In the middle of For the mth phase code within the nth pulse, As a phase modulation function, in The value of the product can be arbitrarily taken, For the symbol width, For pulse repetition interval, the received signal consists of attenuation and time shift frequency offset copies of the transmitted signal, and scattering points are sparsely distributed in a distance-speed dimension, so that sparse vectors of scattering point information are obtained by constructing a proper dictionary and a reconstruction algorithm, K targets are assumed in an nth PRT, and the kth target has time delay: Frequency shift: , wherein, , , The distance and speed of the kth target to the radar respectively, For the carrier frequency of the transmitted signal, Ignoring echo broadening and compression, the received signal within the nth PRT after down-conversion to baseband is represented as: ; Wherein the method comprises the steps of Is the complex reflectivity of the kth target.
  3. 3. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: in the step S12, the change of the doppler shift in the pulse time width is ignored, that is, the echo model adopts the stop-and-go model, and the expression (3) is expressed as: ; Defining a time delay operator Delay the signal : ; Defining frequency offset operators Adding frequency offset phase to the signal: ; and defines the delay-shift operator on the signal as: ; the formula (4) is simplified as: (8)。
  4. 4. the cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S21, the signal finally received by the radar is regarded as a linear superposition of target echoes with different speeds, distances and scattering coefficients in the observation scene, namely (8) the signal is expanded into: ; Wherein omega is the set of all possible values of the target high resolution distance and speed, For distance, speed correspond to The main task of the compressed sensing process is to reconstruct the target scene and estimate the time delay-Doppler two-dimensional plane Target scattering coefficient on ; Generally will be a two-dimensional plane Discretizing, i.e. discretizing the distance and velocity dimensions into P and Q grid points, respectively , The grid should cover all the distance-speed units of interest; After discretization, echo scattering coefficient of scene Represented by a two-dimensional P x Q complex matrix ; Wherein the p-th row and the q-th row in the matrix represent the p-th distance unit and the q-th Doppler unit have an RCS value of Is a point target of (1).
  5. 5. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S22, the discrete echo scattering coefficient matrix in the step S21 is obtained Vectorized representation, and discretized representation of the received signal of the nth PRT of the down-converted baseband echo in step S12; Will be Vectorization, constructing vector , ; Wherein, the Vector is calculated The first element in (a) is recorded as Wherein , , , Formula (8) is rewritten as: ; For the n-th PRT reception interval of discrete echo data, , For the sampling frequency to be the same, For a discretized representation of the nth transmitted signal, of length , Is the pulse width.
  6. 6. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: in the step S23, the first steering vector of the nth echo signal is defined And will be in step S22 Written in matrix form: ; the first steering vector defining the nth echo signal Called atoms: ; representing the transmitted signal And (3) the signal copy subjected to time-delay frequency shift, the formula (12) is written as a matrix form: ; Wherein, the Referred to as a transformation matrix, may be expressed in particular as: ; Representing signals Is satisfied by the time delay matrix of (1) , Expressed as: (16)。
  7. 7. the cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S24, based on the echo matrix representation of the single PRT in the step S23, the echo matrix representation is extended into the CPI: And utilize the measurement matrix Compressing raw echo data Obtaining subsampled echo data : ; Known as a range-doppler sensing matrix; Echo in CPI Expressed as: ; And (3) with The corresponding transformation matrix is : ; The radar observation equation in CPI is written as follows: ; or by measuring matrices Compressing raw echo data Obtaining subsampled echo data : ; Wherein the method comprises the steps of Called the sense matrix, if not sub-sampled Is a unit matrix, and the reconstruction of the radar observation scene is modeled to solve vectors from the equation (19) or (20) , To be satisfied, in which the majority of the elements are zero, meaning that no significant scattering objects are present on the corresponding distance-velocity units, i.e. Is a sparse vector according to The non-zero elements of the corresponding target can be deduced to obtain the estimated values of the distance, the speed and the scattering coefficient of the corresponding target.
  8. 8. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S31, the input is an MxN sensing matrix , Is the echo length in CPI without compression, M x 1 dimension compressed echo Initializing residual error Support set Initial sparsity l=k 0 , iteration number t=1, step index n=1.
  9. 9. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: in the step S32, OSAMP the reconstruction algorithm obtains a scattering coefficient sparse vector estimation And using the transformation matrix to obtain a reconstructed signal; equation (20) is a partial equation with an infinite number of solutions, interesting is to find the sparsest solution, i.e. to make the constraint satisfied while at the same time Vector of Norm minimization, CS theory has demonstrated that in the sense matrix Under the constraint that a certain condition is met, Problem of norm minimization The solution of the norm minimization problem has equivalence, successfully converting the CS signal recovery problem from a non-convex optimization to a convex optimization solution: ; Considering the noise effect, the optimization problem of equation (21) is modified to: ; Wherein, the And Respectively representing the 0 norm and the 2 norm of the vector, Is a parameter determined by the additive noise strength.
  10. 10. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S41, when there is a distance ambiguity, the received echo in the equation (17) is updated as: ; Wherein, the Echo representing the i-th distance segment: ; Wherein the method comprises the steps of A scattering coefficient vector representing the i-th distance segment, A transformation matrix representing the i-th distance segment: ; I.e. a transformation matrix of the first distance segment Cyclically shifting down the row A pulse repetition period; Similarly, the matrix can be measured Compressing raw blurred echo data Obtaining sub-sampling fuzzy echo data : ; Wherein, the For the concatenation of I distance segment transform matrices, Is a concatenation of I scattering coefficient vectors.
  11. 11. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S42, the measurement matrix is equivalent to the truncated matrix in consideration of the pulse truncated effect; The actual situation considers the pulse truncation effect, and the measurement matrix can be a truncation matrix , Actual echo data for the presence of blind spots Can be expressed as: ; Wherein the method comprises the steps of For the construction of a diagonal matrix, Expressed as: 。
  12. 12. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S51, as known from the radar range equation, the magnitude of the backscattering coefficient is inversely proportional to the range, and thus, the scattering coefficient vector of the first range is first solved, where equation (26) may be expressed as: ; Obtaining an estimated value of the scattering coefficient vector of the first distance segment through OSAMP algorithm And reconstructing the sub-echoes Then subtracting the first distance segment from the total echo to reconstruct a sub-echo, and obtaining echo data after the first distance segment blur suppression: ; obtaining the estimated value of the scattering coefficient vector of the second distance segment through (30) and OSAMP reconstruction algorithms And reconstructing the sub-echoes And analogizing is performed until the I range echoes with the ambiguity exist, and one reconstruction is completed.
  13. 13. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S52, the algorithm iteration flow is that for the ith distance segment, the reconstruction sub-module is input, namely, subtracting the reconstruction sub-echo of other distance segments except for the ith distance segment from the total echo, obtaining the estimated value of the backscattering coefficient vector of the ith distance segment and the reconstruction sub-echo by utilizing the OSAMP reconstruction sub-module, wherein I is self-increased by 1, when i=I, the iterative reconstruction is completed, i=1 is reset, and the reconstruction of the sub-echoes of each distance segment is repeated until the difference between adjacent two iteration results is smaller than a preset threshold value.
  14. 14. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein: In the step S53, based on the output after the algorithm in S52 converges, a backscattering coefficient vector and a reconstructed sub-echo of each distance segment are finally obtained, and three radar imaging methods of different applicable scenes are provided; The method 1 comprises the steps of when the signal-to-noise ratio is high and the backward scattering coefficient vector estimation is accurate, carrying out vectorization on the reconstructed one-dimensional backward scattering coefficient vector according to the distance and speed interval division rule of a sensing matrix to obtain two-dimensional distance-Doppler scattering point information, and avoiding side lobe effect of PD processing; The method 2 is that the reconstructed echo error is smaller, the signal to noise ratio is required to be improved, and when two-dimensional accumulation is realized, the reconstructed sub-echoes of each distance section are combined with mismatched filtering treatment, so that the distance sidelobe modulation effect caused by the change of the modulation form between pulses is improved, and a pulse Doppler result is obtained; in the mode 3, when the reconstructed sub-echo possibly has larger loss and needs to be accumulated in two dimensions, the reconstructed sub-echo of the non-own distance section is subtracted by the total echo to obtain the reconstructed sub-echo of the current distance section, and then the combined mismatch filtering processing is carried out to obtain the pulse Doppler result.

Description

Cyclic iteration echo reconstruction and distance ambiguity solving method based on compressed sensing Technical Field The invention relates to the field of pulse Doppler radars of orthogonal agile waveforms, in particular to a method for suppressing folding clutter and solving distance ambiguity based on compressed sensing and loop iteration. Background Pulsed-Doppler (PD) radar can detect objects in more complex environments and obtain accurate information of object distance and speed. The PD radar transmits a periodic coherent pulse sequence, so that the problems of ranging and speed measurement ambiguity are inevitably brought, and large deviation exists in detection and tracking of targets, so that accuracy is reduced. Poor blur suppression results in a more serious false alarm or false alarm. Because no distance ambiguity and no speed ambiguity are mutually exclusive to the requirements of pulse repetition frequency, the ambiguity problem of PD radar is also different in different modes of operation. In order to enhance the detection capability of the radar on a high-speed target and improve the radar transmitting power, a medium-high repetition frequency working mode is generally adopted. So as to obtain a larger range of no-blurring speed measurement, thereby effectively distinguishing clutter and targets in the Doppler dimension. Therefore, it is important to implement a high-precision distance blur suppression algorithm. A typical approach to resolving range ambiguity in radar systems is by transmitting multiple sets of pulse train signals at a staggered pulse repetition frequency (Pulse Repetition Frequency, PRF) and then using the chinese remainder theorem to resolve the ambiguity. But this does not increase the distance and speed resolution and results in an extended period of coherent processing. Therefore, the research of resolving the distance ambiguity under the single pulse repetition frequency condition is increasing. Another method commonly used for resolving range ambiguity is to use different modulated agile waveforms between radar transmit pulses, which requires a lower cross-correlation between the waveforms to effectively distinguish echoes at different range segments, and although correlation studies on orthogonal waveforms optimize the cross-correlation properties between signals well, the effect of doppler shift on the cross-correlation properties between signals is largely not considered in the above studies. In addition, as different modulations exist among the pulses, the sidelobe structures of the pulse matched filtering results are different, and the phenomenon is called a range sidelobe modulation (Range Sidelobe Modulation, RSM) effect, which can cause the lifting of a range-Doppler imaging plane substrate during PD processing and seriously affect the target detection performance of the radar. And when the near-distance section strong wave energy is larger, effective fuzzy inhibition cannot be realized only by the isolation degree between agile waveforms, and the far-distance section target can still be blocked by the near-distance section scattered energy. The compressed sensing (Compressed Sensing, CS) theory breaks through the limitation of the traditional Nyquist sampling law, and by solving the nonlinear optimization problem, accurate signal reconstruction can be realized by using measurement signals with the number lower than the Nyquist sampling point. Extensive research has been conducted in the fields of radar detection, estimation and imaging. Radar imaging uses target echoes to obtain the spatial distribution of the target backscatter coefficients. Radar imaging is thus essentially a process of reconstructing a target characterization using echoes. The existing sparse reconstruction algorithm realizes the distance blur suppression, but does not consider the influence of the blur energy on the accuracy of the reconstruction algorithm, and can cause a certain degree of distortion and blur residues on a target. Therefore, a PD radar system based on transmitting quadrature phase coded signals is developed, a method based on compressed sensing and loop iteration is developed, effective suppression of folding clutter is achieved, accuracy of distance ambiguity suppression is improved, and accordingly targets can be effectively detected, and the method has important practical significance and application value. Disclosure of Invention The invention provides a method for suppressing folding clutter and solving distance ambiguity based on compressed sensing and loop iteration under a PD radar system for transmitting a quadrature phase coded signal. Firstly, a distance-Doppler perception matrix model in a distance fuzzy scene is modeled, the rationality of echo reconstruction by compressed perception is analyzed on the basis, and then, the optimal sparsity adaptive matching pursuit (Optimized SPARSITY ADAPTIVE MATCHING pursuit, OSAMP) algorithm is used for realizing the n