CN111812644A - MIMO radar imaging method based on sparse estimation - Google Patents

MIMO radar imaging method based on sparse estimation Download PDF

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CN111812644A
CN111812644A CN202010890454.6A CN202010890454A CN111812644A CN 111812644 A CN111812644 A CN 111812644A CN 202010890454 A CN202010890454 A CN 202010890454A CN 111812644 A CN111812644 A CN 111812644A
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CN111812644B (en
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王敏
邓晓云
丁杰如
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Xidian University
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Abstract

The invention discloses a sparse estimation-based MIMO radar imaging method, which solves the problem that imaging precision is influenced when sparsity is unknown and solves the problem of large operation amount in the prior art. The implementation comprises the following steps: establishing an MIMO radar imaging model, and acquiring MIMO radar echo data; preprocessing a measurement matrix phi, uniformly dividing the measurement matrix into a plurality of sub-channels, and prejudging each sub-channel to obtain a preprocessed measurement matrix; and combining a sparsity recovery algorithm SAMP or SBL algorithm to complete MIMO radar imaging based on sparse estimation. The invention preprocesses the measuring matrix, sets the measuring matrix of the sub-channel without signals to zero, and reduces the noise influence. According to the invention, the measurement matrix pretreatment is combined with the SAMP or SBL algorithm, so that the accuracy of sparse recovery is improved, the imaging error is reduced, the operation complexity in the sparse recovery process is reduced, and the operation speed is improved. Simulation and experiment prove that the invention has high imaging precision and low running amount. The method is used for MIMO radar imaging.

Description

MIMO radar imaging method based on sparse estimation
Technical Field
The invention relates to the technical field of radar, mainly relates to MIMO radar imaging, and particularly relates to a MIMO radar imaging method based on sparsity estimation. The method is applied to radar imaging.
Background
The Multiple Input Multiple Output (MIMO) radar of the new radar system has the significant advantages of high resolution and real-time performance in imaging, so research on MIMO radar imaging is also continuously proposed. Han and the like have analyzed the problem of distributed multi-channel radar imaging based on the MIMO regime from the perspective of spatial spectrum sampling. The MIMO radar imaging algorithm is comprehensively researched by people of the Wang Huan Jun, the national defense science and technology university, the classic back projection algorithm, the distance offset algorithm and the like are improved and then applied to MIMO radar imaging, the principle verification is carried out, the fusion imaging processing algorithm is provided, and the problem of the MIMO radar imaging spectrum loss is solved. The classic BP algorithm is most widely applied due to the fact that the classic BP algorithm is not limited by an array form and plane wave approximation does not exist, imaging accuracy is highest, but the defect is that operation amount is large when a depth visual angle scene is imaged, and real-time performance of an imaging system is limited. Iterative adaptive methods (IAA) and iterative minimized Sparse Learning (SLIM) are introduced into MIMO radar imaging due to their advantage of ultra-high resolution in radar imaging. However, the two algorithms are proved to have the defect of large calculation amount, and are not easy to be applied in practice like the time domain imaging algorithm. The high calculation amount becomes a main reason for restricting the development of MIMO radar imaging, and is in the need of solving. Although the existing compressed sensing algorithm, such as a greedy algorithm, has the advantage of low computational complexity, sparsity needs to be taken as a known condition, and the sparsity is difficult to acquire in practice and has poor engineering applicability. When a greedy algorithm is used in practical application, if the sparsity is unknown, imaging accuracy is affected, the greedy algorithm is sensitive to noise, interference on radar imaging is increased, and the problem has certain influence on the MIMO radar imaging effect.
Disclosure of Invention
The invention aims to provide a sparse estimation-based MIMO radar imaging method with higher estimation accuracy aiming at the defects and defects of the prior art, which is characterized by comprising the following steps:
the method comprises the following steps: establishing an MIMO radar imaging model: in a rectangular coordinate system, the origin of coordinates is Q, the MIMO radar imaging center is represented by O points, and the transmitting and receiving array elements are respectively represented as
Figure BDA0002656775940000021
RTx,mAnd RRx,nRespectively showing the distance from the Mth transmitting array element and the Nth receiving array element to the O point,
Figure BDA0002656775940000022
and
Figure BDA0002656775940000023
respectively representing the azimuth angles of the Mth transmitting array element and the Nth receiving array element compared with the imaging center; let the rectangular coordinate of the K-th scattering point of the object be rk＝(xk,yk) The scattering coefficient is denoted as xkThe distances from the Mth transmitting array element and the Nth receiving array element to the k-th scattering point are respectively recorded as
Figure BDA0002656775940000024
And
Figure BDA0002656775940000025
the distance from the antenna array baseline to the MIMO radar imaging center is R0(ii) a Establishing a radar echo model on the basis of the MIMO radar geometric image;
Figure BDA0002656775940000026
where n is noise, y is radar echo,
Figure BDA0002656775940000027
t is the transposition calculation, phi is the radar measurement matrix,
Figure BDA0002656775940000028
m is the total number of transmitting array elements, N is the total number of receiving array elements, and x is a scattering coefficient vector which is also the position of a target;
step two: preprocessing a measurement matrix phi: uniformly partitioning the measurement matrix phi into L subchannels; setting a threshold Th, and comparing the coefficient eta with the initial residual r0Multiplying y by two norms to obtain a threshold Th, and setting the coefficient eta to be (0, 1)](ii) a According toThe threshold value pre-judges each subchannel, if the subchannel residual error is smaller than the threshold value, the measurement matrix of the subchannel is set to zero, and if the subchannel residual error is larger than the threshold value, the measurement matrix of the subchannel is kept unchanged; pre-judging each subchannel according to the pre-judging criterion, and forming a new measurement matrix, namely a pre-treated measurement matrix theta after pre-judging all the subchannels, wherein the pre-treated measurement matrix theta has sparsity;
step three: utilizing the preprocessed measurement matrix theta to complete target estimation, namely, using the MIMO radar imaging model
Figure BDA0002656775940000029
The updating is as follows:
Figure BDA00026567759400000210
as a preprocessed radar imaging model; and according to the radar echo y and the preprocessed measurement matrix theta, calculating by combining a sparsity recovery algorithm SAMP or SBL algorithm to obtain the position x of the estimated target, and finishing MIMO radar imaging based on sparse estimation.
The method solves the problems that the signal reconstruction effect is poor and the imaging accuracy is influenced in the case of unknown sparsity of an Orthogonal Matching Pursuit (OMP) algorithm. Meanwhile, the problem of interference of errors caused by noise to radar imaging in the signal reconstruction process is solved.
Compared with the prior art, the invention has the beneficial effects that:
the accuracy is improved: aiming at the problem that the Orthogonal Matching Pursuit (OMP) algorithm is poor in signal reconstruction effect under the condition that the sparsity is unknown, the SAMP algorithm and the SBL algorithm are introduced, and the SAMP algorithm and the SBL algorithm do not need to take the sparsity as a known condition, so that the signal reconstruction effect is better compared with the OMP algorithm. Therefore, the SAMP algorithm or the SBL algorithm is combined with the channelized measurement matrix to solve the problem of unknown sparsity caused by the OMP algorithm and improve the radar imaging accuracy.
And (3) error reduction: aiming at the problem of errors caused by noise in the sparse reconstruction process of the greedy algorithm, the denoising function is achieved by adding the measurement matrix phi for preprocessing, the accuracy of the reconstructed signal is improved, and the imaging errors are reduced.
The calculation amount is reduced: in the channelized preprocessing process, the observation matrix is preprocessed according to the threshold value, and the subchannel observation matrix without the target is set to be zero, so that the operation amount in the signal recovery process is reduced, and the operation speed is improved.
Description of the drawings:
the invention is described in detail below with reference to the figures and the specific embodiments.
FIG. 1 is a flow chart of the algorithm of the present invention;
FIG. 2 is a MIMO radar imaging geometry, which is also applied in embodiments of the present invention;
FIG. 3 is a graph of the present invention and a prior art sparse recovery algorithm at different SNR, wherein FIG. 3(a) is a minimum mean square error graph and FIG. 3(b) is a target background ratio variation graph;
FIG. 4 is a graph of the present invention under different channel numbers and signal-to-noise ratios, wherein FIG. 4(a) is a minimum mean square error graph and FIG. 4(b) is a graph of variation of target background ratio;
fig. 5 is a graph of the present invention and the prior sparse recovery algorithm under different sparse ratios, wherein fig. 5(a) is a minimum mean square error graph, and fig. 5(b) is a target background ratio variation graph.
The invention is described in detail below with reference to the drawings and examples
Detailed Description
Example 1
Traditional radar imaging algorithms, such as a BP algorithm and a range-doppler imaging algorithm, are all based on Synthetic Aperture Radar (SAR) application, and due to the defects of the algorithms, such as large calculation amount of the algorithms, certain limitations are imposed on practical application. With the proposal and application of a Multiple Input Multiple Output (MIMO) radar of a novel radar system, the traditional radar imaging method is gradually introduced into the MIMO radar imaging and achieves certain effect, but the BP algorithm has the defect of large calculation amount and cannot be changed. The Compressed Sensing (CS) technique has the advantage of small calculation amount, and the signal recovery algorithm is mature, and is gradually introduced into MIMO radar application, but for example, although the greedy algorithm has the advantage of small calculation amount, sparsity needs to be used as a known condition to more accurately recover a signal, and the sparsity is not easy to obtain in practical application, so that the imaging accuracy is affected. In addition, since noise is unavoidable and the greedy algorithm is sensitive to noise, imaging may be affected. The invention develops analysis thinking and research aiming at the condition and provides a MIMO radar imaging method based on sparse estimation.
The invention relates to a MIMO radar imaging method based on sparse estimation, which is shown in figure 1 and comprises the following steps:
the method comprises the following steps: establishing an MIMO radar imaging model: the MIMO radar imaging system is composed of M transmitting array elements and N receiving array elements, wherein the transmitting array elements and the receiving array elements are Uniform Linear Arrays (ULAs), and all sensor elements are omnidirectional. MIMO radar geometry fig. 2, fig. 2 is a MIMO radar imaging geometry.
In a rectangular coordinate system, referring to fig. 2, the coordinate origin is Q, the imaging center of the MIMO radar is represented by O point, and the transmitting and receiving array elements are respectively represented as
Figure BDA0002656775940000051
RTx,mAnd RRx,nRespectively showing the distance from the Mth transmitting array element and the Nth receiving array element to the O point,
Figure BDA0002656775940000052
and
Figure BDA0002656775940000053
respectively representing the azimuth angles of the Mth transmitting array element and the Nth receiving array element compared with the imaging center; let the rectangular coordinate of the K-th scattering point of the object be rk＝(xk,yk) The scattering coefficient is denoted as xkThe distances from the Mth transmitting array element and the Nth receiving array element to the k-th scattering point are respectively recorded as
Figure BDA0002656775940000054
And
Figure BDA0002656775940000055
the distance from the antenna array baseline to the MIMO radar imaging center is R0(ii) a Establishing a radar echo model on the basis of the MIMO radar geometric image;
Figure BDA0002656775940000056
where n is noise, y is radar echo,
Figure BDA0002656775940000057
t is the transposition calculation, phi is the radar measurement matrix,
Figure BDA0002656775940000058
m is the total number of transmitting array elements, N is the total number of receiving array elements, and x is a scattering coefficient vector which is also the position of the target.
Step 1.1, a radar echo model is established, and if M transmitting array elements simultaneously transmit signals, the transmitting signal of the Mth transmitting array element is represented as:
Sm(t)＝pm(t)exp(j2πfct)
wherein p ism(t) is the normalized envelope of the transmitted signal, fcIs the carrier frequency, and the transmitting signal adopts a phase coding orthogonal signal.
Setting the image scene center to have K scattering points, the superposition echoes received from the M transmitting signals to the nth receiving array element through the K scattering points are as follows:
Figure BDA0002656775940000059
wherein tau isn,m(k) The path delay of the whole radiation process from the m-th transmitting array element to the k-th scattering point and then to the n-th receiving array element is shown.
And 1.2, forming a radar imaging model. The radar echo and the transmitting signal are subjected to frequency mixing to remove carrier waves, then the carrier waves are processed by a matched filter bank, channel separation is realized by utilizing the orthogonality of the transmitting signal, and the following results are obtained:
Figure BDA0002656775940000061
to Sn,m(t) performing FFT, wherein the conversion result is as follows:
Figure BDA0002656775940000062
wherein
Figure BDA0002656775940000063
Is the wave number, x (r), of the m × n channels of the radark) Is the reflection coefficient of the k-th scattering point. A MIMO radar imaging model can thus be obtained:
Figure BDA0002656775940000064
wherein n is a noise, and n is a noise,
Figure BDA0002656775940000065
is an observation matrix.
Step two: preprocessing a measurement matrix phi: uniformly partitioning the measurement matrix phi into L subchannels; setting a threshold Th, and comparing the coefficient eta with the initial residual r0The threshold value Th is obtained by multiplying two norms, and the coefficient eta belongs to (0, 1)](ii) a Pre-judging each subchannel according to a threshold value, if the residual error of the subchannel is smaller than the threshold value, setting the measurement matrix of the subchannel to zero, and if the residual error of the subchannel is larger than the threshold value, keeping the measurement matrix of the subchannel unchanged; and pre-judging each subchannel according to the pre-judging criterion, and forming a new measurement matrix, namely the pre-treated measurement matrix theta after pre-judging all the subchannels, wherein the pre-treated measurement matrix theta has sparsity.
Step three: utilizing the preprocessed measurement matrix theta with sparsity to complete target estimation through calculation, namely, using the MIMO radar imaging model
Figure BDA0002656775940000066
The updating is as follows:
Figure BDA0002656775940000067
as a preprocessed radar imaging model; and applying a sparsity recovery algorithm SAMP or SBL algorithm to the preprocessed radar imaging model, and calculating to obtain the position x of an estimated target by combining the sparsity recovery algorithm SAMP or SBL algorithm according to the radar echo y and the preprocessed measurement matrix theta to complete the MIMO radar imaging based on sparse estimation.
With the development of a compressed sensing technology (CS), and because an observation area of the MIMO radar has sparsity, the invention introduces the compressed sensing technology into the MIMO radar imaging processing, utilizes the advantage of small calculated amount of the compressed sensing technology, optimizes the algorithm, and simultaneously completes the MIMO radar imaging by combining a sparse recovery algorithm SAMP or SBL algorithm.
The MIMO radar is a novel radar system introduced into the field of radars at the beginning of the century, so that the imaging direction of the radar is greatly broken through, and a lot of research results are obtained. However, the calculated amount of the imaging processing algorithm is a bottleneck for restricting the rapid imaging in the MIMO radar engineering application, for example, although the Back Projection (BP) algorithm can be applied to the limitation of multiple architecture radars and has the advantages of high imaging accuracy and the like, the BP algorithm has a large amount of calculation in a scene with a large depth of field and a wide viewing angle, cannot meet the real-time requirement, and is limited in practical application. The invention introduces the compressive sensing technology into the MIMO radar imaging application, completes the target estimation by using the sparse recovery algorithm, realizes the MIMO radar imaging, and can effectively solve the problem of large radar imaging calculation amount. And the observation matrix is subjected to channelized pretreatment, so that the influence of noise on radar imaging is reduced, and the imaging precision is improved. The invention uses the SAMP or SBL algorithm to reconstruct the signal, avoids the defect that the OMB algorithm takes the sparsity as the known condition, and reduces the imaging error.
Example 2
The MIMO radar imaging target estimation method based on sparsity estimation, which is generally applied to embodiment 1, wherein the preprocessing of the measurement matrix Φ in the step two specifically includes the following steps:
2.1: and (3) partitioning the radar measurement matrix: uniformly partitioning a radar measurement matrix phi, dividing the measurement matrix phi into L blocks as a whole, wherein each block is a subchannel, the length of each subchannel is D, and expressing the measurement matrix phi after partitioning as follows:
Figure BDA0002656775940000071
wherein phikAnd d, a k-th sub-channel measurement matrix is set, wherein k is 1, 2.
2.2: setting a channel threshold Th: ideally, when the subchannel contains the target component, the calculated subchannel residual is equal to the initial residual. When the subchannel does not contain the target component, the calculated subchannel residual value is less than the initial residual. But noise cannot be avoided, eta is used for controlling the influence of the noise on the initial residual error, the eta value is between 0 and 1, and the experimental result is the best when the eta value is 0.98 through a large number of simulation experiments. According to the radar echo, a threshold Th is set by combining an Orthogonal Matching Pursuit (OMP) algorithm;
Th＝η||r0||2
wherein the coefficient eta ∈ (0, 1)]，r0＝y，r0Is the initial residual. | | r0||2Namely the energy of radar echo, in an ideal state, when a subchannel contains a target, the calculated energy of the subchannel residual error is equal to the energy of the radar echo, but in an actual situation, noise is inevitable, and the method controls the influence of the noise on the radar echo, namely the initial residual error, through eta.
Expressing the threshold judgment as:
||rk||＜Th(k∈{1,2,...,L})
where L is the number of subchannels, rkAnd the residual error of the kth channel is represented by Th, a threshold value is represented, each subchannel is pre-judged through the threshold value, if the residual error of the subchannel is smaller than the threshold value, the measurement matrix of the subchannel is set to be zero, and if the residual error is larger than the threshold value, the measurement matrix of the subchannel is kept unchanged.
2.3: denoising the sub-channels by using a threshold value: applying an Orthogonal Matching Pursuit (OMP) algorithm to each subchannel to achieve a denoising function; the OMP algorithm is iterated once, the most closely related parts in the sub-channels are deleted, whether the sub-channels contain signals or not is roughly estimated, namely, a threshold value is obtained through calculation, each sub-channel residual error is calculated in a cycle, and meanwhile, the sub-channels are pre-judged; if the two-norm of the subchannel residual error is smaller than the threshold, the subchannel residual error indicates that the target is not contained in the subchannel, the measurement matrix of the subchannel is set to zero, namely phi [ k ] is 0, otherwise, if the two-norm of the subchannel residual error is larger than the threshold, the subchannel residual error indicates that the signal is contained in the subchannel, and the subchannel measurement matrix is kept unchanged; through circulation, all the sub-channels are pre-judged to form a new measurement matrix, namely a pre-processed measurement matrix theta, and the pre-processed measurement matrix theta has sparsity; assuming that the ith subchannel packet does not contain any component of the signal, the threshold decision is expressed as:
||ri||2＜η||r0||2
where eta ∈ (0, 1)]，η||r0||2This is the threshold Th.
Because the noise can interfere the MIMO radar imaging, the invention denoises by preprocessing the measurement matrix phi, reduces the noise interference and improves the imaging precision. Meanwhile, in the channelized preprocessing process, the subchannel observation matrix is pre-judged according to the threshold value, and the subchannel observation matrix without the target is set to be zero, so that the operation amount in the signal recovery process is reduced, and the operation speed is improved.
Example 3
The method for estimating the imaging target of the MIMO radar based on sparsity estimation is generally applied to embodiment 1, and the sub-channel is denoised in step 2.3, specifically as follows;
2.3.1: initialization processing: channelizing the measurement matrix, i.e. uniformly blocking the measurement matrix and initializing k to 0, r0＝y。
2.3.2: the cycle starts: when k is equal to L, k is equal to k +1 and the cycle is as follows.
2.3.3: calculating subchannel related parameters Pk:
Figure BDA0002656775940000091
The atom in the subchannel that is most correlated with the initial residual is selected, i.e. the column vector in the subchannel that is most correlated with the initial residual is selected.
2.3.4: calculating subchannel residuals:
Figure BDA0002656775940000092
according to calculated PkCalculating the contribution value of the radar echo and the subchannel residual error rk。
2.3.5: judging a threshold value: if it is not
Figure BDA0002656775940000093
Zeroing the measurement matrix of the subchannel, i.e. Φ k]＝0。
2.3.6: and (4) ending the circulation: and when k is larger than L, ending the circulation, ending the preprocessing of the measurement matrix phi, and obtaining a new measurement matrix theta, namely the preprocessed measurement matrix.
The calculated amount is the main reason for restricting the further development of radar imaging, the basic idea of the compressed sensing technology is to extract information as much as possible from data as little as possible, in addition, an MIMO radar observation matrix has sparsity, and the problem of large calculated amount of algorithm is solved to a certain extent by applying the compressed sensing technology to the MIMO radar imaging. The SAMP algorithm or the SBL algorithm is combined with the channelized measurement matrix, the influence of noise on imaging is solved, the defect that the OMP algorithm takes sparsity as a known condition is overcome, and the radar imaging accuracy is improved.
A more detailed example is given below to further illustrate the invention
Example 4
General embodiments 1-3 of the method for estimating an imaging target of an MIMO radar based on sparsity estimation include the steps of establishing an MIMO radar imaging model, referring to fig. 2, including the steps of:
step 1.1, a radar echo model is established, and if M transmitting array elements simultaneously transmit signals, the transmitting signal of the Mth transmitting array element is represented as:
Sm(t)＝pm(t)exp(j2πfct)
wherein p ism(t) is the normalized envelope of the transmitted signal, fcIs the carrier frequency, and employs phase-encoded quadrature signals.
Setting the image scene center to have K scattering points, the superposition echoes received from the M transmitting signals to the nth receiving array element through the K scattering points are as follows:
Figure BDA0002656775940000101
wherein tau isn,m(k) The path delay of the whole radiation process from the m-th transmitting array element to the k-th scattering point and then to the n-th receiving array element is shown.
And 1.2, forming a radar imaging model. The radar echo and the transmitting signal are subjected to frequency mixing to remove carrier waves, then the carrier waves are processed by a matched filter bank, channel separation is realized by utilizing the orthogonality of the transmitting signal, and the following results are obtained:
Figure BDA0002656775940000102
to Sn,m(t) performing FFT, wherein the conversion result is as follows:
Figure BDA0002656775940000103
wherein
Figure BDA0002656775940000111
Is the wave number, x (r), of the m × n channels of the radark) Is the reflection coefficient of the k-th scattering point. A MIMO radar imaging model can thus be obtained:
Figure BDA0002656775940000112
wherein n is a noise, and n is a noise,
Figure BDA0002656775940000113
the matrix is observed for the channel.
Step two, observation matrix preprocessing comprises the following steps:
2.1: and (3) partitioning the radar measurement matrix: uniformly partitioning a radar measurement matrix phi, dividing the measurement matrix phi into L blocks as a whole, wherein each block is a subchannel, the length of each subchannel is D, and expressing the measurement matrix phi after partitioning as follows:
Figure BDA0002656775940000114
wherein phikMeasuring a matrix for a kth subchannel, k being 1, 2.., L;
2.2: setting a channel threshold Th: setting a threshold Th according to radar echo by combining an Orthogonal Matching Pursuit (OMP) algorithm;
Th＝η||r0||2
wherein the coefficient eta ∈ (0, 1)]，r0Y is the initial residual.
Expressing the threshold judgment as:
||rk||＜Th(k∈{1,2,...,L})
where L is the number of subchannels, rkAnd the residual error of the kth channel is represented by Th, a threshold value is represented, each subchannel is pre-judged through the threshold value, if the residual error of the subchannel is smaller than the threshold value, the measurement matrix of the subchannel is set to be zero, and if the residual error is larger than the threshold value, the measurement matrix of the subchannel is kept unchanged.
2.3: denoising the sub-channels by using a threshold value: applying an Orthogonal Matching Pursuit (OMP) algorithm to each subchannel to achieve a denoising function; and the OMP algorithm is iterated once, the part with the closest correlation in the sub-channels is deleted, and whether the sub-channels contain signals or not is judged by utilizing a threshold value. Assuming that the ith subchannel does not contain a signal, the threshold decision is expressed as:
||ri||2＜η||r0||2where eta ∈ (0, 1)]，η||r0||2Is a threshold value.
If the two-norm of the subchannel residual error is smaller than the threshold, the subchannel residual error indicates that the target is not contained in the subchannel, the measurement matrix of the subchannel is set to zero, namely phi [ k ] is 0, otherwise, if the two-norm of the subchannel residual error is larger than the threshold, the subchannel residual error indicates that the signal is contained in the subchannel, and the subchannel measurement matrix is kept unchanged; through circulation, all the sub-channels are pre-judged to form a new measurement matrix, namely a pre-processed measurement matrix theta, and the pre-processed measurement matrix theta has sparsity; the specific algorithm flow is shown in table 1:
TABLE 1 measurement matrix phi preprocessing procedure
Figure BDA0002656775940000121
Step three: utilizing the preprocessed measurement matrix with sparsity to complete target estimation through calculation, namely, using the MIMO radar imaging model
Figure BDA0002656775940000131
The updating is as follows:
Figure BDA0002656775940000132
as a preprocessed radar imaging model; and applying a sparsity recovery algorithm SAMP or SBL algorithm to the preprocessed radar imaging model, and calculating to obtain the position x of an estimated target by combining the sparsity recovery algorithm SAMP or SBL algorithm according to the radar echo y and the preprocessed measurement matrix theta to complete the MIMO radar imaging based on sparse estimation. The specific flow of the SAMP algorithm is shown in Table 2:
TABLE 2 SAMP Algorithm flow
Figure BDA0002656775940000133
The specific flow of the SAMP algorithm can also be used for signal reconstruction by using a sparse recovery algorithm SBL to complete target estimation and realize MIMO radar imaging.
The MIMO radar imaging method based on sparse estimation is mainly used for solving the problems that the signal reconstruction effect is poor and the imaging accuracy is influenced in the case that the sparsity of an Orthogonal Matching Pursuit (OMP) algorithm is unknown, and the radar imaging is interfered by errors caused by noise in the signal reconstruction process. The invention mainly comprises three parts: establishing an MIMO radar imaging model: and acquiring the MIMO radar echo data. Preprocessing a measurement matrix phi to obtain a preprocessed measurement matrix: the radar measurement matrix is processed in a blocking mode and is divided into a plurality of sub-channels; and setting a threshold value to prejudge each subchannel, and setting a subchannel measurement matrix without signals to zero to avoid the occurrence of artifact targets. And finishing target estimation by utilizing the preprocessed measurement matrix with sparsity. And updating the MIMO radar imaging model according to the preprocessed measurement matrix, calculating to obtain the position x of the estimated target by combining a sparsity recovery algorithm SAMP or SBL algorithm, and finishing the MIMO radar imaging based on sparse estimation.
And finally, verifying the MIMO radar imaging method based on sparse signal reconstruction by using a simulation experiment result. Experiments show that the performance of the algorithm is superior to that of an OMP algorithm, an SAMP algorithm and an SBL algorithm.
The technical effects of the present invention will be explained below by simulation experiments and data
Example 5
The MIMO radar imaging method based on sparse estimation is the same as embodiments 1-4,
simulation one:
simulation conditions and contents: the radar system parameters are: radar operating frequency of FcThe operating bandwidth is 50MHz at 12 GHz. The number of target K is 25, and the number of receiving antennas and the number of transmitting antennas are N respectivelyr,MtAll are initialized to 4, the dimensions M of the measurement matrix are 1600 and 7200, N is 1600 and 7200, and the number of selected subchannels is L900, i.e. a matrix of 1600 × 8 subchannels each. Under the condition of different signal-to-noise ratios, minimum mean square error and target background ratio change curves corresponding to an SBL algorithm, an OMP algorithm, an SAMP algorithm, a channelized adaptive matching pursuit (CDN-SAMP) algorithm and an access sparse Bayes (CDN-SBL) algorithm are calculated, and simulation results are shown in FIG. 3.
Simulation result and analysis: fig. 3 is a graph of the present invention and a prior sparse recovery algorithm at different signal-to-noise ratios, wherein fig. 3(a) is a minimum mean square error graph, and fig. 3(b) is a target background ratio variation graph. The existing sparse recovery algorithm is OMP algorithm, SAMP algorithm and SBL algorithm, and the algorithm provided by the invention in the embodiment is channelized adaptive matching pursuit (CDN-SAMP) algorithm and accessibility sparse Bayes (CDN-SBL).
Fig. 3(a) is a plot of minimum mean square error at different signal-to-noise ratios, SNR on the abscissa and minimum mean square error on the ordinate. The red dotted circle line represents the minimum mean square error curve under different signal-to-noise ratios corresponding to different signal-to-noise ratios of the sparse Bayesian algorithm, the blue dotted cross line represents the minimum mean square error curve under different signal-to-noise ratios corresponding to the channelized sparse Bayesian algorithm, the green solid square line represents the minimum mean square error curve under different signal-to-noise ratios corresponding to the adaptive matching tracking algorithm, the black dotted triangle line represents the minimum mean square error curve under different signal-to-noise ratios corresponding to the channelized adaptive matching tracking algorithm, and the purple solid diamond line represents the minimum mean square error curve under different signal-to-noise ratios corresponding to the orthogonal matching tracking algorithm. Fig. 3(b) is a variation curve of the target background ratio under different signal-to-noise ratios, wherein the abscissa is the SNR and the ordinate is the target background ratio. The red dotted circle line represents a target background ratio change curve under different signal-to-noise ratios corresponding to different signal-to-noise ratios of the sparse Bayesian algorithm, the blue cross-hatched line represents a target background ratio change curve under different signal-to-noise ratios corresponding to the channelized sparse Bayesian algorithm, the green square solid line represents a target background ratio change curve under different signal-to-noise ratios corresponding to the adaptive matching tracking algorithm, the black triangular dotted line represents a target background ratio change curve under different signal-to-noise ratios corresponding to the channelized adaptive matching tracking, and the purple diamond solid line represents a target background ratio change curve under different signal-to-noise ratios corresponding to the orthogonal matching tracking algorithm.
It can be seen from fig. 3(a) comparing five curves that the minimum mean square errors of the five algorithms are all reduced as the signal-to-noise ratio is increased, which indicates that the signal-to-noise ratio is increased to reduce the estimation error, and at the same time, it can be seen that the minimum mean square errors of the channelized adaptive matching tracking algorithm (CDN-SAMP) and the channelized sparse bayes algorithm (CDN-SBL) provided by the present invention are smaller than those of the other three algorithms under different signal-to-noise ratios, which indicates that the CDN-SAMP and CDN-SBL algorithms provided by the present invention reduce the sparse recovery error.
As can be seen from the five curve-to-curve ratios in fig. 3(b), as the signal-to-noise ratio increases, the target background ratios of the five algorithms are increased, and meanwhile, the target background ratios of the SDN-SAMP and the CDN-SBL algorithms provided by the present invention are higher than those of the other three algorithms under the condition of different signal-to-noise ratios, which shows that the CDN-SAMP and the CDN-SBL algorithms provided by the present invention improve the sparse recovery accuracy. In summary, as can be obtained from fig. 3(a) and (b), under the same signal-to-noise ratio condition, the sparse reconstruction precision of the CDN-SAMP and CDN-SBL algorithms provided by the present invention is higher than that of other sparse recovery algorithms, so that the target estimation accuracy is improved, and the imaging error is reduced.
Example 6
The MIMO radar imaging method based on sparse estimation is the same as embodiments 1-4,
simulation II:
simulation conditions and contents: the radar system parameters, the number of targets, the number of receiving antennas and the number of reflecting antennas are the same as those in embodiment 5, the dimensions M and N of the measurement matrix are 1600 and 7200 respectively, and the number L of the selected subchannels is 400 and 900 respectively.
And calculating a minimum mean square error and target background ratio change curve chart corresponding to the CDN-SAMP algorithm, the CDN-SBL algorithm, the SBL algorithm and the SAMP algorithm under the condition of different signal-to-noise ratios and different subchannel numbers L, wherein the simulation result is shown in figure 4.
Simulation result and analysis: FIG. 4 is a graph of the present invention under different channel numbers and signal-to-noise ratios, wherein FIG. 4(a) is a minimum mean square error graph and FIG. 4(b) is a target background ratio variation graph.
Fig. 4(a) shows the minimum mean square error of different channel numbers under different signal-to-noise ratios, the abscissa shows the SNR, the ordinate shows the minimum mean square error, the black diamond solid line represents the minimum mean square error curve of the channelized adaptive matching tracking algorithm under different signal-to-noise ratios when the channel number is 400, the blue triangle dotted line represents the minimum mean square error curve of the channelized sparse bayesian algorithm under different signal-to-noise ratios when the channel number is 400, the red cross dotted line represents the minimum mean square error curve of the channelized adaptive matching tracking algorithm under different signal-to-noise ratios when the channel number is 900, and the green square dotted line represents the minimum mean square error curve of the channelized sparse bayesian algorithm under different signal-to-noise ratios when the channel number is 900. Fig. 4(b) is a target background ratio curve of different channel numbers under different signal-to-noise ratios, the abscissa is SNR, the ordinate is minimum mean square error, the black diamond solid line represents the target background ratio curve of the channelized adaptive matching tracking algorithm under different signal-to-noise ratios when the channel number is 400, the blue triangle dotted line represents the target background ratio curve of the channelized sparse bayes algorithm under different signal-to-noise ratios when the channel number is 400, the red cross dotted line represents the target background ratio curve of the channelized adaptive matching tracking algorithm under different signal-to-noise ratios when the channel number is 900, and the green square dotted line represents the target background ratio curve of the channelized sparse bayes algorithm under different signal-to-noise ratios when the channel number is 900.
As can be seen from comparison of the four curves in fig. 4(a), in the case that the number of channels is 400 and 900 respectively under different signal-to-noise ratios, the minimum error of the CDN-SAMP and CDN-SBL algorithms is higher when the number of channels is 400 than when the number of channels is 900, which indicates that increasing the number of channels in the technical solution of the present invention can reduce the sparse recovery error and improve the imaging accuracy.
As can be seen from fig. 4(b), under different signal-to-noise ratios and with the number of channels being 400 and 900 respectively, the target background ratio of the CDN-SAMP and CDN-SBL algorithms is lower when the number of channels is 400 than when the number of channels is 900, which indicates that increasing the number of channels can increase the target background ratio and improve the accuracy of the sparse recovery algorithm.
In summary, as can be obtained from fig. 4(a) and (b), under the same other experimental conditions, the minimum mean square error of the CDN-SAMP and the CDN-SBL is smaller and the target background is higher under the condition that the number of channels is larger, which indicates that the number of channels has an influence on the performance of the sparse reconstruction algorithm, that is, under the same conditions, the number of sparse channels is more, and the precision of sparse recovery is correspondingly improved.
Example 7
The MIMO radar imaging method based on sparse estimation is the same as embodiments 1-4,
and (3) simulation:
simulation conditions and contents: the radar system parameters, the number of targets, the number of receiving antennas and the number of reflecting antennas were the same as in example 5. The dimension M × N of the measurement matrix, k equals M/N, i.e. the number of columns N of the measurement matrix equals 1600 and the number of rows M equals N × k, where k varies from 0.1 to 1. The number of subchannels L is 400. Under different sparsity ratios k, the minimum mean square error and the target background ratio effect graphs corresponding to the SBL algorithm, the SAMP algorithm, the CDN-SAMP algorithm and the CDN-SBL algorithm, and the simulation result is shown in FIG. 5.
Simulation result and analysis: fig. 5 is a graph of the present invention and the prior sparse recovery algorithm under different sparse ratios, wherein fig. 5(a) is a minimum mean square error graph, and fig. 5(b) is a target background ratio variation graph. The existing sparse recovery algorithm is an OMP algorithm, an SAMP algorithm and an SBL algorithm, and the algorithm provided by the invention in the embodiment is a channelized adaptive matching pursuit (CDN-SAMP) algorithm and a reach sparse Bayes (CDN-SBL) algorithm, and has five curves.
Fig. 5(a) is a minimum mean square error curve under different sparsity ratios, with the abscissa being the sparsity ratio and the ordinate being the mean square error. The red circle solid line represents the minimum mean square error curve corresponding to the sparse Bayes algorithm under different sparse ratios, the blue square dotted line represents the minimum mean square error curve corresponding to the channelized sparse Bayes algorithm under different sparse ratios, the black triangle dotted line represents the minimum mean square error curve corresponding to the channelized adaptive matching tracking algorithm under different sparse ratios, the purple diamond dotted line represents the minimum mean square error curve corresponding to the adaptive matching tracking under different sparse ratios, and the green triangle solid line represents the minimum mean square error curve corresponding to the orthogonal matching tracking algorithm under different sparse ratios. Fig. 3(b) is a graph of the target background ratio under different sparsity ratios, with the abscissa being the sparsity ratio and the ordinate being the target background ratio. The solid red circles represent target background curves corresponding to the sparse Bayesian algorithm under different sparse ratios, the dashed blue squares represent target background curves corresponding to the channelized sparse Bayesian algorithm under different sparse ratios, the dashed black triangles represent target background curves corresponding to the channelized adaptive matching tracking algorithm under different sparse ratios, the dashed purple diamonds represent target background curves corresponding to the adaptive matching tracking under different sparse ratios, and the solid green triangles represent target background curves corresponding to the orthogonal matching tracking algorithm under different sparse ratios.
It can be seen from fig. 5(a) that the minimum mean square errors of the five sparse recovery algorithms are all reduced as the sparsity ratio k increases, which indicates that the sparsity ratio increases, that is, the data amount increases, and the error of sparse recovery can be reduced, and when the sparsity ratio is greater than 0.2, the estimation errors of the CDN-SAMP and the CDN-SBL are smaller than those of the other three recovery algorithms, which indicates that the required sparsity of the CDN-SAMP and the CDN-SBL is smaller, that is, the required data amount is smaller, the operation amount is correspondingly reduced, and the CDN-SAMP algorithm and the CDN-SBL algorithm have the advantage of reducing the operation amount.
As can be seen from the five curve-to-curve ratios in fig. 5(b), as the sparsity ratio increases, the target background ratios of the five algorithms are increased, which means that the sparsity ratio increases, that is, the data amount increases, and the error of sparse recovery can be reduced, and meanwhile, when the sparsity ratio is greater than 0.2, the target background ratios of the CDN-SAMP and the CDN-SBL are greater than those of the other three recovery algorithms, which means that the same recovery accuracy is to be achieved, the required sparsity of the CDN-SAMP and the CDN-SBL algorithms proposed by the present invention is smaller, that is, the required data amount is smaller, and the calculation amount is smaller.
As shown by comparing fig. 5(a) and (b), under the same condition, in order to achieve the same sparse recovery accuracy, the data size required by the CDN-SAMP and CDN-SBL algorithms provided by the present invention is smaller than that of other recovery algorithms, that is, the present invention has the advantages of reducing the data size and increasing the operation speed.
The invention relates to a MIMO radar imaging method based on compressed sensing. The method mainly solves some problems brought by reconstructing a coefficient scene of a target by using an OMP algorithm. These problems mainly include: the sparsity of the imaged scene is unknown; and (3) an artifact target brought by OMP algorithm reconstruction. These deficiencies will seriously affect the imaging performance. The invention first presets a threshold, then carries on prejudgement to each sub-channel, and sets zero to the sub-channel without signal. This makes it possible to possibly ghost the appearance of objects in these location areas. Performing sparse reconstruction on the measurement matrix and observation matrix after channelization, and performing adaptive sparse reconstruction; the selected sparse reconstruction algorithms are respectively as follows: adaptive Matching Pursuit (SAMP) and Sparse Bayesian Learning (SBL). And finally, verifying the channelized denoising self-adaptive sparse reconstruction algorithm provided by the text by using simulation data. Experiments show that the performance is superior to that of an OMP algorithm, an SAMP algorithm and an SBL algorithm.
In short, the MIMO radar imaging method based on sparse estimation disclosed by the invention avoids the defects of poor imaging effect under the condition of unknown sparsity by using an OMB algorithm in the prior art and the problem of interference of noise to radar imaging in the signal reconstruction process. The implementation comprises the following steps: establishing an MIMO radar imaging model, and acquiring MIMO radar echo data; preprocessing a measurement matrix phi, uniformly dividing the measurement matrix into a plurality of sub-channels, and prejudging each sub-channel to obtain a preprocessed measurement matrix; and combining a sparsity recovery algorithm SAMP or SBL algorithm to complete MIMO radar imaging based on sparse estimation. The method preprocesses the measurement matrix, sets the subchannel measurement matrix without signals to zero, and reduces the noise influence; the preprocessing of the measurement matrix is combined with the SAMP or SBL algorithm, so that the accuracy of sparse recovery is improved, and the imaging error is effectively reduced; meanwhile, as the measurement matrix is preprocessed, part of the subchannel measurement matrix is set to be zero, so that the operation complexity is reduced in the sparse recovery process, and the operation speed is increased. Simulation and experiment prove that the invention has high imaging precision and low running amount. The method is used for MIMO radar imaging.

Claims (3)

1. A MIMO radar imaging method based on sparse estimation is characterized by comprising the following steps:
the method comprises the following steps: establishing an MIMO radar imaging model: in a rectangular coordinate system, the origin of coordinates is Q, the MIMO radar imaging center is represented by O points, and the transmitting and receiving array elements are respectively represented as
Figure FDA0002656775930000011
RTx,mAnd RRx,nRespectively showing the distance from the Mth transmitting array element and the Nth receiving array element to the O point,
Figure FDA0002656775930000012
and
Figure FDA0002656775930000013
respectively representThe azimuth angles of the Mth transmitting array element and the Nth receiving array element compared with the imaging center; let the rectangular coordinate of the K-th scattering point of the object be rk＝(xk,yk) The scattering coefficient is denoted as xkThe distances from the Mth transmitting array element and the Nth receiving array element to the k-th scattering point are respectively recorded as
Figure FDA0002656775930000014
And
Figure FDA0002656775930000015
the distance from the antenna array baseline to the MIMO radar imaging center is R0(ii) a Establishing a radar echo model on the basis of the MIMO radar geometric image;
Figure FDA0002656775930000016
where n is noise, y is radar echo,
Figure FDA0002656775930000017
t is the transposition calculation, phi is the radar measurement matrix,
Figure FDA0002656775930000018
m is the total number of transmitting array elements, N is the total number of receiving array elements, and x is a scattering coefficient vector which is also the position of a target;
step two: preprocessing a measurement matrix phi: uniformly partitioning the measurement matrix phi into L subchannels; setting a threshold Th, and comparing the coefficient eta with the initial residual r0The threshold value Th is obtained by multiplying two norms, and the coefficient eta belongs to (0, 1)](ii) a Calculating a subchannel residual error, prejudging each subchannel according to a threshold value, if the subchannel residual error is smaller than the threshold value, setting the measurement matrix of the subchannel to zero, and if the subchannel residual error is larger than the threshold value, keeping the measurement matrix of the subchannel unchanged; pre-judging each sub-channel according to the pre-judging criterion, and pre-judging all the sub-channels to form a new measurement matrix, namely a pre-processed measurement matrix theta, wherein the pre-processed measurement matrix theta hasSparsity;
step three: the preprocessed measurement matrix with sparsity is utilized to complete target estimation, namely, the MIMO radar imaging model is imaged according to the preprocessed measurement matrix
Figure FDA0002656775930000019
The updating is as follows:
Figure FDA00026567759300000110
as a preprocessed radar imaging model; and according to the radar echo y and the preprocessed measurement matrix theta, calculating by combining a sparsity recovery algorithm SAMP or SBL algorithm to obtain the position x of the estimated target, and finishing MIMO radar imaging based on sparse estimation.
2. The MIMO radar imaging method based on sparse estimation according to claim 1, wherein the preprocessing the measurement matrix Φ in the step two specifically comprises the following steps:
2.1: and (3) partitioning the radar measurement matrix: uniformly partitioning a radar measurement matrix phi, dividing the measurement matrix phi into L blocks as a whole, wherein each block is a subchannel, the length of each subchannel is D, and expressing the measurement matrix phi after partitioning as follows:
Figure FDA0002656775930000021
wherein phikMeasuring a matrix for a kth subchannel, k being 1, 2.., L;
2.2: setting a channel threshold Th: setting a threshold Th according to radar echo by combining an Orthogonal Matching Pursuit (OMP) algorithm;
Th＝η||r0||2
wherein the coefficient eta ∈ (0, 1)]，r0Y is the initial residual. Expressing the threshold judgment as:
||rk||＜Th(k∈{1,2,...,L})
where L is the number of subchannels, rkIs the residual error of the k channel;
2.3: denoising the sub-channels by using a threshold value: applying an Orthogonal Matching Pursuit (OMP) algorithm to each subchannel to achieve a denoising function; the OMP algorithm is iterated once, the most closely related parts in the subchannels are deleted, whether the subchannels contain signals or not is roughly estimated, namely, a threshold value is obtained through calculation, a residual error is updated in a loop, and meanwhile, the subchannels are pre-judged; if the channel residual is smaller than the threshold, setting the measurement matrix of the subchannel to zero, namely phi [ k ] is 0, and if the subchannel residual is larger than the threshold, keeping the measurement matrix of the subchannel unchanged; pre-judging all the sub-channels to form a new measurement matrix, namely a pre-processed measurement matrix theta, wherein the pre-processed measurement matrix theta has sparsity;
3. the sparsity estimation-based MIMO radar imaging target estimation method of claim 2, wherein said denoising processing is performed on the sub-channels in step 2.3, as described in detail below;
2.3.1: initialization processing: channelizing the measurement matrix, i.e. uniformly dividing the measurement matrix into L blocks and initializing k to 0, r0＝y；
2.3.2: the cycle starts: when k is less than or equal to L, k is k +1, and the following circulation is carried out;
2.3.3: calculating subchannel related parameters Pk:
Figure FDA0002656775930000031
2.3.4: calculating subchannel residuals: according to calculated PkCalculating the subchannel residual rk，
Figure FDA0002656775930000032
2.3.5: judging a threshold value: if it is not
Figure FDA0002656775930000033
Zeroing the measurement matrix of the subchannel, i.e. Φ k]＝0；
2.3.6: and (4) ending the circulation: and when k is larger than L, ending the circulation, ending the pretreatment of the measurement matrix phi, and obtaining the pretreated measurement matrix theta.
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