CN113050059A - Group target focusing super-resolution direction of arrival estimation method by using co-prime array radar - Google Patents

Group target focusing super-resolution direction of arrival estimation method by using co-prime array radar Download PDF

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CN113050059A
CN113050059A CN202110312684.9A CN202110312684A CN113050059A CN 113050059 A CN113050059 A CN 113050059A CN 202110312684 A CN202110312684 A CN 202110312684A CN 113050059 A CN113050059 A CN 113050059A
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prime array
array radar
prime
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targets
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郑纪彬
陈柔暄
杨天园
刘宏伟
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/04—Details
    • G01S3/12—Means for determining sense of direction, e.g. by combining signals from directional antenna or goniometer search coil with those from non-directional antenna
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction

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Abstract

A group target focusing super-resolution direction of arrival estimation method using a co-prime array radar comprises the following steps: constructing a co-prime array radar; forming a co-prime array radar echo wave beam signal; compensating the speed and the acceleration by utilizing a generalized solution frequency modulation-wedge transformation method; performing two-dimensional interpolation on each compensated beam signal; focusing the echo signals by using a long-time coherent accumulation method; detecting the group target by using a CFAR method; respectively reconstructing a signal of a complete uniform linear array corresponding to a co-prime array of each group of targets by utilizing a reverse beam forming technology; estimating the echo power and the direction of arrival of all targets by using an FS-RAM method; estimating the number of real targets in all potential targets by using an SORTE method; the direction of arrival of the target is obtained. The method can be used for performing efficient and robust super-resolution direction-of-arrival estimation on the group target with small radar scattering cross section, long distance and time-varying motion in the region to be monitored.

Description

Group target focusing super-resolution direction of arrival estimation method by using co-prime array radar
Technical Field
The invention belongs to the technical field of direction of arrival estimation, and further relates to a group target focusing super-resolution direction of arrival estimation method by utilizing a co-prime array radar in the technical field of group target direction of arrival estimation. The method can be used for performing efficient and robust super-resolution direction-of-arrival estimation on the group target with small radar scattering cross section, long distance and time-varying motion in the region to be monitored.
Background
Direction of arrival estimation is an important branch of the field of array signal processing. In recent years, due to the development of automatic control and communication technologies, cluster formation of a plurality of unmanned aerial vehicles or missiles is controlled to be possible, so that more advantages are brought, for example, the unmanned aerial vehicle cluster shows great potential in the field of internet of things. At the same time, the advantages of clustering increase the likelihood of its being used maliciously. Radar detection and localization of group targets is therefore an important aspect of national security.
Patent document "a method for detecting a target of a group of unmanned aerial vehicles, an electronic device, and a storage medium" (application No. 202011204492.8 application publication No. CN 112305530 a) filed by shanghai Shen industries ltd. The group target detection method needs to acquire an echo signal of inter-pulse orthogonal phase coding of a target to be detected, and performs pulse compression, digital beam synthesis and slow time dimension fast Fourier transform on the echo signal to obtain Doppler-angle data; and judging the target to be detected according to the Doppler-angle data, and estimating group target parameters and number to obtain the target quantity and target parameters of the target to be detected when the target to be detected is a group target. The method has the following defects: when the Doppler-angle data is used for judging the targets to be detected, the posterior probability distribution of the parameters of each target is estimated by adopting a Gibbs sampling method under the assumption that the number N (N is 1, 2.. multidot.5) of the targets in a group is equal to. Resulting in limited estimation of the number of targets and limited resolution.
A radar target detection method is disclosed in patent document "radar target detection method based on sparse fourier transform" (application No. 201510918409.6 application publication No. CN 105572649B) applied by north and middle university. The radar target detection method comprises eight steps, the detection process also comprises 13 processes, and importantly: firstly, Fourier transform is carried out on a transmitting signal and an echo signal, then the positions of targets with similar frequencies are separated by adopting a sequence rearrangement method, then a filter is adopted for separating the targets, finally, the Fourier transform result of a segmented signal is utilized for determining the delay position and the frequency of the target, and sparse Fourier transform is adopted for target detection. The method has the following defects: because the method performs Fourier transform on the transmitting signal and the echo signal, the fast target moving speed causes the problem of range migration, the echo energy is defocused, and the moving target is difficult to process.
The patent document "arrival direction estimation method based on interpolation co-prime array covariance matrix reconstruction" (application No. 201710735814.3 application publication No. CN 107561484B) applied by the university of zhejiang discloses an arrival direction estimation method based on interpolation co-prime array covariance matrix reconstruction. The method for estimating the direction of arrival comprises the following implementation steps: a receiving end constructs a co-prime array; receiving an incident signal by utilizing a co-prime array and modeling; converting the co-prime array into a uniform linear array according to the interpolation idea, and constructing a corresponding received signal model; calculating a sampling covariance matrix of the interpolated co-prime array; constructing a projection matrix corresponding to the interpolated co-prime array sampling covariance matrix; designing a convex optimization problem based on the minimization of the nuclear norm to realize Toeplitz reconstruction of the interpolation co-prime array covariance matrix; and estimating the direction of arrival according to the reconstructed interpolation co-prime array covariance matrix. The method has the following defects: because the method utilizes the co-prime array to receive the incident signals and model, all targets can appear in the signals to be processed, the number of the targets needing to be processed through convex optimization is large, the calculated amount is large, the robustness is poor, and the method is sensitive to noise.
Disclosure of Invention
The invention aims to provide a group target focusing super-resolution direction-of-arrival estimation method utilizing a co-prime array radar, aiming at overcoming the defects of the prior art, and solving the problems of limited target number estimation, limited resolution, difficulty in processing moving targets, large calculated amount, poor robustness and sensitivity to noise in the prior art.
The idea for realizing the purpose of the invention is that a long-time coherent accumulation method is adopted for focusing, the echo signal of the target can be accumulated, and the noise can not be accumulated, so the problem of low echo signal-to-noise ratio can be solved. And respectively carrying out speed compensation and acceleration compensation on the focused signals by combining a generalized solution frequency modulation-wedge transformation method so as to solve the problem of energy defocusing caused by the fact that the target moves at an excessively high speed and the movement range exceeds one radar beam width. The Doppler resolution and the signal-to-noise ratio can be improved by prolonging the coherent processing interval, but the spatial resolution and the range resolution cannot be improved, so that the spatial resolution is improved by adopting a grid-free sparse method. The FS-RAM method in the grid-free sparse method uses the rough estimation value of the direction of arrival as prior knowledge, and a rough estimation range is planned in advance, so that the robustness of the estimation of the direction of arrival can be improved, and the calculation amount is reduced. And the effectiveness of information extraction is improved by means of interpolation, so that the estimation precision of the group target speed and the distance is improved. Because the super-resolution performance of the non-grid sparse method is reduced along with the increase of the number of targets in a single cluster, a larger array aperture is obtained by using the co-prime array radar under the condition of not increasing the number of array elements so as to improve the resolution and reduce the number of targets in a single wave beam, thereby reducing the calculation amount of the non-grid sparse method and improving the robustness of the non-grid sparse method.
The method comprises the following specific steps:
(1) constructing a co-prime array radar:
the radar receiving end uses M + N-1 antennas and carries out array architecture of the co-prime array radar receiving antenna according to the co-prime array structure; wherein M and N are relatively prime integers;
(2) forming a co-prime array radar echo wave beam signal:
(2a) dividing the space of the group target to be searched
Figure BDA0002990520330000031
A grid point, wherein [. ]]Denotes the rounding operation, θmaxAnd thetaminRespectively representing the maximum and minimum angles, delta, between the space of the group object to be searched and the co-prime array radarθRepresenting the beam width of the co-prime array radar;
(2b) calculating a Hadamard product of the beam steering vector of each grid point angle and an echo signal received by the co-prime array radar as a grid point beam signal;
(3) the generalized FM-wedge transform method is used for compensating the speed and the acceleration:
(3a) performing speed compensation on the beam signal of each grid point by using wedge transformation to obtain a speed-compensated beam signal;
(3b) performing acceleration compensation on each speed-compensated signal by using a generalized frequency demodulation method and a plurality of accelerations respectively to obtain compensated beam signals;
(4) performing two-dimensional interpolation on each compensated beam signal:
carrying out cubic spline interpolation on the slow time dimension of each compensated beam signal and then carrying out cubic spline interpolation on the fast time dimension to obtain an interpolated beam signal;
(5) focusing echo signals by using a long-time coherent accumulation method:
performing two-dimensional Fourier transform on each interpolated beam signal along the fast time dimension and the compensated slow time dimension to obtain a focused signal, and calculating an absolute value of the focused signal;
(6) detecting the group target by using a constant false alarm rate CFAR method:
(6a) when the maximum value of the absolute value of the focused signal is larger than a threshold value, judging that a group target exists;
(6b) obtaining target parameters of each group target;
(7) respectively reconstructing a signal of a complete uniform linear array corresponding to a co-prime array of each group of targets by utilizing a reverse beam forming technology;
(8) estimating the echo power and the direction of arrival of all targets by using an FS-RAM method:
(8a) respectively calculating a frequency interval corresponding to an interval where each group target is located relative to the direction of arrival of the co-prime array radar;
(8b) respectively using an FS-RAM method, regarding each group target, taking a frequency interval corresponding to an interval where the group target is located relative to the direction of arrival of the co-prime array radar as prior information required by the FS-RAM method, and extracting potential target information from a complete uniform linear array signal corresponding to the co-prime array of the group target;
(8c) splicing potential target information extracted from all signals corresponding to the complete uniform linear array of the co-prime array to serve as the power of echo signals of all potential targets and the direction of arrival of all potential targets relative to the co-prime array radar;
(9) estimating the number of real targets in all potential targets by using an SORTE method;
(10) obtaining the direction of arrival of the target:
and sorting the power of the echo signals of all the potential targets according to the descending power, taking the first powers equal to the number of the real targets in the sorting, and taking the arrival direction of the corresponding potential target relative to the co-prime array radar as the arrival direction value of the target.
Compared with the prior art, the invention has the following advantages:
firstly, because the invention uses a long-time coherent accumulation method, the defect of noise sensitivity in the prior art is overcome, so that the invention can keep effectiveness in an environment with low echo signal-to-noise ratio, and can process targets with small radar scattering cross sections and long distances.
Secondly, the generalized de-FM-wedge transform method is adopted, so that the defect of energy defocusing in the prior art is overcome, and the time-varying target of motion can be processed.
Thirdly, as the invention uses the methods of the co-prime array radar and the FS-RAM, the defects of limited resolution, large calculation amount and poor robustness in the prior art are overcome, so that the invention can realize high-efficiency and robust super resolution on the target.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a relatively prime array employed in the present invention;
FIG. 3 is a simulation diagram of the precise detection and positioning of the simulation experiment of the present invention in scenario 1;
FIG. 4 is a graph comparing the performance of the simulation experiment of the present invention in scenario 2 with that of the prior art;
fig. 5 is a simulation diagram of noise robustness in scenario 3 of the simulation experiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The specific implementation steps of the present invention are further described with reference to fig. 1.
Step 1, constructing a co-prime array radar.
The radar receiving end uses M + N-1 antennas and carries out array architecture of the co-prime array radar receiving antenna according to the co-prime array structure; wherein M and N are relatively prime integers.
The specific steps of carrying out the array architecture of the co-prime array radar receiving antenna according to the co-prime array structure are as follows:
the first step is as follows: a pair of relatively prime integers M, N is selected.
The second step is that: and constructing a pair of sparse uniform linear sub-arrays, wherein the first sub-array comprises M antenna array elements with the spacing of Nxd, the second sub-array comprises N antenna array elements with the spacing of Mxd, and d is half of the shortest wavelength of radar receiving signals.
The third step: and combining the two sub-arrays according to the first array element overlapping mode to obtain a non-uniform co-prime array structure actually containing M + N-1 array elements, and performing the array architecture of the co-prime array radar receiving antenna according to the non-uniform co-prime array structure.
The steps of the invention for constructing a co-prime array radar will now be further described with reference to figure 2.
Fig. 2(a) shows a sparse uniform linear subarray including M antenna elements at an N × d pitch, with the leftmost element as a zero point and the array extension direction as the forward direction, and with the coordinate axes established, the antenna elements are located at 0, N × d, …, (M-1) × N × d in this order.
Fig. 2(b) shows a sparse uniform linear subarray including N antenna elements at M × d intervals, where the leftmost element is a zero point and the array extension direction is a forward direction, and coordinate axes are established, and the positions of the antenna elements are 0, M × d, …, (N-1) × M × d in this order.
Fig. 2(c) shows a non-uniform co-prime array structure including M + N-1 array elements, which is obtained by combining the sub-arrays in fig. 2(a) and 2(a) in such a manner that the first array elements are overlapped and the array extension directions are overlapped.
And 2, forming a co-prime array radar echo wave beam signal.
Dividing the space of the group target to be searched
Figure BDA0002990520330000061
A grid point, wherein [. ]]Denotes the rounding operation, θmaxAnd thetaminRespectively representing the maximum and minimum angles, delta, between the space of the group object to be searched and the co-prime array radarθRepresenting the beamwidth of a co-prime array radar.
The group targets refer to a plurality of targets gathered and distributed in a mutual-prime array radar beam in space, the distances between the targets are close, and the speeds and the accelerations of the targets are approximate.
And calculating the Hadamard product of the beam steering vector of each grid point angle and the echo signal received by the co-prime array radar as the grid point beam signal.
And 3, compensating the speed and the acceleration by using a generalized FM-wedge conversion method.
And performing speed compensation on the beam signals of each grid point by using wedge transformation to obtain the beam signals after the speed compensation.
And respectively carrying out acceleration compensation on each speed-compensated signal by using a generalized frequency demodulation method and a plurality of accelerations to obtain a compensated beam signal.
And 4, performing two-dimensional interpolation on each compensated beam signal.
And performing cubic spline interpolation on the slow time dimension of each compensated beam signal and then performing cubic spline interpolation on the fast time dimension to obtain the interpolated beam signal.
And 5, focusing the echo signals by using a long-time coherent accumulation method.
And performing two-dimensional Fourier transform on each interpolated beam signal along the fast time dimension and the compensated slow time dimension to obtain a focused signal, and calculating an absolute value of the focused signal.
And 6, detecting the group target by using a constant false alarm rate CFAR method.
When the maximum value of the absolute value of the focused signal is larger than the threshold value, it is determined that the group target exists.
The threshold is determined by using a constant false alarm rate CFAR method.
Target parameters for each cluster target are obtained.
The target parameters of the group targets are as follows: the method comprises the steps of roughly estimating the direction of arrival of a group target relative to a co-prime array radar, the distance between the group target and the co-prime array radar, the speed of the group target relative to the co-prime array radar, and the speed of the group target relative to the co-prime array radar.
And 7, respectively reconstructing signals of the complete uniform linear array corresponding to the co-prime array of each group of targets by utilizing a reverse beam forming technology.
The inverse beamforming technique is as follows:
firstly, reconstructing an echo signal of each array element of the complete uniform linear array corresponding to the co-prime array.
And secondly, forming an array by the echo signals of all the array elements, and using the array as the echo signal of the complete uniform linear array corresponding to the co-prime array.
And 8, estimating the echo power and the direction of arrival of all targets by using an FS-RAM method.
And respectively calculating the frequency interval corresponding to the interval of the arrival direction of each group target relative to the co-prime array radar.
The specific steps of calculating the frequency interval corresponding to the interval where the direction of arrival of each group target relative to the co-prime array radar is located are as follows:
first, for each group target, respectively calculating the arrival of the group target relative to the co-prime array radarUpper limit f of frequency interval corresponding to interval of directionH：
Figure BDA0002990520330000071
Wherein d represents the minimum array element spacing of the co-prime array radar, cos (·) represents the cosine operation, and θ representszRepresenting a rough estimate of the direction of arrival, δ, of a group target relative to a co-prime array radarθThe beam width of the co-prime array radar is shown, and lambda represents the carrier wavelength of the co-prime array radar signal.
Secondly, for each group target, respectively calculating the lower limit f of a frequency interval corresponding to the interval of the arrival direction of the group target relative to the co-prime array radarL：
Figure BDA0002990520330000072
Third, for each group object, [ f ] is addedL,fH]The frequency range is a frequency range corresponding to a range in which the arrival direction of the group of targets with respect to the co-prime array radar is located.
And respectively using an FS-RAM method, regarding each group target, taking a frequency interval corresponding to an interval where the arrival direction of the group target relative to the co-prime array radar is located as prior information required by the FS-RAM method, and extracting potential target information from a signal of a complete uniform linear array corresponding to the co-prime array of the group target.
The steps of the FS-RAM method are as follows:
first, a weight vector W is calculated.
The method for calculating the weight vector W is as follows:
Figure BDA0002990520330000073
wherein the content of the first and second substances,
Figure BDA0002990520330000074
representation of Toeplitz matrix operationDo, u0A vector formed by a first column of elements of the autocorrelation matrix of the received signal of the cross-prime array radar obtained by reconstructing the group of targets, wherein epsilon > 0 represents a regularization parameter, I represents an identity matrix, (·)-1Representing a matrix inversion operation.
Secondly, solving the following formula:
Figure BDA0002990520330000081
Figure BDA0002990520330000082
wherein:
Figure BDA0002990520330000083
representing a minimization operation, u representing an optimal estimation value of a vector consisting of the elements of the first column of the ideal autocorrelation matrix of the received signal of the uniform linear array radar of the same aperture as that of the co-prime array radar, the number of elements in u being equal to the number of elements of the uniform linear array radar of the same aperture as that of the co-prime array radar, tr [ · n ·]Indicating a rank operation, alpha indicating a free variable, subject to indicating a constraint,
Figure BDA0002990520330000084
represents an ideal received signal of a uniform linear array radar having the same caliber as the co-prime array radar (·)HWhich represents the conjugate transpose operation,
Figure BDA0002990520330000085
is represented by alpha,
Figure BDA0002990520330000086
Figure BDA0002990520330000087
The spliced matrix represents the positive definite of the matrix, | | · | air distribution |, the matrix is more than or equal to 0FRepresents an F norm operation [ ·]ΩIndicating the received signals of the same array elements of the uniform linear array radar and the co-prime array radarOperation, x represents the received signal of the co-prime array radar obtained by reconstructing the group of targets, eta represents a threshold value determined by the environmental noise,
Figure BDA0002990520330000088
the optimal estimation value of the ideal autocorrelation matrix of the received signal of the uniform linear array radar with the same caliber as the co-prime array radar under the condition of the known frequency range is represented by
Figure BDA0002990520330000089
The weighted elements of (c) make up:
Figure BDA00029905203300000810
wherein h is1And h2The weight coefficient is represented by a weight coefficient,
Figure BDA00029905203300000811
h2＝-2cos(π(fH-fL))sign(fH-fL)，e(·)representing exponential operations based on the natural number of layers e, j representing an imaginary symbol, sign (·) representing a symbolic function, fHAnd fLU represents the upper limit and the lower limit of a frequency interval corresponding to the interval in which the direction of arrival of the group of targets with respect to the co-prime array radar is located, respectivelylRepresents the i-th element in u,
Figure BDA00029905203300000812
indicates the number of elements in u.
Thirdly, judging whether the conditions for finishing the circulation are met, if so, executing the fourth step; otherwise, reducing the regularization parameter to obtain a new regularization parameter, recalculating the weight vector W by using the u obtained in the second step and the new regularization parameter, and executing the second step; the condition for ending the loop refers to a case where one of the following two conditions is satisfied: the method comprises the following steps that 1, the circulation frequency is larger than the maximum circulation frequency determined according to computer resources and direction finding precision requirements; in condition 2, u obtained by performing the second step twice in succession is the same.
The method for recalculating the weight vector W is as follows:
Figure BDA0002990520330000091
where e' represents the new regularization parameter.
And fourthly, carrying out Van der Mond decomposition on the Tueplitz matrix of u obtained in the second step, respectively taking each power obtained by the Van der Mond decomposition as the power of the echo signal of each potential target, and enabling the potential target obtained by the Van der Mond decomposition to be opposite to the direction of arrival of the mutual mass array radar.
And splicing potential target information extracted from all signals corresponding to the complete uniform linear array of the co-prime array to obtain the power of echo signals of all potential targets and the direction of arrival of all potential targets relative to the co-prime array radar.
And 9, estimating the number of real targets in all potential targets by using an SORTE method.
The SORTE method is as follows:
in the first step, the power of the echo signals of all potential targets is sorted in descending order.
Second, construct the cumulative difference sequence
Figure BDA0002990520330000092
Each subsequence in the cumulative difference sequence is calculated using the formula:
Figure BDA0002990520330000093
wherein the content of the first and second substances,
Figure BDA0002990520330000094
to represent
Figure BDA0002990520330000095
Represents the constituent sequence operations,
Figure BDA0002990520330000096
represents the difference between the m-th power and the m + 1-th power in the power sorted in descending order,
Figure BDA0002990520330000097
representing constituent sequences
Figure BDA0002990520330000098
M of (b) starts from i, ends at 1 intervals, and ends at W' -1.
Thirdly, calculating the variance of each subsequence of the cumulative difference sequence
Figure BDA0002990520330000099
Fourthly, calculating the reciprocal of the relative attenuation degree of the power sequence in the descending order at the ith element position by using the following formula:
Figure BDA00029905203300000910
wherein SORTE (i) represents the inverse of the relative degree of attenuation of the power sequence sorted in descending order at the ith element position.
And fifthly, taking the serial number corresponding to the minimum value of the SORTE (i) as the number of the real targets.
And step 10, obtaining the arrival direction of the target.
And sorting the power of the echo signals of all the potential targets according to the descending power, taking the first powers equal to the number of the real targets in the sorting, and taking the arrival direction of the corresponding potential target relative to the co-prime array radar as the arrival direction value of the target.
The technical effects of the present invention are further explained by combining simulation experiments as follows:
1. simulation experiment conditions are as follows:
the hardware environment of the simulation experiment of the invention is as follows: the CPU is Inter (R) Xeon (R) CPU E3-1231 v3, the main frequency is 3.40GHz, the memory is 32.0GB, 64-bit operating system.
The software environment of the simulation experiment of the invention is as follows: microsoft windows 10 professional edition, MATLAB 2016b simulation software.
2. And (5) analyzing simulation contents and results thereof.
The simulation experiment of the present invention was performed by using the present invention and one of the prior art (RAM method).
In the simulation experiment, the RAM method in the prior art is the weighted Atomic Norm Minimization planning method proposed by Z Yang et al in "Enhancing spark and Resolution via weighted Atomic Norm Minimization, IEEE Transactions on Signal Processing 64.4(2016): 995-1006", which is referred to as the RAM method for short.
Simulation experiment 1, using the present invention and a prior art (RAM method) to perform direction of arrival estimation on three targets in the following simulation environment, respectively.
Radar carrier frequency in simulation experiment 1 is carrier frequency fcThe antenna is a uniform linear array or a co-prime array, and comprises 16 array elements, the spacing between the array elements is half of the wavelength of signals received by the co-prime array radar, and the propagation speed c of electromagnetic waves is 3 x 108m/s, and a range resolution of 15 m. The number of frequency modulation signals transmitted by the radar is 5000, and the duration of each frequency modulation signal is 500 us.
In the simulation environment of the simulation experiment 1, three moving targets to be detected and uniformly accelerated exist, and the direction angle of each target relative to the direction of arrival of the co-prime array radar, the distance between each target and the co-prime array radar, and the speed and acceleration of each target relative to the co-prime array radar are respectively shown in table 1.
The noise adding mode in the simulation experiment 1 is to use additive complex white Gaussian noise to pollute the echo under the condition that the signal-to-noise ratio is-3 dB.
TABLE 1 summary of parameters of the object to be examined
Figure BDA0002990520330000111
The result of two-dimensional fourier transform along the fast time dimension and the slow time dimension of a signal obtained by the simulation experiment 1 through the step of forming a co-prime array radar echo wave beam signal by using the method of the invention is drawn as a pixel map shown in fig. 3 (a).
The two-dimensional matrix of the projection of the simulation experiment 1 in the distance-angle domain, which is obtained by the method of the present invention through the steps of generalized de-modulation-wedge transformation, is plotted as fig. 3 (b).
The two-dimensional matrix of the projection of the simulation experiment 1 in the velocity-acceleration domain, which is obtained by the method of the present invention through the steps of generalized de-modulation and wedge-shaped transformation, is plotted as fig. 3 (c).
The echo power of the target and the direction of arrival of the target relative to the co-prime array radar, which are obtained by the FS-RAM in the simulation experiment 1 using the method of the present invention, are plotted as fig. 3 (d).
The normalized amplitude of the target echo and the direction of arrival of the target relative to the co-prime array radar obtained by the prior art RAM method in the simulation experiment 1 are plotted as fig. 3 (e).
Simulation experiment 2, using the present invention and a prior art (RAM method) to perform direction of arrival estimation on two nearby targets in the following simulation environment, respectively.
Two adjacent targets exist in the simulation environment in the simulation experiment 2, the two targets are in the same beam of the co-prime array radar, the distance between the two targets is close, and the speed and the acceleration of the two targets are approximate. By varying the angular separation of two targetsθWith the angle of the first target set to 1 ° for each trial, and the second target passing through the interval Δ in the angular dimensionθ×δθAre separated from each other by a factor ofθRepresenting the beamwidth of a co-prime array radar.
The radar, the frequency modulation signal emitted by the radar and the noise adding mode in the simulation experiment 2 are the same as those in the simulation experiment 1.
In the simulation experiment 2, the Monte Carlo experiment is carried out 50 times by respectively adopting the RAM method of the invention and the RAM method of the prior art, the direction of arrival estimation is carried out on two adjacent targets, and the correct separation probability of the two methods for carrying out the direction of arrival estimation on the two adjacent targets is counted.
To compare the accuracy of the direction of arrival estimation for two nearby targets of the present invention versus the prior art RAM method, the Root Mean Square Error (RMSE) is calculated using the following formula:
Figure BDA0002990520330000121
wherein the content of the first and second substances,
Figure BDA0002990520330000122
representing the number of targets, k the target sequence number, Σ (-) representing the summation operation,
Figure BDA0002990520330000123
the actual angle of the kth target is indicated,
Figure BDA0002990520330000124
represents the angle estimate of the kth target in the p-th monte carlo test.
Fig. 4(a) is a graph plotting correct separation probability data of the simulation experiment 2, which is obtained by estimating the direction of arrival of two adjacent targets by using the method of the present invention and the RAM method of the prior art, respectively.
The root mean square error data of simulation experiment 2, which was obtained by estimating the direction of arrival of two adjacent targets using the method of the present invention and the RAM method of the prior art, respectively, is plotted as fig. 4 (b).
Simulation experiment 3, the method of the present invention is adopted to estimate the direction of arrival of two adjacent targets in the following simulation environment.
The noise adding mode in the simulation experiment 3 is that under the condition that the signal-to-noise ratio is 0dB, -10dB, -20dB and-30 dB, additive complex Gaussian white noise is adopted to pollute the echo respectively.
Other simulation parameters were the same as in simulation experiment 2.
Under the conditions that the signal-to-noise ratio is 0dB, -10dB, -20dB and-30 dB respectively, Monte Carlo experiments are carried out for 50 times by adopting the method, the direction of arrival estimation is carried out on two adjacent targets, and the correct separation probability of the two methods on the two adjacent targets is counted.
The correct separation probability data of the simulation experiment 3 for estimating the direction of arrival of two adjacent targets by adopting the method of the invention under the conditions that the signal-to-noise ratio is 0dB, -10dB, -20dB and-30 dB respectively is drawn as a graph 5.
The simulation experiment 1 result is shown in fig. 3, fig. 3(a) is a distance-slow time domain simulation diagram after the beam forming operation of the present invention, the abscissa is the pulse cumulative number (number), and the ordinate is the distance (m) between the target and the co-prime array radar; fig. 3(b) is a projection simulation diagram of data obtained through the generalized solution frequency modulation-wedge transformation step in the distance-angle domain, x and y coordinates are respectively a distance (m) between a target and a co-prime array radar and an included angle (degree) of the target relative to the co-prime array radar, and z coordinate is a projection amplitude of the data obtained through the generalized solution frequency modulation-wedge transformation step in the distance-angle domain. FIG. 3(c) is a projection simulation diagram of data obtained by the generalized de-FM-wedge transformation step in the velocity-acceleration domain, and the x and y coordinates are the velocity (m/s) and acceleration (m/s) of the target relative to the co-prime array radar respectively2) And the z coordinate is the projection amplitude of the data obtained by the generalized solution frequency modulation-wedge shape transformation step in the speed-acceleration domain. Fig. 3(d) is a simulation diagram of the result of estimation of the direction of arrival through the FS-RAM by using the method of the present invention, the abscissa is the angle (degree) of the target relative to the co-prime array radar, and the ordinate is the normalized amplitude of the target echo. Fig. 3(e) is a simulation diagram of a result of estimation of a direction of arrival based on the RAM method, in which the abscissa is an angle (degree) of a target relative to a co-prime matrix radar, and the ordinate is a normalized amplitude of a target echo.
As can be seen from the distance value distribution corresponding to the light color pixels in different pulse accumulation number regions in fig. 3(a), different pulse accumulation numbers of the echo signal of the co-prime array radar correspond to different distances, and energy defocusing may be generated if two-dimensional fourier transform is directly performed.
As can be seen from fig. 3(b) that the targets 1,2, and 3 exist in the same peak, the data obtained through the generalized de-fm-wedge transform step cannot separate the three targets in the distance-angle domain.
As can be seen from fig. 3(c) that target 1 is present in one peak, target 2 and target 3 is present in the other peak, it can be seen that the data obtained through the generalized dechirp-wedge transform step can separate targets 2, 3 from target 1 in the velocity-acceleration domain, but target 2 and target 3 are not separable.
As can be seen from the fact that the angle estimated by the method of the present invention in fig. 3(d) is very close to the true value, the method of the present invention can separate two adjacent targets, and the error of estimating the direction of arrival of the adjacent targets is small.
As can be seen from the error between the angle estimated by the RAM method in fig. 3(e) and the true value, the RAM method in the prior art can separate two adjacent targets, but the error in estimating the direction of arrival of the adjacent targets is large.
Comparing the real values in fig. 3(d) and fig. 3(e) with the estimated values of the directions of arrival given by the two methods, it can be seen that the present invention has better resolution performance when there is a target with a closer direction of arrival among the detected group targets.
The results of simulation experiment 2 are shown in fig. 4, in which fig. 4(a) is a simulation graph of the probability of successful resolution, fig. 4(b) is a simulation graph of the estimation error, and the abscissa is the angular interval Δ between two targetsθ(times), the results are distributed within 0.1 to 1, the ordinate is success rate (%), the solid line plus the cross sign represents the simulation result of the invention, and the solid line plus the circle represents the simulation result of the prior art.
As can be seen from fig. 4(a) the success rate of the present invention is consistently higher than or equal to the prior art RAM approach, the present invention has a higher probability of correct separation of spatially adjacent targets than the prior art at a signal-to-noise ratio of-3 dB.
As can be seen from fig. 4(b) the RMSE of the present invention is smaller than the prior art RAM method, the present invention has a smaller error in separating spatially adjacent targets than the prior art at a signal-to-noise ratio of-3 dB.
The results of simulation experiment 3 are shown in FIG. 5, where the abscissa of FIG. 5 is the angular interval Δ between two targetsθ(times), the results are distributed within 0.1 to 1, the ordinate is success rate (%), and the solid line plus the circle, the solid line plus the cross, the solid line plus the star, and the solid line plus the square respectively represent the simulation results that the echo signal-to-noise ratio is 0dB, -10dB, -20dB, and-30 dB.
As can be seen from fig. 5, when the echo signal-to-noise ratio is less than-20 dB, the super-resolution reconstruction performance is closely related to the echo signal-to-noise ratio. The higher the echo signal-to-noise ratio, the better the super-resolution reconstruction performance. When the signal-to-noise ratio of the echo is-20 dB, the super-resolution performance of the method is still close to 5 times. Although the-30 dB case is slightly worse than the-20 dB case, the super-resolution performance of this strategy is still close to 3.3 times. Therefore, the invention discloses a noise robust direction of arrival estimation method.

Claims (9)

1. A group target focusing super-resolution direction-of-arrival estimation method utilizing a co-prime array radar is characterized in that a co-prime array radar for enlarging the aperture of an array antenna is constructed, a generalized solution frequency modulation-wedge transform method is utilized to respectively carry out distance compensation and acceleration compensation on focused signals, interpolation is utilized to improve information extraction performance, a long-time coherent accumulation method is utilized to focus echo signals, and a meshless FS-RAM method is utilized to carry out super-resolution direction-of-arrival estimation on group targets, and the method comprises the following steps:
(1) constructing a co-prime array radar:
the radar receiving end uses M + N-1 antennas and carries out array architecture of the co-prime array radar receiving antenna according to the co-prime array structure; wherein M and N are relatively prime integers;
(2) forming a co-prime array radar echo wave beam signal:
(2a) dividing the space of the group target to be searched
Figure FDA0002990520320000011
A grid point, wherein [. ]]Denotes the rounding operation, θmaxAnd thetaminRespectively representing the maximum and minimum angles, delta, between the space of the group object to be searched and the co-prime array radarθRepresenting the beam width of the co-prime array radar;
(2b) calculating a Hadamard product of the beam steering vector of each grid point angle and an echo signal received by the co-prime array radar as a grid point beam signal;
(3) the generalized FM-wedge transform method is used for compensating the speed and the acceleration:
(3a) performing speed compensation on the beam signal of each grid point by using wedge transformation to obtain a speed-compensated beam signal;
(3b) performing acceleration compensation on each speed-compensated signal by using a generalized frequency demodulation method and a plurality of accelerations respectively to obtain compensated beam signals;
(4) performing two-dimensional interpolation on each compensated beam signal:
carrying out cubic spline interpolation on the slow time dimension of each compensated beam signal and then carrying out cubic spline interpolation on the fast time dimension to obtain an interpolated beam signal;
(5) focusing echo signals by using a long-time coherent accumulation method:
performing two-dimensional Fourier transform on each interpolated beam signal along the fast time dimension and the compensated slow time dimension to obtain a focused signal, and calculating an absolute value of the focused signal;
(6) detecting the group target by using a constant false alarm rate CFAR method:
(6a) when the maximum value of the absolute value of the focused signal is larger than a threshold value, judging that a group target exists;
(6b) obtaining target parameters of each group target;
(7) respectively reconstructing a signal of a complete uniform linear array corresponding to a co-prime array of each group of targets by utilizing a reverse beam forming technology;
(8) the echo power and the direction of arrival of all potential targets are estimated using the FS-RAM method:
(8a) respectively calculating a frequency interval corresponding to an interval where each group target is located relative to the direction of arrival of the co-prime array radar;
(8b) respectively using an FS-RAM method, regarding each group target, taking a frequency interval corresponding to an interval where the group target is located relative to the direction of arrival of the co-prime array radar as prior information required by the FS-RAM method, and extracting potential target information from a complete uniform linear array signal corresponding to the co-prime array of the group target;
(8c) splicing potential target information extracted from all signals corresponding to the complete uniform linear array of the co-prime array to serve as the power of echo signals of all potential targets and the direction of arrival of all potential targets relative to the co-prime array radar;
(9) estimating the number of real targets in all potential targets by using an SORTE method;
(10) obtaining the direction of arrival of the target:
and sorting the power of the echo signals of all the potential targets according to the descending power, taking the first powers equal to the number of the real targets in the sorting, and taking the arrival direction of the corresponding potential target relative to the co-prime array radar as the arrival direction value of the target.
2. The method for estimating direction of arrival (DOA) of group targets focused by using a co-prime array radar as claimed in claim 1, wherein the step (1a) of constructing the array of the receiving antennas of the co-prime array radar according to the co-prime array structure comprises the following steps:
the first step is as follows: selecting a pair of coprime integers M, N;
the second step is that: constructing a pair of sparse uniform linear sub-arrays, the first sub-array comprising M spaced nxd antenna elements at positions 0, nxd, …, (M-1) xnd, the second sub-array comprising N spaced mxd antenna elements at positions 0, mxd, …, (N-1) xmd, wherein d is half of the shortest wavelength of the radar received signal;
the third step: and combining the two sub-arrays according to the first array element overlapping mode to obtain a non-uniform co-prime array structure actually containing M + N-1 array elements, and performing the array architecture of the co-prime array radar receiving antenna according to the non-uniform co-prime array structure.
3. The method according to claim 1, wherein the group targets in step (2a) are multiple targets clustered in space and distributed in a beam of the co-prime array radar, and the distances between the targets are close, and the velocities and accelerations of several targets are similar.
4. The method of claim 1, wherein the threshold in step (6a) is determined by a Constant False Alarm Rate (CFAR) method.
5. The method according to claim 1, wherein the target parameters of the group target in step (6b) are: the method comprises the steps of roughly estimating the direction of arrival of a group target relative to a co-prime array radar, the distance between the group target and the co-prime array radar, the speed of the group target relative to the co-prime array radar, and the speed of the group target relative to the co-prime array radar.
6. The method of estimating direction of arrival of group targets focused by co-prime array radar as claimed in claim 1, wherein the inverse beamforming technique in step (7) is as follows:
firstly, reconstructing an echo signal of each array element of a complete uniform linear array corresponding to a co-prime array;
and secondly, forming an array by the echo signals of all the array elements, and using the array as the echo signal of the complete uniform linear array corresponding to the co-prime array.
7. The method according to claim 1, wherein the step (8a) of calculating the frequency interval corresponding to the interval where the direction of arrival of each group target relative to the co-prime array radar is located comprises the following steps:
the first step is that for each group target, the upper limit f of the frequency interval corresponding to the interval where the direction of arrival of the group target relative to the co-prime array radar is located is calculatedH：
Figure FDA0002990520320000031
Wherein d represents the minimum array element spacing of the co-prime array radar, cos (·) represents the cosine operation, and θ representszRepresenting a rough estimate of the direction of arrival, δ, of a group target relative to a co-prime array radarθThe wave beam width of the co-prime array radar is represented, and lambda represents the carrier wave length of the co-prime array radar signal;
secondly, for each group target, respectively calculating the lower limit f of a frequency interval corresponding to the interval of the arrival direction of the group target relative to the co-prime array radarL：
Figure FDA0002990520320000041
Third, for each group object, [ f ] is addedL,fH]The frequency range is a frequency range corresponding to a range in which the arrival direction of the group of targets with respect to the co-prime array radar is located.
8. The method of estimating direction of arrival of group targets focused super-resolution using co-prime array radar as claimed in claim 1, wherein the step of the FS-RAM method in step (8b) is as follows:
firstly, calculating a weight vector W;
secondly, solving the following formula:
Figure FDA0002990520320000042
Figure FDA0002990520320000043
wherein:
Figure FDA0002990520320000044
represents the minimization operation, u represents the optimal estimation value of the vector formed by the first column elements of the ideal autocorrelation matrix of the uniform linear array radar receiving signal with the same aperture as the co-prime array radar, tr [ ·]Which means that the rank-finding operation is performed,
Figure FDA0002990520320000045
representing the topolitz matrix operation, alpha representing a free variable, subject to representing a constraint,
Figure FDA0002990520320000046
represents an ideal received signal of a uniform linear array radar having the same caliber as the co-prime array radar (·)HWhich represents the conjugate transpose operation,
Figure FDA0002990520320000047
is represented by alpha,
Figure FDA0002990520320000048
The spliced matrix represents the positive definite of the matrix, | | · | air distribution |, the matrix is more than or equal to 0FRepresents an F norm operation [ ·]ΩThe operation of taking out the received signals of the same array elements of the uniform linear array radar and the co-prime array radar is shown, x is the received signal of the co-prime array radar obtained by reconstructing a group target, eta is a threshold value determined by environmental noise,
Figure FDA0002990520320000049
the optimal estimation value of an ideal autocorrelation matrix of a receiving signal of the uniform linear array radar with the same caliber as the co-prime array radar under the condition of a known frequency range is represented;
thirdly, judging whether the conditions for finishing the circulation are met, if so, executing the fourth step; otherwise, the weight vector W is recalculated by using u obtained in the second step, and the second step is executed; the condition for ending the loop refers to a case where one of the following two conditions is satisfied: the method comprises the following steps that 1, the circulation frequency is larger than the maximum circulation frequency determined according to computer resources and direction finding precision requirements; condition 2, u obtained by continuously executing the second step twice is the same;
and fourthly, carrying out Van der Mond decomposition on the Tueplitz matrix of u obtained in the second step, respectively taking each power obtained by the Van der Mond decomposition as the power of the echo signal of each potential target, and enabling the potential target obtained by the Van der Mond decomposition to be opposite to the direction of arrival of the mutual mass array radar.
9. The method for estimating direction of arrival of group targets focused super-resolution using co-prime array radar as claimed in claim 1, wherein the SORTE method in step (9) is as follows:
the method comprises the following steps that firstly, the power of echo signals of all potential targets is sorted according to a descending order;
second, construct the cumulative difference sequence
Figure FDA0002990520320000051
Each subsequence in the cumulative difference sequence is calculated using the formula:
Figure FDA0002990520320000052
wherein the content of the first and second substances,
Figure FDA0002990520320000053
to represent
Figure FDA0002990520320000054
Denotes a composition sequence operation, # γ { }mRepresents the difference between the m-th power and the m + 1-th power in the power sorted in descending order,
Figure FDA0002990520320000055
denotes ^ gamma of a constituent sequencemThe value range of m is from i, takes 1 as an interval and ends with W' -1;
thirdly, calculating the variance of each subsequence of the cumulative difference sequence
Figure FDA0002990520320000056
Fourthly, calculating the reciprocal of the relative attenuation degree of the power sequence in the descending order at the ith element position by using the following formula:
Figure FDA0002990520320000057
wherein SORTE (i) represents the inverse of the relative degree of attenuation of the power sequence sorted in descending order at the ith element position;
and fifthly, taking the serial number corresponding to the minimum value of the SORTE (i) as the number of the real targets.
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