CN116299551A - Terahertz SAR two-dimensional self-focusing imaging algorithm - Google Patents

Terahertz SAR two-dimensional self-focusing imaging algorithm Download PDF

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CN116299551A
CN116299551A CN202211089077.1A CN202211089077A CN116299551A CN 116299551 A CN116299551 A CN 116299551A CN 202211089077 A CN202211089077 A CN 202211089077A CN 116299551 A CN116299551 A CN 116299551A
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distance
phase error
azimuth
sar
compensation
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李银伟
郑其斌
朱亦鸣
吴琦
罗绍文
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University of Shanghai for Science and Technology
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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
    • G01S17/00—Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
    • G01S17/88—Lidar systems specially adapted for specific applications
    • G01S17/89—Lidar systems specially adapted for specific applications for mapping or imaging
    • G01S17/90—Lidar systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques
    • 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
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/4802—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00 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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/497—Means for monitoring or calibrating

Abstract

The terahertz SAR two-dimensional self-focusing imaging algorithm provided by the invention sequentially comprises the following steps: establishing a terahertz SAR echo signal model; removing the residual video phase items and the oblique phase items; estimating a distance nonlinear phase error; performing distance compensation based on the estimated nonlinear phase error; performing distance compression on the echo signals subjected to distance compensation; performing azimuth coarse compensation on the echo signals after the distance compression; performing range migration correction on the echo signals after the azimuth coarse compensation; estimating azimuth residual phase errors; performing azimuth fine compensation based on the estimated residual phase error; and carrying out azimuth compression on the echo signals subjected to azimuth fine compensation to obtain THz-SAR focusing images. In the application, estimating and compensating the distance-direction nonlinear phase error and the azimuth-direction motion phase error to obtain a high-resolution THz-SAR focusing image; based on the combined use of IMU/GPS measurement data and MEA self-focusing algorithm, the calculation amount can be reduced compared with the direct adoption of the self-focusing algorithm.

Description

Terahertz SAR two-dimensional self-focusing imaging algorithm
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a terahertz SAR two-dimensional self-focusing imaging algorithm.
Background
Terahertz (THz) waves refer to electromagnetic waves with the frequency spectrum between 100GHz and 10THz, and have the characteristics of high carrier frequency, large communication capacity, good penetrability, low photon energy, no biological ionization and the like. Terahertz synthetic aperture radar (THz-SAR) imaging has significant advantages such as higher resolution, higher frame rate, higher detection probability, easier recognition, and the like compared with microwave synthetic aperture radar (Synthetic Aperture Radar, SAR) imaging, which makes it receiving more and more attention in the field of modern radar imaging.
THz-SAR imaging is often affected by some non-ideal factors, introducing phase errors in the radar echo signal. The error can be divided into a distance direction and an azimuth direction. The distance phase error is caused by the fact that the terahertz radar system based on the solid-state source can only generate terahertz signals through multiple times of frequency multiplication, and nonlinear phase error is introduced into the terahertz signals due to the non-ideal characteristics of the sweep frequency source and the transceiver link frequency multiplier. These nonlinear phase errors will directly affect the phase of the target echo, resulting in distortion of the range profile and reduced resolution, which results in an unrealistic target support. The azimuth phase error is caused by platform motion error caused by deviation of the flight track from an ideal state due to the influence of factors such as air flow and the like on the carrier platform. In modern SAR systems, the motion state data of the platform can be measured by a combination of an inertial measurement unit (Inertial Measurement Unit, IMU) and a global positioning system (Global Positioning System, GPS), and then the echoes are compensated by the measurement data. For THz-SAR, the shorter wavelength makes the influence of smaller vibration error on echo phase not be ignored, which makes the existing sensor not reach the required precision requirement for compensation. Therefore, for the above-mentioned distance-direction and azimuth-direction phase errors, it is also necessary to improve the imaging quality by using a self-focusing algorithm after performing compensation based on the measurement data.
Sub-aperture correlation (Map Drift, MD) and phase gradient self-focusing (Phase Gradient Autofocus, PGA) are two of the more important self-focusing algorithms. The MD method has the defect that only secondary phase errors can be estimated, and the improved multi-sub-aperture correlation algorithm can in principle estimate higher-order phase errors, but the deviation of estimation results is larger due to the fact that sub-apertures are too short, and the method cannot meet the requirement of high-resolution imaging. The PGA has good robustness and high imaging efficiency, but the PGA must effectively compensate for errors in the presence of a special display point, and has limitations in practical applications. The minimum entropy (Minimum Entropy Algorithm, MEA) algorithm is based on the whole image entropy value without special display points, and has wider application range and practicability.
Disclosure of Invention
The invention aims to provide a terahertz SAR two-dimensional self-focusing imaging algorithm, which obtains a THz-SAR high-resolution focusing image through the combination of measurement data compensation and an MEA-based two-dimensional self-focusing algorithm.
In order to achieve the above purpose, the invention provides a terahertz SAR two-dimensional self-focusing imaging algorithm, which comprises the following steps:
s1: establishing a model of an echo signal of the terahertz SAR;
s2: removing the residual video phase items and the oblique phase items in the echo signals;
s3: estimating a nonlinear phase error of the distance direction;
s4: performing distance compensation based on the estimated nonlinear phase error;
s5: performing distance compression on the echo signals subjected to distance compensation;
s6: based on IMU/GPS measurement data, performing azimuth coarse compensation on the echo signals after distance compression;
s7: performing range migration correction on the echo signals after the azimuth coarse compensation;
s8: estimating a residual phase error of the azimuth direction;
s9: performing azimuth fine compensation based on the estimated residual phase error;
s10: and carrying out azimuth compression on the echo signals subjected to azimuth fine compensation to obtain THz-SAR focusing images.
Further, in the two-dimensional autofocus imaging algorithm of the terahertz SAR, in step S1, the terahertz SAR transmits a chirp pulse signal, and carries out de-chirp on a received echo signal, and a model expression of the generated echo signal is:
Figure BDA0003836325010000031
wherein: τ is distance-wise fast time; t is azimuth slow time; t (T) p Is pulse width; c is the speed of light; lambda is the wavelength; r is R i Is the actual distance of the radar; r is R ref Is the reference distance of the radar; r is R Δ Is the difference between the actual distance of the radar and the reference distance; j is an imaginary unit; gamma is the frequency modulation slope.
Further, in the terahertz SAR two-dimensional self-focusing imaging algorithm, in step S2, a distance fourier transform (FFT) is performed on equation (1), so as to obtain:
Figure BDA0003836325010000032
wherein: f (f) r Is distance frequency; f (f) c Is the center frequency;
Figure BDA0003836325010000033
is a Doppler term;
Figure BDA0003836325010000041
is the remaining video phase term; />
Figure BDA0003836325010000042
A diagonal phase term that is an echo envelope;
the remaining video phase term and the diagonal phase term in equation (2) are expressed as:
Figure BDA0003836325010000043
equation (2) multiplied by the compensation function of the residual video phase term and the diagonal phase term
Figure BDA0003836325010000044
The method can obtain:
Figure BDA0003836325010000045
performing Inverse Fast Fourier Transform (IFFT) on equation (4), i.e. the model expression of the echo signal after transformation is:
Figure BDA0003836325010000046
further, in the terahertz SAR two-dimensional self-focusing imaging algorithm, in step S3, it is assumed that the function of the nonlinear phase error of the distance direction is
Figure BDA0003836325010000047
The model expression of the echo signal for which the nonlinear phase error exists is:
Figure BDA0003836325010000048
wherein: τ is distance-wise fast time; t is azimuth slow time;
discretizing τ and t into t, respectively n (n=0:n-1) and t m (m= 0:M-1), then discretization of formula (6) can yield:
Figure BDA0003836325010000051
taking the minimum entropy criterion as an evaluation criterion, and estimating the nonlinear phase error through iterative optimization, wherein the method comprises the following specific steps of:
s3.1: hypothesis estimationIs the distance direction of the nonlinear phase error of
Figure BDA0003836325010000052
And->
Figure BDA0003836325010000053
Initializing and setting to 0, namely, the compensated range profile expression is as follows:
Figure BDA0003836325010000054
wherein: k is the distance frequency; m is the number of echo pulses; n is a distance unit; n is the total distance unit number;
s3.2: based on the minimum entropy criterion, a phase error model is established, and the expression is:
Figure BDA0003836325010000055
wherein: ent is the image entropy value, and the expression is:
Figure BDA0003836325010000056
wherein: e is the range profile energy, and the expression is:
Figure BDA0003836325010000057
s3.3: solving the expression (9) based on Newton's method, the expression for iterating the phase error can be obtained as follows:
Figure BDA0003836325010000061
wherein:
Figure BDA0003836325010000062
Figure BDA0003836325010000063
wherein: s is(s) 0 (l-1) (n, m) is the echo data corrected using the phase error estimated by the (l-1) th iteration;
Figure BDA0003836325010000064
is G k，m Each element of the (B) is complex conjugated;
s3.4: judging whether the estimated phase error is accurate enough, namely judging the image entropy values Ent and Ent respectively obtained after the first iteration and the (l-1) th iteration (l-1) Whether the difference between them is lower than a preset threshold value J, namely:
|Ent (l) -Ent (l-1) |≤J (13)
if equation (13) is satisfied, the nonlinear phase error in the distance direction that needs to be compensated is:
Figure BDA0003836325010000065
in step S4, the nonlinear phase error estimated according to step S3
Figure BDA0003836325010000066
The compensation function of the nonlinear phase error of the distance direction is +>
Figure BDA0003836325010000067
And multiplying the echo signal by equation (7) to compensate the distance direction, the method can obtain:
Figure BDA0003836325010000071
further, in the terahertz SAR two-dimensional autofocus imaging algorithm, in step S5, a distance fourier transform (FFT) is performed on the echo signal after distance compensation, and a model expression of the echo signal after distance compression is completed is:
Figure BDA0003836325010000072
wherein: t is t i Discrete delay fast time for target to radar;
Figure BDA0003836325010000073
discrete slow time for the beam center to pass through the target; b is the distance signal bandwidth; w (w) a (. Cndot.) is the azimuthal envelope;
based on motion phase error
Figure BDA0003836325010000074
The model expression of the echo signal that actually completes the distance compression is:
Figure BDA0003836325010000075
further, in the terahertz SAR two-dimensional self-focusing imaging algorithm, in step S6, based on IMU/GPS measurement data, a difference d between the actual tilt of the antenna and the scene and the ideal tilt is calculated los (t n ，t m ) To perform corresponding motion phase compensation, and the compensation function of the motion phase error is as follows:
Figure BDA0003836325010000076
equation (17) is multiplied by equation (18) to perform coarse azimuthal compensation on the echo signal, to obtain:
s a，com1 (t n ，t m )＝s a (t n ， t m)·D com
Figure BDA0003836325010000081
residual phase error due to the IMU/GPS measurement data based on azimuth
Figure BDA0003836325010000082
By transforming the formula (19), it is possible to obtain:
Figure BDA0003836325010000083
further, in the terahertz SAR two-dimensional self-focusing imaging algorithm, in step S7, the azimuth fourier transform (FFT) is performed on the echo signal after the azimuth coarse compensation, the echo signal is transformed to the range-doppler domain, the range migration correction is performed on the echo signal by interpolation, and after the influence of the range migration is eliminated, the inverse azimuth fourier transform (IFFT) is performed on the echo signal, so that it is possible to obtain:
Figure BDA0003836325010000084
wherein:
Figure BDA0003836325010000086
a discrete delay fast time for the target to radar closest slope distance.
Further, in the terahertz SAR two-dimensional autofocus imaging algorithm, in step S8, based on a minimum entropy criterion, estimation of a residual phase error in a azimuth direction is performed by the phase error model in step S3.2, after l iterations, it is determined whether the obtained image entropy value Ent satisfies the formula (13), and if so, the residual phase error in the azimuth direction to be compensated is:
Figure BDA0003836325010000085
in step S9, the residual phase error estimated according to step S8
Figure BDA0003836325010000091
The compensation function of said residual phase error in azimuth direction is +.>
Figure BDA0003836325010000092
And multiplying the echo signals by the equation (21) to perform azimuth fine compensation, so that the echo signals can be obtained:
Figure BDA0003836325010000093
further, in the terahertz SAR two-dimensional self-focusing imaging algorithm, in step S10, the echo signal after the fine compensation is subjected to matched filtering, and after azimuth compression is completed, the model expression of the obtained THz-SAR focusing image is:
Figure BDA0003836325010000094
wherein: b (B) d Is the doppler bandwidth.
Compared with the prior art, the invention has the beneficial effects that: comprehensively considering nonlinear phase errors in the distance direction and motion phase errors in the azimuth direction, and correspondingly compensating after estimation to obtain a high-resolution THz-SAR focusing image; meanwhile, based on the combined use of IMU/GPS measurement data and MEA self-focusing algorithm, the calculation amount can be effectively reduced compared with the direct adoption of the self-focusing algorithm.
Drawings
Fig. 1 is a schematic structural diagram of a terahertz SAR two-dimensional self-focusing imaging algorithm in the present invention.
Detailed Description
The terahertz SAR two-dimensional autofocus imaging algorithm of the present invention will be described in more detail below in conjunction with the schematic diagram, in which the preferred embodiments of the present invention are shown, it being understood that the invention described herein can be modified by those skilled in the art, while still achieving the advantageous effects of the present invention. Accordingly, the following description is to be construed as broadly known to those skilled in the art and not as limiting the invention.
The invention is more particularly described by way of example in the following paragraphs with reference to the drawings. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are in a very simplified form and are all to a non-precise scale, merely for convenience and clarity in aiding in the description of embodiments of the invention.
As shown in fig. 1, the invention provides a terahertz SAR two-dimensional self-focusing imaging algorithm, which comprises the following steps:
s1: establishing a model of an echo signal of the terahertz SAR;
in step S1, the terahertz SAR transmits a chirp signal, and carries out de-chirp on a received echo signal, and a model expression of the generated echo signal is:
Figure BDA0003836325010000101
wherein: τ is distance-wise fast time; t is azimuth slow time; t (T) p Is pulse width; c is the speed of light; lambda is the wavelength; r is R i Is the actual distance of the radar; r is R ref Is the reference distance of the radar; rΔ is the difference between the actual range of the radar and the reference range; j is an imaginary unit; gamma is the frequency modulation slope;
s2: removing the residual video phase items and the oblique phase items in the echo signals;
in step S2, the fourier transform of the distance direction is performed on equation (1), and it is possible to obtain:
Figure BDA0003836325010000102
Figure BDA0003836325010000111
wherein: f (f) r Is distance frequency; f (f) c Is the center frequency;
Figure BDA0003836325010000112
is a Doppler term;
Figure BDA0003836325010000113
is the remaining video phase term; />
Figure BDA0003836325010000114
A diagonal phase term that is an echo envelope; because the Doppler value is deviated due to the residual video phase term and the oblique phase term, the two terms are required to be removed;
the remaining video phase term and the diagonal phase term in equation (2) are expressed as:
Figure BDA0003836325010000115
the compensation function of the residual video phase term and the diagonal phase term is
Figure BDA0003836325010000116
And multiplying by formula (2):
Figure BDA0003836325010000117
performing Inverse Fast Fourier Transform (IFFT) on equation (4), i.e., the model expression of the transformed echo signal is:
Figure BDA0003836325010000118
s3: estimating a nonlinear phase error of the distance direction based on the MEA;
in step S3, the linear phase is not ideal due to the nonlinear phase error of the distance, so that the distribution and focusing of the distance image are affected.Assume that the function of the nonlinear phase error of the range direction is
Figure BDA0003836325010000119
The model expression for the echo signal with nonlinear phase error is:
Figure BDA0003836325010000121
discretizing the distance direction fast time tau and the azimuth direction slow time t into t respectively n (n=0:n-1) and t m (m= 0:M-1), then discretization of formula (6) can yield:
Figure BDA0003836325010000122
taking the minimum entropy as an evaluation criterion, and estimating the nonlinear phase error through iterative optimization, wherein the method comprises the following specific steps of:
s3.1: assume that the estimated range-wise nonlinear phase error is
Figure BDA0003836325010000123
And->
Figure BDA0003836325010000124
Initializing and setting to 0, namely, the compensated range profile expression is as follows:
Figure BDA0003836325010000125
wherein: k is the distance frequency; m is the number of echo pulses; n is a distance unit; n is the total distance unit number;
s3.2: based on the minimum entropy criterion, an optimization model of the phase error is established, and the expression is:
Figure BDA0003836325010000126
wherein: ent is the image entropy value, and the expression is:
Figure BDA0003836325010000127
wherein: e is the range profile energy, and the expression is:
Figure BDA0003836325010000131
s3.3: solving the expression (9) based on Newton's method, the expression for iteration of the phase error can be obtained as follows:
Figure BDA0003836325010000132
wherein:
Figure BDA0003836325010000133
Figure BDA0003836325010000134
wherein: s is(s) 0 (l-1 ) (n, m) is echo data corrected by the phase error estimated by the (l-1) th iteration:
Figure BDA0003836325010000135
is G k，m Each element of the (B) is complex conjugated;
s3.4: judging whether the estimated phase error is accurate enough, namely judging the image entropy values Ent and Ent respectively obtained after the first iteration and the (l-1) th iteration (l-1 ) Whether the difference between them is lower than a preset threshold value J, namely:
|Ent (l) -Ent (l-1) |≤J (13)
wherein: the smaller the preset threshold J is, the more accurate the estimated phase error is, but the corresponding iteration times are increased;
if equation (13) is satisfied, the nonlinear phase error in the distance direction to be compensated is:
Figure BDA0003836325010000141
s4: performing distance compensation based on the estimated nonlinear phase error;
in step S4, the nonlinear phase error estimated according to step S3
Figure BDA0003836325010000142
The compensation function of the nonlinear phase error of the distance direction is +.>
Figure BDA0003836325010000143
And multiplying the echo signal by equation (7) to compensate the distance direction, the method can obtain:
Figure BDA0003836325010000144
s5: performing distance compression on the echo signals subjected to distance compensation;
in step S5, the distance-compensated echo signal is subjected to a distance-wise fourier transform (FFT), and distance compression is completed, that is, the model expression of the echo signal is:
Figure BDA0003836325010000145
wherein: t is t i Discrete delay fast time for target to radar;
Figure BDA0003836325010000146
discrete slow time for the beam center to pass through the target; b is the distance signal bandwidth; w (w) a (. Cndot.) is the azimuthal envelope; r is R Δ The difference between the actual distance and the reference distance of the radar is the ideal slant distance;
based on motion phase error
Figure BDA0003836325010000147
The model expression of the echo signal that actually completes the distance compression is:
Figure BDA0003836325010000148
s6: based on IMU/GPS measurement data, performing azimuth coarse compensation on the echo signals after distance compression;
in step S6, based on IMU/GPS measurement data, calculating the actual track of the antenna by combining the geometric position of the antenna, and obtaining the reference track of the antenna by straight line fitting; the actual inclined distance and the ideal inclined distance between the antenna and the scene are calculated according to the actual track and the reference track of the antenna, so as to obtain a difference d between the actual inclined distance and the ideal inclined distance los (t n ，t m ) For motion phase errors
Figure BDA0003836325010000151
And performing corresponding motion phase compensation, wherein the compensation function of the motion phase error is as follows:
Figure BDA0003836325010000152
equation (17) is multiplied by equation (18) to perform coarse azimuthal compensation on the echo signal, and it is obtained that:
Figure BDA0003836325010000153
in the formula (19), when
Figure BDA0003836325010000154
When the phase error is 0, the phase error of the azimuth direction is completely compensated; however, due to the limitation of IMU/GPS measurement data, the azimuth direction has residual phase error +.>
Figure BDA0003836325010000155
Therefore, by converting the formula (19), it is possible to obtain:
Figure BDA0003836325010000156
s7: performing range migration correction on the echo signals after the azimuth coarse compensation;
in step S7, the azimuth fourier transform (FFT) is performed on the echo signal after the azimuth coarse compensation, the echo signal at this time is transformed into the range-doppler domain, the range migration correction is performed on the echo signal by interpolation, and after the influence of the range migration is eliminated, the azimuth inverse fourier transform (IFFT) is performed on the echo signal, so that it is possible to obtain:
Figure BDA0003836325010000161
wherein:
Figure BDA0003836325010000162
discrete delay fast time for target to radar nearest ramp; it can be seen that the azimuth is still subject to residual phase error after the range migration correction>
Figure BDA0003836325010000163
Is effective for modulation.
S8: estimating a residual phase error of the azimuth based on the MEA;
in step S8, based on the minimum entropy criterion, estimation of the azimuth residual phase error is performed by the phase error model in step S3.2, and after i iterations, it is determined whether the obtained image entropy value Ent satisfies the formula (13), and if so, the azimuth residual phase error to be compensated is:
Figure BDA0003836325010000164
s9: performing azimuth fine compensation based on the estimated residual phase error;
in step S9, the residual phase error estimated according to step S8
Figure BDA0003836325010000165
The compensation function of the residual phase error in azimuth is +.>
Figure BDA0003836325010000166
And multiplying the echo signals by the equation (21) to perform azimuth fine compensation, so that the echo signals can be obtained:
Figure BDA0003836325010000167
s10: carrying out azimuth compression on the echo signals subjected to azimuth fine compensation to obtain THz-SAR focusing images;
in step S10, the echo signal after the fine compensation is matched and filtered, and after the azimuth compression is completed, the model expression of the THz-SAR focusing image is obtained as follows:
Figure BDA0003836325010000171
wherein: b (B) d Is the doppler bandwidth.
In summary, in the embodiment, the proposed terahertz SAR two-dimensional self-focusing imaging algorithm comprehensively considers the nonlinear phase error in the distance direction and the motion phase error in the azimuth direction, and correspondingly compensates after estimation to obtain a high-resolution THz-SAR focusing image; meanwhile, based on the combined use of IMU/GPS measurement data and MEA self-focusing algorithm, the calculation amount can be effectively reduced compared with the direct adoption of the self-focusing algorithm.
The foregoing is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any person skilled in the art will make any equivalent substitution or modification to the technical solution and technical content disclosed in the invention without departing from the scope of the technical solution of the invention, and the technical solution of the invention is not departing from the scope of the invention.

Claims (9)

1. The terahertz SAR two-dimensional self-focusing imaging algorithm is characterized by comprising the following steps of:
s1: establishing a model of an echo signal of the terahertz SAR;
s2: removing the residual video phase items and the oblique phase items in the echo signals;
s3: estimating a nonlinear phase error of the distance direction;
s4: performing distance compensation based on the estimated nonlinear phase error;
s5: performing distance compression on the echo signals subjected to distance compensation;
s6: based on IMU/GPS measurement data, performing azimuth coarse compensation on the echo signals after distance compression;
s7: performing range migration correction on the echo signals after the azimuth coarse compensation;
s8: estimating a residual phase error of the azimuth direction;
s9: performing azimuth fine compensation based on the estimated residual phase error;
s10: and carrying out azimuth compression on the echo signals subjected to azimuth fine compensation to obtain THz-SAR focusing images.
2. The terahertz SAR two-dimensional self-focusing imaging algorithm according to claim 1, wherein in step S1, the terahertz SAR transmits a chirp signal, and de-chirps the received echo signal, and the model expression of the generated echo signal is:
Figure FDA0003836322000000011
wherein: τ is distance-wise fast time; t is azimuth slow time; t (T) p Is pulse width; c isLight velocity; lambda is the wavelength; r is R i Is the actual distance of the radar; r is R ref Is the reference distance of the radar; r is R Δ Is the difference between the actual distance of the radar and the reference distance; j is an imaginary unit; gamma is the frequency modulation slope.
3. The terahertz SAR two-dimensional self-focusing imaging algorithm according to claim 2, wherein in step S2, a fourier transform (FFT) of the range direction is performed on equation (1), which can be obtained:
Figure FDA0003836322000000021
wherein: f (f) r Is distance frequency; f (f) c Is the center frequency;
Figure FDA0003836322000000022
is a Doppler term;
Figure FDA0003836322000000023
is the remaining video phase term; />
Figure FDA0003836322000000024
A diagonal phase term that is an echo envelope;
the remaining video phase term and the diagonal phase term in equation (2) are expressed as:
Figure FDA0003836322000000025
equation (2) multiplied by the compensation function of the residual video phase term and the diagonal phase term
Figure FDA0003836322000000026
The method can obtain:
Figure FDA0003836322000000027
performing Inverse Fast Fourier Transform (IFFT) on equation (4), i.e. the model expression of the echo signal after transformation is:
Figure FDA0003836322000000028
4. the terahertz SAR two-dimensional self-focusing imaging algorithm according to claim 1, wherein in step S3, it is assumed that the function of the nonlinear phase error of the range direction is
Figure FDA0003836322000000031
The model expression of the echo signal for which the nonlinear phase error exists is:
Figure FDA0003836322000000032
wherein: τ is distance-wise fast time; t is azimuth slow time;
discretizing τ and t into t, respectively n (n=0:n-1) and t m (m= 0:M-1), then discretization of formula (6) can yield:
Figure FDA0003836322000000033
taking the minimum entropy criterion as an evaluation criterion, and estimating the nonlinear phase error through iterative optimization, wherein the method comprises the following specific steps of:
s3.1: assuming that the nonlinear phase error of the estimated distance direction is
Figure FDA0003836322000000034
And->
Figure FDA0003836322000000035
Initializing and setting to 0, namely, the compensated range profile expression is as follows:
Figure FDA0003836322000000036
wherein: k is the distance frequency; m is the number of echo pulses; n is a distance unit; n is the total distance unit number;
s3.2: based on the minimum entropy criterion, a phase error model is established, and the expression is:
Figure FDA0003836322000000037
wherein: ent is the image entropy value, and the expression is:
Figure FDA0003836322000000041
wherein: e is the range profile energy, and the expression is:
Figure FDA0003836322000000042
s3.3: solving the expression (9) based on Newton's method, the expression for iterating the phase error can be obtained as follows:
Figure FDA0003836322000000043
wherein:
Figure FDA0003836322000000044
Figure FDA0003836322000000045
wherein: s is(s) 0 (l-1) (n, m) is the echo data corrected using the phase error estimated by the (l-1) th iteration;
Figure FDA0003836322000000046
is G k，m Each element of the (B) is complex conjugated;
s3.4: judging whether the estimated phase error is accurate enough, namely judging the image entropy values Ent and Ent respectively obtained after the first iteration and the (l-1) th iteration (l-1) Whether the difference between them is lower than a preset threshold value J, namely:
|Enr (l) -Ent (1-1) |≤J (13)
if equation (13) is satisfied, the nonlinear phase error in the distance direction that needs to be compensated is:
Figure FDA0003836322000000051
in step S4, the nonlinear phase error estimated according to step S3
Figure FDA0003836322000000052
The compensation function of the nonlinear phase error of the distance direction is +>
Figure FDA0003836322000000053
And multiplying the echo signal by equation (7) to compensate the distance direction, the method can obtain:
Figure FDA0003836322000000054
5. the terahertz SAR two-dimensional self-focusing imaging algorithm according to claim 4, wherein in step S5, the distance-compensated echo signal is subjected to a distance-wise fourier transform (FFT), and the model expression of the distance-compressed echo signal is:
Figure FDA0003836322000000055
wherein: t is t i Discrete delay fast time for target to radar;
Figure FDA0003836322000000056
discrete slow time for the beam center to pass through the target; b is the distance signal bandwidth; w (w) a (. Cndot.) is the azimuthal envelope;
based on motion phase error
Figure FDA0003836322000000057
The model expression of the echo signal that actually completes the distance compression is:
Figure FDA0003836322000000061
6. the terahertz SAR two-dimensional self-focusing imaging algorithm according to claim 5, wherein in step S6, the difference d between the actual and ideal tilt of the antenna and scene is calculated based on IMU/GPS measurement data los (t n ，t m ) To perform corresponding motion phase compensation, and the compensation function of the motion phase error is as follows:
Figure FDA0003836322000000062
equation (17) is multiplied by equation (18) to perform coarse azimuthal compensation on the echo signal, to obtain:
Figure FDA0003836322000000063
residual phase error due to the IMU/GPS measurement data based on azimuth
Figure FDA0003836322000000064
By transforming the formula (19), it is possible to obtain:
Figure FDA0003836322000000065
7. the terahertz SAR two-dimensional self-focusing imaging algorithm according to claim 6, wherein in step S7, the echo signal after the orientation coarse compensation is subjected to an orientation fourier transform (FFT), the echo signal is transformed into a range-doppler domain, the echo signal is subjected to range migration correction by interpolation, and after the influence of the range migration is eliminated, the echo signal is subjected to an orientation inverse fourier transform (IFFT), so that it is obtained:
Figure FDA0003836322000000066
Figure FDA0003836322000000071
wherein:
Figure FDA0003836322000000072
a discrete delay fast time for the target to radar closest slope distance.
8. The terahertz SAR two-dimensional self-focusing imaging algorithm according to claim 7, wherein in step S8, based on a minimum entropy criterion, estimation of the residual phase error in azimuth is performed by the phase error model in step S3.2, and after i iterations, it is determined whether the obtained image entropy value Ent satisfies equation (13), and if so, the residual phase error in azimuth to be compensated is:
Figure FDA0003836322000000073
in step S9, the residual phase error estimated according to step S8
Figure FDA0003836322000000074
The compensation function of said residual phase error in azimuth direction is +.>
Figure FDA0003836322000000075
And multiplying the echo signals by the equation (21) to perform azimuth fine compensation, so that the echo signals can be obtained:
Figure FDA0003836322000000076
9. the terahertz SAR two-dimensional self-focusing imaging algorithm according to claim 1, wherein in step S10, the echo signal after fine compensation is subjected to matched filtering, and after azimuth compression is completed, the model expression of the obtained THz-SAR focusing image is:
Figure FDA0003836322000000077
wherein: b (B) d Is the doppler bandwidth.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116990777A (en) * 2023-09-27 2023-11-03 中国人民解放军国防科技大学 Terahertz RCS high-precision measurement method, system, device and equipment
CN117129994A (en) * 2023-10-26 2023-11-28 中国石油大学(华东) Improved backward projection imaging method based on phase compensation nuclear GNSS-SAR

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116990777A (en) * 2023-09-27 2023-11-03 中国人民解放军国防科技大学 Terahertz RCS high-precision measurement method, system, device and equipment
CN116990777B (en) * 2023-09-27 2023-12-12 中国人民解放军国防科技大学 Terahertz RCS high-precision measurement method, system, device and equipment
CN117129994A (en) * 2023-10-26 2023-11-28 中国石油大学(华东) Improved backward projection imaging method based on phase compensation nuclear GNSS-SAR
CN117129994B (en) * 2023-10-26 2024-01-30 中国石油大学(华东) Improved backward projection imaging method based on phase compensation nuclear GNSS-SAR

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