CN114063071B - Compressed sensing vortex imaging method based on mode selection, storage medium and application - Google Patents
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Abstract
The invention belongs to the technical field of radar imaging, and discloses a compressed sensing vortex imaging method based on mode selection, a storage medium and application thereof, wherein the phase excitation mode of a uniform circular array is adjusted so that vortex waves of different modes have the same beam direction, and thus a target can be irradiated by all vortex beams; performing correlation operation on a two-dimensional imaging result obtained based on Fourier transformation and a two-dimensional imaging result (a randomly selected modal sequence) obtained by a compressed sensing algorithm, and optimizing the modal sequence through a genetic algorithm to obtain an optimized two-dimensional imaging result; the first-order term coefficient can be obtained through fitting the change curve of the azimuth angle of the target, so that the y-axis information corresponding to the target is obtained, and finally, the three-dimensional imaging of the target is realized. The invention considers the influence of field intensity change after the vortex wave of different modes turns on the imaging effect, and combines compressive sensing and genetic algorithm at the same time, thereby effectively reducing the requirements of vortex imaging on the mode quantity.
Description
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to a compressed sensing vortex imaging method based on mode selection, a storage medium and application.
Background
At present, compared with the light imaging technology, the radar imaging technology has the capability of overcoming the influence of natural conditions such as atmospheric disturbance, cloud and fog and the like to continue imaging, and is an information acquisition means capable of playing a role in all-time and all-weather conditions. Compared with the traditional plane wave Radar which only has difference in distance and cannot provide azimuth resolution under the staring observation geometric condition, the vortex electromagnetic Radar has the phase difference in the distance direction and the azimuth direction at the same time because of transmitting vortex electromagnetic waves with spiral phase wave fronts because of carrying orbital angular momentum (Orbital Angular Momentum, OAM), and the two-dimensional imaging of the distance direction and the azimuth direction of a target can be realized by utilizing the phase difference, and a novel imaging mode can be provided by combining the technology of synthetic Aperture (SYNTHETIC APERTURE RADAR, SAR)/inverse synthetic Aperture (INVERSE SYNTHETIC Aperture Radar).
The azimuth resolution of vortex electromagnetic imaging based on traditional imaging algorithms such as fast Fourier transform (Fast Fourier Transform, FFT) is related to the range of the used orbital angular momentum mode l, the more the number of modes is adopted, the higher the azimuth resolution is, otherwise, the higher side lobe or even aliasing can be generated on the target azimuth image contour, and in order to reduce the requirement on the OAM mode range during azimuth imaging, sparse recovery methods such as sparse Bayesian learning (Sparse Bayesian Learning,SBL)"Liu K,Li X,Gao Y,et al.High-resolution electromagnetic vortex imaging based on sparse Bayesian learning[J].IEEE Sensors Journal,2017,17(21):6918-6927."、 orthogonal matching pursuit (Orthogonal Matching Pursuit,OMP)"Guo S,He Z,Chen R.High resolution 2-D electromagnetic vortex imaging using uniform circular arrays[J].IEEE Access,2019,7:132430-132437." are researched. However, the effect of vortex wave field intensity and mode selection on imaging effect is not considered in the current research on compressed sensing (compressed sensing, CS) vortex imaging, and due to the fact that main lobe directions of different modes are different, the main lobe directions of different modes cannot be irradiated by all mode main lobes for a remote target, which will affect information acquisition and imaging, documents "Yuan T,Cheng Y,Wang H,et al.Beam steering for electromagnetic vortex imaging using uniform circular arrays[J].IEEE Antennas and Wireless Propagation Letters,2016,16:704-707." and "Yuan T,Wang H,Qin Y,et al.Electromagnetic vortex imaging using uniform concentric circular arrays[J].IEEE Antennas and Wireless Propagation Letters,2015,15:1024-1027." propose vortex beam main lobe steering technology to enable the target to be irradiated by vortex waves of different modes, but due to the fact that residual errors exist after main lobe steering, and the residual errors of different modes are different, imaging results obtained by different mode sequences in vortex electromagnetic wave CS imaging are different. Therefore, further investigation is required to select a modality sequence to ensure the compression imaging effect when considering the influence of the vortex field intensity.
Through the above analysis, the problems and defects existing in the prior art are as follows: because field intensity difference exists after the different-mode vortex waves are subjected to beam control steering, the influence on imaging quality by using different-mode sequences after the beam steering is not considered in the current vortex imaging compression sensing algorithm.
The difficulty of solving the problems and the defects is as follows: and combining compressed sensing with a genetic algorithm, and establishing a genetic algorithm model suitable for modal sequence change and selection.
The meaning of solving the problems and the defects is as follows: on the basis of considering the beam directions of vortex waves of different modes, the method capable of selecting the optimal mode sequence is provided, so that the number of modes required by imaging is reduced, and the imaging quality is improved.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a compressed sensing vortex imaging method based on mode selection, a storage medium and application.
The invention is realized in such a way that a compressed sensing vortex imaging method based on mode selection comprises the following steps:
Step one, an imaging model is established, so that a radar is positioned at an origin O (0, 0) of a coordinate system O-xyz, an x-axis represents an azimuth direction, and a y-axis represents a distance direction; the uniform annular array for generating vortex electromagnetic waves consists of N array elements, and the center of the uniform annular array is positioned at an origin O; (the imaging model established in this step is the basis for theoretical derivation in the overall scheme)
Secondly, the target consists of a plurality of scattering points, and moves positively along the x-axis at a speed v on a plane with a height H from the radar; the linear frequency modulation signals are used for bearing orbital angular momentum, and the phase excitation mode of the uniform circular columns is adjusted so that vortex waves of different modes have the same beam direction, and therefore the target can be irradiated by all vortex beams; (in this step, the vortex waves of different modes are subjected to beam control, and the premise of performing compressed sensing and genetic algorithm optimization on the echo is that follows
Performing correlation operation on the two-dimensional imaging result obtained based on Fourier transformation and the two-dimensional imaging result (randomly selecting a modal sequence) obtained by a compressed sensing algorithm, and optimizing the modal sequence through a genetic algorithm to obtain an optimized two-dimensional imaging result; (this step is the core of the solution, reducing the imaging modality number requirements by compressed sensing, and optimizing imaging quality using genetic algorithms)
And step four, according to the optimized two-dimensional imaging result, a first-order term coefficient can be obtained through fitting a change curve of the azimuth angle of the target, so that y-axis information corresponding to the target is obtained, and finally, three-dimensional imaging of the target is realized (the step is perfection of the last part of the scheme, final one-dimensional information of the target is obtained through analysis of the azimuth angle curve, and three-dimensional information reconstruction of the target is realized).
Further, in the second step, the target is composed of a plurality of scattering points, and the specific process of moving along the x-axis forward direction at the speed v in the plane with the height H of the radar is as follows:
Assuming that the equivalent phase center of the target is O ', the relative coordinate system in which the target is located is O' -x 'y' z 'and the pointing direction coincides with the radar coordinate system O-xyz, the ideal scattering point being denoted in the relative coordinate system as a' T(x'T,y'T,z'T) T e1, 2, M, which can be denoted in the coordinate system O-xyz as a T(xT,yT,zT), and For the distance of the connecting line between the radar and the scattering point, the two satisfy the following relationship:
the chirp signal is used to carry orbital angular momentum and the transmitted signal is expressed as:
Wherein T p and K represent the pulse width of the signal and the frequency modulation rate of the LFM, T m and Respectively representing a slow time domain and a fast time domain, f c is the center frequency of the signal, l is an OAM mode value, Φ n =2n/N, n=0, 1,2 …, N-1 represents the phase of the nth array element, and ψ n＝lφn is the phase excitation corresponding to each array element; turning the main lobe of the vortex electromagnetic wave under different modal values, wherein the excitation phase of each array element needs to be changed into:
Ψn＝lφn+kasinθ0cosφn；
Wherein the method comprises the steps of The wave number, a, is the radius of the array, and θ 0 is the deflection angle compared to the primary lobe direction of the vortex wave.
Further, since the relationship between the vortex wave main lobe orientation and the mode satisfies the following formula:
thus θ 0＝θT-θmax, where θ T is the direction to which it is desired to turn; from the above analysis, the corresponding intensity function can be expressed as:
Wherein ζ= kasin θ, ζ 0＝kasinθ0, and when the deflection angle θ 0 =0, the above formula can be expressed as a bessel function J l (kasin θ); when the deflection angle is smaller, the phase of the vortex electromagnetic wave still accords with the spiral distribution, and the target azimuth angle The dual relationship with the OAM mode may be considered as unchanged.
Further, in the third step, the specific distance compression process is as follows:
assuming that the target consists of M scattering points and the array is in MIMO mode, the received echoes within one pulse can be expressed as:
Where τ T＝2rT/c is the echo delay for each scattering point, Azimuth angle of scattering point at slow time t m; assuming that the distance from the radar to the target equivalent phase center O' is r ref, the intermediate frequency echo signal after the demodulation frequency processing is:
Wherein the method comprises the steps of Is the time referenced to the phase center O', τ ΔT＝τT-τref is the relative echo delay in one pulse and τ ref＝2rref/c; compensating the residual video phase term and the diagonal term in the above method, and then carrying out fast time domain/>Fourier variations can yield one-dimensional range profiles:
Further, the sparse representation model of the radar echo signal in the azimuth angle domain simplifies the echo signal as follows:
Wherein l k (k=1, 2,., K) is the corresponding modality number, α T＝sinc[TP(f+KτΔT)]·exp(-j2πfcτΔT); assuming that the region where the target is located is divided into N discrete grids, N > M and Will be a sampling grid of the azimuth angles at which all targets are likely to be located, expressed in vector form as follows:
S＝Pα；
The vector S is an echo received under different modal values, and the vector P and the vector α are respectively represented as follows:
P＝[p1,p2,···,pN]
according to the compressed sensing theory, the reconstruction vector alpha is a convex optimization problem, and the following convex problem is solved by solving:
Wherein |· | 2 represents Norm, Φ represents the measurement matrix.
In the third step, the modal sequence is optimized through a genetic algorithm, and the specific process of obtaining the optimized two-dimensional imaging result is as follows:
Designing each parameter of the genetic algorithm, and selecting a relatively optimal modal sequence; assuming that the maximum and minimum modes of the total mode sequence L ord are L m and-L m respectively, the mode stepping value is 1, and the total mode number is K=2l m +1; the measurement matrix phi is regarded as population individuals in a genetic algorithm to complete the processes of selection, crossing and mutation, the dimension of phi is related to the total mode number and the required mode sequence length, and the dimension of phi is m multiplied by K on the assumption that the mode sequence length is m; in order for the modalities in the modality sequence to be uniquely non-repetitive, the measurement matrix Φ must satisfy the condition of rank m, namely:
r(Φ)＝m；
At this time, the measurement matrix Φ is multiplied by the dictionary matrix P to obtain:
Am×N＝Φ·P；
the matrix A is an echo sequence which is selected from the total modal echo sequences and used for imaging;
The genetic algorithm needs to construct a suitable fitness function, assuming that the distance-azimuth two-dimensional image Q tra of the target at a certain slow time is obtained by a conventional method such as fourier transform, and Q cs represents the two-dimensional image obtained by the modal sequence L according to the proposed compressed sensing algorithm at that slow time, where L represents the combination of the modal sequences selected by the genetic algorithm, so as to satisfy:
L＝Φ·Lord；
the corresponding fitness function F fit can thus be defined as:
Ffit＝cor(Qtra,Qcs)；
Where cor (·) represents the correlation, i.e. the correlation of Q tra with Q cs is greatest when the modality sequence is relatively optimal, the optimal sequence L op at this time can be expressed as:
Lop＝argmax(cor(Qtra,Qcs))s.t.len(Lop)＝m。
further, according to the sequence L op, a two-dimensional image of the target in the distance direction and the azimuth direction is obtained; to obtain a three-dimensional image of the target, information of the target on the y-axis is obtained due to the azimuth angle of the target The method meets the following conditions:
The equation represents the trend of the azimuth angle of the target along with the change of the slow time t m, and x 0 is the abscissa of the target at the beginning of the slow time; since the initial azimuth of the target is obtained, and the following relationship is satisfied as can be seen from the above equation:
y is the y-axis information of the target, the following relation can be obtained:
So it can be known that the starting time abscissa and the target ordinate satisfy the relation
Since the first equation can be approximated as:
therefore, the first-order term coefficients of the method can be obtained by simplifying the method to satisfy the following conditions:
the first-order term coefficient c 1 can be obtained by fitting a change curve of the azimuth angle of the target, so that y-axis information corresponding to the target is obtained, and finally, three-dimensional imaging of the target is realized.
It is another object of the present invention to provide a storage medium for receiving user input, the stored computer program causing an electronic device to execute the compressed sensing vortex imaging method based on modality selection, comprising:
Step one, an imaging model is established, so that a radar is positioned at an origin O (0, 0) of a coordinate system O-xyz, an x-axis represents an azimuth direction, and a y-axis represents a distance direction; the uniform annular array for generating vortex electromagnetic waves consists of N array elements, and the center of the uniform annular array is positioned at an origin O;
Secondly, the target consists of a plurality of scattering points, and moves positively along the x-axis at a speed v on a plane with a height H from the radar; the linear frequency modulation signals are used for bearing orbital angular momentum, and the phase excitation mode of the uniform circular columns is adjusted so that vortex waves of different modes have the same beam direction, and therefore the target can be irradiated by all vortex beams;
Performing correlation operation on the two-dimensional imaging result obtained based on Fourier transformation and the two-dimensional imaging result (randomly selecting a modal sequence) obtained by a compressed sensing algorithm, and optimizing the modal sequence through a genetic algorithm to obtain an optimized two-dimensional imaging result;
and step four, according to the optimized two-dimensional imaging result, a first-order term coefficient can be obtained by fitting a change curve of the azimuth angle of the target, so that y-axis information corresponding to the target is obtained, and finally, three-dimensional imaging of the target is realized.
The invention further aims to provide an application of the compressed sensing vortex imaging method based on mode selection in radar imaging.
By combining all the technical schemes, the invention has the advantages and positive effects that: according to the invention, the influence of vortex wave field intensity caused by a wave beam control technology is considered in a traditional compressed sensing imaging algorithm, and imaging quality is different according to different imaging mode sequences, so that a genetic algorithm suitable for mode selection is constructed to optimize the imaging mode sequence, and the imaging quality can be effectively improved while the number of modes required by imaging is reduced.
Drawings
Fig. 1 is a flow chart of a compressed sensing vortex imaging method based on mode selection provided by an embodiment of the invention.
Fig. 2 is a schematic process diagram of a compressed sensing vortex imaging method based on mode selection according to an embodiment of the present invention.
Fig. 3 is a schematic view of an imaging model according to an embodiment of the present invention.
Fig. 4 is a schematic diagram showing contrast of imaging effects provided by the embodiment of the invention.
In the figure: figure a, random modality sequence imaging; figure b, optimized modality sequence imaging.
Fig. 5 is a schematic diagram of a three-dimensional imaging result provided by an embodiment of the present invention.
Fig. 6 is a schematic diagram of three-dimensional imaging of a target provided by an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Aiming at the problems existing in the prior art, the invention provides a compressed sensing vortex imaging method based on mode selection, a storage medium and application, and the invention is described in detail below with reference to the accompanying drawings.
Other steps may be performed by those skilled in the art of the compressed sensing vortex imaging method based on mode selection provided by the present invention, and the compressed sensing vortex imaging method based on mode selection provided by the present invention of fig. 1 is merely a specific embodiment.
As shown in fig. 1, a compressed sensing vortex imaging method based on mode selection provided by an embodiment of the present invention includes:
S101: establishing an imaging model, enabling the radar to be located at an origin O (0, 0) of a coordinate system O-xyz, wherein an x-axis represents a direction and a y-axis represents a distance direction; the uniform circular ring array for generating vortex electromagnetic waves consists of N array elements, and the center of the uniform circular ring array is positioned at an origin O.
S102: the target consists of a plurality of scattering points, and moves positively along the x-axis at a speed v in a plane at a height H from the radar; the chirp signal is used to carry orbital angular momentum and the phase excitation pattern of the uniform circular array is adjusted so that the vortex waves of different modes have the same beam direction, so that the target can be irradiated by all the vortex beams.
S103: and performing correlation operation on a two-dimensional imaging result obtained based on Fourier transformation and a two-dimensional imaging result (randomly selected modal sequence) obtained by a compressed sensing algorithm, and optimizing the modal sequence through a genetic algorithm to obtain an optimized two-dimensional imaging result.
S104: according to the optimized two-dimensional imaging result, a first-order term coefficient can be obtained through fitting a change curve of the azimuth angle of the target, so that y-axis information corresponding to the target is obtained, and finally three-dimensional imaging of the target is realized.
In S102 provided by the embodiment of the present invention, the target is composed of a plurality of scattering points, and the specific process of moving at a speed v along the x-axis forward direction in a plane with a height H from the radar is:
Assuming that the equivalent phase center of the target is O ', the relative coordinate system in which the target is located is O' -x 'y' z 'and the pointing direction coincides with the radar coordinate system O-xyz, the ideal scattering point may be represented as a' T(x'T,y'T,z'T) T e1, 2 in the relative coordinate system, M may be represented as a T(xT,yT,zT in the coordinate system O-xyz, and For the distance of the connecting line between the radar and the scattering point, the two satisfy the following relation:
in S102 provided in the embodiment of the present invention, the chirp signal is used to carry orbital angular momentum, and the transmitting signal is expressed as:
Wherein T p and K represent the pulse width of the signal and the frequency modulation rate of the LFM, T m and Respectively representing a slow time domain and a fast time domain, f c is the center frequency of the signal, l is an OAM mode value, Φ n =2n/N, n=0, 1,2 …, N-1 represents the phase of the nth array element, and ψ n＝lφn is the phase excitation corresponding to each array element; turning the main lobe of the vortex electromagnetic wave under different modal values, wherein the excitation phase of each array element needs to be changed into:
Ψn＝lφn+kasinθ0cosφn；
Wherein the method comprises the steps of The wave number, a, is the radius of the array, and θ 0 is the deflection angle compared to the primary lobe direction of the vortex wave.
Because the relationship between the vortex wave main lobe direction and the mode satisfies the following formula:
thus θ 0＝θT-θmax, where θ T is the direction to which it is desired to turn; from the above analysis, the corresponding intensity function can be expressed as:
Wherein ζ= kasin θ, ζ 0＝kasinθ0, and when the deflection angle θ 0 =0, the above formula can be expressed as a bessel function J l (kasin θ); when the deflection angle is smaller, the phase of the vortex electromagnetic wave still accords with the spiral distribution, and the target azimuth angle The dual relationship with the OAM mode may be considered as unchanged.
The specific distance compression process provided by the embodiment of the invention comprises the following steps:
Assuming that the target consists of M scattering points and the array is in MIMO (multiple input multiple output) mode, the received echoes within one pulse can be expressed as:
Where τ T＝2rT/c is the echo delay for each scattering point, Azimuth angle of scattering point at slow time t m; assuming that the distance from the radar to the target equivalent phase center O' is r ref, the intermediate frequency echo signal after the demodulation frequency processing is:
Wherein the method comprises the steps of Is the time referenced to the phase center O', τ ΔT＝τT-τref is the relative echo delay in one pulse and τ ref＝2rref/c; compensating the residual video phase term (RVP) and the diagonal terms in the above method and then carrying out fast time domain/>Fourier variations can yield one-dimensional range profiles:
The sparse representation model of the radar echo signal in the azimuth angle domain simplifies the echo signal as follows:
Wherein l k (k=1, 2,., K) is the corresponding modality number, α T＝sinc[TP(f+KτΔT)]·exp(-j2πfcτΔT); assuming that the region where the target is located is divided into N discrete grids, N > M and Will be a sampling grid of the azimuth angles at which all targets are likely to be located, expressed in vector form as follows:
S＝Pα；
The vector S is an echo received under different modal values, and the vector P and the vector α are respectively represented as follows:
P＝[p1,p2,···,pN]
according to the compressed sensing theory, the reconstruction vector alpha is a convex optimization problem, and the following convex problem is solved by solving:
Wherein |· | 2 represents Norm, Φ represents the measurement matrix.
In S103 provided by the embodiment of the present invention, the specific process of optimizing the modal sequence by genetic algorithm to obtain the optimized two-dimensional imaging result is:
designing each parameter of the genetic algorithm, and selecting a relatively optimal modal sequence; assuming that the maximum and minimum modes of the total mode sequence L ord are L m and-L m respectively, the mode stepping value is 1, so that the total mode number is k=2l m +1; the measurement matrix phi is regarded as population individuals in a genetic algorithm to complete the processes of selection, crossing and mutation, the dimension of phi is related to the total mode number and the required mode sequence length, and the dimension of phi is m multiplied by K on the assumption that the mode sequence length is m; the mode in the mode sequence is unique and not repeated, and the measurement matrix phi must meet the condition of m rank, namely:
r(Φ)＝m；
At this time, the measurement matrix Φ is multiplied by the dictionary matrix P to obtain:
Am×N＝Φ·P；
the matrix A is an echo sequence which is selected from the total modal echo sequences and used for imaging;
The genetic algorithm needs to construct a suitable fitness function, and it is assumed that a distance-azimuth two-dimensional image Q tra of a target at a certain slow time is obtained by a traditional method, and Q cs represents a two-dimensional image obtained by a modal sequence L at the slow time according to the proposed compressed sensing algorithm, where L represents a modal sequence combination selected by the genetic algorithm, and the requirements are satisfied:
L＝Φ·Lord；
the corresponding fitness function F fit can thus be defined as:
Ffit＝cor(Qtra,Qcs)；
Where cor (·) represents the correlation, i.e. the correlation of Q tra with Q cs is greatest when the modality sequence is relatively optimal, the optimal sequence L op at this time can be expressed as:
Lop＝argmax(cor(Qtra,Qcs))s.t.len(Lop)＝m。
In the embodiment of the invention, according to the sequence L op, a two-dimensional image of the target in the distance direction and the azimuth direction is obtained; to obtain a three-dimensional image of the target, information of the target on the y-axis is obtained due to the azimuth angle of the target The method meets the following conditions:
The equation represents the trend of the azimuth angle of the target along with the change of the slow time t m, and x 0 is the abscissa of the target at the beginning of the slow time; since the initial azimuth of the target is obtained, and the following relationship is satisfied as can be seen from the above equation:
y is the y-axis information of the target, the following relation can be obtained:
So it can be known that the starting time abscissa and the target ordinate satisfy the relation
Since the first equation can be approximated as:
therefore, the first-order term coefficients of the method can be obtained by simplifying the method to satisfy the following conditions:
the first-order term coefficient c 1 can be obtained by fitting a change curve of the azimuth angle of the target, so that y-axis information corresponding to the target is obtained, and finally, three-dimensional imaging of the target is realized.
The technical scheme of the invention is further described below with reference to specific embodiments.
1. The radar is located at the origin O (0, 0) of the coordinate system O-xyz, the x-axis represents the azimuth direction, the y-axis represents the distance direction, t m andRepresenting the slow time domain and the fast time domain, respectively. A Uniform Circular Array (UCA) for generating vortex electromagnetic waves is composed of N array elements, the center of the UCA is positioned at an origin O, and the z axis is perpendicular to the plane of the array.
2. The object consists of a plurality of scattering points, moving forward along the x-axis at a velocity v in a plane at a height H from the radar. Assuming that the equivalent phase center of the target is O ', the relative coordinate system in which the target is located is O' -x 'y' z 'and the pointing direction coincides with the radar coordinate system O-xyz, the ideal scattering point may be represented as a' T(x'T,y'T,z'T) T e 1,2 in the relative coordinate system, M may be represented as a T(xT,yT,zT in the coordinate system O-xyz, andFor the distance of the connecting line between the radar and the scattering point, the two satisfy the following relation:
fig. 3 is a corresponding object imaging model.
3. A chirped signal (LFM) is used to carry orbital angular momentum, and the transmitted signal can be expressed as:
Where T p and K represent the pulse width of the signal and the frequency modulation rate of the LFM, respectively. f c is the center frequency of the signal, l is the OAM mode value and Φ n =2n/N, n=0, 1,2 …, N-1 represents the phase of the nth element, ψ n＝lφn is the phase excitation corresponding to each element. In order to steer the main lobe of the vortex electromagnetic wave under different modal values, the excitation phase of each array element needs to be changed into:
Ψn＝lφn+kasinθ0cosφn；
Wherein the method comprises the steps of The wave number, a, is the radius of the array and θ 0 is the deflection angle compared to the primary lobe direction of the vortex wave.
4. Because the relationship between the vortex wave main lobe direction and the mode satisfies the following formula:
And therefore θ 0＝θT-θmax, where θ T is the direction to which it is desired to turn. From the above analysis, the corresponding intensity function can be expressed as:
Where ζ= kasin θ, ζ 0＝kasinθ0, and when the deflection angle θ 0 =0, the above formula can be expressed as a bessel function J l (kasin θ). When the deflection angle is smaller, the phase of the vortex electromagnetic wave still accords with spiral distribution and the target azimuth angle The dual relationship with the OAM mode may be considered as unchanged.
5. Assuming that the target consists of M scattering points and the array is in MIMO (multiple input multiple output) mode, the received echoes within one pulse can be expressed as:
Where τ T＝2rT/c is the echo delay for each scattering point, Is the azimuth of the scattering point at slow time t m. Assuming that the distance from the radar to the target equivalent phase center O' is r ref, the intermediate frequency echo signal after the demodulation frequency processing is: /(I)
Wherein the method comprises the steps ofIs the time referenced to the phase center O', τ ΔT＝τT-τref is the relative echo delay within one pulse and τ ref＝2rref/c. Compensating the residual video phase term (RVP) and the diagonal terms in the above method and then carrying out fast time domain/>Fourier variations can yield one-dimensional range profiles:
6. in order to establish a sparse representation model of radar echo signals in an azimuth angle domain, the echo signals are simplified as follows:
Where l k (k=1, 2,., K) is the corresponding number of modes, and α T＝sinc[TP(f+KτΔT)]·exp(-j2πfcτΔT). Assuming that the region where the target is located is divided into N discrete grids, N > M and Will be a sampling grid of the azimuth angles at which all targets are likely to be located, expressed in vector form as follows:
S＝Pα；
The vector S is an echo received under different modal values, and the vector P and the vector α are respectively represented as follows:
P＝[p1,p2,···,pN]
according to the compressed sensing theory, the reconstruction vector alpha is a convex optimization problem, which can be solved by solving the following convex problem:
Wherein |· | 2 represents Norm, Φ represents the measurement matrix.
7. Because the dictionary matrix P considers the influence of the intensity of the vortex waves of different modes after the main lobe is turned, parameters of the mode sequence selected for imaging, such as the maximum mode value, the length of the mode sequence, the value of the mode sequence and the like, may influence the imaging effect when changing, so that a genetic algorithm is used to select a proper mode sequence to obtain a better imaging effect.
8. In order to better adapt to genetic algorithm rules, a relatively optimal modal sequence is selected, and each parameter of compressed sensing needs to be designed. Assuming that the maximum and minimum modes of the total mode sequence L ord are L m and-L m, respectively, the mode step value is 1, so the total mode number is k=2l m +1. The measurement matrix phi is regarded as population individuals in a genetic algorithm to complete the processes of selection, crossing and mutation, the dimension of phi is related to the total mode number and the required mode sequence length, and the dimension of phi is m multiplied by K on the assumption that the mode sequence length is m. In order for the modalities in the modality sequence to be uniquely non-repetitive, the measurement matrix Φ must satisfy the condition of rank m, namely:
r(Φ)＝m；
At this time, the measurement matrix Φ is multiplied by the dictionary matrix P to obtain:
Am×N＝Φ·P；
wherein matrix a is the echo sequence selected from the total modality echo sequences for imaging.
Then, a suitable fitness function needs to be constructed, and it is assumed that a distance-azimuth two-dimensional image Q tra of the target at a certain slow time is obtained by a conventional method, and Q cs represents a two-dimensional image obtained by a modal sequence L at the slow time according to the proposed compressed sensing algorithm, where L represents a modal sequence combination selected by a genetic algorithm, and the following are satisfied:
L＝Φ·Lord；
the corresponding fitness function F fit can thus be defined as:
Ffit＝cor(Qtra,Qcs)；
Where cor (·) represents the correlation, i.e. the correlation of Q tra with Q cs is greatest when the modality sequence is relatively optimal, the optimal sequence L op at this time can be expressed as:
Lop＝argmax(cor(Qtra,Qcs))s.t.len(Lop)＝m；
9. from the sequence L op, two-dimensional images of the object in the distance direction as well as in the azimuth direction can be obtained. In order to obtain the three-dimensional image of the target, the information of the target on the y-axis needs to be acquired, because of the azimuth angle of the target The method meets the following conditions:
The equation represents the trend of the azimuth of the target over the slow time t m, x 0 being the abscissa of the target at the start of the slow time. Since the initial azimuth of the target can be obtained, the following relationship is satisfied as can be seen from the above equation:
y is the y-axis information of the target, the following relation can be obtained:
So it can be known that the starting time abscissa and the target ordinate satisfy the relation
Since the first equation can be approximated as:
therefore, the first-order term coefficients of the method can be obtained by simplifying the method to satisfy the following conditions:
the first-order term coefficient c 1 can be obtained by fitting a change curve of the azimuth angle of the target, so that y-axis information corresponding to the target is obtained, and finally, three-dimensional imaging of the target is realized.
The technical effects of the present invention will be described in detail with reference to simulation experiments.
Fig. 4 (a) is a two-dimensional image of a target obtained by performing imaging processing using a randomly selected imaging modality sequence, in order to effectively improve imaging quality, the imaging modality sequence is optimized by using the method described in the scheme, and the target is imaged according to the optimized modality sequence, as shown in fig. 4 (b), it can be seen that the imaging quality is significantly improved, and error peaks and side lobes are effectively suppressed; fig. 5 (a) is an image fitted to the azimuth change curve of a certain scattering center, and y-axis information of the target can be calculated according to the first-order coefficient value obtained in the figure, and fig. 5 (b) is imaging information of the target in the x-axis and z-axis, so that three-dimensional imaging of the target as shown in fig. 6 is obtained.
It should be noted that the embodiments of the present invention can be realized in hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or special purpose design hardware. Those of ordinary skill in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such as provided on a carrier medium such as a magnetic disk, CD or DVD-ROM, a programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The device of the present invention and its modules may be implemented by hardware circuitry, such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., as well as software executed by various types of processors, or by a combination of the above hardware circuitry and software, such as firmware.
The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.
Claims (9)
1. The compressed sensing vortex imaging method based on the mode selection is characterized by comprising the following steps of:
Step one, an imaging model is established, so that a radar is positioned at an origin O (0, 0) of a coordinate system O-xyz, an x-axis represents an azimuth direction, and a y-axis represents a distance direction; the uniform annular array for generating vortex electromagnetic waves consists of N array elements, and the center of the uniform annular array is positioned at an origin O;
Secondly, the target consists of a plurality of scattering points, and moves positively along the x-axis at a speed v on a plane with a height H from the radar; the linear frequency modulation signals are used for bearing orbital angular momentum, and the phase excitation mode of the uniform circular columns is adjusted so that vortex waves of different modes have the same beam direction, and thus the target can be irradiated by all vortex beams;
thirdly, randomly selecting a modal sequence to perform correlation operation based on a two-dimensional imaging result obtained by Fourier transformation and a two-dimensional imaging result obtained by a compressed sensing algorithm, and optimizing the modal sequence through a genetic algorithm to obtain an optimized two-dimensional imaging result;
Step four, according to the optimized two-dimensional imaging result, a first-order term coefficient can be obtained through fitting a change curve of a target azimuth angle, so that y-axis information corresponding to the target is obtained, and finally three-dimensional imaging of the target is realized;
In the third step, the modal sequence is optimized through a genetic algorithm, and the specific process of obtaining the optimized two-dimensional imaging result is as follows: designing each parameter of the genetic algorithm, and selecting a relatively optimal modal sequence; assuming that the maximum and minimum modes of the total mode sequence L ord are L m and-L m respectively, and the mode stepping value is 1, the total mode number is K=2l m +1; the measurement matrix phi is regarded as population individuals in a genetic algorithm to complete the processes of selection, crossing and mutation, the dimension of phi is related to the total mode number and the required mode sequence length, and the dimension of phi is m multiplied by K on the assumption that the mode sequence length is m; in order to make the modes in the mode sequence unique and not repeated, the measurement matrix phi meets the condition of m rank, namely:
r(Φ)＝m；
At this time, the measurement matrix Φ is multiplied by the dictionary matrix P to obtain:
Am×N＝Φ·P；
the matrix A is an echo sequence which is selected from the total modal echo sequences and used for imaging;
The genetic algorithm needs to construct a suitable fitness function, assuming that the distance-azimuth two-dimensional image Q tra of the target at a certain slow time is obtained by a conventional method such as fourier transform, and Q cs represents the two-dimensional image obtained by the modal sequence L according to the proposed compressed sensing algorithm at that slow time, where L represents the combination of the modal sequences selected by the genetic algorithm, so as to satisfy:
L＝Φ·Lord；
the corresponding fitness function F fit can thus be defined as:
Ffit＝cor(Qtra,Qcs)；
Where cor (·) represents the correlation, i.e. the correlation of Q tra with Q cs is greatest when the modality sequence is relatively optimal, the optimal sequence L op at this time can be expressed as:
Lop＝arg max(cor(Qtra,Qcs))s.t.len(Lop)＝m。
2. The compressed sensing vortex imaging method based on mode selection according to claim 1 wherein in the second step, the target is composed of a plurality of scattering points, and the specific process of moving at a speed v along the x-axis in a plane with a height H from the radar is as follows: the equivalent phase center of the target is O ', the relative coordinate system in which the target is located is O' -x 'y' z 'and the pointing direction is consistent with the radar coordinate system O-xyz, the ideal scattering point is denoted in the relative coordinate system as a' T(x'T,y'T,z'T) T e1, 2, M, which can be denoted in the coordinate system O-xyz as a T(xT,yT,zT), and For the distance of the connecting line between the radar and the scattering point, the two satisfy the following relationship:
3. The compressed sensing vortex imaging method based on modality selection of claim 1 wherein in step two, a chirp signal is used to carry orbital angular momentum, and the transmitted signal is represented as:
Wherein T p and K represent the pulse width of the signal and the frequency modulation rate of the LFM, T m and Respectively representing a slow time domain and a fast time domain, f c is the center frequency of the signal, l is an OAM mode value, Φ n =2n/N, n=0, 1,2 …, N-1 represents the phase of the nth array element, and ψ n＝lφn is the phase excitation corresponding to each array element; turning the main lobe of the vortex electromagnetic wave under different modal values, wherein the excitation phase of each array element needs to be changed into:
Ψn＝lφn+ka sinθ0cosφn；
Wherein the method comprises the steps of The wave number, a, is the radius of the array, and θ 0 is the deflection angle compared to the primary lobe direction of the vortex wave.
4. A compressed sensing vortex imaging method based on mode selection according to claim 3 wherein the relationship between the main lobe direction and the mode due to vortex wave satisfies the following formula:
thus θ 0＝θT-θmax, where θ T is the direction to which it is desired to turn; from the above analysis, the corresponding intensity function can be expressed as:
Wherein ζ=ka sin θ, ζ 0＝ka sinθ0, and when the deflection angle θ 0 =0, the above formula can be expressed as a bessel function J l (ka sin θ); when the deflection angle is smaller, the phase of the vortex electromagnetic wave still accords with the spiral distribution, and the target azimuth angle The dual relationship with the OAM mode may be considered as unchanged.
5. The compressed sensing vortex imaging method based on mode selection according to claim 1 wherein the specific process of distance compression is: the target consists of M scattering points, and the array is in a multiple-input multiple-output (MIMO) echo receiving mode, the received echo in one pulse is expressed as:
Where τ T＝2rT/c is the echo delay for each scattering point, Azimuth angle for the scattering point at each pulse time t m; assuming that the distance from the radar to the target equivalent phase center O' is r ref, the intermediate frequency echo signal after the demodulation processing is:
Wherein the method comprises the steps of Is the time referenced to the phase center O', τ ΔT＝τT-τref is the relative echo delay in one pulse and τ ref＝2rref/c; compensating the residual video phase term and the diagonal term in the above method, and then carrying out fast time domain/>Fourier variations can yield one-dimensional range profiles:
6. the compressed sensing vortex imaging method based on modality selection of claim 5 wherein the sparse representation of the radar echo signals in the azimuth domain is simplified by:
Wherein l k (k=1, 2,., K) is the corresponding modality number, α T＝sinc[TP(f+KτΔT)]·exp(-j2πfcτΔT); assuming that the region where the target is located is divided into N discrete grids, N > M and Will be a sampling grid of the azimuth angles at which all targets are likely to be located, expressed in vector form as follows:
S＝Pα；
The vector S is an echo received under different modal values, and the vector P and the vector α are respectively represented as follows:
according to the compressed sensing theory, the reconstruction vector alpha is a convex optimization problem, and the following convex problem is solved by solving:
Wherein |· | 2 represents Norm, Φ represents the measurement matrix.
7. The compressed sensing vortex imaging method based on modality selection of claim 1 wherein the obtaining of a two-dimensional image of the target in the range direction and azimuth direction is based on sequence L op; to obtain a three-dimensional image of the target, information of the target on the y-axis is obtained due to the azimuth angle of the targetThe method meets the following conditions:
The equation represents the trend of the azimuth angle of the target along with the change of the slow time t m, and x 0 is the abscissa of the target at the beginning of the slow time; since the initial azimuth of the target can be obtained by processing the echo, the following relationship is satisfied as can be seen from the above equation:
y is the y-axis information of the target, the following relation can be obtained:
So it can be known that the starting time abscissa and the target ordinate satisfy the relation
The expression for the target azimuth angle can be approximated as:
therefore, the first-order term coefficients of the method can be obtained by simplifying the method to satisfy the following conditions:
the first-order term coefficient c 1 can be obtained by fitting a change curve of the azimuth angle of the target, so that y-axis information corresponding to the target is obtained, and finally, three-dimensional imaging of the target is realized.
8. A storage medium receiving a user input program, the stored computer program causing an electronic device to perform the compressed sensing vortex imaging method based on modality selection of any one of claims 1 to 7, comprising:
Step one, an imaging model is established, so that a radar is positioned at an origin O (0, 0) of a coordinate system O-xyz, an x-axis represents an azimuth direction, and a y-axis represents a distance direction; the uniform annular array for generating vortex electromagnetic waves consists of N array elements, and the center of the uniform annular array is positioned at an origin O;
Secondly, the target consists of a plurality of scattering points, and moves positively along the x-axis at a speed v on a plane with a height H from the radar; the linear frequency modulation signals are used for bearing orbital angular momentum, and the phase excitation mode of the uniform circular columns is adjusted so that vortex waves of different modes have the same beam direction, and therefore the target can be irradiated by all vortex beams;
Performing correlation operation on the two-dimensional imaging result obtained based on Fourier transformation and the two-dimensional imaging result (randomly selecting a modal sequence) obtained by a compressed sensing algorithm, and optimizing the modal sequence through a genetic algorithm to obtain an optimized two-dimensional imaging result;
and step four, according to the optimized two-dimensional imaging result, a first-order term coefficient can be obtained by fitting a change curve of the azimuth angle of the target, so that y-axis information corresponding to the target is obtained, and finally, three-dimensional imaging of the target is realized.
9. Use of a compressed sensing vortex imaging method based on modality selection according to any one of claims 1 to 7 in radar imaging.
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