A method for estimating and refocusing parameters of a terahertz circular SAR moving target

Abstract

The present application belongs to the technical field of radar moving target imaging, and particularly relates to a terahertz circular SAR moving target parameter estimation and refocusing method. The present application reduces two-dimensional coupling in the range and azimuth by dividing sub-apertures, performs range compression on the echo under each sub-aperture by performing inverse Fourier transform in the range direction and after slant correction, estimates the Doppler center by using the spectral peak measurement method and combining the shadow position, estimates the Doppler frequency by using the fractional Fourier transform, estimates the along-track speed and radial speed information of the moving target according to the estimated results, constructs a first-order and second-order phase compensation function, corrects the azimuth direction offset, partial defocusing and additional range migration, and compensates the residual quadratic and higher-order phase by using the phase gradient autofocus algorithm. The refocusing effect of the moving target in the simulation data verifies the effectiveness of the present method.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar moving target imaging, and particularly relates to a terahertz circular SAR moving target parameter estimation and refocusing method. BACKGROUND

[0002] The terahertz circular synthetic aperture radar (SAR) is a radar working in a circular beam scanning mode and transmitting a terahertz wave. In the mode, a carrier platform performs circular motion at a certain height, the beam center is always directed to the same imaging scene, and long-time and all-directional observation of a key area and a moving target can be achieved to obtain more target information. Relative motion between the radar and a stationary target will cause occurrence of range migration, which is caused by the inherent motion characteristics of the SAR and can be eliminated by constructing a compensation function based on the motion speed of the carrier. However, for a moving target, the motion of the target will introduce additional range migration, and due to the unknown motion parameters of the moving target, the radar will be offset and defocused when directly imaging the moving target. In the modern battlefield, we hope to identify the information of enemy tanks, armored vehicles, ships and other moving equipment, and therefore the parameter estimation and refocusing of the moving target need to be solved.

[0003] To realize refocusing imaging of the moving target, two problems need to be solved. One is to eliminate the two-dimensional coupling in the range and azimuth directions. The circular SAR provides more target information, but due to the curved motion form of the carrier, more complex azimuth-range coupling is also introduced. The other is to estimate the motion parameters of the target and then construct an azimuth phase compensation function for refocusing of the moving target. Due to the complex coupling between the motion parameters in the circular mode, the motion parameter information is coupled in the azimuth phase of the echo, which causes the traditional refocusing method to fail. In the terahertz band, the shadow left at the original position after the defocusing of the azimuth energy of the moving target can be observed, which lays a foundation for estimating the Doppler center offset of the moving target. However, the current research on the parameter estimation and refocusing of the moving target is mostly for strip Ku band, C band and W band SAR, and there is less research on the terahertz circular SAR moving target. Therefore, it is of great significance to research a method for parameter estimation and refocusing of the terahertz circular SAR moving target. SUMMARY

[0004] The purpose of the present application is to provide a terahertz circular SAR moving target parameter estimation and refocusing method to solve the above problems.

[0005] The technical scheme of the present application is as follows: a terahertz circular SAR moving target parameter estimation and refocusing method, comprising the following steps:

[0006] S1, sub-aperture division is carried out on a terahertz circumferential SAR original echo signal s (t, t a ) to reduce two-dimensional coupling in the range and azimuth directions;

[0007] S2, echo data of each sub-aperture scene is subjected to desquaring processing to reduce the requirement for azimuth sampling frequency;

[0008] S3, inverse Fourier transform is performed on the echo data in each sub-aperture in the range direction to complete range compression and remove a video residual phase (RVP) term, so that the target echo is compressed to the same range cell;

[0009] S4, the instantaneous slant range (R (t a )) of the target to the carrier is obtained by performing quadratic fitting on the carrier motion trajectory under each sub-aperture by using Taylor expansion;

[0010] S5, Fourier transform is performed along the azimuth direction to extract data of the distance cell where the moving target is located, to improve the estimation accuracy, data of multiple distance cells can be extracted for accumulation, the spectrum peak measurement method is used to estimate the azimuth Doppler center in combination with the shadow position of the moving target, to obtain an estimation value of the along-track speed, and then a first-order phase compensation function is constructed to correct the Doppler center shift, so that the moving target is repositioned;

[0011] S6, fractional Fourier transform is used to estimate the Doppler frequency, to obtain an estimation value of the radial speed, and a second-order phase compensation function is constructed to correct the defocusing of the moving target, so that the moving target is preliminarily refocused;

[0012] S7, azimuth Fourier transform is performed on the result of step S6, and then a phase gradient autofocus (PGA) algorithm is used to correct residual quadratic and high-order phase errors caused by a series of approximations, so that the moving target is refocused;

[0013] The present application reduces the two-dimensional coupling in the azimuth and range directions by dividing the sub-aperture, uses the second-order Taylor expansion to approximate the parabolic trajectory of the carrier, combines the parameter estimation with the shadow position of the moving target to eliminate the coupling of each motion parameter, and combines the phase gradient autofocus algorithm to achieve good focusing effect of the moving target.

[0014] The present application has the beneficial effects of reducing the two-dimensional coupling in the azimuth and range directions, eliminating the coupling of each motion parameter, realizing the parameter estimation and refocusing of the moving target, and improving the imaging quality of the moving target. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 It is a carrier observation geometric model diagram of the present application;

[0016] Figure 2This is a diagram of the aircraft observation geometry after dividing the aperture into sub-apertures;

[0017] Figure 3 This is a flowchart of the present invention;

[0018] Figure 4 It is the imaging result of a moving car target and its shadow in the simulation data;

[0019] Figure 5 This is a diagram showing the Doppler center estimation results of the moving vehicle target in the simulation data;

[0020] Figure 6 This is a diagram showing the Doppler modulation frequency estimation results of the moving target vehicle in the simulation data;

[0021] Figure 7 This is a diagram showing the corrected Doppler shift of the moving car target in the simulation data;

[0022] Figure 8 This is a refocusing effect diagram of the moving car target in the simulation data; Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings to demonstrate its practicality.

[0024] As attached Figure 1 As shown, the radar operates in terahertz CSAR mode, performing 360° all-around, long-term observation of moving targets in the scene. Figure 2 This is a geometric observation model diagram after sub-aperture division. Sub-aperture division reduces azimuth accumulation time and decreases coupling in azimuth range. Figure 3 The flowchart of this invention illustrates a circular terahertz SAR moving target parameter estimation and refocusing method proposed in this invention. This method can effectively refocus moving targets with azimuth offset and defocus, and estimate the target's motion parameters. The specific implementation steps are as follows:

[0025] Step 1: Process the raw echo signal s(t,t) from the terahertz circular SAR. a Sub-apertures are defined, and the resulting sub-apertures are as follows: Figure 2 As shown, under each sub-aperture, since the azimuth time change is relatively small, the radar coordinates at the center time of each sub-aperture can be fitted with a quadratic parabola using Taylor's theorem, thereby reducing the two-dimensional coupling of range and azimuth.

[0026] Step 2: Construct a reference function to de-skew the echo data for each sub-aperture scene, reducing the requirement for the azimuth sampling frequency, and obtain the de-skewed echo signal as follows:

[0027]

[0028] where ω r is the range window, τ is the fast time, t a is the slow time, R(t a ) is the instantaneous slant range from the target to the carrier, c is the speed of light, K r is the range chirp rate, R ref is the reference range, R Δ is the instantaneous slant range from the radar to the target minus the reference range R ref , i.e., R Δ = R(t a )-R ref , f c is the carrier center frequency, the first exponential term is the range phase, the second exponential term is the azimuth phase, and the third exponential term is the video residual phase RVP term, which needs to be removed in subsequent processing.

[0029] Step 3: Perform inverse Fourier transform on the echo data in each sub-aperture in the range direction to complete range compression and remove the video residual phase RVP term, to obtain the processed echo signal:

[0030]

[0031] Step 4: Perform quadratic parabolic fitting on the carrier motion trajectory under each sub-aperture using Taylor's theorem to obtain the instantaneous slant range R(t a ) from the target to the carrier, taking the nth sub-aperture as an example, R n (t a ) is obtained as:

[0032]

[0033] where x n (t a ), y n (t a ) represent the azimuth and range positions of the target under the nth sub-aperture, x p,n (t a ), y n (t a ) represent the azimuth and range positions of the radar under the nth sub-aperture, and H is the flight height of the carrier, whose expressions are respectively:

[0034]

[0035] where (x0, y0) represents the original coordinates of the target under the sub-aperture, (v x , v y ) is the speed information of the target, represents the azimuth center time of the nth sub-aperture, and θ nis the azimuth center angle of the nth aperture, R is the moving radius of circular SAR, V is the flight speed of the carrier, for the convenience of analysis, it is assumed that n = 0, and it is noted that its range satisfies T sub is a synthetic aperture time, then the coordinates of the radar can be expressed as Substituting the slant range equation R n (t a ) and performing Taylor expansion at t n = 0 can obtain:

[0036]

[0037] where R n1 (0), R n2 (0), and R n3 (0) are the first-order, second-order, and third-order coefficients of the Taylor expansion polynomial, respectively:

[0038]

[0039] where is the pitch angle of the carrier to the center of the imaging scene, R n (0) is a phase constant term, which has no effect on the imaging quality, R n1 (0) is a first-order phase term, which will cause the offset of the imaging and determines the azimuth Doppler center, which is determined by the azimuth velocity and the original position of the target, since there is rich shadow information of moving targets in the terahertz CSAR imaging scene, and the shadow position is the real position of the moving target, therefore, the influence of the original position of the target on the Doppler center can be eliminated by detecting the shadow position of the moving target, so the influence of this term is ignored in the subsequent analysis; R n2 (0) is a second-order phase term, which determines the azimuth Doppler frequency modulation, according to the relationship between the phase and the frequency, the expression of the azimuth Doppler center frequency and the Doppler frequency modulation can be obtained as follows:

[0040]

[0041] The above approximation process uses the far-field approximation, considers that v x << V, v y << V, and ignores the influence of the original position of the target, from the above formula, the along-track speed of the target can be obtained by estimating the Doppler center, and the radial speed of the target can be obtained by estimating the Doppler frequency modulation and the Doppler center;

[0042] Step 5: Fourier transform is performed in the azimuth direction to extract the data of the distance unit where the moving target is located. To improve the estimation accuracy, the data of multiple distance units can be extracted and accumulated. The Doppler center is estimated by using the spectral peak measurement method. The estimation result of the Doppler center is as shown in the following table: Figure 5 The frequency corresponding to the peak position is the Doppler center frequency. As shown in the following figure, Figure 5 The estimated value of the target speed along the heading direction is 7.09 m / s. The accuracy of the estimated parameters is determined in combination with the shadow position of the moving target. Then, a first-order phase compensation function is constructed to correct the Doppler center offset, and the repositioning of the moving target is realized. The first-order phase compensation function is as follows:

[0043]

[0044] The echo signal after removing the RVP is subjected to the distance direction Fourier transform, and the above first-order compensation function is multiplied by the echo signal. The two-dimensional time domain echo signal after the first-order phase error compensation is as follows:

[0045]

[0046] As can be seen from the above formula, the first-order phase compensation not only eliminates the azimuth offset, but also corrects the distance walk. As shown in the following figure, Figure 7 It can be seen that the target and the shadow are overlapped after the Doppler offset is corrected, which proves the accuracy of the estimated parameters.

[0047] Step 6: The fractional Fourier transform is used to estimate the Doppler frequency, and then the radial velocity of the target can be obtained. The transformation result is as shown in the following table: Figure 6 The peak position contains the Doppler frequency information, and the estimated value of the Doppler frequency can be obtained by peak search. A second-order phase compensation function is constructed to correct the defocusing of the moving target, and the re-focusing of the moving target is preliminarily realized. The second-order phase compensation function is as follows:

[0048]

[0049] The above formula is multiplied by the echo signal after the first-order phase compensation in step 5, and the echo signal after the second-order phase compensation is as follows:

[0050]

[0051] The inverse Fourier transform is performed on the compensated echo signal in the distance direction, and the following formula is obtained:

[0052]

[0053] As can be seen from the above formula, the second-order phase compensation not only eliminates the quadratic error of the azimuth phase, but also corrects the distance curvature. At this time, the target echo is compressed to the same distance unit.

[0054] Step 7: The echo after step 6 still contains higher-order phase and residual second-order phase errors caused by a series of approximations. Therefore, the echo after step 6 is subjected to azimuth Fourier transform to the image domain, and the phase gradient autofocus (PGA) algorithm is used to correct the remaining second-order and higher-order phase errors caused by a series of approximations, so as to achieve the final refocusing of the moving target.

[0055] Simulation data description

[0056] The above method is attached. Figure 3 The illustrated procedure was validated using simulation data. The refocusing results demonstrate the effectiveness of this method. The specific parameter settings for the simulation data are shown in Table 1.

[0057] Operating mode Bunching circumferential mode Center frequency 220 GHz Distance sampling rate 8 MHz Pulse repetition frequency 3000 Hz Platform average velocity 136.3 m / s Reference distance 8000m Motion radius 5656.84m Sub-aperture time 0.2s Moving target along course velocity 7 m / s Moving target radial velocity 4 m / s

[0058] Figure 8 The image shows the refocusing effect of the method on a moving car target in simulation data, compared with the image before refocusing. Figure 4 The comparison shows that the moving target focusing effect after processing by this method is good, which proves the practical value of the method proposed in this invention.

Claims

1. A method for estimating and refocusing parameters of a moving target using terahertz circular SAR, characterized in that, Includes the following steps: S1, the raw echo signal s(t,t) from the terahertz circular SAR a Perform sub-aperture division; S2. Construct a reference function to de-skew the echo data for each sub-aperture scene, obtaining the de-skewed echo signal as follows: Where, ω r Let τ be the distance window function, t be the fast time, and t be the distance window function. a For slow time, R(t) a Let ) be the instantaneous slant distance from the target to the carrier aircraft, c be the speed of light, and K be the distance from the target to the carrier aircraft. r For distance frequency modulation, R ref For reference distance, R Δ The instantaneous slant range and reference distance R of the radar reaching the target ref The difference, i.e., R Δ =R(t) a )-R ref f c The carrier center frequency is represented by the first exponential term, which represents the range phase, the second exponential term represents the azimuth phase, and the third exponential term represents the video residual phase (RVP). S3. Perform an inverse Fourier transform in the range direction on the echo data in each sub-aperture to complete range compression and remove the residual phase (RVP) term from the video. At this time, the target echo is compressed into the same range unit. S4. Apply Taylor's theorem to perform a quadratic fitting of the aircraft's trajectory under each sub-aperture to obtain the instantaneous slant distance R(t) from the target to the aircraft. a The instantaneous slope R of the nth sub-aperture is obtained by performing a quadratic fitting on the nth sub-aperture. n (t a )for: Where, x n (t a ), y n (t a ) represents the t under the nth sub-aperture a The position and distance of the target at any given time, x p,n (t a ), y p,n (t a ) represent the t values ​​at the nth sub-aperture. a The azimuth and range positions of the radar at any given time, where H is the flight altitude of the carrier aircraft, are expressed as follows: Where (x0, y0) represents the original coordinates of the target under this sub-aperture, (v x ,v y This is the target's speed information. θ represents the azimuth center time of the nth sub-aperture. n Let θ be the azimuth center angle of the nth aperture, R be the radius of motion of the circular SAR, V be the flight speed of the carrier aircraft, and let θ be... n =0, and record Range satisfies T sub Given a synthetic aperture time, the radar coordinates can be expressed as: Substitute into the slope distance equation R n (t a ) and in t n Performing a Taylor expansion at the point = 0 yields: Among them, R n1 (0), R n2 (0), R n3 (0) represents the first, second, and third order coefficients of the Taylor expansion polynomial; S5. Perform a Fourier transform along the azimuth direction to extract the data from the range cell where the moving target is located. To improve estimation accuracy, data from multiple range cells can be extracted and accumulated. The azimuth Doppler center is estimated using the spectral peak measurement method combined with the moving target's shadow position, yielding an estimated value for the velocity along the heading. A first-order phase compensation function is then constructed to correct the Doppler center offset, achieving repositioning of the moving target. The first-order phase compensation function H... com1 (t n )as follows: S6. Using fractional Fourier transform to estimate the Doppler modulation frequency, the radial velocity is estimated. A second-order phase compensation function is constructed to correct the defocusing of the moving target, thus initially achieving refocusing of the moving target. The second-order phase compensation function H... com2 (t n )as follows: S7. Perform an azimuth-to-Fourier transform on the result of step S6, and then use the phase gradient autofocus algorithm to correct the remaining second-order and higher-order phase errors caused by a series of approximations, thereby achieving refocusing of the moving target.

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