CN115453536A - Forward-looking azimuth pitching two-dimensional super-resolution imaging method for motion platform - Google Patents

Forward-looking azimuth pitching two-dimensional super-resolution imaging method for motion platform Download PDF

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CN115453536A
CN115453536A CN202211207454.7A CN202211207454A CN115453536A CN 115453536 A CN115453536 A CN 115453536A CN 202211207454 A CN202211207454 A CN 202211207454A CN 115453536 A CN115453536 A CN 115453536A
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杨建宇
黄钰林
马彦晶
杨海光
罗嘉伟
张寅�
张永超
张永伟
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a method for two-dimensional super-resolution imaging of a forward-looking direction and a pitching direction of a motion platform. The method solves the problems that the existing real-aperture radar is low in azimuth-elevation two-dimensional resolution and is not suitable for a moving platform, and compared with the existing two-dimensional scanning radar super-resolution method, the method not only can be used for two-dimensional super-resolution imaging of the moving platform, but also has excellent target resolution capability and lower calculation complexity and is suitable for engineering realization.

Description

Forward-looking azimuth pitching two-dimensional super-resolution imaging method for motion platform
Technical Field
The invention belongs to the technical field of radar imaging, and particularly relates to a forward-looking azimuth pitching two-dimensional super-resolution imaging method for a motion platform.
Background
The Real Aperture Radar (RAR) has forward-looking target detection capability which cannot be realized by a Synthetic Aperture Radar (SAR) and a Doppler Beam Sharpening (DBS) in the aspect of an imaging mechanism, and is widely applied to civil fields such as topographic mapping, autonomous landing, material airdrop and the like. Existing RAR super-resolution methods can improve azimuth imaging resolution, but the result is typically an azimuth-distance two-dimensional image with a fixed pitch angle, regardless of the scanning modulation of the pitch beam antenna pattern.
To obtain high azimuthal resolution matching range resolution, the literature "Zhang Y, li J, li M, et al, online space Reconstruction for Scanning Radar Using Beam-Updating q-spice, ieee Geoscience and Remote Sensing Letters,2021, 19: 1-5' provides a generalized spatial-based estimation (SPICE) method based on beam updating, the method utilizes the sparsity of a target scene, compared with an iterative adaptive method, the method further improves the azimuth resolution, but the processing sequence of the method to the azimuth and the pitch direction can seriously deteriorate the imaging result, and the method can not be directly used for two-dimensional super-resolution imaging; the literature "Tuo X, xia Y, zhang Y, et al. Super-Resolution Imaging for Real Aperture radio by Two-Dimensional resolution.2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS. IEEE,2021:6630-6633 "proposes a two-dimensional super-resolution imaging Method based on sparse Alternating Direction multiplier (ADMM), which uses regularized 1 norm constraint and uses ADMM Method to solve, improving the two-dimensional resolution of RAR, but the Method is only effective for fixed platform, but is difficult to realize airborne moving platform radar azimuth pitching two-dimensional resolution.
Disclosure of Invention
In order to solve the technical problem, the invention provides a two-dimensional super-resolution imaging method for pitching a forward-looking direction of a motion platform.
The technical scheme adopted by the invention is as follows: a forward-looking azimuth pitching two-dimensional super-resolution imaging method for a motion platform comprises the following specific steps:
s1, an orientation-pitching two-dimensional scanning echo model of an airborne radar platform;
if the airborne radar platform is located at the point A (0, gamma) when t =0 and moves at a constant speed along the y-axis direction at the speed v, gamma represents the height of the airborne platform, and if the airborne platform moves to the point B at the moment t, AB = vt can be obtained, and if a point P (x) in the scanning area is set P ,y P ,z P ) The projection on the xOy plane is the Q point, R P The distance between the radar platform and the target at the initial moment,
Figure BDA0003874623660000011
is the pitch angle, θ, of the target relative to the radar platform P Is the azimuth angle of the target with respect to the y-axis direction. According to the geometrical relationship, the distance R (t) between the airborne platform and the target at the time t can be represented as follows:
Figure BDA0003874623660000021
according to the following geometrical relationship:
Figure BDA0003874623660000022
substituting the formula (2) into the formula (1) to obtain:
Figure BDA0003874623660000023
taylor unfolding of R (t) gives:
Figure BDA0003874623660000024
wherein, O (t) 2 ) Denotes t 2 In the coherent accumulation time (CPI) of an arbitrary point target, satisfies vt < R P Thus, the quadratic and higher order terms of the distance history are negligible, and equation (4) can be approximated as:
Figure BDA0003874623660000025
setting a scanning radar to transmit a chirp signal:
Figure BDA0003874623660000026
where τ is the distance time variable, T p For the pulse width, rect (-) represents a rectangular window function, f c Denotes the carrier frequency, K r Indicating the chirp rate. According to the platform motion, beam scanning, signal transmitting and receiving processes, the echo signal of the target P point can be expressed as:
Figure BDA0003874623660000027
where t is the platform motion time variable (slow time), τ is the distance time variable (fast time), σ P The scattering coefficient of the target P is represented by k, a constant containing various gains and losses, c is the propagation speed of the electromagnetic wave, and h (t) is the antenna pattern modulation function. In distance, high distance resolution is achieved through pulse compression, and after carrier frequency removal and pulse compression processing, echoes can be written as:
Figure BDA0003874623660000031
wherein, B r Represents the signal bandwidth and satisfies B r ＝K r T p And sinc (·) represents a distance signal envelope after pulse compression, and is particularly marked as sinc (γ) = sin (π γ)/π γ, the last term exp { -j4 π R (t)/λ } represents a Doppler phase term caused by stage motion, and λ represents wavelength.
The method for scanning the target airspace omega is as follows: for the first pitch dimension, scanning along the azimuth direction, jumping to the second pitch dimension, scanning along the azimuth direction, and so on, and scanning densely in a Z shape line by line, wherein the sum of delta theta and delta theta
Figure BDA0003874623660000032
Respectively representing the azimuth and elevation wave position jump, phi θ And
Figure BDA0003874623660000033
respectively representing azimuth and elevation sweep ranges, N θ And
Figure BDA0003874623660000034
respectively representing the number of azimuth and pitch samples. In the scanning process of the airborne radar platform, the fast time tau and the slow time t respectively meet the following conditions:
Figure BDA0003874623660000035
Figure BDA0003874623660000036
wherein PRF denotes the pulse repetition frequency, θ and
Figure BDA0003874623660000037
representing the azimuth pitch angle variable and R the range variable.
S2, echo pretreatment;
substituting the formula (9) and the formula (10) into the echo formula (8) can obtain a distance-azimuth-pitch three-dimensional echo expression:
Figure BDA0003874623660000038
wherein the content of the first and second substances,
Figure BDA0003874623660000039
representing a two-dimensional antenna pattern, in order to eliminate the range walk created by the relative motion of the platform and target, the range walk amount can be expressed as:
Figure BDA00038746236600000310
constructing a phase compensation factor in the distance frequency domain:
Figure BDA00038746236600000311
wherein f is R And (3) representing a distance frequency variable, performing Fast Fourier Transform (FFT) on the distance direction of the formula (11), multiplying the distance direction by the formula (13), and performing Inverse Fast Fourier Transform (IFFT) on the distance direction to obtain an echo after walking correction:
Figure BDA0003874623660000041
wherein, the fourth term in the formula
Figure BDA0003874623660000042
A constant term related to the initial slope distance is expressed, the azimuth and elevation two-dimensional processing is not influenced and can be approximately ignored, and a fifth term expresses Doppler phase modulation generated in the relative motion process. When the target is located in the forward looking range of the airborne platform,
Figure BDA0003874623660000043
in this case, the doppler history of each target in the forward-looking region is approximately equal, so equation (14) can be approximated as:
Figure BDA0003874623660000044
is located in an airspace omega
Figure BDA0003874623660000045
Has a target backscattering coefficient of
Figure BDA0003874623660000046
R 0 ,θ 0 ,
Figure BDA0003874623660000047
Respectively represent objects
Figure BDA0003874623660000048
The total echo of the detection airspace can be written as:
Figure BDA0003874623660000049
for a fixed range unit, only azimuth and pitch changes are considered. The azimuth-elevation two-dimensional scanning of the detection area is equivalent to the two-dimensional convolution of a two-dimensional antenna directional diagram and each scattering point of the detection area by a target scattering coefficient and an azimuth elevation two-dimensional antenna directional diagram. Thus, equation (16) can be simplified to an echo model for a single range bin as:
Figure BDA00038746236600000410
wherein the content of the first and second substances,
Figure BDA00038746236600000411
is equivalent to a two-dimensional convolution kernel,
Figure BDA00038746236600000412
representing the target azimuth pitch scatter distribution for the corresponding range bin.
Considering additive noise, there are:
Figure BDA00038746236600000413
wherein, denotes a two-dimensional convolution,
Figure BDA00038746236600000414
is equivalent to a two-dimensional convolution kernel,
Figure BDA00038746236600000415
representing additive gaussian noise.
For simplicity of presentation, the two-dimensional convolution model (18) can be discretized as:
Y＝AXB T +N (19)
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00038746236600000416
an echo matrix representing a slice at a certain distance,
Figure BDA00038746236600000417
is a backscattering coefficient matrix of the target, K 1 、K 2 Respectively representing the number of azimuth and elevation sampling points of the backscatter coefficient matrix,
Figure BDA0003874623660000051
in order to be an additive noise, the noise is,
Figure BDA0003874623660000052
representing a real space, T represents the transpose of a matrix,
Figure BDA0003874623660000053
and
Figure BDA0003874623660000054
the azimuth and elevation antenna pattern modulation matrices are represented separately, written specifically as:
Figure BDA0003874623660000055
Figure BDA0003874623660000056
wherein the content of the first and second substances,
Figure BDA0003874623660000059
representing the azimuth dimension antenna pattern sampling points,
Figure BDA0003874623660000057
representing the antenna pattern sample point, L, in elevation 1 And L 2 Respectively representing the sampling points of the directional diagram and the pitching-dimensional antenna directional diagram, and the sampling points M, N and K 1 ，K 2 ，L 1 ，L 2 Satisfies the relationship:
Figure BDA0003874623660000058
s3, calculating an autocorrelation matrix R;
scattering result x from the target (q+1) Can be written as:
x (q+1) ＝P (q) F H (R (q) ) -1 y (23)
wherein q represents the number of iterations, R (q) ＝F H P (q) F is P by the q-th iteration (q) Is obtained by calculation, P (q) ＝diag(x (q) ) Diag (·) denotes the construction of a diagonal matrix from a vector, H denotes the conjugate transpose operation, and Y = vec (Y) is the one-dimensional vectorized version of the echo Y. For simplicity of representation, the number of iterations of R is omitted from equation (24) and onward. Furthermore, due to the particular structure of the scan matrix F, it can be seen that R is actually a singular matrix, which results in R -1 Is wrong. In order to ensure the accuracy of the angle estimation and prevent the noise amplification problem, R is diagonally loaded:
R＝FPF H +μI (24)
wherein μ represents a regularization parameterA number, which balances noise and resolution performance, I denotes a unit matrix. Because the dimension of the matrix R is overlarge, R is directly solved -1 The computational complexity is too high, and R is first reduced by CG algorithm -1 The computational complexity of (2).
S4, iteratively updating U;
defining variables
Figure BDA0003874623660000061
According to the Fletcher-Reeves conjugate gradient algorithm, the variable u can be updated by the following formula:
u l+1 ＝u l +α l d l (25)
wherein l represents the number of CG iterations, d l Denotes the direction of conjugation, α, with respect to R l Represents a step size, satisfies
Figure BDA0003874623660000062
ρ l Representing an intermediate variable, a weight vector w l Satisfies the following conditions:
w l ＝Rd l+1 (26)
equation (25) is written in two-dimensional form:
Figure BDA0003874623660000063
wherein, U l 、D l Represents u l And d l In two-dimensional form of (1), satisfy u l ＝vec(U l )，d l ＝vec(D l ) Thus, there are:
U l+1 ＝U l +α l D l (28)
wherein the content of the first and second substances,
Figure BDA0003874623660000064
wherein an indicates a conjugate operation, an indicates a Hadamard product of the matrix,
Figure BDA0003874623660000065
and
Figure BDA0003874623660000066
respectively represent vectors d l+1 And w l The (i) th element of (a),
Figure BDA0003874623660000067
represent
Figure BDA0003874623660000068
The full 1 vector of row 1 and column,
Figure BDA0003874623660000069
represents N θ All 1 vectors, W, of row 1 column l Satisfy w l ＝vec(W l ) And can be derived by the following steps.
S5, iteratively updating W;
from the Kronecker product property, equation (26) is written as a two-dimensional form:
Figure BDA00038746236600000610
wherein, sigma is the target scattering power, and satisfies the condition of sigma ij ＝|X ij | 2 The relation P = diag { vec (Σ) }, Σ is satisfied with the matrix P ij I row j column element representing the target scattering power matrix Σ, i =1 1 ，j＝1,...,K 2 ，X ij Representing the ith row and jth column of matrix object X. Since P is a diagonal array, P is converted into sigma-and (A) H D l+1 B * ) Hadamard product relationship of (a), thus:
W l ＝A(Σ⊙(A H D l+1 B * ))B T +μD l+1 (31)
s6, iteratively updating D;
d l the one-dimensional update expression can be written as:
d l+1 ＝g l +β l d l (32)
wherein, g l Representing gradient vectors, intermediate variable beta l+1 ＝ρ l+1 /ρ l 。
Figure BDA0003874623660000071
Writing equation (32) in two dimensions:
Figure BDA0003874623660000072
wherein G is l Is represented by g l In two-dimensional form of (1), satisfies g l ＝vec(G l ) Thus, there are:
D l+1 ＝G l +β l D l (35)
wherein, beta l+1 The update method of (2) is the same as that of (32), and
Figure BDA0003874623660000073
||·|| F representing the matrix Frobenius norm.
S7, iteratively updating G;
in the formula (32), the gradient g l The update formula of (c) is as follows:
g l+1 ＝g l -α l w l (36)
converting the above formula to a two-dimensional form:
Figure BDA0003874623660000074
thus, the following results are obtained:
G l+1 ＝G l -α l W l (38)
when it is satisfied with
Figure BDA0003874623660000075
Or stopping CG iteration after reaching the specified iteration times, wherein epsilon represents a small positive number, and outputting a two-dimensional CG iteration nodeFruit
Figure BDA0003874623660000076
S8, iterating a two-dimensional form of an estimation result;
according to equation (23), the two-dimensional representation of the scattering of the target can be written as:
Figure BDA0003874623660000081
similar to formula (30), wherein P is used (q) ＝diag{vec(Σ (q) ) And obtaining a two-dimensional target scattering iteration formula:
X (q+1) ＝Σ (q) ⊙(A H U (q) B * ) (40)
wherein, U (q) Satisfy vec (U) (q) )＝R -1 y. At the start of the target scatter iteration, the variable Σ is initialized to: sigma (0) ＝A H YB H . At the start of a CG iteration, variables are initialized as: u shape 0 ＝0，D 0 ＝0，β 0 ＝0，G 0 ＝Y，
Figure BDA0003874623660000082
By repeated iterations of two-dimensional target scatter (equation (40)) and CG (equations (28), (29), (31), (35), and (38)), X in model equation (19) can be solved directly.
The invention has the beneficial effects that: the method comprises the steps of establishing an orientation-pitching two-dimensional scanning echo model of the airborne radar platform, then carrying out distance walking correction on the orientation-pitching-distance echo, enabling the echo model to be approximate to a two-dimensional convolution model, and finally utilizing a conjugate gradient method and the Kronecker product property of a matrix to derive the scattering intensity of an orientation-pitching two-dimensional target. The method solves the problems that the existing real aperture radar is low in azimuth-elevation two-dimensional resolution and is not suitable for a motion platform, and compared with the existing two-dimensional scanning radar super-resolution method, the method not only can be used for two-dimensional super-resolution imaging of the motion platform, but also has excellent target resolution capability and lower calculation complexity, and is suitable for engineering implementation.
Drawings
FIG. 1 is a flow chart of a forward-looking azimuth elevation two-dimensional super-resolution imaging method of a motion platform according to the invention.
Fig. 2 is a geometric model of the movement of the airborne radar platform in the embodiment of the invention.
FIG. 3 is a schematic diagram of a spatial domain target two-dimensional scanning mode according to an embodiment of the present invention.
Fig. 4 is an azimuthally tilted two-dimensional antenna pattern in an embodiment of the present invention.
FIG. 5 is a diagram of original scene three-dimensional point target layout in an embodiment of the present invention.
FIG. 6 is a diagram of the setting of an azimuth-elevation two-dimensional point target in an embodiment of the invention.
FIG. 7 is a diagram of the results of the pre-processed azimuth-elevation two-dimensional real beam echo in the embodiment of the present invention.
FIG. 8 is a diagram of super-resolution results of two-dimensional wiener inverse filtering in the embodiment of the present invention.
FIG. 9 is a graph of super-resolution results according to an embodiment of the present invention.
Detailed Description
The method of the present invention is further illustrated by the following examples in conjunction with the accompanying drawings.
In the embodiment, the effectiveness of the proposed method for the two-dimensional super-resolution imaging of the pitching of the forward-looking direction of the motion platform is verified through a simulation experiment. The steps and results in this embodiment are verified on a MATLAB 2018b simulation platform.
As shown in fig. 1, a flow chart of a two-dimensional super-resolution imaging method for pitching a forward-looking azimuth of a motion platform of the present invention includes the following specific steps:
s1, establishing a signal geometric model;
as shown in table 1, simulation parameters of the radar motion platform are listed. The sampling rate satisfies the nyquist sampling law.
TABLE 1
Figure BDA0003874623660000091
The airborne radar platform is located at a point A (0, Γ) when t =0, Γ =1000m, and moves at a uniform velocity in the y-axis direction with a velocity v =90 m/s. And when the airborne platform moves to the point B at the moment t, AB = vt can be obtained. Let a point P (x) in the scanning area P ,y P ,z P ) The projection on the xOy plane is the Q point. R is P =30000m is the distance between the radar platform and the target at the initial moment,
Figure BDA0003874623660000092
is the pitch angle, theta, of the target relative to the radar platform P For the azimuth angle of the target relative to the y-axis direction, as shown in fig. 2, according to the geometric relationship, the distance R (t) between the airborne platform and the target at time t can be written as:
Figure BDA0003874623660000101
according to fig. 2, there are the following geometrical relations:
Figure BDA0003874623660000102
substituting formula (42) for formula (41) yields:
Figure BDA0003874623660000103
taylor expansion of R (t) and neglecting the quadratic and higher terms of the distance history, we can:
Figure BDA0003874623660000104
according to the platform motion, beam scanning, signal transmitting and receiving processes, the echo signal of the target P point can be expressed as:
Figure BDA0003874623660000105
wherein tau is a distance time variable, rect (-) represents a rectangular window function, K r Expressing the chirp slope, t is the platform motion time variable (slow time), τ is the distance time variable (fast time), σ P The scattering coefficient of the target P is represented by k, a constant containing various gains and losses, c is the propagation speed of the electromagnetic wave, and h (t) is the antenna pattern modulation function.
After carrier frequency removal and after pulse compression processing, the echo can be written as:
Figure BDA0003874623660000106
wherein, sinc (·) represents the distance direction signal envelope after pulse compression, and is specifically denoted as sinc (γ) = sin (π γ)/π γ, the last term exp { -j4 π R (t)/λ } represents the Doppler phase term caused by stage motion, and λ represents the wavelength.
As shown in fig. 3, the target airspace Ω is scanned in the following manner: and for the first pitch dimension, scanning along the azimuth direction, jumping to the second pitch dimension, scanning along the azimuth direction, and so on, and performing Z-shaped dense scanning line by line. Wherein N is θ And
Figure BDA0003874623660000107
respectively representing the number of azimuth and pitch samples. In the scanning process of the airborne radar platform, the fast time tau and the slow time t respectively meet the following requirements:
Figure BDA0003874623660000111
Figure BDA0003874623660000112
wherein PRF denotes the pulse repetition frequency, θ and
Figure BDA0003874623660000113
representing the azimuth pitch angle variable and R the range variable.
S2, preprocessing an echo;
as can be seen from equations (46), (47) and (48), the range-azimuth-pitch three-dimensional echo expression can be written as:
Figure BDA0003874623660000114
wherein the content of the first and second substances,
Figure BDA0003874623660000115
representing a two-dimensional antenna pattern function with an energy distribution as shown in figure 4. The phase compensation factors are constructed in the distance frequency domain as follows:
Figure BDA0003874623660000116
wherein, f R And (3) representing a distance frequency variable, performing Fast Fourier Transform (FFT) on the distance direction of the formula (49), multiplying the distance direction by the formula (50), and performing Inverse Fast Fourier Transform (IFFT) on the distance direction to obtain an echo after walking correction:
Figure BDA0003874623660000117
when the target is located in the direct forward-looking range of the airborne platform,
Figure BDA0003874623660000118
the doppler history of each target in the forward-looking region is approximately equal, so equation (51) can be approximated as:
Figure BDA0003874623660000119
is located in an airspace omega
Figure BDA00038746236600001113
Has a target backscattering coefficient of
Figure BDA00038746236600001110
R 0 ,θ 0 ,
Figure BDA00038746236600001111
Respectively representing objects
Figure BDA00038746236600001112
The target setting is shown in fig. 5 and 6. The total echo in the probe space domain can be written as:
Figure BDA0003874623660000121
according to the above equation, the two-dimensional scanning convolution model can be discretized as:
Y＝AXB T +N (54)
wherein the content of the first and second substances,
Figure BDA0003874623660000122
an echo matrix representing a slice at a certain distance,
Figure BDA0003874623660000123
is a backscattering coefficient matrix of the target, K 1 、K 2 Respectively representing the number of azimuth and elevation sampling points of the backscatter coefficient matrix,
Figure BDA0003874623660000124
in order to be additive to the noise,
Figure BDA0003874623660000125
representing a real space, T represents the transpose of a matrix,
Figure BDA0003874623660000126
and
Figure BDA00038746236600001213
representing azimuth and elevation antenna pattern modulation matrices, respectively, in particularWrite as:
Figure BDA0003874623660000127
Figure BDA0003874623660000128
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00038746236600001214
the azimuth dimension antenna pattern sampling points are represented,
Figure BDA0003874623660000129
represents the elevation dimension antenna pattern sample point, L 1 And L 2 Respectively representing the sampling point number of the antenna directional diagram in the azimuth dimension and the elevation dimension.
S3, iteratively updating U;
defining variables
Figure BDA00038746236600001210
The variable u is updated by the following formula:
u l+1 ＝u l +α l d l (57)
wherein l represents the number of CG iterations, d l Denotes the conjugation direction, α, with respect to R l Represents a step size, satisfies
Figure BDA00038746236600001211
ρ l Represents an intermediate variable, w l Representing a weight vector.
Writing equation (58) in two-dimensional form:
Figure BDA00038746236600001212
wherein, U l 、D l Denotes u l And d l In two-dimensional form of (1), satisfy u l ＝vec(U l )，d l ＝vec(D l ) Thus, there are:
U l+1 ＝U l +α l D l (59)
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003874623660000131
wherein, indicates a conjugate operation, indicates a Hadamard product,
Figure BDA0003874623660000132
and
Figure BDA0003874623660000133
respectively represent vectors d l+1 And w l The (i) th element of (2),
Figure BDA0003874623660000134
to represent
Figure BDA0003874623660000135
The full 1 vector of row 1 and column,
Figure BDA0003874623660000136
represents N θ All 1 vectors, W, of row 1 column l Satisfy w l ＝vec(W l )。
S4, iteratively updating W;
in equation (57):
w l ＝Rd l+1 (61)
equation (61) is written in two dimensions:
Figure BDA0003874623660000137
wherein, the sigma is the target scattering power, and the requirement of sigma is satisfied ij ＝|X ij | 2 The relation P = diag { vec (Σ) }, Σ is satisfied with the matrix P ij I row j column element representing the target scattering power matrix Σ, i =1 1 ，j＝1,...,K 2 ，X ij Representing the ith row and the jth column of matrix object X. Since P is a diagonal array, P is converted into sigma-and (A) H D l+1 B * ) Hadamard product relationship of (a), thus:
W l ＝A(Σ⊙(A H D l+1 B * ))B T +μD l+1 (63)
s5, iteratively updating D;
d l+1 and d l Is updated by:
d l+1 ＝g l +β l d l (64)
wherein, g l Representing gradient vectors, intermediate variable beta l+1 ＝ρ l+1 /ρ l 。
Figure BDA0003874623660000141
Writing equation (64) in two dimensions:
Figure BDA0003874623660000142
wherein, G l Is represented by g l In two-dimensional form of (b), satisfies g l ＝vec(G l ) Thus, there are:
D l+1 ＝G l +β l D l (67)
wherein beta is l+1 The update method of (1) is the same as formula (64), and
Figure BDA0003874623660000143
||·|| F representing the Frobenius norm of the matrix.
S6, iteratively updating G;
in equation (64), the gradient g may be updated by the equation l ：
g l+1 ＝g l -α l w l (68)
Converting the above formula to a two-dimensional form:
Figure BDA0003874623660000144
thus, the following results were obtained:
G l+1 ＝G l -α l W l (70)
when it is satisfied with
Figure BDA0003874623660000145
Or terminate the CG iteration after up to 10 iterations, e =10 -3 Representing a small positive number and outputting a two-dimensional CG iteration result
Figure BDA0003874623660000146
S7, iterating a two-dimensional form of an estimation result;
after the CG iteration is terminated, outputting a CG iteration result u (q) ＝u l Substituting the formula (23) to obtain the q-th iteration result of the target scattering:
Figure BDA0003874623660000147
wherein u is (q) R in the q-th target scattering iteration (23) derived by CG iteration -1 y。
According to equation (23), the two-dimensional iterative representation of the target scatter can be written as:
Figure BDA0003874623660000151
therefore, there are:
X (q+1) ＝Σ (q) ⊙(A H U (q) B * ) (73)
wherein, U (q) Satisfy vec (U) (q) )＝R -1 y. At the start of the target scatter iteration, the variable Σ is initialized to: sigma-shaped (0) ＝A H YB H . At the start of a CG iterationWhen, the variables are initialized to: u shape 0 ＝0，D 0 ＝0，β 0 ＝0，G 0 ＝Y，
Figure BDA0003874623660000152
By repeated iterations of two-dimensional target scatter (equation (73)) and CG (equations (59), (60), (63), (67), and (70)), X in model equation (54) can be solved directly. On one hand, the method does not need matrix inversion, on the other hand, the method does not need to construct and calculate multiplication of high-dimensional matrix and vector, and can greatly reduce the calculation complexity of the target scattering iteration method.
The complexity of the method is specifically analyzed: in the CG iteration, four matrices, U respectively, need to be stored l ，W l ，D l And G l . Each CG iteration requires 4 matrix-matrix multiplications (A (Sigma |, A) H D l+1 B * ))B T ) 2 matrix-matrix Hadamard multiplication (one-time as in equation (63) & Sigma & (A) H D l+1 B * ) In another case in formula (60)
Figure BDA0003874623660000153
) 4 matrix-scalar multiplication (U) l ,D l ,G l Update of (2) and μ D in equation (63) l+1 ) And 1 scalar multiplication
Figure BDA0003874623660000154
If L iterations are required, the computational complexity of the two-dimensional CG algorithm is
Figure BDA0003874623660000155
Two matrix multiplications (sigma) are required for each iteration of the target scatter (q) ⊙(A H U (q) B * ) And a scalar multiplication (∑ y) (q) ＝X (q) ⊙X (q) ). Assuming that Q target scattering iterations are performed, the overall computational complexity of the algorithm is:
Figure BDA0003874623660000156
fig. 7, 8 and 9 show the point target super-resolution results of different methods. Limited by the internal memory of the platform, the number of azimuth and pitch sampling points is reduced, wherein,
Figure BDA0003874623660000157
fig. 7 shows the real beam results, and it can be seen that 4 targets are completely indistinguishable. Fig. 8 is a processing result of the two-dimensional wiener inverse filtering method. The method has high processing speed. It can be seen that although the four targets are substantially separated, the method has poor resolution performance and also has strong side lobe effects near the 0 ° azimuth and 0 ° pitch dimensions. Both methods can be implemented quickly in the frequency domain by FFT, but with limited resolution. Fig. 9 is a processing result of the method proposed by the present invention, and it can be seen that the resolution performance is significantly better than the real beam result and the two-dimensional wiener filtering method.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (1)

1. A method for two-dimensional super-resolution imaging of pitching of a forward-looking azimuth of a motion platform comprises the following specific steps:
s1, an orientation-pitching two-dimensional scanning echo model of an airborne radar platform;
assuming that the airborne radar platform is located at a point A (0, gamma) when t =0 and moves at a constant speed along the y-axis direction at a speed v, gamma represents the height of the airborne platform, and the airborne platform moves to a point B at the time t, AB = vt can be obtained, and a point P (x) in a scanning area is assumed P ,y P ,z P ) The projection on the xOy plane is the Q point, R P The distance between the radar platform and the target at the initial moment,
Figure FDA0003874623650000011
is the pitch angle, θ, of the target relative to the radar platform P According to the geometrical relationship, the distance R (t) between the airborne platform and the target at the time t is expressed as follows:
Figure FDA0003874623650000012
according to the following geometrical relationship:
Figure FDA0003874623650000013
substituting formula (2) into formula (1) to obtain:
Figure FDA0003874623650000014
taylor unfolding R (t) gives:
Figure FDA0003874623650000015
wherein, O (t) 2 ) Denotes t 2 Satisfies vt & lt R within the coherent accumulation time (CPI) of an arbitrary point target P Equation (4) is approximated as:
Figure FDA0003874623650000016
setting a scanning radar to transmit a chirp signal:
Figure FDA0003874623650000017
where τ is the distance time variable, T p For pulse width, rect (·)Representing a rectangular window function, f c Denotes the carrier frequency, K r Representing the chirp slope, the echo signal at target P point is represented as:
Figure FDA0003874623650000021
where t is the platform motion time variable (slow time), τ is the distance time variable (fast time), σ P For the target scattering coefficient of the target P, κ represents a constant containing various gains and losses, c is the electromagnetic wave propagation speed, h (t) is the antenna pattern modulation function, high range resolution is achieved by pulse compression over distance, and after carrier frequency removal and pulse compression processing, the echo is written as:
Figure FDA0003874623650000022
wherein, B r Represents the signal bandwidth and satisfies B r ＝K r T p Sine (·) represents the distance-wise signal envelope after pulse compression, and is specifically denoted as sine (γ) = sin (π γ)/π γ, and the last term exp { -j4 π R (t)/λ } represents the Doppler phase term due to stage motion, and λ represents wavelength;
scanning a target space domain omega, wherein delta theta and
Figure FDA0003874623650000023
respectively representing the azimuth and elevation wave position jump, phi θ And
Figure FDA0003874623650000024
respectively representing azimuth and elevation sweep ranges, N θ And
Figure FDA0003874623650000025
respectively representing the number of azimuth sampling points and the number of pitching sampling points, wherein in the scanning process of the airborne radar platform, the fast time tau and the slow time t respectively meet the following requirements:
Figure FDA0003874623650000026
Figure FDA0003874623650000027
wherein PRF denotes the pulse repetition frequency, θ and
Figure FDA0003874623650000028
representing an azimuth pitch angle variable, and R representing a distance variable;
s2, echo pretreatment;
substituting the formula (9) and the formula (10) into the echo formula (8) can obtain a distance-azimuth-pitch three-dimensional echo expression:
Figure FDA0003874623650000029
wherein the content of the first and second substances,
Figure FDA00038746236500000210
representing a two-dimensional antenna pattern, the distance walk is represented as:
Figure FDA0003874623650000031
constructing a phase compensation factor in the distance frequency domain:
Figure FDA0003874623650000032
wherein f is R And (3) representing a distance frequency variable, performing Fast Fourier Transform (FFT) on the distance direction of the formula (11), multiplying the distance direction by the formula (13), and performing Inverse Fast Fourier Transform (IFFT) on the distance direction to obtain an echo after walking correction:
Figure FDA0003874623650000033
wherein, the fourth term in the formula
Figure FDA0003874623650000034
A constant term related to the initial slope distance is shown, a fifth term represents Doppler phase modulation generated by the relative motion process, when the target is positioned in the forward looking range of the airborne platform,
Figure FDA0003874623650000035
the approximation is:
Figure FDA0003874623650000036
locate in omega of airspace
Figure FDA0003874623650000037
Has a target backscattering coefficient of
Figure FDA0003874623650000038
R 0 ,θ 0 ,
Figure FDA0003874623650000039
Respectively representing objects
Figure FDA00038746236500000310
The total echo of the detection airspace is written as:
Figure FDA00038746236500000311
equation (16) reduces to the echo model for a single range bin:
Figure FDA00038746236500000312
wherein the content of the first and second substances,
Figure FDA00038746236500000313
is equivalent to a two-dimensional convolution kernel,
Figure FDA00038746236500000314
representing the target azimuth pitch scattering distribution of the corresponding range unit;
considering additive noise, there are:
Figure FDA00038746236500000315
wherein, denotes a two-dimensional convolution,
Figure FDA00038746236500000316
is equivalent to a two-dimensional convolution kernel,
Figure FDA00038746236500000317
representing additive gaussian noise;
discretization of the two-dimensional convolution model (18) is:
Y＝AXB T +N (19)
wherein the content of the first and second substances,
Figure FDA0003874623650000041
an echo matrix representing a slice at a certain distance,
Figure FDA0003874623650000042
is a backscattering coefficient matrix of the target, K 1 、K 2 Respectively representing the position of the backscattering coefficient matrix and the number of pitching sampling points,
Figure FDA0003874623650000043
in order to be additive to the noise,
Figure FDA0003874623650000044
representing a real space, T represents the transpose of a matrix,
Figure FDA0003874623650000045
and
Figure FDA0003874623650000046
the azimuth and elevation antenna pattern modulation matrices are represented separately, written specifically as:
Figure FDA0003874623650000047
Figure FDA0003874623650000048
wherein, [ a (θ) ] L1 ),a(θ L1-1 ),…,a(θ 1 )]The azimuth dimension antenna pattern sampling points are represented,
Figure FDA0003874623650000049
representing the antenna pattern sample point, L, in elevation 1 And L 2 Respectively representing the number of sampling points of an azimuth dimension antenna directional diagram and a pitching dimension antenna directional diagram, and the number of the sampling points M, N and K 1 ，K 2 ，L 1 ，L 2 Satisfies the relationship:
Figure FDA00038746236500000410
s3, calculating an autocorrelation matrix R;
scattering result x from the target (q+1) Writing as follows:
x (q+1) ＝P (q) F H (R (q) ) -1 y (23)
whereinQ denotes the number of iterations, R (q) ＝F H P (q) F is P by the q-th iteration (q) Is obtained by calculation, P (q) ＝diag(x (q) ) Diag (·) denotes constructing a diagonal matrix from a certain vector, H denotes a conjugate transpose operation, Y = vec (Y) is a one-dimensional vectorization form of the echo Y, and R is diagonally loaded:
R＝FPF H +μI (24)
where μ represents a regularization parameter, I represents a unit matrix, and R is reduced by the CG algorithm -1 The computational complexity of (2);
s4, updating U in an iterative manner;
defining variables
Figure FDA0003874623650000051
The variable u is updated by the following formula:
u l+1 ＝u l +α l d l (25)
wherein l represents the number of CG iterations, d l Denotes the direction of conjugation, α, with respect to R l Represents a step size, satisfies
Figure FDA0003874623650000052
ρ l Representing an intermediate variable, a weight vector w l Satisfies the following conditions:
w l ＝Rd l+1 (26)
equation (25) is written in two-dimensional form:
Figure FDA0003874623650000053
wherein, U l 、D l Represents u l And d l In two-dimensional form of (1), satisfy u l ＝vec(U l )，d l ＝vec(D l ) Thus, there are:
U l+1 ＝U l +α l D l (28)
wherein the content of the first and second substances,
Figure FDA0003874623650000054
wherein an indicates a conjugate operation, an indicates a Hadamard product of the matrix,
Figure FDA0003874623650000055
and
Figure FDA0003874623650000056
respectively represent vectors d l+1 And w l The (i) th element of (a),
Figure FDA0003874623650000057
to represent
Figure FDA0003874623650000058
The full 1 vector of row 1 and column,
Figure FDA0003874623650000059
represents N θ All 1 vectors, w, of row 1 column l Satisfy w l ＝vec(W l )；
S5, iteratively updating W;
equation (26) is written in two dimensions:
Figure FDA00038746236500000510
wherein, the sigma is the target scattering power, and the requirement of sigma is satisfied ij ＝|X ij | 2 The relation P = diag { vec (Σ) }, Σ is satisfied with the matrix P ij I row j column element representing the target scattering power matrix Σ, i =1 1 ，j＝1,...,K 2 ，X ij The ith row and the jth column of the matrix target X are represented, P is a diagonal matrix, and P is converted into sigma-sum (A) H D l+1 B * ) Hadamard product relationship of (a), thus:
W l ＝A(Σ⊙(A H D l+1 B * ))B T +μD l+1 (31)
s6, iteratively updating D;
d l the one-dimensional update expression is written as:
d l+1 ＝g l +β l d l (32)
wherein, g l Representing gradient vectors, intermediate variable beta l+1 ＝ρ l+1 /ρ l ；
Figure FDA0003874623650000061
Writing equation (32) in two dimensions:
Figure FDA0003874623650000062
wherein, G l Denotes g l In two-dimensional form of (b), satisfies g l ＝vec(G l ) Thus, there are:
D l+1 ＝G l +β l D l (35)
wherein, beta l+1 The update method of (2) is the same as formula (32), and
Figure FDA0003874623650000063
||·|| F representing a matrix Frobenius norm;
s7, iteratively updating G;
in the formula (32), the gradient g l The update formula of (2) is as follows:
g l+1 ＝g l -α l w l (36)
converting the above formula to a two-dimensional form:
Figure FDA0003874623650000064
obtaining:
G l+1 ＝G l -α l W l (38)
when it satisfies
Figure FDA0003874623650000065
Or stopping CG iteration after reaching the specified iteration times, wherein epsilon represents a small positive number, and outputting a two-dimensional CG iteration result
Figure FDA0003874623650000066
S8, iterating a two-dimensional form of an estimation result;
according to equation (23), the two-dimensional representation of the scattering of the target is written as:
Figure FDA0003874623650000071
obtaining a two-dimensional target scattering iterative formula:
X (q+1) ＝Σ (q) ⊙(A H U (q) B * ) (40)
wherein, U (q) Satisfy vec (U) (q) )＝R -1 y, at the start of the target scatter iteration, the variable Σ is initialized to: sigma-shaped (0) ＝A H YB H At the start of a CG iteration, variables are initialized to: u shape 0 ＝0，D 0 ＝0，β 0 ＝0，G 0 ＝Y，
Figure FDA0003874623650000072
By repeated iterations of two-dimensional object scatter (equation (40)) and CG (equations (28), (29), (31), (35), and (38)), X in model equation (19) can be solved directly.
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CN117090989A (en) * 2022-12-22 2023-11-21 浙江德卡控制阀仪表有限公司 Electric gate valve with monitoring system
CN117090989B (en) * 2022-12-22 2024-06-07 浙江德卡控制阀仪表有限公司 Electric gate valve with monitoring system

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117090989A (en) * 2022-12-22 2023-11-21 浙江德卡控制阀仪表有限公司 Electric gate valve with monitoring system
CN117090989B (en) * 2022-12-22 2024-06-07 浙江德卡控制阀仪表有限公司 Electric gate valve with monitoring system

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