Phased array system space-borne SAR non-stripline mode beam control method

Abstract

The application discloses a phased array system space-borne SAR non-trace mode beam control method and relates to the technical field of synthetic aperture radar. The specific implementation of the method comprises the following steps: for the phased array system space-borne SAR, a satellite orbit coordinate system, an antenna body coordinate system and a SAR coordinate system are established; a second transfer matrix HAnt2sar from the antenna body coordinate system to the SAR antenna coordinate system is expressed by a phased array beam control angle; a phased array constraint condition and a corresponding relationship between the phased array beam control angle and a satellite attitude angle are solved according to a first transfer matrix HAnt2Sat from the satellite orbit coordinate system to the antenna body coordinate system; and an observation angle of an observed target under the phased array system is converted into a corresponding satellite attitude angle, so that the observed target is observed according to different observation angles. The implementation is suitable for the change characteristics of the phased array beam, realizes the beam control of the phased array system space-borne SAR non-trace mode, and completes tasks such as target search, tracking, capture and identification.

Description

Technical Field

[0001] This invention belongs to the field of Synthetic Aperture Radar (SAR) technology, and particularly relates to a non-track mode beam control method for phased array spaceborne SAR. Background Technology

[0002] Non-track mode (or non-track imaging mode) refers to the adaptive adjustment of the beam transmitted by the spaceborne SAR according to the terrain changes of the imaging scene during satellite operation. Compared with traditional spaceborne SAR generating mapping strips along the satellite orbit, spaceborne SAR non-track imaging can directly generate mapping strips along the target terrain by continuously adjusting the beam pointing in the elevation and azimuth dimensions. This fundamentally reduces the redundancy of echo data when imaging certain "non-track scenes" such as earthquake zones and coastlines, and significantly improves the observation efficiency of spaceborne SAR for narrow scenes.

[0003] Phased array antennas (or phased array antennas) are a type of SAR array arrangement. They possess spatial filtering capabilities, enabling the transmission and reception of electromagnetic waves across various frequency bands throughout space. They intelligently achieve beam scanning over a large spatial area, exhibiting strong signal gain. Within a defined spatial domain, they acquire target information and rapidly and flexibly adjust the antenna beam's direction and shape according to the target, accurately performing tasks such as target search, tracking, acquisition, and identification. Existing beam control methods for non-tracking modes in spaceborne SAR are based on profile antenna designs and lack the ability to control phased array beams, thus rendering them unsuitable for phased array spaceborne SAR. Summary of the Invention

[0004] In view of this, the present invention provides a beam control method for non-tracking mode of phased array spaceborne SAR. Based on the variation characteristics of phased array beams, it combines with the configuration design method of non-tracking mode of spaceborne SAR to realize beam control of non-tracking mode of phased array spaceborne SAR, and complete the target search, tracking, acquisition and identification tasks of non-tracking mode in phased array system.

[0005] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0006] For the aforementioned phased array-based spaceborne SAR, establish the satellite orbit coordinate system, the antenna body coordinate system, and the SAR coordinate system;

[0007] The second transition matrix H from the antenna body coordinate system to the SAR antenna coordinate system Ant2sar Represented by the phased array beam control angle;

[0008] According to the first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system Ant2SatThe value of is used to solve the phased array constraint conditions and the correspondence between the phased array beam control angle and the satellite attitude angle;

[0009] Based on the correspondence between the phased array beam control angle and the satellite attitude angle, the observation angle of the target under the phased array system is converted into the corresponding satellite attitude angle, so as to observe the target according to different observation angles.

[0010] Optionally, the second transfer matrix H that transforms the antenna body coordinate system to the SAR antenna coordinate system... Ant2sar Represented by the phased array beam control angle, including:

[0011] Using the phased array beam control angle, the normal vector n of the range profile of the beam is represented. r and the normal vector n of the azimuth profile a :

[0012]

[0013] The vector in the positive direction of the Z' axis of the SAR antenna coordinate system is used with the normal vector n r and the normal vector n a This means that Z′=n a ×n r =[cosαsinβ,-sinαcosβ,cosαcosβ] T The direction vector n pointing to the antenna phase center is obtained. Z :

[0014]

[0015] Based on the vector of the positive direction of the Z' axis in the SAR antenna coordinate system, and the normal vector n r and the normal vector n a Determine the range profile vector l of the beam. r and azimuth profile vector l a :

[0016]

[0017] Choose mutually orthogonal azimuth profile vectors l a The normal vector n a Using the basis vectors of the SAR antenna coordinate system, the second transition matrix H from the antenna body coordinate system to the SAR antenna coordinate system is determined. Ant2sar :

[0018]

[0019] Optionally, the first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system... Ant2Sat The value of is used to solve the phased array constraint conditions and the correspondence between the phased array beam control angle and the satellite attitude angle, including:

[0020] In the first transition matrix H Ant2Sat In the case of an identity array, the second transfer matrix H that transforms the antenna body coordinate system to the SAR antenna coordinate system. Ant2sar Using the satellite's yaw angle The pitch angle θ and roll angle ψ are represented by rotation matrix functions:

[0021]

[0022] Determine the second transition matrix H Ant2sar The correspondence between the phased array beam control angles α and β is as follows:

[0023]

[0024] The constraints of the phased array antenna are obtained as follows:

[0025]

[0026] Accordingly, the phased array beam control angles α and β and the satellite yaw angle are obtained. The correspondence between pitch angle θ and roll angle ψ:

[0027]

[0028] Optionally, the first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system... Ant2Sat The value of is used to solve the phased array constraint conditions and the correspondence between the phased array beam control angle and the satellite attitude angle, including:

[0029] In the first transition matrix H Ant2Sat In the case of an identity matrix, the second transition matrix H is... Ant2sar Using the adjusted yaw angle The pitch angle θ1 and roll angle ψ1 are represented by rotation matrix functions:

[0030]

[0031] According to the adjusted yaw angle Pitch angle θ1, roll angle ψ1 and yaw angle before adjustment The correspondence between pitch angle θ0 and roll angle ψ0:

[0032] The constraints of the phased array antenna are obtained as follows:

[0033]

[0034] The correspondence between the phased array beam control angles α and β and the satellite attitude angles:

[0035]

[0036] Optionally, establishing the satellite orbit coordinate system, antenna body coordinate system, and SAR coordinate system for the phased array-based spaceborne SAR includes:

[0037] Based on the satellite's direction of motion, construct the satellite orbit coordinate system and the antenna body coordinate system;

[0038] The first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system Ant2Sat The SAR antenna coordinate system is obtained by setting it to a unit array, where the antenna body coordinate system coincides with the satellite body coordinate system.

[0039] Beneficial effects:

[0040] (1) This invention establishes the antenna body coordinate system and SAR antenna coordinate system for phased array antennas, solves the phased array constraint conditions and the relationship between yaw, pitch, roll and phased array beam control angle, and can be applied to the joint design and optimization method of spaceborne SAR non-track multi-target imaging configuration based on phased array antennas, solving the problems of high configuration freedom and high design difficulty in spaceborne SAR non-track bending imaging mode.

[0041] (2) This invention solves the problem that existing satellite SAR non-track mode beam control methods are based on profile antenna design and cannot be applied to phased array satellite SAR. It provides the transition matrix from the satellite body coordinate system to the SAR antenna coordinate system, obtains the phased array constraints and the relationship between yaw, pitch, roll and phased array beam control angle. Furthermore, it solves the problem that the range and azimuth profiles are not perpendicular in the phased array system and cannot be directly used as the basis vectors of the SAR system. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the main process of the phased array-based spaceborne SAR non-track mode beam control method according to an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of the satellite orbit coordinate system, antenna body coordinate system, and SAR coordinate system according to an embodiment of the present invention;

[0044] Figure 3(a) is a schematic diagram of the wave foot trajectory according to an embodiment of the present invention;

[0045] Figure 3(b) is a schematic diagram of the deviation between the wave foot trajectory and the observation target point according to an embodiment of the present invention;

[0046] Figure 4(a) is a schematic diagram of the azimuth resolution of each observation target point according to an embodiment of the present invention;

[0047] Figure 4(b) is a schematic diagram of the distance swath of each observation target point according to an embodiment of the present invention;

[0048] Figure 5(a) and 5(b) This is a simulation diagram illustrating the change of the phased array beam control angle over time according to an embodiment of the present invention. Detailed Implementation

[0049] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

[0050] Azimuth: When the beam center is transmitted along the direction of the satellite orbit, the direction of the beam center indicates the azimuth of the beam. The azimuth profile is the profile passing through the azimuth.

[0051] Range direction: The direction perpendicular to the azimuth direction of the beam represents the range direction of the beam. The range profile is the profile passing through the range direction.

[0052] In embodiments of the present invention, such as Figure 1 As shown, the phased array-based spaceborne SAR non-track mode beam control method of the present invention includes the following steps:

[0053] Step 1: For the phased array-based spaceborne SAR, establish the satellite orbit coordinate system, the antenna body coordinate system, and the SAR coordinate system.

[0054] Step 11: Construct the satellite orbit coordinate system and the antenna body coordinate system according to the satellite's motion direction.

[0055] In this embodiment of the invention, the relationship between the satellite orbit coordinate system, the antenna body coordinate system, and the SAR coordinate system is as follows: Figure 2 As shown, where:

[0056] The satellite orbit coordinate system is a three-dimensional coordinate system with the origin at O. The positive direction of the X1 axis is the direction of satellite motion, and the positive direction of the Z1 axis is in the satellite orbit plane and points towards the Earth's center. The positive direction of the Y1 axis is determined by the right-hand rule. The four fingers of the right hand bend from the positive direction of Z1 to the positive direction of X1, and the direction of the right thumb is the positive direction of the Y1 axis.

[0057] The antenna body coordinate system is a three-dimensional coordinate system with its origin at O. The dot product of the positive X2 axis and the satellite's motion direction is positive. The X2OZ2 plane is a cross-section of the phased array antenna along the azimuth direction of the beam. The positive Z2 axis is the antenna pointing direction of the phased array antenna. The positive Y2 axis is determined according to the right-hand rule: the four fingers of the right hand bend from the positive Z2 direction to the positive X2 direction, and the direction of the right thumb is the positive Y2 axis direction. The first transition matrix H from the satellite orbit coordinate system to the antenna body coordinate system is... Ant2Sat Euler angles are generally used for description.

[0058] Step 12, using the first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system. Ant2Sat The coordinate system of the SAR antenna is determined.

[0059] In this embodiment of the invention, unlike traditional profile antennas which are one-dimensional linear arrays, the phase array antenna of this invention is a two-dimensional planar array. In the phased array antenna system, the phased array antenna system achieves two-dimensional beam sweeping (i.e., pointing arbitrarily to a location in two-dimensional space) through phase matching (i.e., the second transfer matrix from the antenna body coordinate system to the SAR antenna coordinate system). The first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system... Ant2Sat By setting it to an identity array, and ensuring that the antenna coordinate system coincides with the satellite coordinate system, the SAR antenna coordinate system is obtained. Specifically:

[0060] When the first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system Ant2Sat When using a unit array, the antenna coordinate system coincides with the satellite coordinate system. Representing this coincident coordinate system as XYZ, XOZ is the azimuth profile and YOZ is the range profile. In the phased array SAR antenna coordinate system X'Y'Z', the positive direction of the Z' axis is the intersection vector of the range and azimuth profiles, indicating the direction of the antenna phase center. The positive direction of the X' axis lies within the azimuth profile and is perpendicular to the Z' axis. The positive direction of the Y' axis is determined using the right-hand rule: the four fingers of the right hand bend from the positive direction of the Z' axis towards the positive direction of the X' axis, and the direction of the right thumb is the positive direction of the Y' axis.

[0061] Step 2, transfer the second transition matrix H from the antenna body coordinate system to the SAR antenna coordinate system. Ant2sar Represented by the phased array beam control angle.

[0062] Step 21: Using the phased array beam control angle, represent the normal vector n of the range profile of the beam. r and the normal vector n of the azimuth profile a .

[0063] In this embodiment of the invention, the phased array beam control angle includes the angle α between the azimuth profile of the beam and the Z-axis of the SAR antenna coordinate system and the angle β between the range profile of the beam and the Z-axis, and the normal vector n of the range profile of the beam. r The normal vector n of the azimuth profile of the beam a It can be expressed by the phased array beam control angle, as shown in equation (1) below:

[0064]

[0065] In the above formula, H X (), H Y () is the rotation matrix function, H X (-α) indicates a counterclockwise rotation of α° around the X-axis using the right-hand rule; H Y (-β) indicates a counterclockwise rotation of β° around the Y-axis using the right-hand rule.

[0066] Step 22, use the normal vector n to transform the vector of the positive Z' axis of the SAR antenna coordinate system. r and the normal vector n a This means that the direction vector n pointing to the antenna phase center is obtained. Z .

[0067] In this embodiment of the invention, the positive direction of the Z' axis is the intersection vector of the range profile and the azimuth profile, and the normal vector n of the range profile and azimuth profile of the beam can be used. r n a It is represented as shown in equation (2) below:

[0068] Z′=n a ×n r =[cosαsinβ,-sinαcosβ,cosαcosβ] T (2)

[0069] Then the direction vector n pointed to by the antenna phase center Z It can be expressed by the following formula (3):

[0070]

[0071] In the above formula, ||Z′|| is the L2 norm, which represents the modulus of vector Z'.

[0072] Step 23, based on the vector of the positive direction of the Z' axis of the SAR antenna coordinate system and the normal vector n r and the normal vector n a Determine the range profile vector l of the beam. r and azimuth profile vector l a .

[0073] In this embodiment of the invention, the range profile vector l is used. r The direction vector of the range profile and the azimuth profile vector l represent the direction vector of the range profile and the direction vector of the azimuth profile, respectively. a The direction vector l represents the azimuth direction of the profile. r and l a Perpendicular to the Z' axis, the positive direction vector of the Z' axis and the distance profile normal vector n can be obtained. r and azimuth profile normal vector n a This is represented as shown in equation (4):

[0074]

[0075] Step 24, select mutually orthogonal azimuth profile vectors l a The normal vector n a Using the basis vectors of the SAR antenna coordinate system, the second transition matrix H from the antenna body coordinate system to the SAR antenna coordinate system is determined. Ant2sar .

[0076] In this embodiment of the invention, it can be seen from equation (4) that the distance profile vector l r and azimuth profile vector l a The range and azimuth profiles are not perpendicular; that is, in the SAR antenna coordinate system, they are not perpendicular and cannot be used as basis vectors of the SAR antenna coordinate system. Therefore, a mutually orthogonal azimuth profile normal vector n is chosen. a azimuth profile vector l a Using the basis vectors of the SAR antenna coordinate system, the second transition matrix H is determined from the antenna body coordinate system to the SAR antenna coordinate system. Ant2sar As shown in equation (5):

[0077]

[0078] Then, the range profile vector l r It can be expressed as shown in the following formula (6):

[0079]

[0080] Range profile vector l r The angle between the antenna and the X' axis of the SAR antenna coordinate system is shown in equation (7):

[0081]

[0082] To facilitate use in practical engineering, the distance profile vector l r azimuth profile normal vector n a azimuth profile vector l a The relationship is expressed as shown in equation (8):

[0083]

[0084] Step 3, based on the first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system Ant2Sat The value of is used to solve the phased array constraint conditions and the correspondence between the phased array beam control angle and the satellite attitude angle.

[0085] In this embodiment of the invention, according to the first transition matrix H Ant2Sat Whether it is a unit array or not, the control problem of the phased array antenna is divided into two cases, in which:

[0086] Step 311, in the first transition matrix H Ant2Sat In the case of an identity array, the second transfer matrix H that transforms the antenna body coordinate system to the SAR antenna coordinate system. Ant2sar Using the satellite's yaw angle The pitch angle θ and roll angle ψ are represented by rotation matrix functions.

[0087] (1) In the first transition matrix H Ant2Sat When the phased array is always an identity array, there is no need to adjust the satellite's attitude angle before each observation mission. The observation can be completed by adjusting the phased array antenna. That is, by adjusting the second transfer matrix H from the antenna body coordinate system to the SAR antenna coordinate system. Ant2sar The value is sufficient to complete the observation. A phased array antenna consists of multiple sub-antennas. By controlling the movement of the sub-antennas through phase shifters and delayers, the direction of the synthesized beam of the phased array antenna can be achieved, enabling observation tasks at different observation angles.

[0088] Phased array antennas are controlled by the phased array beam control angles α and β of a two-dimensional linear array. That is, the phased array antenna uses two degrees of freedom α and β to constrain the beam attitude in three-dimensional space. However, existing beam control methods for non-tracking modes of spaceborne SAR are Euler angle control. Therefore, to integrate the beam control problem of phased array antennas with existing Euler angle control, it is necessary to add another degree of freedom constraint to the phased array antenna. For this purpose, the second transition matrix H from the antenna body coordinate system to the SAR antenna coordinate system is... Ant2sar Using the satellite's yaw angle The rotation matrix functions for pitch angle θ and roll angle ψ are expressed as shown in equation (9):

[0089]

[0090] In the above formula, This indicates rotation clockwise around the X-axis using the right-hand rule. H Y (θ), H Z (ψ) Synonyms.

[0091] Step 312, determine the second transition matrix H Ant2sar The correspondence between the phased array beam control angles α and β.

[0092] In this embodiment of the invention, the phased array beam control angles α and β are related to the second transfer matrix H from the antenna body coordinate system to the SAR antenna coordinate system. Ant2sar The relationship is shown in equation (10):

[0093]

[0094] In the above formula, a ij H represents the second transition matrix. Ant2sar The element in the i-th row and j-th column.

[0095] Step 313: Obtain the constraint conditions of the phased array antenna and the phased array beam control angles α and β.

[0096] From equations (9) and (10), the constraint condition (11) for the phased array antenna can be obtained:

[0097]

[0098] Accordingly, the phased array beam control angles α and β and the satellite yaw angle are obtained. The relationship between pitch angle θ and roll angle ψ is shown in equation (12) below:

[0099]

[0100] Step 321, in the first transition matrix H Ant2Sat In the case of an identity matrix, the second transition matrix H is... Ant2sar Using the adjusted yaw angle The pitch angle θ1 and roll angle ψ1 are represented by rotation matrix functions.

[0101] (2) In the first transition matrix H Ant2Sat In the case of a constant, time-invariant, non-unit array, the satellite's attitude angle needs to be adjusted and the phased array antenna adjusted before each observation mission. Assume the initial attitude angle adjustment before each observation mission is... After one adjustment, the second transition matrix H is obtained from θ0 and ψ0. Ant2sar It can be expressed as shown in the following formula (13):

[0102]

[0103] Step 322, based on the adjusted yaw angle Pitch angle θ1, roll angle ψ1 and yaw angle before adjustment By determining the correspondence between the pitch angle θ0 and the roll angle ψ0, the constraint conditions of the phased array antenna and the phased array beam control angles α and β are obtained.

[0104] In this embodiment of the invention, after the satellite adjusts its attitude angle, it completes the observation using a phased array scan, as shown in equation (14) below:

[0105]

[0106] Equation (14) leads to the following equation (15):

[0107]

[0108] Substituting into equation (13), we can obtain the constraints of the phased array antenna and the correspondence between the phased array beam control angles α and β and the satellite attitude angle, as shown in equation (16) below:

[0109]

[0110] Step 4: Based on the correspondence between the phased array beam control angle and the satellite attitude angle, the observation angle of the observation target under the phased array system is converted into the corresponding satellite attitude angle, so as to observe the observation target according to different observation angles.

[0111] In this embodiment of the invention, based on the correspondence between the phased array beam control angle and the satellite attitude angle, the observation angle of the observed target is converted into the corresponding satellite attitude angle. At the same time, the yaw angle, pitch angle and roll angle of the satellite must meet the corresponding phased array constraints in order to achieve target observation under different observation angles.

[0112] Furthermore, when this invention is applied to the joint design and optimization method of spaceborne SAR non-track multi-target imaging space-ground configuration, the corresponding projection ellipse rotation angle η needs to be given by the user. The relationship between η and the yaw angle is η = -ψ. Moreover, since the beam of the phased array system is directly abrupt (for example, the phased array beam control angles α and β abruptly change by 0.1° each time), there is no need to constrain the attitude angular velocity and attitude angular acceleration.

[0113] In this embodiment of the invention, during simulation experiments, for example, the simulation parameters of the phased array-based spaceborne SAR non-track mode beam control method of the present invention are shown in Table 1 below:

[0114] Table 1

[0115] Parameter name numerical values unit orbital altitude 500 km track inclination 97.4 ° Orbital eccentricity 0.005 / carrier frequency 10 GHz Width 3.8 Km Beam Jump 0.1 °

[0116] The observation targets include 22 observation target points. The wave foot trajectory obtained by the phased array-based spaceborne SAR non-track mode beam control method of the present invention is shown in Figure 3(a). Figure 3(b) shows the actual deviation between the wave foot trajectory and the observation target points. The horizontal axis is the sequence number of the observation target points, and the vertical axis is the deviation value of each observation target point. As can be seen from Figure 3(b), the wave foot trajectory obtained by the method of the present invention closely matches the observation target points.

[0117] Figure 4(a) shows the azimuth resolution of each observation target point, and Figure 4(b) shows the range swath of each observation target point. Compared with the existing method which has high beam center resolution and lower resolution further away from the beam center, as shown in Figure 4(a), the azimuth resolution of the method of the present invention is all within 0.5m, which satisfies the uniformity of resolution, the resolution is relatively close, the resolution is better, and the imaging quality is better. As shown in Figure 4(b), compared with the existing range swath (about 2km), the range swath of the imaging strip of the method of the present invention is wider (about 5km), and the target scene that can be captured is larger.

[0118] Figures 5(a) and 5(b) show the trends of phased array beam control angles α and β over time, which can realize the design of non-track imaging modes under given platform maneuver constraints.

[0119] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for controlling a non-stripline mode beam of a space-borne SAR based on a phased array system, characterized in that, Comprise: For the phased array system spaceborne SAR, a satellite orbit coordinate system, an antenna body coordinate system and a SAR antenna coordinate system are established; a second transfer matrix H of the antenna body coordinate system to the SAR antenna coordinate system Ant2sar by a phased array beam control angle representation; According to the first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system Ant2Sat The value of is used to solve the phased array constraint conditions and the correspondence between the phased array beam control angle and the satellite attitude angle; According to the corresponding relationship between the phased array beam control angle and the satellite attitude angle, the observation angle of the observation target under the phased array system is converted into the corresponding satellite attitude angle, so that the observation target is observed according to different observation angles; said second transfer matrix H of the antenna body coordinate system to the SAR antenna coordinate system Ant2sar by means of a phased array beam control angle representation, comprising: The phase array beam control angle represents a normal vector of a range profile of the beam n r and an azimuth profile n a : In the above formula, H X ( ), H Y ( ) is a rotation matrix function, H X ( - α ) means rotating anticlockwise by α ° around the X axis with the right-hand rule; H Y ( - β ) means rotating anticlockwise by β ° around the Y axis with the right-hand rule; a vector of a positive direction of a Z' axis of the SAR antenna coordinate system is utilized to calculate a direction vector of the antenna phase center pointing direction by using the normal vector n r and the normal vector n a represents, a direction vector of the antenna phase center pointing direction n Z : a vector according to a positive direction of a Z' axis of the SAR antenna coordinate system, the normal vector n r and the normal vector n a determining a range profile vector of the beam l r and an azimuth profile vector l a : selecting said azimuth profile vectors to be mutually orthogonal l a , said normal vectors n a determining a second transfer matrix H of the antenna body coordinate system to the SAR antenna coordinate system as base vectors of the SAR antenna coordinate system Ant2sar :

2. The method of claim 1, wherein, said first transfer matrix H from said satellite orbital coordinate system to said antenna body coordinate system Ant2Sat solving the phased array constraint condition and the correspondence between the phased array beam control angle and the satellite attitude angle, comprising: In the first transition matrix H Ant2Sat In the case of an identity array, the second transfer matrix H that transforms the antenna body coordinate system to the SAR antenna coordinate system. Ant2sar Using the satellite's yaw angle Phi Pitch angle Theta Roll angle Psi Represented by the rotation matrix function: determining the second transfer matrix H Ant2sar corresponding relationship between the phased array beam control angles α, β: In the above formula, a ij denotes the element in the i-th row and j-th column of the second transfer matrix H Ant2sar . The constraint condition of the phased array antenna is obtained: Correspondingly, the corresponding relationship between the phased array beam control angle α, β and the yaw angle Phi , the pitch angle Theta , the roll angle Psi of the satellite is obtained.

3. The method of claim 1, wherein, the first transfer matrix H from the satellite orbital coordinate system to the antenna body coordinate system Ant2Sat solving the phased array constraint condition and the correspondence between the phased array beam control angle and the satellite attitude angle, comprising: In the case of the first transition matrix H Ant2Sat In the case of the second transition matrix H Ant2sar With the adjusted yaw angle Phi 1, the pitch angle Theta 1, the roll angle Psi 1 is represented by the rotation matrix function: ； adjusted yaw angle Phi 1, pitch angle Theta 1, roll angle Psi 1 and pre-adjusted yaw angle Phi 0, pitch angle Theta 0, roll angle Psi 0 The constraint condition of the phased array antenna is obtained: and the correspondence between the phased array beam control angles a, b and the satellite's attitude angles:

4. The method of claim 1, wherein, For the phased array system spaceborne SAR, a satellite orbit coordinate system, an antenna body coordinate system and a SAR coordinate system are established, comprising: According to the satellite motion direction, the satellite orbit coordinate system and the antenna body coordinate system are constructed; a first transfer matrix H from the satellite orbit coordinate system to the antenna body coordinate system Ant2Sat is set to the identity matrix, in case the antenna body coordinate system coincides with the satellite body coordinate system, the SAR antenna coordinate system is obtained.

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