Two-dimensional baseline estimation method for vertical track of spaceborne SAR based on least squares method

Abstract

The present invention discloses a method for estimating the two-dimensional baseline of a satellite-borne SAR vertical track based on the least squares method. It belongs to the field of synthetic aperture radar interferometry, and the steps are as follows: performing BP imaging processing on the echo data of the two channels of the satellite-borne SAR system; finding three or more calibration areas on the SAR image, calculating the interference phase of each calibration area, and constructing a set of equations for calculating the interference phase according to the height information and position information of the SAR platform during the imaging process, combined with the spatial geometric relationship during the interferometry measurement of the satellite-borne SAR system; using the least squares method to solve the set of interference phase equations, and realizing the estimation of the length of the two-dimensional baseline of the vertical track. The present invention directly performs phase compensation based on the measured vertical track baseline, which often leads to more serious speed measurement errors; it realizes the method for estimating the length of the two-dimensional baseline of the vertical track of the satellite-borne SAR, and effectively removes the phase interference caused by the vertical track baseline during the speed measurement of the interferometry of the ocean current along the track.

Description

Technical Field

[0001] The invention belongs to the field of synthetic aperture radar interferometry and relates to a two-dimensional baseline estimation method of a satellite-borne SAR vertical track based on a least squares method. Background Art

[0002] In the existing technology, marine resources are a new field that countries are competing to develop, and marine remote sensing is a hot topic in radar research today. As one of the important forms of seawater movement, the sea surface flow field describes the large-scale relatively stable flow of seawater, which can directly affect the weather and climate of the relevant sea areas. The detection of sea surface flow fields is still a difficult problem in marine environmental detection. Conventional observation methods can only observe specific areas at fixed points, which is difficult to meet the global and continuous observation needs of sea surface flow fields.

[0003] Synthetic Aperture Radar (SAR) is an active high-resolution microwave imaging sensor. The SAR system emits linear frequency modulation signals with a large time-bandwidth product. It has great advantages in ocean observation due to its all-day, all-weather and wide-coverage capabilities. Along-Track Interferometric Synthetic Aperture Radar (ATI-SAR) is based on SAR. Two antennas are placed along the flight direction to achieve two observations of the same area in a very short time. The echo information is obtained after the two observations, and the interference phase related to the height of the observation area is obtained by certain technical means.

[0004] The sea surface velocity can be extracted through the interferometric phase, but the obtained interferometric phase is interfered and affected by many factors - the amplitude and phase error between channels, the additional phase value caused by the vertical track baseline, etc. Among them, the additional phase value caused by the vertical track baseline has a greater influence. In order to obtain a more accurate ocean current velocity value, the additional phase value introduced by the vertical track baseline must be effectively removed, that is, the two-dimensional baseline length of the vertical track must be accurately estimated. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a method for estimating the two-dimensional baseline of the vertical track of a space-borne SAR based on the least squares method. The present invention accurately estimates the length of the two-dimensional baseline of the vertical track based on the echo data and the known calibration points in the SAR imaging scene to the centimeter level or even the millimeter level.

[0006] Technical solution: The method for estimating two-dimensional baselines of vertical tracks of spaceborne SAR based on the least squares method described in the present invention has the following specific operating steps:

[0007] (1) First, the echo data of the two channels of the spaceborne SAR system are processed by BP imaging;

[0008] (2) Then, three or more calibration areas are found on the SAR image, the interferometric phase of each calibration area is calculated, and a set of equations for calculating the interferometric phase is constructed based on the height information and position information of the SAR platform during the imaging process and the spatial geometric relationship during the interferometric measurement process of the spaceborne SAR system;

[0009] (3) Finally, the least squares method is used to solve the interference phase equations to estimate the two-dimensional baseline length of the vertical track.

[0010] Furthermore, in step (1), the specific operation steps of performing BP imaging processing on the echo data of the two channels of the spaceborne SAR system are as follows:

[0011] (1.1) Range compression: The radar echo pulse signal is processed by pulse compression through a matched filter;

[0012] (1.2) Range interpolation: Calculate the slant distance between each pixel in the imaging area and the radar antenna at each pulse time. This is usually done by using the method of zero padding in the frequency domain followed by an inverse Fourier transform.

[0013] (1.3) Grid division: Divide the imaging area into grids to obtain all grid point targets. Each pixel in the final SAR image represents a grid.

[0014] (1.4) Back projection: Calculate the distance R between the radar and each grid point at the moment of each transmitted pulse (u,v) , where u and v represent the corresponding points in the range and azimuth directions of the imaging area, respectively;

[0015] (1.5) Coherent superposition: For the pixel point (u, v) in the imaging space, the corresponding echo value is calculated by interpolation and superimposed with the echo value of the grid point in the previous azimuth to form an image.

[0016] Furthermore, in step (2), the spatial geometric relationship during the interferometric measurement of the spaceborne SAR system is as follows:

[0017]

[0018] Among them, θ is the angle between the two channels transmitting signals to the calibration point, R 1 is the distance from channel 1 to the calibration area, R 2 is the distance from channel 2 to the calibration area, and B is the baseline length between the two channels;

[0019]

[0020] Among them, θ' is the angle between the two channels that transmit signals to the projection point of the calibration point, R 1 ' is the distance from channel 1 to the projection point of the calibration area, R 2 ' is the distance from channel 2 to the projection point of the calibration area, and B is the baseline length;

[0021] After transforming equations (1) and (2), we get:

[0022]

[0023]

[0024] Subtracting equation (3) from equation (4) yields the distance history difference ΔR:

[0025] ΔR=(R 1 -R 1 ')-(R 2 -R 2 ')=B(cosθ-cosθ') (5)

[0026] According to the geometric relationship between the dual channels of the spaceborne SAR system and the target:

[0027] θ=α-β=Δθ+θ' (6)

[0028] Among them, α is the angle between the line connecting channel 1 and the target and the z-axis, β is the angle between the line connecting channel 1 and the target projection point and the z-axis, and Δθ is the angle of rotation of channel 1 from the calibration point to the calibration point projection point;

[0029]

[0030] Where H is the altitude of the satellite, h is the altitude of the calibration point, R_x is the horizontal distance between the satellite and the target, and R is the slant distance between the satellite and the target;

[0031]

[0032] Since Δθ→0, then cosΔθ→1, substituting the infinitesimal relation, equations (6) and (10) into equation (5), we obtain:

[0033]

[0034] Among them, B y is the component of the vertical track baseline along the y-axis, B z is the component of the vertical track baseline along the z-axis;

[0035]

[0036] Where φ is the phase error caused by the vertical track baseline.

[0037] Furthermore, in step (2), the equation group of the interference phase is as follows:

[0038]

[0039] Furthermore, in step (3), the least square method is as follows:

[0040] According to formula (12), the relationship between slant distance and viewing angle is obtained. According to the data pair of viewing angle and interference phase, recorded as (M, N), the best fitting function between the two is found by the minimum sum of squares of errors, where M = (m 1 , m 2 , ..., m l ) is the viewing angle between different calibration points and the satellite-borne SAR system, N = (n 1 , n 2 ,……,n l ) is the interference phase obtained by conjugate multiplication of the dual-channel echo signals at different calibration points, l is the data logarithm, and the specific solution process is as follows:

[0041] (3.1), according to the data pair of viewing angle and interference phase, take the i-th historical data sampling point, denoted as (u i ,v i ), determine the fitting function V = a × U + b, and select the sum of squares of errors as the error function. When the error function is the minimum, the calculated fitting function coefficients a and b are optimal;

[0042] (3.2) According to the data pair of viewing angle and interference phase, the error function is calculated, and the partial derivatives of the error function with respect to coefficients a and b are calculated respectively according to the error function:

[0043]

[0044] (3.3), calculate the coefficients a* and b* of the fitting coefficients. To minimize the error function, set the values ​​of formulas (15) and (16) to 0, and obtain the coefficients a* and b*:

[0045]

[0046]

[0047] in, is the average value of the viewing angle, is the average value of the interference phase, a* and b* are the coefficients of the fitting curve, and according to the fitting coefficients, the relationship between the interference phase and the viewing angle is: V = a* × U + b*, B y is the component of the vertical track baseline along the y-axis, that is, a*, B zis the component of the vertical track baseline along the z-axis, that is, b*.

[0048] Beneficial effect: Compared with the prior art, the present invention introduces a phase error to the vertical track baseline for the mixed baseline when actually performing channel interferometry processing, and the phase error needs to be eliminated when measuring the ocean current velocity. The two-dimensional baseline length of the vertical track of the satellite-borne SAR system can be measured by corresponding equipment, but the cost and complexity of the system will be increased. Therefore, the present invention proposes a method for estimating the two-dimensional baseline length of the vertical track based on SAR echo data and known calibration points in the SAR scene, which can realize the two-dimensional baseline estimation of the vertical track of the satellite-borne SAR based on the least squares method, and remove the extra phase value by the estimated value of the two-dimensional baseline length of the vertical track, so as to ensure the accuracy of the ocean current velocity measurement along the track interferometry system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is an operation flow chart of the present invention;

[0050] Figure 2 is the echogram after the distance pulse pressure of channel 1 in the embodiment of the present invention;

[0051] Figure 3 is the echogram after the distance pulse pressure of channel 2 in the embodiment of the present invention;

[0052] Figure 4 is a BP imaging result diagram of channel 1 in an embodiment of the present invention;

[0053] Figure 5 is the BP imaging result of channel 2 in an embodiment of the present invention;

[0054] Figure 6 1 is a spatial geometric relationship diagram of space-borne SAR interferometry in an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In order to more clearly illustrate the technical solution of the present invention, the technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0056] The present invention designs a two-dimensional baseline estimation method for vertical track of spaceborne SAR based on the least squares method. The method flow is as follows: Figure 1 shown.

[0057] This embodiment uses simulated spaceborne SAR echo data for verification and analysis; the computer CPU used in the experiment is i7-9700@3.00GHz eight-core and the memory is 16GB; the specific SAR system simulation parameters are shown in Table 1.

[0058] Table 1

[0059]

[0060]

[0061] Reference Figure 1 ,The two-dimensional baseline estimation method for the vertical track of spaceborne SAR based on the least square method includes the following steps:

[0062] Step 1: First, perform BP imaging processing on the echo data of the two channels of the spaceborne SAR system;

[0063] Specifically, step 1 can be achieved by:

[0064] The most important thing about BP imaging is the distance R(p,n) from the scattering point to the antenna phase center. The calculation formula is as follows:

[0065] R(p,n)=||pp A (n)|| 2 (19)

[0066] Where p represents the position of the scattering point, n represents the number of radar pulses, and p A (n) represents the position of the antenna phase center at the nth pulse repetition interval, ||*|| 2 represents the 2-norm;

[0067] (1.1) Distance compression: The radar echo pulse signal is processed by pulse compression through a matched filter. The echo data of different pulse repetition periods after compression can be expressed as:

[0068]

[0069] Among them, T Delay represents the gate delay, T Pulse represents the pulse duration, κ represents the frequency domain difference multiple, f s Indicates the sampling frequency;

[0070] (1.2) Range interpolation: Calculate the slant distance between each pixel in the imaging area and the radar antenna at each pulse time. Usually, the range interpolation calculation can be performed by using the method of zero padding in the frequency domain followed by inverse Fourier transform.

[0071] (1.3) Grid division: Divide the imaging area into grids to obtain all grid point targets. Each pixel in the final SAR image represents a grid.

[0072] (1.4) Back projection: Calculate the distance R between the radar and each grid point at the moment of each transmitted pulse (u,v) , where u and v represent the corresponding points in the range and azimuth directions of the imaging area, respectively;

[0073] (1.5) Coherent superposition: For the pixel point (u, v) in the imaging space, the corresponding echo value is calculated by interpolation and superimposed with the echo value of the grid point in the previous azimuth. The result of SAR imaging can be expressed as:

[0074]

[0075] Where s represents the echo data after the range pulse compression, K represents the wave number, K = 2π / λ, λ is the radar wavelength;

[0076] Step 2: Then, find three or more calibration areas (with known height and position information) on the SAR image, calculate the interferometric phase of each calibration area, and construct a set of equations for calculating the interferometric phase based on the height and position information of the SAR platform during the imaging process and the spatial geometric relationship during the interferometric measurement of the spaceborne SAR system;

[0077] Specifically, the geometric relationship of step 2 is as follows:

[0078]

[0079] Among them, θ is the angle between the two channels transmitting signals to the calibration point, R 1 is the distance from channel 1 to the calibration area, R 2 is the distance from channel 2 to the calibration area, and B is the baseline length between the two channels;

[0080]

[0081] Among them, θ' is the angle between the two channels that transmit signals to the projection point of the calibration point, R 1 ' is the distance from channel 1 to the projection point of the calibration area, R 2 ' is the distance from channel 2 to the projection point of the calibration area, and B is the baseline length;

[0082] After transforming equations (22) and (23), we can obtain:

[0083]

[0084] Subtracting equation (24) from equation (25) yields the distance history difference ΔR:

[0085] ΔR=(R 1 -R 1 ')-(R 2 -R 2 ')=B(cosθ-cosθ') (26)

[0086] according to Figure 6 Geometric relations in:

[0087] θ=α-β=Δθ+θ' (27)

[0088] Among them, α is the angle between the line connecting channel 1 and the target and the z-axis, β is the angle between the line connecting channel 1 and the target projection point and the z-axis, and Δθ is the angle of rotation of channel 1 from the calibration point to the calibration point projection point;

[0089]

[0090] Where H is the altitude of the satellite, h is the altitude of the calibration point, R_x is the horizontal distance between the satellite and the target, and R is the slant distance between the satellite and the target;

[0091]

[0092] Since Δθ→0, then cosΔθ→1, substituting the infinitesimal relation, equations (27) and (31) into equation (26), we obtain:

[0093]

[0094] Among them, B y is the component of the vertical track baseline along the y-axis, B z is the component of the vertical track baseline along the z-axis;

[0095]

[0096] Where φ is the phase error value caused by the vertical track baseline;

[0097] The interference phase equations in step (2) are as follows:

[0098]

[0099] Step 3: Finally, the least square method is used to solve the interferometric phase equations to estimate the two-dimensional baseline length of the vertical track;

[0100] In this embodiment, the least square method in step 3 is implemented using the following preferred solution:

[0101] According to the data pair of viewing angle and interference phase, recorded as (M, N), the best fitting function of the two is found by the minimum sum of squares of the error, where M = (m 1 , m 2 , ..., m l ) is the viewing angle between different calibration points and the satellite-borne SAR system, N = (n 1 , n 2 ,……,n l ) is the interference phase obtained by conjugate multiplication of the dual-channel echo signals at different calibration points, l is the data logarithm, and the specific solution process is as follows:

[0102] (3.1), according to the data pair of viewing angle and interference phase, take the i-th historical data sampling point, denoted as (u i ,v i ), determine the fitting function V = a × U + b, and select the sum of squares of errors as the error function. When the error function is the minimum, the calculated fitting function coefficients a and b are optimal;

[0103] (3.2) According to the data pair of viewing angle and interference phase, the error function is calculated, and the partial derivatives of the error function with respect to coefficients a and b are calculated respectively according to the error function:

[0104]

[0105] (3.3), calculate the coefficients a* and b* of the fitting coefficients. To minimize the error function, set the values ​​of formulas (36) and (37) to 0, and obtain the coefficients a* and b*:

[0106]

[0107]

[0108] in, is the average value of the viewing angle, is the average value of the interference phase, a* and b* are the coefficients of the fitting curve, and according to the fitting coefficients, the relationship between the interference phase and the viewing angle is: V = a* × U + b*.

[0109] Through the interference phase simulation and baseline estimation of the calibration points at five different slant ranges in Table 2, by comparing the theoretical values ​​with the actual values, it can be found that there is a centimeter-level error between the estimated value and the true value of the vertical track baseline in the y-axis and z-axis components, which is in line with the quantitative indicators in engineering. Therefore, the effectiveness of the above vertical track baseline length estimation method can be verified.

[0110] Table 2

[0111]

[0112] The component B of the vertical track baseline on the y-axis y and the z-axis component B z The accuracy is determined by the actual value setting, the distance history between the spaceborne SAR system and the calibration area, the flight altitude of the spaceborne SAR system, the altitude of the calibration points and the number of calibration points. Table 2 shows the estimated values ​​of the two-dimensional baseline length obtained by experimental calculation after giving some important parameters.

[0113] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A two-dimensional baseline estimation method for vertical track of spaceborne SAR based on least squares method, characterized by: The specific steps are as follows: (1) First, the echo data of the two channels of the spaceborne SAR system are processed by BP imaging; (2) Then, three or more calibration areas are found on the SAR image, the interferometric phase of each calibration area is calculated, and a set of equations for calculating the interferometric phase is constructed based on the height information and position information of the SAR platform during the imaging process and the spatial geometric relationship during the interferometric measurement process of the spaceborne SAR system; (3) Finally, the least square method is used to solve the interferometric phase equations to estimate the two-dimensional baseline length of the vertical track; In step (1), the specific operation steps of performing BP imaging processing on the echo data of the two channels of the spaceborne SAR system are as follows: (1.1) Range compression: The radar echo pulse signal is processed by pulse compression through a matched filter; (1.2) Range interpolation: Calculate the slant distance between each pixel in the imaging area and the radar antenna at each pulse time. This is usually done by using the method of zero padding in the frequency domain followed by an inverse Fourier transform. (1.3) Grid division: Divide the imaging area into grids to obtain all grid point targets. Each pixel in the final SAR image represents a grid. (1.4) Back projection: Calculate the distance R between the radar and each grid point at the moment of each transmitted pulse (u,v) , where u and v represent the corresponding points in the range and azimuth directions of the imaging area, respectively; (1.5) Coherent superposition: For the pixel point (u, v) in the imaging space, the corresponding echo value is calculated by interpolation, and then superimposed with the echo value of the grid point in the previous azimuth to form an image; In step (2), the spatial geometric relationship during the interferometric measurement of the spaceborne SAR system is as follows: Where θ is the angle between the two channels transmitting signals to the calibration point, R1 is the distance from channel 1 to the calibration area, R2 is the distance from channel 2 to the calibration area, and B is the baseline length between the two channels; Where θ' is the angle between the two channels that transmit signals to the projection point of the calibration point, R1' is the distance from channel 1 to the projection point of the calibration area, R2' is the distance from channel 2 to the projection point of the calibration area, and B is the baseline length; After transforming equations (1) and (2), we get: Subtracting equation (3) from equation (4) yields the distance history difference ΔR: ΔR=(R1-R1')-(R2-R2')=B(cosθ-cosθ') (5) According to the geometric relationship between the dual channels of the spaceborne SAR system and the target: θ=α-β=Δθ+θ' (6) Among them, α is the angle between the line connecting channel 1 and the target and the z-axis, β is the angle between the line connecting channel 1 and the target projection point and the z-axis, and Δθ is the angle of rotation of channel 1 from the calibration point to the calibration point projection point; Where H is the altitude of the satellite, h is the altitude of the calibration point, R_x is the horizontal distance between the satellite and the target, and R is the slant distance between the satellite and the target; Since Δθ→0, then cosΔθ→1, substituting the infinitesimal relation, equations (6) and (10) into equation (5), we obtain: Among them, B y is the component of the vertical track baseline along the y-axis, B z is the component of the vertical track baseline along the z-axis; Where φ is the phase error value caused by the vertical track baseline; In step (2), the equations of the interference phase are as follows: In step (3), the least square method is as follows: The relationship between the slant distance and the viewing angle is obtained according to formula (12). According to the data pair of viewing angle and interference phase, recorded as (M, N), the best fitting function between the two is found by the minimum sum of squares of the error, where M = (m1, m2, ..., m l ) is the viewing angle of different calibration points and the spaceborne SAR system, N = (n1, n2, ..., n l ) is the interference phase obtained by conjugate multiplication of the dual-channel echo signals at different calibration points, l is the data logarithm, and the specific solution process is as follows: (3.1), according to the data pair of viewing angle and interference phase, take the i-th historical data sampling point, denoted as (u i ,v i ), determine the fitting function V = a × U + b, and select the sum of squares of errors as the error function. When the error function is the minimum, the calculated fitting function coefficients a and b are optimal; (3.2) According to the data pair of viewing angle and interference phase, the error function is calculated, and the partial derivatives of the error function with respect to coefficients a and b are calculated respectively according to the error function: (3.3), calculate the coefficients a* and b* of the fitting coefficients. To minimize the error function, set the values ​​of formulas (15) and (16) to 0, and obtain the coefficients a* and b*: in, is the average value of the viewing angle, is the average value of the interference phase, a* and b* are the coefficients of the fitting curve, and according to the fitting coefficients, the relationship between the interference phase and the viewing angle is: V = a* × U + b*, B y is the component of the vertical track baseline along the y-axis, that is, a*, B z is the component of the vertical track baseline along the z-axis, that is, b*.

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