CN116794625A - Cyclic iteration echo reconstruction and distance ambiguity solving method based on compressed sensing - Google Patents

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 sensing matrix model under a distance fuzzy scene is constructed, and feasibility of echo reconstruction by compressed sensing is analyzed; an optimized sparsity self-adaptive matching pursuit (OSAMP) algorithm is provided for realizing the non-fuzzy information estimation and echo reconstruction of scattering points; embedding an OSAMP algorithm into a loop iteration framework to form a CI-OSAMP algorithm, gradually reducing the influence of fuzzy energy, and improving reconstruction accuracy and fuzzy inhibition performance; and can be applied to compressed samples, breaking through the limitation between radar signal bandwidth and sampling rate.

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 the spread 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 the pulses have different modulations, 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, modeling a distance-Doppler perception matrix model under a distance-blurred scene, analyzing the rationality of echo reconstruction by compressed perception on the basis, and then, elaborating the optimal sparsity self-adaptive matching pursuit (Optimized sparsity adaptive matching pursuit, OSAMP) algorithm to realize the non-blurred information estimation and echo reconstruction of scattering points, thereby effectively reducing reconstruction errors. And finally, combining an OSAMP algorithm with a Cyclic Iteration (CI) method to form a complete echo reconstruction solution distance fuzzy CI-OSAMP algorithm, suppressing fuzzy energy of a non-local distance segment, reducing reconstruction errors and improving reconstruction precision and fuzzy suppression performance. In addition, the reconstruction algorithm can be directly applied to compressed samples, the relation between the radar signal bandwidth and the sampling rate is broken, and the reconstruction accuracy under different compression rates and signal-to-noise ratios is analyzed. The method ensures the echo reconstruction precision and the fuzzy inhibition performance by using a compressed sensing and cyclic iteration method. Simulation experiments and actual measurement data processing show that the method can effectively inhibit folding clutter and realize echo decorrelation at different distance segments while improving reconstruction effects.

The invention discloses a cyclic iteration echo reconstruction and distance ambiguity solving method based on compressed sensing, which is realized by the following technical scheme:

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, an OSAMP reconstruction algorithm is provided, and information estimation and echo reconstruction of scattering points are achieved;

s4, constructing a distance-Doppler sensing matrix model in a distance fuzzy scene, and considering the pulse cut-off effect in practice;

and 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.

The step S1 includes the steps of:

step S11, performing down-conversion on the radar echo to obtain a baseband echo;

and step S12, converting the baseband echo to obtain a linear echo model applicable to the compressed sensing algorithm.

The step S2 includes the steps of:

step S21, target dispersion on delay-Doppler two-dimensional plane (τ, v)Coefficient of emission sigma _(τ,v) Discretizing to obtain a discrete echo scattering coefficient matrix Λ of the scene;

step S22, vectorizing the discrete echo scattering coefficient matrix Λ in the step S21, and discretizing the received signal of the nth PRT of the down-converted baseband echo in the step S12;

step S23, defining the first steering vector (vector) ψ of the nth echo signal _n,l And r in step S22 _n Can be written in matrix form: r is (r) _n ＝Ψ _n σ；

Step S24, based on the echo matrix representation of the single PRT of step S23, expanding into an echo matrix representation within the CPI: r=ψσ. And compressing the original echo data r by using the measurement matrix phi to obtain sub-sampling echo data y: y=Φr=Φψσ=aσ, a being referred to as the range-doppler sensing matrix.

The 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 using an OSAMP reconstruction algorithmAnd the reconstructed signal can be obtained by using the transformation matrix.

The step S4 includes the steps of:

s41, constructing a distance-Doppler sensing matrix model in a distance fuzzy scene;

in step S42, the measurement matrix is equivalent to the truncation matrix in consideration of the pulse truncation effect.

The step S5 includes the steps of:

step S51, based on the echo data and the distance-Doppler sensing matrix model in the distance fuzzy scene obtained in step S4, the OSAMP echo reconstruction and deblurring without loop iteration is completed;

step S52, a CI-OSAMP algorithm is provided, and the influence of fuzzy energy of a non-local distance segment is gradually reduced in a cyclic iteration mode, so that cyclic iteration echo reconstruction solution blurring is realized;

step S53, three radar imaging methods of different application scenes are provided based on the output after the algorithm in S52 converges.

The beneficial effects are that:

under the PD radar system of the orthogonal agile waveform, the invention provides a method based on compressed sensing and loop iteration to inhibit folding clutter and solve the problem of distance ambiguity. Compared with the traditional multi-pulse-train spread spectrum repeated frequency de-blurring method, only one pulse train is needed, and the coherent processing period is shortened. Firstly, establishing an underdetermined range Doppler recovery problem under a range-blurred scene, and estimating the unblurred information of a scattering point and reconstructing an echo through an OSAMP algorithm on the basis. And finally, combining the OSAMP with a cyclic iteration method to form a CI-OSAMP algorithm, so that reconstruction errors are reduced. The invention improves the echo reconstruction precision and the fuzzy inhibition performance by using the compressed sensing and cyclic iteration method, and realizes the effective inhibition of the folded clutter.

Drawings

FIG. 1 is a graphical summary of the inventive content herein;

FIG. 2 is a schematic diagram of pulse Doppler results based on constant pulses and agile pulses;

FIG. 3 is a flow chart of echo reconstruction and distance blur suppression based on the CI-OSAMP algorithm;

fig. 4 (a) shows the result of the first three-distance segment PD processing before blur suppression (three-dimensional view);

fig. 4 (b) shows the result of the first three-distance PD processing before blur suppression (distance-speed projection diagram);

fig. 4 (c) shows the processing result (three-dimensional view) of the first three distance segments PD after blur suppression;

fig. 4 (d) shows the processing result (distance-velocity projection diagram) of the first three distance segments PD after blur suppression;

the echo reconstruction residual for the third distance segment of fig. 5;

FIG. 6 shows the unambiguous distance-velocity estimation of scattering points in the first three distance segments;

FIG. 7 reconstructed powers for different signal-to-noise ratios at different compression ratios;

FIG. 8 (a) shows the result of the PD stitching of the measured blurred echo distance segments before CI-OSAMP processing (three-dimensional view);

FIG. 8 (b) shows the measured fuzzy echo over each distance segment PD splice (distance-velocity projection plot) prior to CI-OSAMP processing;

FIG. 8 (c) reconstructed sub-echo joint mismatch filter imaging (three-dimensional view) after CI-OSAMP processing;

FIG. 8 (d) reconstructed sub-echo joint mismatch filter imaging (distance-velocity projection map) after CI-OSAMP processing;

FIG. 8 (e) CI-OSAMP processed total echo and non-local range bin reconstructed sub-echo difference joint mismatch filtered imaging (three-dimensional view);

FIG. 8 (f) CI-OSAMP processed total echo and non-local range bin reconstructed sub-echo difference joint mismatch filter imaging (range-velocity projection view);

figure 9 shows the blur-free distance-velocity estimation of the scattering points at the first 11 distance segments.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. And provides a graphical summary of the objects and solutions of the present invention as shown in figure 1. The distance ambiguity suppression method based on the joint reversible mismatch filter and the nonlinear processing comprises the following specific 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, wherein the method comprises the following steps:

step S11, down-converting the radar echo to obtain a baseband echo.

Assuming that the radar transmit signal is a quadrature-phase encoded signal, there is a different pulse sequence in a CPI, each pulse signal is modulated by a different M-phase code, and the nth transmit pulse signal time domain may be expressed as:

in the formula For the mth phase code in the nth pulse _n (m) is a phase modulation function, and is arbitrarily valued at [0,2 pi ], T _c For symbol width, T _r For the pulse repetition interval.

The received signal is composed of attenuation of the transmitted signal and time-shift frequency offset copies, and scattering points are sparsely distributed in a distance-speed dimension, so that sparse vectors of scattering point information can be obtained by constructing a proper dictionary and a reconstruction algorithm. K targets are assumed in the nth PRT, and the kth target has time delay: τ _k ＝2R _k And/c, frequency shift: upsilon (v) _k ＝2f _c v _k Wherein, K is more than or equal to 1 and less than or equal to K, R _k ，v _k Distance and speed from kth target to radar, f _c For transmitting carrier frequencies c is the speed of light. Ignoring echo broadening and compression, the received signal within the nth PRT after down-conversion to baseband can be expressed as:

wherein σ_k Is the complex reflectivity of the kth target.

And step S12, converting the baseband echo to obtain a linear echo model applicable to the compressed sensing algorithm.

The doppler shift varies negligibly over the pulse time width, i.e. using a stop-and-go model, equation (3) can be expressed as:

defining a time delay operator T _τ [·]Signal delay τ:

T _τ [u _n (t)]＝u _n (t-τ _k ) (5)

defining frequency offset operatorsAdding frequency offset phase to the signal:

and defines the delay-shift operator on the signal as:

formula (4) can be simplified as:

step S2, based on the linear echo model obtained in the step S1 in the non-distance-blur scene, constructing a distance-Doppler perception matrix model in the non-distance-blur scene, wherein the method comprises the following steps of:

step S21, target scattering coefficient sigma on time delay-Doppler two-dimensional plane (τ, v) _(τ,v) Discretizing to obtain a discrete echo scattering coefficient matrix Λ of the scene.

The signal finally received by the radar can be seen as a linear superposition of target echoes with different velocities, distances, scattering coefficients within the observation scene, i.e. (8) expands to:

wherein omega is the set of all possible values of the target high resolution distance and speed, sigma _(τ,v) The scattering coefficient of the target corresponding to (τ, v) for distance, velocity. The main task of the compressed sensing process is to reconstruct the target scene and estimate the delay-DopplerTarget scattering coefficient sigma in two-dimensional plane (tau, v) _(τ,v) 。

The two-dimensional plane [ tau ] is usually taken _begin ,τ _end ]×[v _begin ,v _end ]Discretizing, i.e. discretizing the distance and velocity dimensions into P and Q grid points, respectively, i.e. τ ₀ ,τ ₁ ,…τ _P-1 ，v ₀ ,v ₁ ,…v _P-1 . The grid should be valued to cover all the distance-speed cells of interest.

After discretization, the echo scattering coefficient sigma (τ, v) of the scene can be represented by a two-dimensional p×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 ofIs a point target of (1).

Step S22, vectorizing the discrete echo scattering coefficient matrix Λ in step S21, and discretizing the received signal of the nth PRT of the down-converted baseband echo in step S12.

Vectorizing lambda to form vector

wherein ,the first element in the vector sigma is noted as

Wherein P is more than or equal to 0 and less than or equal to P-1,q is more than or equal to 0 and less than or equal to Q-1, l=q+pQ, and l is more than or equal to 0 and less than or equal to PQ-1, and the formula (8) is rewritten as follows:

discrete echo data for the nth PRT reception interval, N _s ＝f _s T _r ，f _s For sampling frequency u _n ＝[u _n,0 ,u _n,1 ,…u _n,L-1 ] ^T For a discretized representation of the nth transmitted signal, a length of l=f _s T _p ，T _p ＝MT _c Is the pulse width.

Step S23, defining the first steering vector (vector) ψ of the nth echo signal _n,l And r in step S22 _n Can be written in matrix form: r is (r) _n ＝Ψ _n σ。

Defining the first pilot vector (vector) ψ of the nth echo signal _n,l May also be referred to as an atom:

representing the transmitted signal u _n And (2) the time-shifted signal replica, equation (12) can be written in matrix form:

r _n ＝Ψ _n σ (14)

wherein ,referred to as a transformation matrix, may be expressed in particular as:

representing signal U _n Is a time delay matrix of (1), satisfy N _s ＝P+L-1，U _n Expressed as:

step S24, based on the echo matrix representation of the single PRT of step S23, expanding into an echo matrix representation within the CPI: r=ψσ. And compressing the original echo data r by using the measurement matrix phi to obtain sub-sampling echo data y: y=Φr=Φψσ=aσ. A is referred to as the range-doppler sensing matrix.

Echo in CPIExpressed as:

the transformation matrix corresponding to r is

The radar observation equation in CPI can be written in the form of a matrix as follows:

r＝Ψσ (19)

the original echo data r can also be compressed by the measurement matrix Φ to obtain sub-sampled echo data y:

y＝Φr＝ΦΨσ＝Aσ (20)

wherein A is called a sensing matrix, and if subsampling is not performed, phi is a unitary matrix. The reconstruction of the radar observation scene can be modeled as solving the vector σ from equation (19) or (20), σ being required to satisfy that most of the elements are zero, representing that no significant scattering objects are present on the corresponding range-velocity units, i.e., σ is a sparse vector. From the non-zero elements in σ, estimates of the distance, velocity, scattering coefficient of the corresponding target can be inferred.

Step S3, based on the echo data and the distance-Doppler sensing matrix model in step S2, an OSAMP reconstruction algorithm is provided to realize information estimation and echo reconstruction of scattering points, and the method comprises the following steps:

step S31, input data is obtained based on step S2 and parameter initialization is performed.

The input is: m×n perceptual matrices a=Φψ, n=n _s N _prt The echo y is compressed M x 1 dimensions for the echo length in the CPI without compression. Initializing: residual r ₀ Support set =yInitial sparsity l=k ₀ The iteration number t=1, the step index n=1.

Step S32, obtaining scattering coefficient sparse vector estimation by using an OSAMP reconstruction algorithmAnd the reconstructed signal can be obtained by using the transformation matrix.

Equation (20) is a partial equation with infinite number of solutions, interested in finding the sparsest solution, i.e. let l of the sigma vector while satisfying the constraint ₀ The norm is minimized. CS theory has demonstrated that under the constraint that the perceptual matrix A satisfies certain conditions, l ₁ Norm minimization problem and l ₀ 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 I ₁ and ||||₂ The 1 norm and the 2 norm of the vector are respectively expressed, and E.gtoreq.o is a parameter determined by the additive noise intensity. Solving for l above using the OSAMP algorithm set forth below ₁ The norm minimizes the problem. It is a greedy algorithm that achieves approximation of signal vectors by selecting the appropriate atoms and passing through a series of stepwise increasing methods.

The thought of the OSAMP algorithm is mainly derived from a subspace tracking (SP) algorithm, but the optimal value is difficult to determine when the step size is selected, the number of scattering points is difficult to determine, and the improvement of the algorithm is as follows on the premise of unknown sparsity: 1) The number of scattering points in the estimated environment is processed through PD, nonlinear step length is adopted, the step length is gradually adjusted to approach the number of real scattering points, the algorithm is facilitated to rapidly approach the real sparsity, and the convergence speed is improved; 2) And setting a sparsity judgment sub-process, and carrying out sparsity judgment by setting a threshold to weaken the influence of noise, so as to obtain final sparse solution and improve the reconstruction precision of sparse vectors. The specific algorithm flow is as follows:

wherein ,r_t Representing residual error, t representing iteration number,Representing empty set, Λ _t An atomic position index (column number) set (the number of elements is L, L is the step length corresponding to each iteration) representing the support set of the t-th iteration, the symbol U represents the set and operates, abs [. Cndot.]Representing absolute values.

The OSAMP algorithm does not require accurate knowledge of sparsity. On the premise of unknown sparsity, an initial sparsity estimation value K is utilized ₀ And a nonlinear step length set S, which approaches the original signal sparsity K segment by segment. Obtained by a suitable threshold valueSparsity estimate K. And selecting an atom which is most matched with the signal from the observation matrix, and solving a signal residual error. Then, the atom that best matches the signal residual is selected and iterated. Each iteration process is required to satisfy regularization constraint to ensure that each round result is an optimal solution, and the final signal can be represented by the linear sum of the atoms and the final residual value, namely, the transformation matrix and the scattering coefficient vector estimation value are utilizedAvailable reconstruction signal +.>

Step S4, constructing a distance-Doppler perception matrix model under a distance fuzzy scene, and considering the pulse cut-off effect in practice, comprising the following steps:

step S41, constructing a distance-Doppler sensing matrix model in a distance fuzzy scene.

When the target distance exceeds a PRT interval length, there is a distance ambiguity phenomenon in which the measured distance of the radar obtained by the pulse time interval of the adjacent transmitted wave and echo cannot be determined as the actual distance. When using a constant waveform, it is not possible to distinguish from which distance segment the target comes, resulting in a great reduction in imaging and detection performance, and a long-distance weak target is easily blocked by the energy spread of a close-distance strong target. When using agile waveforms, the range gating characteristics are obtained by the isolation between pulses, and echoes of different range segments are distinguished over the waveform domain, as schematically shown in fig. 2.

When there is a distance ambiguity, the received echo in equation (17) is updated as:

wherein ,rⁱ Echo representing the i-th distance segment:

r ⁱ ＝Ψ ⁱ σ ⁱ (24)

wherein σⁱ Scattering coefficient vector, ψ, representing the i-th distance segment ⁱ A transformation matrix representing the i-th distance segment:

Ψ ⁱ i.e. a transformation matrix of the first distance segmentI-1 pulse repetition periods are cyclically shifted down the row.

Similarly, the original fuzzy echo data r can be compressed through the measurement matrix phi to obtain sub-sampling fuzzy echo data y:

in step S42, the measurement matrix is equivalent to the truncation matrix in consideration of the pulse truncation effect.

The actual situation considers the pulse truncation effect, and the measurement matrix can be a truncation matrixN _J The sample length of the actual echo data y for the presence of the dead zone can be expressed as:

wherein diag []For constructing diagonal matrix, J _j Expressed as:

during processing, the speed interval and the speed resolution of scattering points in an actual scene need to be comprehensively considered due to the large dimension of the matrix. And carrying out block parallel processing according to the Doppler unit channels and carrying out block parallel processing on the data according to the PRT interval so as to reduce the calculation load and improve the operation speed.

And 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. The method comprises the following steps:

and step S51, based on the echo data and the distance-Doppler sensing matrix model in the distance blurred scene obtained in the step S4, the OSAMP echo reconstruction deblurring without loop iteration is completed.

As can be seen from the radar range equation, the magnitude of the backscatter coefficient is inversely proportional to the range, so we first solve for the scatter coefficient vector for the first range bin, and equation (26) can be expressed as:

obtaining an estimated value of a scattering coefficient vector of the first distance segment through an OSAMP algorithmAnd reconstructing the sub-echoesAnd then subtracting the first distance segment from the total echo to reconstruct a sub-echo, and obtaining echo data after the first distance segment is subjected to fuzzy inhibition:

obtaining an estimated value of the scattering coefficient vector of the second distance segment through (30) and an OSAMP reconstruction algorithmAnd reconstruct sub-echo->And analogizing is performed until the fuzzy I distance segment echoes are reconstructed once.

And step S52, providing a CI-OSAMP algorithm, and gradually reducing the influence of the fuzzy energy of the non-local distance section in a cyclic iteration mode to realize the cyclic iteration echo reconstruction and the fuzzy.

The second term of (30) can know that the fuzzy component can necessarily influence the reconstruction effect, so that the influence of the fuzzy energy of the non-local distance section cannot be avoided through single reconstruction, errors exist in the reconstruction, the fuzzy inhibition effect is further influenced, and therefore, the influence of the fuzzy energy of the non-local distance section is gradually reduced in a cyclic iteration mode, and the reconstruction precision is improved. The algorithm iteration flow is shown in fig. 3.

For the ith distance segment, the inputs of the reconstruction sub-module are: the total echo is subtracted by the reconstructed sub-echoes of the other distance segments than the i-th distance segment. And obtaining an estimated value of a backscattering coefficient vector of the ith distance segment and a reconstructed sub-echo by using an OSAMP reconstruction sub-module. And the I is increased by 1, and when i=i, one iteration reconstruction is completed. And resetting i=1, and repeating the reconstruction of the sub-echoes of each distance segment until the difference between the adjacent two iteration results is smaller than a preset threshold value.

Step S53, three radar imaging methods of different application scenes are provided based on the output after the algorithm in S52 converges.

Based on the output after the algorithm in S52 is converged, the backscattering coefficient vector and the reconstructed sub-echo of each distance segment are finally obtained, and three radar imaging methods of different applicable scenes are provided.

Mode 1): when the signal-to-noise ratio is higher and the backward scattering coefficient vector estimation is more accurate, the reconstructed one-dimensional backward scattering coefficient vector is matrixed according to the distance and speed interval division rule of the sensing matrix to obtain two-dimensional distance-Doppler scattering point information, and no side lobe effect of PD processing exists;

mode 2): 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 subjected to combined mismatch filtering treatment, so that the range side lobe modulation effect caused by the change of the modulation form between pulses is improved, and a pulse Doppler result is obtained;

mode 3): when the two-dimensional accumulation is needed, the total echo is used for subtracting the reconstructed sub-echo of the non-own distance section 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.

The invention is illustrated by the following examples:

the effectiveness of the CI-OSAMP algorithm is verified by using the inter-pulse phase coding signals by using a point target simulation experiment and an actual scene experiment, the reconstruction performance and the fuzzy inhibition capability of the algorithm are analyzed, and the noise robustness of the reconstruction algorithm under different compression ratios is analyzed through Monte Carlo simulation. As shown in the following table, specific parameters of the radar and scene are listed.

First, the reconstruction and blur suppression performance of the CI-OSAMP algorithm proposed by the present invention is validated and analyzed. Clutter is distributed in the first two distance segments, the second and third distance segments have 4 point targets, firstly, fuzzy echo is processed by the traditional PD of the distance segments, and as shown in fig. 4a and 4b, the second and third distance segments are blocked by the scattered energy of strong clutter in the first short distance segment, because the echo of the receiving filter bank to other distance segments is in a mismatch state, the energy of folding clutter is scattered in the whole imaging plane, and the detection and imaging performance of radar targets are seriously affected.

The reconstruction errors of the echoes of each distance segment are gradually reduced by using a CI-OSAMP algorithm. With the imaging mode 2 in step S53, i.e. the unambiguous reconstructed echoes of each distance segment are subjected to joint mismatch filtering, and PD results are shown in fig. 4c and 4 d. The problems of RSM are solved, the problem that pulse pressure side lobe structures are different due to waveform diversity and side lobe energy is scattered in Doppler dimension due to the fact that phase-coherent accumulation cannot be achieved in slow time dimension is avoided, fuzzy inhibition is achieved, targets in a long distance section can be imaged and detected, and the problem of clutter folding in a traditional PD radar is effectively solved.

For the purpose of quantifying the blur suppression effect of the analysis algorithm, the residual energy of the i-th distance segment reconstructed signal and the true signal is used herein as an evaluation criterion:

as shown in fig. 5, the reconstruction residual error result of the third distance segment is reduced along with iteration, the reconstruction accuracy gradually rises, that is, the distance blur suppression performance gradually rises, the convergence condition is satisfied in the 12 th iteration, the echo reconstruction residual error is almost 0, the calculated amount is small, the complexity is low, and the blur-free echo of each distance segment is recovered from the blur echo.

The CI-OSAMP algorithm outputs the two-dimensional distance-speed information of the scattering points by matrixing the scattering coefficient vector of each distance segment except the reconstructed echo data in the imaging mode 1 in the step S53, and the splicing result of the scattering point information of the three distance segments is shown in fig. 6, so that 4 targets marked by red circles in the graph can be clearly seen.

First, the noise robustness of the reconstruction algorithm proposed by the present invention is analyzed. The 5 point targets are set randomly, and the signal to noise ratio after the fast and slow time accumulation is increased from-10 dB to 35dB at 1dB intervals. And obtaining an echo without compression at a Nyquist sampling rate, and obtaining sub-Nyquist echo data by using compression ratios of 50%, 25%, 10% and 5% of the echo by using a random Gaussian matrix. 100 Monte Carlo simulation experiments are carried out under different compression ratios and signal to noise ratios, if the distance-speed estimation of each point target is correct and the complex amplitude estimation error is smaller than a certain threshold value, the reconstruction is judged to be successful, and the reconstructed power curve is shown in figure 7.

The recovery performance of the nyquist mode is observed to be superior to that of the sub-nyquist mode, which decreases with decreasing compression rate. This is because sub-nyquist sampling results in sample reduction and SNR loss. Nevertheless, the sub-nyquist mode ensures successful recovery of the target parameters at high signal-to-noise ratios.

Finally, in order to further verify the effectiveness of the algorithm, a certain ground-based radar measured data is adopted for verification analysis, the transmitted waveform is an inter-pulse phase coded signal, the measured echo data clutter and the target echo are folded into the same fuzzy distance section, the distance ambiguity phenomenon is serious, and as shown in fig. 8a and 8b, the scattering energy of the near-range strong clutter seriously affects the imaging result of the far-range section.

After being processed by the CI-OSAMP method, clutter echoes from different distance segments can be effectively reconstructed, and effective suppression of folding clutter is achieved, so that targets can be effectively detected. During processing, the echo data is not compressed, the pulse cut-off effect of the actual echo data is considered, namely the measurement matrix is the cut-off matrix, the speed interval of the scattering points is primarily analyzed through the PD result before fuzzy inhibition, the Doppler unit channels in the interval are subjected to block processing, invalid speed grid redundancy values are avoided, the calculation load is reduced, and the operation speed is improved.

With the imaging mode 2 in step S53, the reconstructed sub-echoes of each distance segment are directly processed in the distance segment PD, and the result is as shown in fig. 8c and 8d, because there is no subtraction operation of the imaging mode 3, there is no noise and residual components of other distance segments, and the imaging effect is better. But such processing relies on the accuracy of the algorithm reconstruction. If the imaging mode 3 in step S53 is adopted, for each distance segment, the total echo is used to subtract the reconstructed clutter of the non-local distance segment, so as to complete the suppression of the folded clutter, and the reconstructed echo after the blur suppression of each distance segment is obtained. And then the distance segment PD processing is conducted, and the result is shown in fig. 8e and 8f, so that effective suppression of folding clutter is achieved, the target can be effectively detected, and the method has the advantages of small calculated amount, low complexity, no clutter priori statistical information, good robustness and the like. The target was detected in the 11 th distance segment, with distances and speeds of 117.48km and 99.4463m/s, respectively.

In the same way, the imaging mode 1 in the step S53 is adopted, the scattering coefficient vector of each distance segment is matrixed to obtain the two-dimensional distance-speed information of the scattering points, the splicing result of the scattering point information of 11 distance segments is shown in fig. 9, the red circle marked target can be seen, and the non-fuzzy ranging and speed measurement of the target are realized.

The invention provides a novel method for suppressing folding clutter and solving distance ambiguity based on compressed sensing and loop iteration under a PD radar system adopting a single PRF and a quadrature phase coded signal. Firstly, a compressed sensing model of the range-Doppler recovery under the range-free fuzzy scene is deduced, and the compressed sensing model is popularized to the range fuzzy scene. An OSAMP algorithm is then proposed to estimate the unambiguous information of the scatterers and reconstruct the corresponding echoes. And finally, combining the OSAMP and a cyclic iteration method to form a CI-OSAMP algorithm, reducing reconstruction errors, and improving echo reconstruction precision and fuzzy inhibition performance. Furthermore, three radar imaging methods are presented herein that are suitable for different scene requirements. The simulation analysis and the measured data processing both prove the effectiveness of the method, analyze the algorithm reconstruction accuracy under different compression rates and signal to noise ratios, and provide the parameter selection basis of the algorithm.

In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (14)

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, an OSAMP reconstruction algorithm is provided, and information estimation and echo reconstruction of scattering points are achieved;

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, target scattering coefficient sigma on time delay-Doppler two-dimensional plane (τ, v) _(τ,v) Discretizing to obtain a discrete echo scattering coefficient matrix Λ of the scene;

step S22, vectorizing the discrete echo scattering coefficient matrix Λ in the step S21, and discretizing the received signal of the nth PRT of the down-converted baseband echo in the step S12;

step S23, defining the first steering vector (vector) ψ of the nth echo signal _n,l And r in step S22 _n Can be written in matrix form: r is (r) _n ＝Ψ _n σ；

Step S24, based on the echo matrix representation of the single PRT of step S23, expanding into an echo matrix representation within the CPI: r=ψσ; and compressing the original echo data r by using the measurement matrix phi to obtain sub-sampling echo data y: y=Φr=Φψσ=aσ, a being referred to as the 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 using OSAMP reconstruction algorithmAnd a transformation matrix is utilized to obtain a reconstruction 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 sensing matrix model in the distance fuzzy scene obtained in step S4, the OSAMP echo reconstruction and deblurring without loop iteration is completed;

step S52, a CI-OSAMP algorithm is provided, and the influence of fuzzy energy of a non-local distance segment is gradually reduced in a cyclic iteration mode, so that cyclic iteration echo reconstruction solution blurring 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. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein:

in the step S11, assuming that the radar transmit signal is a quadrature phase encoded signal, there is a different pulse sequence in a CPI, each pulse signal is modulated by a different M-phase code, and the nth transmit pulse signal time domain may be expressed as:

in the formula For the mth phase code in the nth pulse _n (m) is a phase modulation function, and is arbitrarily valued at [0,2 pi ], T _c For symbol width, T _r For pulse repetition interval, the received signal consists of attenuation of the transmitted signal and time shift frequency offset copies, and scattering points are sparsely distributed in a distance-speed dimension, so that sparse vectors of scattering point information can be obtained by constructing a proper dictionary and a reconstruction algorithm; k targets are assumed in the nth PRT, and the kth target has time delay: />Frequency shift:wherein K is more than or equal to 1 and less than or equal to K, R _k ，v _k Distance and speed from kth target to radar, f _c C is the speed of light for transmitting carrier frequency; ignoring echo broadening and compression, the received signal within the nth PRT after down-conversion to baseband can be expressed as:

wherein σ_k Is the complex reflectivity of the kth target.

3. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein:

in the step S12, the doppler shift can be ignored in the pulse time width, that is, the stop-and-go model is adopted, and the expression (3) can be expressed as:

defining a time delay operatorSignal delay τ:

T _τ [u _n (t)]＝u _n (t-τ _k ) (5)

defining frequency offset operatorsAdding frequency offset phase to the signal:

and defines the delay-shift operator on the signal as:

formula (4) can be simplified as:

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 can be regarded as a linear superposition of target echoes with different speeds, distances and scattering coefficients in the observation scene, namely (8) the expansion is as follows:

wherein omega is the set of all possible values of the target high resolution distance and speed, sigma _(τ,v) Scattering coefficients for targets whose distance, velocity corresponds to (τ, v); the main task of the compressed sensing process is to reconstruct the target scene and estimate the target scattering coefficient sigma on the delay-Doppler two-dimensional plane (τ, v) _(τ,v) ；

The two-dimensional plane [ tau ] is usually taken _begin ,τ _end ]×[v _begin ,v _end ]Discretizing, i.e. discretizing the distance and velocity dimensions into P and Q grid points, respectively, i.e. τ ₀ ,τ ₁ ,…τ _P-1 ，v ₀ ,v ₁ ,…v _P-1 The method comprises the steps of carrying out a first treatment on the surface of the The grid should be valued to cover all the distance-speed cells of interest;

after discretization, the echo scattering coefficient sigma (τ, v) of the scene can be represented by a two-dimensional p×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 ofIs a point target of (1).

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 Λ in the step S21 is represented in a vectorization manner, and the received signal of the nth PRT of the baseband echo after the down-conversion in the step S12 is represented in a discretization manner;

vectorizing lambda to form vector

wherein ,let the/th element in vector sigma be +.> Wherein P is more than or equal to 0 and less than or equal to P-1, Q is more than or equal to 0 and less than or equal to Q-1, l=q+pQ, l is more than or equal to 0 and less than or equal to PQ-1, and the formula (8) is rewritten as:

discrete echo data for the nth PRT reception interval, N _s ＝f _s T _r ，f _s For sampling frequency u _n ＝[u _n,0 ,u _n,1 ,…u _n,L-1 ] ^T For a discretized representation of the nth transmitted signal, a length of l=f _s T _p ，T _p ＝MT _c Is the pulse width.

6. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein:

in the step S23, the first pilot vector (step) ψ of the nth echo signal is defined _n,l And r in step S22 _n Can be written in matrix form: r is (r) _n ＝Ψ _n σ；

Defining the nth pilot vector (phi) of its nth echo signal _n,l May also be referred to as an atom:

representing the transmitted signal u _n And (2) the time-shifted signal replica, equation (12) can be written in matrix form:

r _n ＝Ψ _n σ (14)

wherein ,referred to as a transformation matrix, may be expressed in particular as:

representing signal U _n Is a time delay matrix of (1), satisfy N _s ＝P+L-1，U _n Expressed as:

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: r=ψσ; and compressing the original echo data r by using the measurement matrix phi to obtain sub-sampling echo data y: y=Φr=Φψσ=aσ; a is called a range-doppler sensing matrix;

echo in CPIExpressed as:

the transformation matrix corresponding to r is

The radar observation equation in CPI can be written in the form of a matrix as follows:

r＝Ψσ (19)

the original echo data r can also be compressed by the measurement matrix Φ to obtain sub-sampled echo data y:

y＝Φr＝ΦΨσ＝Aσ (20)

wherein A is called as a sensing matrix, and if subsampling is not performed, phi is a unit matrix; the reconstruction of the radar observation scene can be modeled as solving the vector σ from equation (19) or (20), where σ is required to satisfy that most of the elements are zero, representing that no significant scattering target exists on the corresponding range-speed unit, i.e., σ is a sparse vector; from the non-zero elements in σ, estimates of the distance, velocity, scattering coefficient of the corresponding target can be inferred.

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: m×n perceptual matrices a=Φψ, n=n _s N _prt An M x 1-dimensional compressed echo y is the echo length in the CPI without compression; initializing: residual r ₀ Support set =yInitial sparsity l=k ₀ The iteration number t=1, the step index n=1.

9. The cyclic iterative echo reconstruction solution distance ambiguity method based on compressed sensing of claim 1, wherein:

in the step S32, an OSAMP reconstruction algorithm obtains a sparse vector estimation of the scattering coefficientAnd a transformation matrix is utilized to obtain a reconstruction signal;

equation (20) is a partial equation with infinite number of solutions, of interest is findingThe sparsest solution, i.e. having l of the sigma vector while satisfying the constraint ₀ Norm minimization; CS theory has demonstrated that under the constraint that the perceptual matrix A satisfies certain conditions, l ₁ Norm minimization problem and l ₀ 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 ,‖‖₁ and ‖‖₂ The 0 norm and the 2 norm of the vector are respectively represented, and E.gtoreq.0 is a parameter determined by the additive noise intensity.

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 ,rⁱ Echo representing the i-th distance segment:

r ⁱ ＝Ψ ⁱ σ ⁱ (24)

wherein σⁱ Scattering coefficient vector, ψ, representing the i-th distance segment ⁱ A transformation matrix representing the i-th distance segment:

Ψ ⁱ i.e. a transformation matrix of the first distance segmentCircularly shifting i-1 pulse repetition periods downwards along the row;

similarly, the original fuzzy echo data r can be compressed through the measurement matrix phi to obtain sub-sampling fuzzy echo data y:

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 N _J The sample length of the actual echo data y for the presence of the dead zone can be expressed as:

wherein diag []For constructing diagonal matrix, J _j Expressed as:

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 a scattering coefficient vector of the first distance segment through an OSAMP algorithmAnd reconstructing the sub-echoesAnd then subtracting the first distance segment from the total echo to reconstruct a sub-echo, and obtaining echo data after the first distance segment is subjected to fuzzy inhibition:

obtaining an estimated value of the scattering coefficient vector of the second distance segment through (30) and an OSAMP reconstruction algorithmAnd reconstruct sub-echo->And analogizing is performed until the fuzzy I distance segment echoes are reconstructed once.

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 process is as follows: for the ith distance segment, the inputs of the reconstruction sub-module are: subtracting the reconstructed sub-echoes of the other distance segments except the ith distance segment from the total echo; obtaining an estimated value of a backscattering coefficient vector of an ith distance segment and a reconstructed sub-echo by using an OSAMP reconstruction sub-module; the I is increased by 1, and when i=i, one iteration reconstruction is completed; and resetting i=1, and repeating the reconstruction of the sub-echoes of each distance segment until the difference between the adjacent two iteration results is smaller than a preset threshold value.

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;

mode 1): when the signal-to-noise ratio is higher and the backward scattering coefficient vector estimation is more accurate, the reconstructed one-dimensional backward scattering coefficient vector is matrixed according to the distance and speed interval division rule of the sensing matrix to obtain two-dimensional distance-Doppler scattering point information, and no side lobe effect of PD processing exists;

mode 2): 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 subjected to combined mismatch filtering treatment, so that the range side lobe modulation effect caused by the change of the modulation form between pulses is improved, and a pulse Doppler result is obtained;

mode 3): when the two-dimensional accumulation is needed, the total echo is used for subtracting the reconstructed sub-echo of the non-own distance section 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.