Three-dimensional imaging method of spaceborne polar ice radar

Abstract

The present invention discloses a spaceborne polar ice radar three-dimensional imaging method. The method first acquires antenna echo signals and superimposes signals received by the same antenna. The superimposed image is then subjected to secondary range compression and center point range migration correction. Complementary range migration correction is further performed. Azimuth compression is performed through phase multiplication to obtain a two-dimensional under-ice image. After corresponding additional phase multiplication, the two-dimensional under-ice image is subjected to cross-track range migration correction to ensure that the range signals of all antennas are consistent with the center antenna. The corrected two-dimensional images are written into a three-dimensional array to obtain a three-dimensional image. The three-dimensional image is multiplied by a reference function in the cross-track direction, and the additional phase in the two-dimensional image is compensated in the cross-track direction. Finally, the three-dimensional image is Fourier transformed in the cross-track direction to obtain a three-dimensional focused image. The method has high computational efficiency and can obtain richer under-ice data through compressed imaging in the third dimension.

Description

Technical Field

[0001] The present invention relates to the field of polar ice exploration synthetic aperture radar imaging, and in particular to a three-dimensional imaging method of a spaceborne polar ice radar. Background Art

[0002] Synthetic Aperture Radar (SAR) is a high-resolution microwave imaging system that transmits microwave signals and receives scattered echoes from ground targets. Polar ice radar transmits electromagnetic pulses and receives reflected waves from beneath the ice, then processes them to produce images of the ice layer.

[0003] By transmitting broadband signals and combining synthetic aperture technology, SAR (Synthetic Aperture Radar) can simultaneously acquire high-resolution two-dimensional images in both range and azimuth. Compared to traditional optical and hyperspectral remote sensing, SAR offers all-weather and all-day imaging capabilities and possesses a certain degree of penetration. The images it acquires reflect the microwave scattering characteristics of targets, making it a crucial means for humans to acquire information about ground objects. With advances in science and technology, spaceborne SAR is developing towards providing broader, richer, and more detailed target information. Due to variations in observation altitude, the echoes received by spaceborne SAR are affected by cross-track scattering, necessitating focusing in the third dimension.

[0004] The polar regions are a crucial component of Earth's environmental system, reflecting and influencing global climate and sea level changes. Therefore, research on ice-penetrating radars is of crucial practical significance. Due to environmental constraints, the polar ice caps remain one of the least understood regions on Earth. Compared to traditional SAR, ice-penetrating radar offers superior ice penetration capabilities and greater flexibility and efficiency in measurement, making it an effective method for studying and analyzing subsurface ice. However, due to changes in the observation regime, low-frequency electromagnetic waves in ice-penetrating radars penetrate several kilometers of ice, leading to more complex propagation mechanisms and demanding system performance requirements. Furthermore, ice-penetrating radars are affected by subglacial clutter. Furthermore, for spaceborne ice-penetrating radars, the reduced cross-track resolution due to increased observation altitudes is a major challenge. This makes research on spaceborne ice-penetrating radars even more challenging. In existing technologies, in vehicle-based scenarios, a range migration algorithm based on the inverse scaled Fourier transform (ISFT) replaces the traditional Stolt interpolation operation in the two-dimensional frequency domain. This simultaneous combination of Stolt interpolation and IFFT transform solves the computational inefficiency caused by the need to continuously update the distance between the radar and point targets. Currently, this algorithm is only applicable to vehicle-based two-dimensional imaging. The present invention considers implementing a space-based three-dimensional imaging method. Summary of the Invention

[0005] In response to the above-mentioned existing technologies, the present invention provides a spaceborne polar SAR 3D imaging method. This method utilizes a satellite array to achieve 3D imaging of sub-ice areas. First, each radar in the array receives a 2D echo from beneath the ice and processes it to complete the 2D image. Phases are then added to the 2D image, and all 2D signals are written into a 3D array to obtain a 3D signal. Finally, the 3D signal is processed in the cross-track direction to obtain the final 3D image.

[0006] The three-dimensional imaging method of spaceborne polar SAR comprises the following specific steps:

[0007] Step 1: Place multiple point targets in the range and cross-track directions, build a satellite antenna array, and transmit pulse signals through the polar ice-penetrating radar on the center antenna. All antennas simultaneously receive echoes from under the ice. The collected echo signals are:

[0008] S m,n (τ,t)

[0009] Where m represents the position of each antenna in the antenna array, n represents the target point in each cross-track direction, τ represents the time in range, and t represents the time in azimuth. All signals received by the same antenna are superimposed to obtain a superimposed two-dimensional image S m (τ,t).

[0010]

[0011] Step 2: Transform the time domain image S m After (τ, t) is transformed into the two-dimensional frequency domain, it is multiplied by the reference function to complete the distance secondary compression and center point distance migration correction;

[0012] The inverse scale Fourier transform (ISFT) is applied to transform the signal into the range Doppler domain while completing the complementary range migration correction. The azimuth compression is completed by phase multiplication to obtain a superimposed two-dimensional image, which is recorded as the two-dimensional image Z under the ice. m (τ,t);

[0013] Step 3: Each set of superimposed two-dimensional images Z m (τ, t) are multiplied by the corresponding additional phase, and the reference function is: H m (τ, d), where d represents the ice depth, updated along the distance to time;

[0014] Z m (τ,t)=Z m (τ,t)*H m (τ,d)

[0015] Step 4: All two-dimensional images Z m(τ, t) are corrected for cross-track range migration so that the range signals of all antennas are consistent with the center antenna; the corrected two-dimensional images are written into a three-dimensional array to obtain a three-dimensional image Z(τ, t, m);

[0016] Step 5: Multiply the three-dimensional image by the reference function in the cross-track direction. The reference function is Compensate the additional phase H in the 2D image along the cross-track direction m (τ, d);

[0017] Step 6: Perform a cross-track Fourier transform on the phase-compensated three-dimensional image to obtain a three-dimensional focused image, which is the three-dimensional image under the ice.

[0018] The advantages of the present invention are:

[0019] 1. The present invention's spaceborne polar ice radar 3D imaging method, based on the existing ISFT-based 2D vehicle-borne algorithm, verifies the applicability of the algorithm in spaceborne scenarios, and constructs a satellite array to achieve 3D imaging under ice.

[0020] 2. The spaceborne polar ice radar three-dimensional imaging method of the present invention has high computational efficiency and can be implemented effectively and quickly. At the same time, through compressed imaging of the third dimension, richer sub-ice data can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a flow chart of the spaceborne polar ice radar three-dimensional imaging method of the present invention;

[0022] Figure 2 This is a schematic diagram of the geometric relationship of the echo received by the space-borne radar system;

[0023] Figure 3 A schematic diagram of the geometric relationship between the antenna array and the arrangement point matrix used in simulation in an embodiment of the present invention;

[0024] Figure 4 The three-dimensional imaging result of the point target extracted in the embodiment of the present invention;

[0025] Figure 5a It is the range profile of the imaging result of the center point target;

[0026] Figure 5b It is the azimuth profile of the imaging result of the center point target;

[0027] Figure 6a The range profile of the imaging result of the upper left corner point target

[0028] Figure 6b It is the azimuth profile of the imaging result of the upper left corner point target;

[0029] Figure 7 The cross-track profile of the imaging results for three adjacent point targets. DETAILED DESCRIPTION

[0030] The present invention will be described in further detail below with reference to the accompanying drawings.

[0031] The present invention provides a spaceborne polar three-dimensional SAR imaging method, such as Figure 1 The specific steps are as follows:

[0032] Step 1: Arrange multiple point targets in the range direction and cross-track direction, build a satellite-borne antenna array, transmit pulse signals through the polar ice-penetrating radar on the central antenna, and all antennas simultaneously receive the echo from under the ice and collect the resulting echo signals.

[0033] The geometric relationship between the radar system's transmitted pulse and received echo signal is deduced, and the radar parameters used in the present invention are shown in the table:

[0034] Table 1 Radar parameters

[0035] Parameter Type Numerical unit Radar type Linear frequency modulation pulse --- Carrier frequency 300 MHz Transmit pulse width 30 μs bandwidth 10 MHz Sampling rate 12 MHz PRF 360 Hz Distance antenna length 1 m Radar speed 7563 m / s synthetic aperture length 13000 m

[0036] The geometric relationship between the radar system receiving and transmitting pulse echo signals used in the present invention is as follows: Figure 2 As shown, the coordinate origin O is the point where the radar pulse penetrates the ice layer, A is the radar position, and B is the point target position; x represents the projection of the distance between the radar and the point target in the azimuth direction; y represents the projection of the distance between the radar and the point target in the cross-track direction; θ 1，m，n and θ 2，m，n are the incident angle and reflection angle of the ice-penetrating radar pulse passing through the ice layer; α 1，m，n With α2 ,m，n is θ 1,m，n and θ 2，m，n In the upward projection across the track, the antenna array composed of all radars is arranged along the y direction, and the α between adjacent radars is 1，m，n The angle difference is the same, that is, Δα1 is a constant; m represents the radar number on different antennas, n represents the cross-track point target position; h1 and h2 represent the height of the radar to the ground and the depth of the point target under the ice respectively; the three directions x, y, and z are azimuth, cross-track, and range respectively.

[0037] The specific process of deducing the geometric relationship between the radar system's transmitted pulse and received echo signal is as follows:

[0038] A. Geometric relationship of the emission pulse process.

[0039] rect() represents a square wave signal, K represents the frequency modulation, T represents the transmit pulse width, ω cis the center frequency, j is the imaginary unit, and the linear frequency modulation pulse emitted by the radar is:

[0040] s(τ)=rect(τ / T)exp(jπKτ 2 )exp(jω c τ)

[0041] Where τ represents the distance time.

[0042] According to the law of refraction, the relative dielectric constant of ice is ε r , assuming the radar speed is v, then:

[0043]

[0044] x=vt

[0045] y=h1*tanα 1，m +h2*tanα 2，m

[0046] Where t represents the azimuth time.

[0047] Points D and C are the projections of points O and B in the distance direction. AC and DC are denoted as x1 and x2, and they have the following geometric relationship:

[0048]

[0049] Arranging it, we can get the equation about x2:

[0050]

[0051] x2 has only one physically meaningful solution. Considering the change in the propagation speed of the pulse signal in the ice layer, since only the central radar transmits the signal, the distance is only related to the cross-track point n, and the equivalent distance R between the radar and the point target can be obtained 1,n (t,h2) is:

[0052]

[0053] B. Geometric relationship of the pulse receiving process.

[0054] Similar to the geometric relationship when transmitting the pulse, since all radars on the antenna will receive the signal, the received signal is also related to the position of the radar. The equivalent distance is recorded as R 2，m，n (t, h2), L represents the synthetic aperture length, c represents the speed of light, and the echo signal is obtained as:

[0055]

[0056] All the echo signals received by the same radar that are directed upward across the track are superimposed to obtain the final echo signal:

[0057]

[0058] Based on the echo data obtained above, the three-dimensional imaging method of the spaceborne polar SAR of the present invention is as follows: Figure 2 As shown, the specific steps are:

[0059] Step 2: Realize 2D imaging based on ISFT

[0060] Since the distance between different point targets across the track is much smaller than the radar angle, the superimposed echo signal can be directly processed by the parameter approximation of the center point target across the track, h m is the equivalent altitude of the radar, dref m The reference depth under the ice is dref0, and the reference depth of the received signal is dref m，2 , the distance of the linear frequency modulation signal under the ice is d m , Rmid m The shortest slant distance from each radar to the center point of the scene, the slant distance of the center radar is recorded as Rmid0;

[0061] h m ≈(h1+h1 / cosα 1，m ) / 2

[0062] dref0=h2

[0063] dref m，2 =h2 / cosα 1，m

[0064] dref m ≈(dref0+dref m，2 ) / 2

[0065]

[0066] The specific process of the algorithm is:

[0067] 1) Transform the received echo signal into the two-dimensional frequency domain and obtain the spectrum as follows:

[0068]

[0069] Among them, f c represents the radar carrier frequency, f τ Represents the range frequency, f t Indicates the azimuth frequency; j is the imaginary unit;

[0070] 2) The obtained two-dimensional spectrum G m (f τ , f t) is multiplied by the reference function to achieve focusing at the reference depth. The reference function is:

[0071]

[0072] 3) Apply ISFT to compensate for the residual range migration and transform the signal into the range time domain. The range migration parameter is recorded as D m (f t , v);

[0073]

[0074] Specifically:

[0075] 3.1 Resize the original signal about f by scaling τ / D m (f τ , v) perform inverse Fourier transform, specifically:

[0076]

[0077] Where, is the updated distance time after scaling back to the time domain.

[0078] 3.2 Residual range-azimuth coupling, the phase function used is:

[0079]

[0080] Where B is the signal bandwidth, F m (B) is the phase reduction factor of the signal, which is expressed as:

[0081]

[0082] 3.3 Residual azimuth compression, the reference function is:

[0083]

[0084] 3.4 Perform inverse Fourier transform on the signal in the azimuth direction and return it to the time domain to obtain a two-dimensional image Z m (τ, t).

[0085] Step 3: Two-dimensional image Z m (τ, t) plus the depth d under the ice m The linear phase H m (τ, d), the purpose is to calculate the d of different cross-track points m Different signals can be distinguished in the third dimension, and subsequent processing can enable the signals to be focused in the third dimension;

[0086] H m (τ, d) = exp(-j2ωc d m / c)

[0087] Z m (τ, t) = Z m (τ, t)*H m (τ, d)

[0088] Step 4: Add H m Z after (τ, d) m (τ, t) is used to perform cross-track range migration correction so that the range signals of all antennas are consistent with the central antenna. This compensates for the phase difference caused by the different distances between each radar and the point target in the same cross-track direction:

[0089]

[0090] The compensation phase function is:

[0091] F m (τ, d) = exp(-j2ω c ΔRmid m (h2) / c)

[0092] Z m (τ, t) = Z m (τ, t)*F m (τ, d)

[0093] Write the two-dimensional image after cross-track range migration correction into the three-dimensional array Z(τ, t, m)

[0094] Step 5: Add linear phase H in step 4 m Z after (τ, d) m (τ,t) is focused in the cross-track direction, and the depth under the ice is d m , its minimum value is recorded as d0, and the calculation formula is as follows:

[0095]

[0096] Step 6: Perform Fourier transform on Z(τ, t, m) processed in step 5 in the cross-track direction to complete the compression of the third dimension and obtain a three-dimensional focused image, which is the three-dimensional image under the ice. The compressed signal is z(τ, t, f m ):

[0097] z(τ, t, f m )=F m {Z(τ, t, m)}

[0098] Among them, F m {·} means to perform Fourier transform on m, f mIndicates the cross-track frequency.

[0099] Example:

[0100] like Figure 3 As shown in the figure, simulation software is used to arrange a 3×3×3 dot matrix in the cross-track direction and the range direction. The center point O is located directly below the central radar. The distance Δα between point targets in the cross-track direction is 0.025 degrees, and the distance between point targets in the range direction is 500 meters. A total of 41 radars are arranged in the antenna array, and the distance between adjacent radars is 0.01 degrees. When the central radar transmits a signal, all radars will receive the echo signal from the 3×3×3 point targets. Figure 4 is the superimposed echo of all point targets received by the radar at the edge of the antenna array, that is,

[0101] α 1，1，1 =0.225

[0102] α 1，1，2 =0.2

[0103] α 1，1，3 =0.175

[0104] The following table shows the parameters of the geometric relationship between the radar and the point target used in the simulation:

[0105] Table 2 Geometric relationship between radar and point target used in simulation

[0106] Parameter Type Numerical unit Radar height to the ground 600 Km Depth of point target under ice 2000 m Total length of antenna array 0.4 deg Number of antennas 41 --- Radar spacing 0.01 deg

[0107] Step 1: Get the echo signal S 1，1 (τ, t), S 1，2 (τ, t) and S 1，3 (τ, t);

[0108] Superposition gives:

[0109]

[0110] Step 2: Taking one of the antenna echoes S1(τ, t) as an example, the ISFT-based range migration algorithm is used to achieve two-dimensional imaging. The resulting two-dimensional image Z1(τ, t) is focused in both range and azimuth. The parameter d1 used approximates the position of the application center point, which is the actual position when n=2.

[0111]

[0112] Step 3: Add the linear phase H1(τ, d) to the two-dimensional image Z1(τ, t); then repeat the above operation for antennas at other positions to obtain the two-dimensional images Z m (τ, t).

[0113] Step 4: After making the distance migration correction in the cross-track direction, set Z m (τ, t) is written into a three-dimensional array to obtain Z(τ, t, m);

[0114] Step 5: Perform phase processing in the cross-track direction;

[0115]

[0116] Step 6: Perform Fourier transform on the cross-track direction to obtain a three-dimensional image, such as Figure 4 The figure shows a 3×3 point matrix collected in one of the azimuth directions, in which 2048 sampling points are arranged in the range direction, 1024 sampling points are arranged in the azimuth direction, and 82 sampling points are arranged in the cross-track direction.

[0117] The results show that the present invention can collect three-dimensional data under the ice, as shown in Figures 5 and 6, which are the cross-sections of the center point target and the upper left corner edge point target in the range and azimuth directions. Figure 7 The cross-track profiles of three point targets are shown in Figure 2. By analyzing the profiles, we can obtain the resolution of the point targets in the range, azimuth, and cross-track directions, and compare them with the theoretical resolution. The theoretical resolution calculation formula is as follows:

[0118]

[0119] Among them, ρ r represents the range resolution, ρ a represents the azimuth resolution, ρ m represents the cross-track resolution, B r is the range signal bandwidth, L is the synthetic aperture length, L m is the total length of the antenna array. The theoretical value of resolution obtained by calculation and the actual value obtained by analyzing the cross section are shown in the following table:

[0120] Table 3 Theoretical resolution values ​​and actual values ​​obtained from analytical profiles

[0121]

[0122]

[0123] It can be seen that the imaging method of the present invention can achieve three-dimensional imaging, and the resolution of the simulation results is good.

Claims

1. A spaceborne polar ice radar three-dimensional imaging method, characterized by: The specific steps are: Step 1: Arrange multiple point targets in the range direction and cross-track direction, build a satellite antenna array, transmit pulse signals through the polar ice-penetrating radar on the center antenna, and all antennas receive the echo from under the ice at the same time. S m,n (τ,t); Where m represents the position of each antenna in the antenna array, n represents the target point in each cross-track direction, τ represents the time in range, and t represents the time in azimuth. All echo signals received by the same antenna are superimposed to obtain a superimposed two-dimensional image S m (τ,t); Step 2: Transform the two-dimensional image S m (τ, t) is transformed into the two-dimensional frequency domain and then multiplied with the reference function to complete the distance secondary compression and center point distance migration correction to obtain the two-dimensional image Z under the ice. m (τ,t); Step 3: Each set of two-dimensional images Z under the ice m (τ,t) adds a linear phase H with respect to the depth under the ice m (τ,d), where d represents the ice depth and is updated along the distance to time; Step 4: Combine with H m All two-dimensional images Z after multiplication of (τ, d) m (τ, t) are corrected for cross-track range migration so that the range signals of all antennas are consistent with the center antenna; the corrected two-dimensional images are further written into a three-dimensional array to obtain a three-dimensional image Z(τ, t, m); Step 5: Multiply the 3D image in the cross-track direction with the reference function. The reference function is Compensate the additional phase H in the 2D image along the cross-track direction m (τ,d); Step 6: Perform a cross-track Fourier transform on the phase-compensated three-dimensional image to obtain a three-dimensional focused image, which is the three-dimensional image under the ice.

2. The spaceborne polar ice radar 3D imaging method according to claim 1, wherein: The specific method of step 2 is: 1) Transform the received echo signal into the two-dimensional frequency domain and obtain the spectrum as follows: Among them, rect() represents a square wave signal; f c represents the radar carrier frequency, f τ Represents the range frequency, f t Indicates the azimuth frequency; h m is the equivalent height of the radar; j is the imaginary unit; c is the speed of light; v is the operating speed of the radar; d m is the distance of the linear FM signal under the ice; ε r is the relative dielectric constant of the ice layer; K represents the modulation frequency; 2) The obtained two-dimensional spectrum G m (f τ ,f t ) is multiplied by the reference function to achieve focusing at the reference depth; the reference function is: Where dref m is the reference depth under the ice; 3) Apply ISFT to compensate for the residual range migration and transform the signal into the range time domain. The range migration parameter is recorded as D m (f t ,v); Specifically: 3.1 Resize the original signal about f by scaling τ / D m (f τ ,f t ) to perform the inverse Fourier transform: Where, is the updated distance time after the scale transformation back to the time domain; 3.2 Residual range-azimuth coupling, the phase function used is: Where B is the signal bandwidth, F m (B) is the phase reduction factor of the signal, which is expressed as: 3.3 Residual azimuth compression, the reference function is: 3.4 Perform azimuth Fourier transform on the signal and return it to the time domain to obtain a two-dimensional image Z m (τ,t).

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