A method for three-dimensional positioning of a spaceborne curved trajectory SAR target based on FrFT

Abstract

The application provides a FrFT-based three-dimensional positioning method for a spaceborne curve track SAR target, which comprises the following steps: firstly, a reference spectrum is established, and the reference spectrum is multiplied by a conjugate echo spectrum to obtain an imaging result; secondly, a fractional Fourier transform (FrFT) is performed on a target azimuth signal to estimate a Doppler frequency and an initial frequency; and finally, three-dimensional coordinates of the target are calculated according to the estimated parameters. The application combines the FrFT, and can effectively improve the estimation speed and reduce the signal-to-noise ratio loss compared with a traditional method.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture radar technology, and particularly relates to a three-dimensional localization method for spaceborne curved trajectory SAR targets based on fractional Fourier transform (FrFT). Background Technology

[0002] Synthetic Aperture Radar (SAR) possesses all-weather, all-day observation capabilities and boasts high resolution, currently holding a crucial position in Earth observation. Conventional SAR two-dimensional images can only present the approximate location of targets, suffering from problems such as overlay and top-bottom inversion, and failing to reflect target height information. This overlay phenomenon is particularly pronounced in urban areas with numerous high-rise buildings and complex structures, and cities are strategically vital areas in modern warfare. Due to these issues, SAR three-dimensional imaging technology has become a research hotspot both domestically and internationally in recent years.

[0003] Currently, commonly used techniques in SAR 3D imaging include tomographic SAR, array interferometric SAR, and circular SAR. Tomographic SAR, also known as multi-baseline SAR, involves the radar observation platform repeatedly flying at different altitudes to form a synthetic aperture in the altitude direction, achieving high resolution in the range-altitude two-dimensional plane. Array interferometric SAR involves mounting multiple antennas on the observation platform and acquiring multi-channel SAR images through multiple-input multiple-output (MIMO) technology, enabling single-flight 3D imaging. Circular SAR involves the observation platform orbiting the target in a circular motion to acquire omnidirectional information. Similarly, it only requires a single flight to form a synthetic aperture in both the range-azimuth and range-elevation two-dimensional planes, achieving high resolution and solving the time-consuming problem of tomographic SAR.

[0004] However, the existing SAR 3D imaging methods all require a large amount of data, which takes a long time to acquire and is quite cumbersome to process. Curved trajectory SAR, on the other hand, only needs a portion of the trajectory from circular trajectory SAR to reconstruct a single-flight target, requiring less data and saving acquisition time. However, existing curved trajectory SAR imaging methods extract the Doppler frequency modulation residual of the target by dividing the aperture into sub-apertures, which not only results in a loss of signal-to-noise ratio but also has a relatively slow processing speed. Therefore, there is an urgent need for a method to quickly estimate the 3D position of the target. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a three-dimensional positioning method for spaceborne curved trajectory SAR targets based on fractional Fourier transform (FrFT). This method can quickly estimate the Doppler modulation frequency residual and the target's initial frequency using FrFT. By combining the relationship between the Doppler modulation frequency residual and the target's altitude, and the relationship between the target's initial frequency and its azimuth position, the three-dimensional positioning of the target can be completed quickly.

[0006] The FrFT-based three-dimensional localization method for spaceborne curved trajectory SAR targets of the present invention includes:

[0007] S1. Obtain the satellite's spatial parameters, including its trajectory, velocity v in the geocentrically fixed (ECF) coordinate system at the synthetic aperture center time, and beam center position. Obtain the satellite's payload parameters, including wavelength λ, bandwidth B, and synthetic aperture time T. s , Pulse repetition frequency (PRF).

[0008] S2. Imaging the observed target, the specific steps include:

[0009] S21. Construct a scene coordinate system with the beam center position as the scene center point O, the line connecting the Earth's center and the scene center point as the z-axis, the satellite velocity direction as the x-axis, and the Earth distance direction as the y-axis. Perform polynomial fitting on the slant range history R(η) of the scene center point.

[0010] R(η) = R0 + k1η + k2η 2 +k3η 3 +k4η 4 (1)

[0011] Where η is the slow time, k1-k4 are the coefficients of the first to fourth order polynomials, and R0 is the zero-order term.

[0012] S22, Construct the two-dimensional spectrum of the reference point as follows:

[0013]

[0014] Where K r Here, f is the distance-modulated frequency, c is the speed of light, and f is the frequency. c For carrier frequency, f r For the range frequency, f a This refers to the azimuth frequency.

[0015] S23. Compare the spectrum of the echo signal with the reference two-dimensional spectrum S(f r ,f a By multiplying the conjugates and then performing an inverse Fourier transform, the imaging result can be obtained.

[0016] S3. Estimate the target's Doppler modulation frequency and initial frequency. Specific steps include:

[0017] S31. Locate the target's location based on the imaged SAR image, and then extract its azimuth signal for Fast Fourier Transform (FFT).

[0018] S32. Normalize the dimensions of the frequency domain signal after FFT by introducing a scaling factor Q:

[0019]

[0020] The original signal's time domain (t) and frequency domain (f) are transformed into the dimensionless domain (ul) to obtain new scaled coordinates. The transformation relationship is as follows:

[0021] u=t / Q,l=f·Q (4)

[0022] S33. Perform FrFT transformations of different orders p on the scaled signal to form a two-dimensional energy distribution map of the pu plane. Then, search for the location of the energy peak point and calculate the initial frequency of the signal based on the peak position. With frequency modulation The definition of FrFT is:

[0023]

[0024] In the formula, For the kernel function of FrFT, α = pπ / 2, where n is an integer.

[0025] The relationship between the peak position and the Doppler modulation frequency and the initial frequency estimate is as follows:

[0026]

[0027] S4. Calculate the three-dimensional coordinates of the target. The specific steps include:

[0028] S41. Calculate the target's azimuth coordinates. The calculation method is as follows:

[0029]

[0030] S42. To calculate the difference in Doppler modulation frequencies between points O and B, we first need to calculate the time-domain modulation frequency of B. The calculation method is as follows:

[0031]

[0032] Then, the difference in Doppler modulation frequency between points O and B in the time domain is calculated as follows:

[0033] K OB =K O -K B (9)

[0034] Where K O It can be obtained from the polynomial fitting coefficients k2.

[0035] S43. To calculate the difference in Doppler modulation frequencies between points A and B, first calculate the position of point A in the distance from the ground. The calculation method is as follows:

[0036]

[0037] Where S y Let S be the y-coordinate of the satellite at the center of the synthetic aperture. h Let R be the z-coordinate of the satellite at the time of the synthetic aperture center. B The slant distance from the satellite to the target point at the aperture center time is given.

[0038] The slant distance history is calculated using the coordinates of point A, and the tuning frequency K of reference point A is determined by fitting the second-order coefficients in the polynomial. A Then we can determine the difference in frequency modulation between points A and B as follows:

[0039] ΔK a =K OB -(K A -K0) (11)

[0040] S44. Calculate the height coordinates of the target point. The calculation method is as follows:

[0041]

[0042] Where λ is the wavelength, R A R is the slant distance from the satellite to the ground reference point A at the aperture center time. e H is the Earth's radius. s β1 is the altitude of the satellite orbit above the ground, and β1 is the angle between the geocenter-satellite and the geocenter-ground reference point A.

[0043] S45. Finally, calculate the ground distance coordinates of target B. The calculation method is as follows:

[0044]

[0045] The beneficial effects of this invention are as follows:

[0046] Compared to traditional point-by-point estimation, this invention combines FrFT to estimate the Doppler frequency modulation residuals of multiple target points column by column, thereby accurately and quickly estimating the three-dimensional position of the target. Attached Figure Description

[0047] Figure 1 This is a flowchart of the three-dimensional positioning method of the present invention;

[0048] Figure 2 A geometric schematic diagram of the motion trajectory of a spaceborne curved SAR;

[0049] Figure 3 Schematic diagram of the geometry of satellite-borne curve SAR observation

[0050] Figure 4 A schematic diagram of the coordinate system for the observed target scene;

[0051] Figure 5This is a multi-point imaging result image obtained using this patent;

[0052] Figure 6 This is a graph showing the FrFT results for columns containing T1 and T2 obtained using this patent.

[0053] Figure 7 This is a graph of the FrFT results for the column containing T3 obtained using this patent. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0055] The spaceborne curved trajectory SAR target three-dimensional localization method of the present invention is based on FrFT and consists of two parts: target imaging and parameter estimation. Specific steps are detailed below. Figure 1 ,include:

[0056] S1. Obtain the satellite's spatial parameters, including its trajectory, velocity v in the geocentrically fixed (ECF) coordinate system at the synthetic aperture center time, and beam center position. Obtain the satellite's payload parameters, including wavelength λ, bandwidth B, and synthetic aperture time T. s Pulse repetition frequency (PRF). In the ECF coordinate system, the trajectory of the satellite-borne curved SAR is as follows: Figure 2 As shown, the geometry of spaceborne curve SAR observation is as follows: Figure 3 As shown.

[0057] Since the target's frequency modulation residual has a linear relationship with its altitude, it is necessary to generate Doppler residuals through imaging operations. At the same time, imaging operations can also determine the target's location.

[0058] S2. Imaging the observed target, the specific steps include:

[0059] S21. Construct a scene coordinate system with the beam center position as the scene center point O, the line connecting the Earth's center and the scene center point as the z-axis, the satellite velocity direction as the x-axis, and the Earth distance direction as the y-axis. The observation target scene coordinate system is as follows: Figure 4 As shown, a polynomial fitting is performed on the slant distance history R(η) of the scene center point.

[0060] R(η) = R0 + k1η + k2η 2 +k3η 3 +k4η 4 (1)

[0061] Where η is the slow time, k1-k4 are the coefficients of the first to fourth order polynomials, and R0 is the zero-order term.

[0062] The purpose of constructing a scene coordinate system is to better demonstrate the data processing flow and make operations simpler.

[0063] S22, Construct the two-dimensional spectrum of the reference point as follows:

[0064]

[0065] Where K r Here, f is the distance-modulated frequency, c is the speed of light, and f is the frequency. c For carrier frequency, f r For the range frequency, f a This refers to the azimuth frequency. The principle is as follows: under curved trajectories, traditional RD imaging methods are no longer applicable; therefore, this patent employs a frequency domain imaging method. Based on the reference point spectrum proposed in the literature: C. Hu, T. Long, Z. Liu, T. Zeng, and Y. Tian, ​​"An Improved Frequency Domain Focusing Method in Geosynchronous SAR," IEEE Transactions on Geoscience and Remote Sensing, vol. 52, no. 9, pp. 5514-5528, 2014, this patent extends the spectrum to f... a The sixth order can more accurately calculate the frequency modulation residual.

[0066] S23. Compare the spectrum of the echo signal with the reference two-dimensional spectrum S(f r ,f a By multiplying the conjugates and then performing an inverse Fourier transform, the imaging result can be obtained.

[0067] S3. Estimate the target's Doppler modulation frequency and initial frequency. Specific steps include:

[0068] S31. Locate the target's location based on the imaged SAR image, and then extract its azimuth signal for Fast Fourier Transform (FFT).

[0069] The principle is that the frequency domain signal has a Doppler modulation frequency residual between the target point and the center point of the scene, and it is easy to calculate.

[0070] S32. Normalize the dimensions of the frequency domain signal after FFT by introducing a scaling factor Q:

[0071]

[0072] The original signal's time domain (t) and frequency domain (f) are transformed into the dimensionless domain (ul) to obtain new scaled coordinates. The transformation relationship is as follows:

[0073] u=t / Q,l=f·Q (4)

[0074] S33. Perform FrFT transformations of different orders p on the scaled signal to form a two-dimensional energy distribution map of the pu plane. Then, search for the location of the energy peak point and calculate the initial frequency of the signal based on the peak position. With frequency modulation

[0075] According to the literature: HM, O. Ankan, MAKutay, and G. Bozdagi. "Digital Computation of the Fractional Fourier Transform." IEEE Transactions on Signal Processing, vol. 44, pp. 2141-2150, 1996., the definition of FrFT is:

[0076]

[0077] In the formula, For the kernel function of FrFT, α = pπ / 2, where n is an integer.

[0078] The relationship between the peak position and the Doppler modulation frequency and the initial frequency estimate is as follows:

[0079]

[0080] The principle of selecting FrFT is as follows: When estimating target parameters, FrFT can process column by column. If there are multiple targets in a column of the imaged SAR image, the Doppler modulation frequency and initial frequency of multiple targets can be estimated with just one FrFT.

[0081] S4. Calculate the three-dimensional coordinates of the target. The specific steps include:

[0082] S41. Calculate the target's azimuth coordinates. The calculation method is as follows:

[0083]

[0084] S42. To calculate the difference in Doppler modulation frequencies between points O and B, we first need to calculate the time-domain modulation frequency of B. The calculation method is as follows:

[0085]

[0086] Then, the difference in Doppler modulation frequency between points O and B in the time domain is calculated as follows:

[0087] K OB =K O -K B (9)

[0088] Where K O It can be obtained from the polynomial fitting coefficients k2.

[0089] S43. To calculate the difference in Doppler modulation frequencies between points A and B, first calculate the position of point A in the distance from the ground. The calculation method is as follows:

[0090]

[0091] Where S y Let S be the y-coordinate of the satellite at the center of the synthetic aperture. h Let z be the z-coordinate of the satellite at the center of the synthetic aperture.

[0092] The slant distance history is calculated using the coordinates of point A, and the tuning frequency K of reference point A is determined by fitting the second-order coefficients in the polynomial. A Then we can determine the difference in frequency modulation between points A and B as follows:

[0093] ΔK a =K OB -(K A -K0) (11)

[0094] The purpose of S42 and S43 is to calculate Figure 3 The difference in Doppler modulation frequency between ground reference point A and observation target point B.

[0095] S44. Calculate the height coordinates of the target point. The calculation method is as follows:

[0096]

[0097] Where λ is the wavelength, R A R is the slant distance from the satellite to the ground reference point A at the aperture center time. e H is the Earth's radius. s β1 is the altitude of the satellite orbit above the ground, and β1 is the angle between the geocenter-satellite and the geocenter-ground reference point A.

[0098] The principle is as follows:

[0099] Because the satellite's orbital altitude is low, the Earth's rotation effect is negligible, and the target can be considered stationary during the observation period. When the synthetic aperture time is small, the satellite rotation angle θ is small, and the satellite's coordinates at a given instant can be calculated based on its velocity at the center of the synthetic aperture. The rotation angle θ can be expressed as:

[0100]

[0101] Where t a For slow time, and t a ∈(-T s / 2,Ts / 2).

[0102] The satellite's coordinates can then be represented as: By differentiating the satellite's trajectory, we can obtain the satellite's velocity vector.

[0103] according to Figure 3 From the geometric relationships in the diagram, we can obtain the coordinates of point A: A = [0, R]. e sinβ1,R e cosβ1], the coordinates of point B are B=[0,(R) e +Δh)sinβ2,(R e +Δh)cosβ2]. Where β1 is ∠SOA and β2 is ∠SOB.

[0104] From the satellite's position coordinates and the point target's position coordinates, the distance vectors between SA and SB can be derived:

[0105]

[0106]

[0107] Then calculate the Doppler frequencies at the two points:

[0108]

[0109]

[0110] And calculate the Doppler bandwidth at points A and B:

[0111]

[0112] And the difference in Doppler bandwidth between the two:

[0113]

[0114] Then calculate the difference ΔK between the two points in Doppler modulation frequency. a :

[0115]

[0116] Therefore, the height difference Δh between target point B and ground reference point A can be obtained.

[0117]

[0118] S45. Finally, calculate the ground distance coordinates of target B. The calculation method is as follows:

[0119]

[0120] Its principle is Figure 4 The geometric relationship between the satellite and the observation target.

[0121] This completes all the steps.

[0122] The following provides an implementation example with specific parameters.

[0123] In this example, the satellite trajectory and velocity were read from the Satellite Tool Kit (STK), and the orbital root numbers are shown in Table 1. Other simulation parameters are shown in Table 2, with a range resolution of 1.5m and an azimuth resolution of 0.2m. To better observe the imaging effect of the target point, the sampling rate was appropriately increased (bandwidth increased by 2.5 times instead of 1.2 times).

[0124] Table 1

[0125]

[0126] Table 2

[0127]

[0128] In modern cities, many buildings have a lot of glass on their exteriors. Glass has dihedral angles, which can create isolated strong points on the building. Therefore, by estimating the three-dimensional positions of these isolated strong points, the three-dimensional structure of the building can be reconstructed. This patent simulates the case of multiple isolated strong points, demonstrating that the method has the ability to estimate multiple points. The observed target positions are shown in Table 3.

[0129] Table 1

[0130]

[0131] After performing step S2, the resulting imaging is as follows: Figure 5 As shown in the figure, T1 and T3 are in the same direction and upward, while T1 and T2 are at the same distance and upward. Therefore, when estimating these two points, only this column needs to be taken.

[0132] After performing step S3, the FrFT results for columns containing T1 and T2 are as follows: Figure 6 As shown in the figure, if there are multiple points upwards at a certain distance, the FrFT result will also show multiple peaks. Based on the peak positions, the target parameters can be estimated. The FrFT result in the column containing T3 is shown below. Figure 7 As shown.

[0133] After performing step S4, the multi-point estimation results are shown in Table 4:

[0134] Table 4

[0135]

[0136] The above results demonstrate that this patent can process multiple targets simultaneously, and when the target points are spaced apart, the estimation results for multi-point targets are relatively accurate, with errors in all three dimensions within 1m, thus proving the effectiveness of this method.

[0137] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A three-dimensional localization method for spaceborne curved trajectory SAR targets based on FrFT, characterized in that, Includes the following steps: S1. Obtain the satellite's spatial parameters, including the satellite's trajectory and velocity in the geocentric fixed coordinate system at the time of the synthetic aperture center. and beam center position; obtain satellite payload parameters, including wavelength. ,bandwidth Synthesis pore size time Pulse repetition frequency (PRF); S2. Imaging the observed target, the specific steps include: S21. The scene center point is the position of the beam center. The line connecting the Earth's center and the center of the scene is... The axis, the direction of satellite velocity is Axis, distance from the ground is The axes construct the scene coordinate system; S22. Construct the two-dimensional spectrum of the reference point; S23. Compare the spectrum of the echo signal with the reference two-dimensional spectrum. Conjugate multiplication followed by inverse Fourier transform yields the imaging result, where... For range frequency, For azimuth frequency; S3. Estimate the target's Doppler modulation frequency and initial frequency; specific steps include: S31. Locate the target's location based on the imaged SAR image, and then extract its azimuth signal for fast Fourier transform. S32. Normalize the dimensions of the frequency domain signal after FFT by introducing a scaling factor. The original signal in the time domain Frequency domain Transformation into a dimensionless field This yields new scaled coordinates; S33. Scale the signal to different orders. The FrFT transform forms The system first obtains a two-dimensional energy distribution map of the plane, then searches for the location of the energy peak point, and calculates the initial frequency of the signal based on the peak location. With frequency modulation ; S4. Calculate the three-dimensional coordinates of the target. The specific steps include: S41. Calculate the target's azimuth coordinates; S42. Calculate the difference in Doppler modulation frequency between points O and B. A is the center point of the scene, and B is the target point; S43. Calculate the difference in Doppler modulation frequency between points A and B, where A is the ground reference point and B is the target point; S44. Calculate the height coordinate of the target point; S45. Finally, calculate the ground distance coordinates of target B.

2. The method for three-dimensional localization of spaceborne curved trajectory SAR targets based on FrFT as described in claim 1, characterized in that, In step S21, the beam center position is taken as the scene center point. The line connecting the Earth's center and the center of the scene is... The axis, the direction of satellite velocity is Axis, distance from the ground is The axes construct the scene coordinate system; Slant distance history of scene center point Perform polynomial fitting ； in For slow time, For polynomials Order coefficient, It is a term of order 0.

3. The method for three-dimensional localization of spaceborne curved trajectory SAR targets based on FrFT as described in claim 1, characterized in that, In step S22, the two-dimensional spectrum of the reference point is constructed as follows: ； in For range-directed frequency modulation, At the speed of light, For carrier frequency, For range frequency, This refers to the azimuth frequency.

4. The FrFT-based three-dimensional positioning method for spaceborne curved trajectory SAR targets as described in claim 1, characterized in that, In step S22, a frequency domain imaging method is used to extend the spectrum. The sixth order.

5. The method for three-dimensional localization of spaceborne curved trajectory SAR targets based on FrFT as described in claim 1, characterized in that, In step S44, the height coordinates of the target point are calculated as follows: ； in, For wavelength, The slant distance from the satellite to the ground reference point A at the aperture center time is... For the Earth's radius, The altitude of the satellite's orbit above the ground. Let θ be the angle between the geocentric satellite and the geocentric ground reference point A, and v be the satellite's velocity.

6. The method for three-dimensional localization of spaceborne curved trajectory SAR targets based on FrFT as described in claim 1, characterized in that, In step S45, the ground distance coordinates of target B are calculated as follows: ； in, Let y be the satellite's position at the center of the synthetic aperture. Let z be the z-coordinate of the satellite at the center of the synthetic aperture. The slant distance from the satellite to the ground reference point B at the aperture center time. Let x be the x-coordinate of the target point. The target point's height coordinates.

Images