CN112924965B - Clustering coherent superposition-based frequency diversity array radar target imaging method - Google Patents

Clustering coherent superposition-based frequency diversity array radar target imaging method Download PDF

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CN112924965B
CN112924965B CN202110137151.1A CN202110137151A CN112924965B CN 112924965 B CN112924965 B CN 112924965B CN 202110137151 A CN202110137151 A CN 202110137151A CN 112924965 B CN112924965 B CN 112924965B
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CN112924965A (en
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谢宁波
罗晓萍
廖可非
欧阳缮
王海涛
王辉
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Guilin University of Electronic Technology
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Abstract

The invention discloses a frequency diversity array radar target imaging method based on cluster coherent superposition, which adopts the fusion of K-means clustering and a BP algorithm and solves the problems of fuzzy imaging and high side lobe of the traditional BP algorithm when FDA radar positions and images multiple targets. In the method, each time the frequency offset is changed to perform new scanning on the imaging area, the time delay compensation in the data processing process only needs to perform time delay compensation calculation on the grid point marked with the last clustering classification cluster as 1 without traversing the full grid space, so that the improved method provided by the invention can effectively reduce the operation amount compared with the existing method; meanwhile, the improved method provided by the invention fully utilizes the energy concentration characteristic of the target point and the difference of the energy of the target point and the virtual image point, can effectively eliminate the target virtual false image and effectively improve the accuracy of the imaging result.

Description

Clustering coherent superposition-based frequency diversity array radar target imaging method
Technical Field
The invention relates to the technical field of radar signal processing, in particular to an improved method for radar target imaging based on a Frequency Diversity Array (FDA) of clustering coherent superposition.
Background
The frequency diversity array radar is a new system radar evolved from phased array radar, and the biggest difference relative to a common uniform linear array is that a frequency offset which is far smaller than a reference carrier frequency is arranged between two adjacent array elements. This makes its beam pattern not only angle-dependent but also distance and time-dependent, so FDA radar has a wide application prospect in radar target detection imaging.
At present, FDA radar target imaging method is generally based on array element single-frequency receiving mode, and BP and MUSIC algorithm is adopted to realize target positioning and imaging. However, the inherent distance and angle coupling characteristics of the linear frequency offset FDA beam pattern require that the frequency offset is changed for multiple times to realize a multi-target imaging task, and the method has the problems of high side lobe and imaging blur, and the effect is not ideal when the multi-target is accurately positioned and imaged.
On the other hand, a target echo signal of the radar has the characteristic of energy concentration at a specific position through coherent accumulation. By utilizing the characteristic, the clustering method is combined with a back projection algorithm (BP algorithm) to extract and classify the characteristics of the scanning area according to the echo response amplitude, and the algorithm is a radar target imaging improvement algorithm with low calculated amount and side lobe elimination.
Disclosure of Invention
The invention aims to solve the technical problems of high side lobe and imaging fuzziness of the existing FDA radar adopting a BP algorithm to perform target imaging in a single-frequency receiving mode, and provides a frequency diversity array radar target imaging method based on clustering coherent superposition.
In order to solve the problems, the invention is realized by the following technical scheme:
a frequency diversity array radar target imaging method based on clustering coherent superposition comprises the following steps:
step 1, constructing a single-frequency receiving frequency diversity array;
the frequency diversity array is composed of N antenna array elements which are linearly arranged at equal intervals, and a single-frequency receiving mechanism is adopted, namely, each array element only receives an echo corresponding to a signal sent by the array element;
the transmitting frequency of each array element of the constructed frequency diversity array is sequentially and linearly increased, and the frequency f of the transmitting signal of the nth array element isnComprises the following steps:
fn＝f0+nΔf1 n＝0,1,…,N-1
in the formula (f)0Setting the initial transmitting frequency of the frequency diversity array, namely the central frequency of the signal transmitted by the first array elementFor reference array elements,. DELTA.f1The frequency offset is the frequency offset of the frequency diversity array, and N is the number of array elements of the frequency diversity array;
step 2, dividing the imaging area into grid points according to distance and angle, initializing a grid point cluster mark, and initializing the cluster mark to 1;
step 3, scanning an imaging area by using the frequency diversity array in the step 1 to transmit narrow-band signals, and receiving echo data by adopting a single-frequency receiving mechanism;
step 4, carrying out time delay compensation on the grid points marked with the clusters as 1 in the imaging area to obtain echo amplitudes of each array element of the frequency diversity array at each grid point;
step 5, overlapping the echo amplitudes of the grid points in the step 4 relative to the N array elements to obtain the total echo response of the frequency diversity array relative to each grid point;
step 6, vectorizing a data matrix formed by the total echo response data of the grid points in the step 5, clustering and dividing a data set obtained by matrix vectorization by using a K-means clustering algorithm, updating grid point cluster marks, selecting a cluster with the largest clustering center as a next search path, and setting a grid point cluster mark corresponding to the cluster with the largest clustering center value as 1;
the concrete substeps of step 6 are:
the data set obtained by vectorizing the obtained echo response data matrix is represented as D ═ x1,x2,…,xmRandomly selecting k echo response data from D to initialize a mean vector (mu) formed by cluster centers1,μ2,…,μkThen echo response data xjAnd cluster center muiHas a squared difference of cji：
cji＝(xj-μi)2
Center of cluster muiIn the middle, i is more than or equal to 1 and less than or equal to k;
determining x according to the difference between each echo response data and the cluster centerjCluster mark of (2)jComprises the following steps:
λj＝arg mini∈{1,2,...,k}cji
wherein k is the number of clusters, cjiFor echo response data xjAnd cluster center muiThe squared difference of (d);
echo response data x according to the least square error criterionjPartitioning into respective clusters:
Figure GDA0003513569090000031
updating cluster centers:
Figure GDA0003513569090000032
judging whether the clustering centers of the two times before and after iteration are the same, and when mu is equali (k'+1)≠μi (k')Then, k' is iteration number, and echo response data x is calculatedjCarrying out cluster division on the data according to the difference with the cluster center;
when mu isi (k'+1)＝μi (k')When the cluster division is stopped, the cluster division C is output as (C)1，C2，…，Ck)；
Step 7, changing the frequency offset of the frequency diversity array, repeating the steps 3-6 to perform new scanning on the imaging area, receiving new echo data by using the array and performing corresponding processing, and totally finishing M times of frequency offset change, radar imaging scanning and data processing;
completing the M frequency offset changes, radar imaging scans and data processing as described in step 7, finally with respect to the grid points (R)q,θq) Obtaining M time delay compensation echo response values in total, and obtaining the pixel value p (R) at the grid point by performing modulo superposition on all the M echo response valuesq,θq)：
Figure GDA0003513569090000041
In the formula (f)0Frequency of transmitted signal, Δ f, for reference array elements of frequency diversity arraymFor the frequency offset of the frequency diversity array, N is the number of array elements of the frequency diversity array, d is the spacing of the array elements, m represents the corresponding serial number during the mth frequency offset scanning, (R)q,θq) Is the two-dimensional position of grid point q in the scan area;
and 8, taking the grid point marked as 1 in the final cluster as a search object, and calculating the pixel value of the corresponding grid point in the imaging scene, namely finishing the imaging of the frequency diversity array radar target.
The radar target imaging method is further improved on the basis of the prior art, and the key point of the improvement is in the steps 6-8.
Compared with the prior art, the invention has the beneficial effects that:
1) the method adopts the fusion of K-means clustering and BP algorithm, and solves the problems of fuzzy imaging and high side lobe of the traditional BP algorithm when FDA radar positions and images multiple targets;
2) the FDA radar target imaging improvement method provided by the invention does not need to traverse all grid points of an imaging area in multiple iterations in the implementation process, can effectively reduce the calculated amount, and is easy to implement.
Drawings
FIG. 1 is a flow chart of a method of imaging an object of the present invention.
Fig. 2 is a schematic diagram of a frequency diversity array according to an embodiment.
Fig. 3 is a schematic diagram of a receiving end of a frequency diversity array in a single frequency receiving system according to an embodiment.
Fig. 4 is a schematic diagram of imaging region meshing.
Fig. 5 is a schematic view of the target position of the imaging region.
FIG. 6 is a two-dimensional display of multi-target imaging with 3 sets of frequency offset scans for an unmodified algorithm.
FIG. 7 is a two-dimensional display of multi-target imaging when the improved algorithm employs 3 sets of frequency offset scans.
FIG. 8 is a three-dimensional display of multi-target imaging with 3 sets of frequency offset sweeps employed by the unmodified algorithm.
FIG. 9 is a three-dimensional display of multi-target imaging when the improved algorithm employs 3 sets of frequency offset scans.
Detailed Description
The present invention will be further described with reference to the following examples and drawings, but the present invention is not limited thereto.
Examples
A flow chart of the frequency diversity array radar target imaging method based on clustering coherent superposition is shown in figure 1, and the specific steps are as follows:
step 1, constructing a single-frequency receiving frequency diversity array, wherein the array structure and the receiving end schematic diagram of the single-frequency receiving frequency diversity array are respectively shown in fig. 2 and fig. 3;
the frequency diversity array has an initial transmission frequency f0Initial frequency bias is Δ f1The array element interval is d, and the frequency diversity array is a one-dimensional uniformly-arranged linear array with N array elements;
the transmitting frequency of each array element of the FDA radar antenna array is sequentially and linearly increased, and the carrier frequency f of the transmitting signal of the nth array element of the array isnExpressed as:
fn＝f0+nΔf1 n＝0,1,…,N-1
in the formula (f)0Setting the initial transmitting frequency of the frequency diversity array, namely the central frequency of the signal transmitted by the first array element as a reference array element, delta f1The frequency offset is the frequency offset of the frequency diversity array, and N is the number of array elements of the frequency diversity array;
in order to realize that each array element of the frequency diversity array only receives the signal sent by itself, a narrow-band filter which only allows the signal sent by itself to pass is connected with the receiving end of each array element of the frequency diversity array.
Step 2, dividing the imaging area into grid points according to distance and angle, wherein the grid division of the imaging area is shown in fig. 4, wherein Δ x is the distance of the grid division in the x-axis direction, Δ y is the distance of the grid division in the y-axis direction, and NrTotal number of divisions of grid, N, for x-axis directiontDividing the total number of grids for the y-axis direction, initializing a cluster mark of grid points of an imaging area, and initializing the cluster mark to be1。
Step 3, scanning the imaging area by using the frequency diversity array in the step 1 to transmit the narrow-band signal, and when the frequency offset is delta f1When the transmitting signal of the nth array element is s1,n(t) the received signal is r1,n(t), N is 0,1,2, …, N-1, t represents a time variable.
The specific substeps in step 3 are:
the frequency diversity array is used for transmitting a narrow-band signal, and the signal s transmitted by the nth array element of the FDAn(t) can be simply expressed as a complex exponential function:
sn(t)＝a(t)exp{j2πfnt}
wherein a (t) is a signal complex envelope, and because a narrow-band signal is transmitted, the envelope fluctuation is very slow, and the difference between each array element can be ignored; for an observed target point p in the far field imaging area, the normal included angle of the observed target point p along the array ray is thetapAnd a distance R from the reference array elementpThe observation target point p is the position of the imaging target, thetapAnd RpA fixed quantity in the whole imaging process, which is contained in the received echo signal, the echo signal time delay tau of the nth array elementnComprises the following steps:
Figure GDA0003513569090000061
receiving far-field target echo signals by using a frequency diversity array, wherein the echo signals received by the nth array element are as follows:
Figure GDA0003513569090000062
step 4, carrying out time delay compensation on the grid point q marked as 1 in the cluster in the imaging area to obtain the echo amplitude r of the nth array element of the array after time delay compensation at the point qn(Rq,θq) Wherein (R)q,θq) Is the two-dimensional position of grid point q in the scan area.
The specific substeps in step 4 are:
for any point in the imaging region with cluster label 1 (R)q,θq) The distance between the frequency diversity array and the nth array element is Rq-nd sinθqAnd calculating the two-way time delay:
Figure GDA0003513569090000063
the time delay compensation is carried out on the echo signal of each array element, and the point (R) of the nth array element of the frequency diversity array can be obtainedq,θq) Echo amplitude r after time delay compensationcomp,n(Rq,θq)：
Figure GDA0003513569090000071
Step 5, all N array elements of the array are related to the scanning grid point (R)q,θq) The time delay compensation echo amplitudes are superposed to obtain the point (R) of the arrayq,θq) Compensating the echo response x for the time delaym(Rq,θq)；
Figure GDA0003513569090000072
Due to f0> N Δ f, then
Figure GDA0003513569090000073
The term can be ignored, and the property of accumulation can be simplified into:
Figure GDA0003513569090000074
wherein the content of the first and second substances,
Figure GDA0003513569090000075
Figure GDA0003513569090000076
where m represents the corresponding sequence number at the time of the mth frequency offset sweep.
Step 6, carrying out vectorization on a data matrix formed by the total echo response data of the grid points in the step 5, carrying out clustering division on a data set obtained by the matrix vectorization by using a K-means clustering algorithm, updating grid point cluster marks, selecting a cluster with the largest clustering center as a next search path, and setting a grid point cluster mark corresponding to the cluster with the largest clustering center value as 1;
the concrete substeps of step 6 are:
the data set obtained by vectorizing the obtained echo response data matrix is represented as D ═ x1,x2,...,xmRandomly selecting k echo response data from D to initialize a mean vector (mu) formed by cluster centers1,μ2,...,μkThen echo response data xjAnd cluster center mui(1. ltoreq. i. ltoreq.k) has a square error of cji：
cji＝(xj-μi)2
Determining x according to the difference between each echo response data and the cluster centerjCluster mark of (2)jComprises the following steps:
λj＝argmini∈{1,2,...,k}cji
wherein k is the number of clusters, cjiFor echo response data xjAnd cluster center mui(1. ltoreq. i. ltoreq.k);
echo response data x according to the least square error criterionjPartitioning into respective clusters:
Figure GDA0003513569090000083
updating cluster centers:
Figure GDA0003513569090000081
judging whether the clustering centers of the two times before and after iteration are the same, and when mu is equali (k'+1)≠μi (k')Then, the echo response data x is calculatedjCarrying out cluster division on the data according to the difference with the cluster center;
when mu isi (k'+1)＝μi (k')When the cluster division is stopped, the cluster division C is output as (C)1，C2，…，Ck)。
Step 7, changing the frequency offset of the frequency diversity array, repeating the steps 3-6 to perform new scanning on the imaging area, using the array to receive and obtain new echo data and perform corresponding processing, totally completing M times of frequency offset change, radar imaging scanning and data processing, and finally regarding the grid point (R)q,θq) Obtaining M time delay compensation echo response values in total, and obtaining the pixel value p (R) at the grid point by performing modulo superposition on all the M echo response valuesq,θq)：
Figure GDA0003513569090000082
And 8, taking the grid point marked as 1 in the final cluster as a search object, and calculating the pixel value of the corresponding grid point in the imaging scene, namely finishing FDA radar target imaging.
In the method, the imaging area is newly scanned by changing the frequency offset every time, and the time delay compensation in the data processing process only needs to carry out time delay compensation calculation on the grid point marked as 1 in the last clustering classification cluster without traversing the full grid space, so that the improved method provided by the invention can effectively reduce the operation amount compared with the existing method; meanwhile, the improved method provided by the invention fully utilizes the energy concentration characteristic of the target point and the difference of the energy of the target point and the virtual image point, can effectively eliminate the target virtual false image and effectively improve the accuracy of the imaging result.
The effect of the present invention can be further illustrated by the following simulation results:
1) simulation conditions
The frequency diversity array antenna model adopts a one-dimensional uniformly-arranged linear array as shown in fig. 2, wherein the number of array elements is N-80, and the radar signal carrier frequency reference is f010GHz with array element spacing
Figure GDA0003513569090000091
The initial frequency offset is 600 KHz.
Imaging area distance range: 9.6km to 9.9km, and the distance domain scanning interval is 3 m; azimuth angle range: 6 degrees to 6 degrees, and the interval of azimuth angle scanning angles is 0.2 degrees.
The target is a 5-point target, the position diagram of which is shown in fig. 5, and the position information is respectively: object 1 (x)1,y1) = (9750m, -2 °); object 2 (x)2,y2) (9750m, 0); target 3 (x)3,y3) = (9750m,2 °); target 4 (x)4,y4) = (9775m,0 °); target 5 (x)5,y5)＝(9725m,0°)；
2) Simulation result
Experiment 1, multi-target imaging was performed using the traditional BP algorithm. The imaging area is scanned by using 3 sets of frequency offsets, and the imaging simulation results are shown in fig. 6 and 8, wherein the radar imaging results of 5 targets are shown in a manner that the targets can be distinguished, but the images are blurred and the side lobes are high.
Experiment 2, the improved method proposed by the present invention was used for multi-objective imaging. The simulation conditions are the same as those of experiment 1, and the imaging simulation results are shown in fig. 7 and 9, wherein the radar imaging results of the 5 targets show that the targets are clearly visible, the images are clear, and the target positioning positions are consistent with the actual positions.
In conclusion, the frequency diversity array radar target imaging method based on cluster coherent superposition effectively solves the problems of fuzzy and high side lobe of the traditional linear frequency offset FDA radar target imaging image based on the BP algorithm, and the effectiveness of the method is verified through a simulation experiment.

Claims (1)

1. A frequency diversity array radar target imaging method based on clustering coherent superposition is characterized by comprising the following steps:
step 1, constructing a single-frequency receiving frequency diversity array;
step 2, dividing the imaging area into grid points according to distance and angle, initializing a grid point cluster mark, and initializing the cluster mark to 1;
step 3, scanning an imaging area by using the frequency diversity array in the step 1 to transmit narrow-band signals, and receiving echo data by adopting a single-frequency receiving mechanism;
step 4, carrying out time delay compensation on the grid points marked with the clusters as 1 in the imaging area to obtain echo amplitudes of each array element of the frequency diversity array at each grid point;
step 5, overlapping the echo amplitudes of the grid points in the step 4 relative to the N array elements to obtain the total echo response of the frequency diversity array relative to each grid point;
step 6, vectorizing a data matrix formed by the total echo response data of the grid points in the step 5, clustering and dividing a data set obtained by matrix vectorization by using a K-means clustering algorithm, updating grid point cluster marks, selecting a cluster with the largest clustering center as a next search path, and setting a grid point cluster mark corresponding to the cluster with the largest clustering center value as 1;
the concrete substeps of step 6 are:
the data set obtained by vectorizing the obtained echo response data matrix is represented as D ═ x1,x2,...,xmRandomly selecting k echo response data from D to initialize a mean vector (mu) formed by cluster centers1,μ2,…,μkThen echo response data xjAnd cluster center muiHas a squared difference of cji：
cji＝(xj-μi)2
Center of cluster muiIn the middle, i is more than or equal to 1 and less than or equal to k;
determining x according to the difference between each echo response data and the cluster centerjCluster mark of (2)jComprises the following steps:
λj＝arg mini∈{1,2,...,k}cji
wherein k is the number of clusters, cjiFor echo response data xjAnd cluster center muiThe squared difference of (d);
echo response data x according to the least square error criterionjPartitioning into respective clusters:
Figure FDA0003513569080000021
updating cluster centers:
Figure FDA0003513569080000022
judging whether the clustering centers of the two times before and after iteration are the same, and when mu is equali (k'+1)≠μi (k')Then, the echo response data x is calculatedjCarrying out cluster division on the data according to the difference with the cluster center;
when mu isi (k'+1)＝μi (k')When the cluster division is stopped, the cluster division C is output as (C)1，C2，...，Ck)；
Step 7, changing the frequency offset of the frequency diversity array, repeating the steps 3-6 to perform new scanning on the imaging area, using the array to receive and obtain new echo data and perform corresponding processing, totally completing M times of frequency offset change, radar imaging scanning and data processing, and finally regarding the grid point (R)q,θq) Obtaining M time delay compensation echo response values in total, and obtaining the pixel value p (R) at the grid point by performing modulo superposition on all the M echo response valuesq,θq)：
Figure FDA0003513569080000023
In the formula (f)0Frequency of transmitted signal, Δ f, for reference array elements of frequency diversity arraymFor the frequency offset of the frequency diversity array, N is the number of array elements of the frequency diversity array, d is the spacing of the array elements, m represents the corresponding serial number during the mth frequency offset scanning, (R)q,θq) Is the two-dimensional position of grid point q in the scan area;
and 8, taking the grid point marked as 1 in the final cluster as a search object, and calculating the pixel value of the corresponding grid point in the imaging scene, namely finishing the imaging of the frequency diversity array radar target.
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