Complex configuration interferometer antenna array measurement and control method based on multi-coordinate conversion

Abstract

The invention discloses a complex-configuration interferometer antenna array measurement and control method based on multi-coordinate conversion, and the method comprises the steps: carrying out the phase consistency test of array element antennas of an interferometer antenna array, and carrying out the statistics of the equivalent phase centers of a plurality of array element antennas under the same coordinate system; and for the array element antennas with different configurations, combining the equivalent phase center, and performing step-by-step conversion through the transfer matrix among the plurality of coordinate systems so as to obtain the positions and directions of the array element antennas. According to the method, the relatively accurate spatial position of the array element antenna is obtained by utilizing the step-by-step conversion of the transfer matrixes among the coordinate systems, so that the problem of testing the phase center positions of fixed and expanded array element antennas in an interferometer antenna array with a complex configuration can be solved, and the array model precision of the interferometer antenna array is improved; and the direction finding precision of the system is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of interferometer direction finding technology, and in particular to a complex configuration interferometer antenna array measurement and control method based on multi-coordinate conversion. BACKGROUND

[0002] Interferometer direction finding technology is a kind of high-precision direction finding technology that is widely used at present. In an interferometer direction finding system, the direction finding accuracy can be represented by formula (1):

[0003] wherein, is the direction finding accuracy, is the wavelength, is the angle of view, is the phase measurement error, is the baseline length.

[0004] As can be seen from the above formula, the direction finding accuracy is proportional to the phase measurement error and inversely proportional to the baseline length, that is, the smaller the phase measurement error, the higher the direction finding accuracy, and the longer the baseline, the higher the direction finding accuracy. Therefore, long baseline design is an effective means to improve the direction finding accuracy of the interferometer. However, long baseline interferometers require more short baselines for direction finding de-masking (reference: Ouxin, Design method of multi-baseline phase interferometer [J] Electronic information countermeasure technology, 2021, 36(6): 105-109). Therefore, high-precision interferometer direction finding systems necessarily increase the complexity of the design of the interferometer antenna array.

[0005] Under the condition of limited weight and space of the bearing platform, a retractable / expandable movable mechanism is often used to construct a long baseline interferometer antenna array. However, the movable mechanism and its arm in the case of large spatial span and insufficient gravity unloading will result in a large measurement error of the array antenna expansion position, and the real position parameters of the interferometer antenna array cannot be accurately obtained. SUMMARY

[0006] In order to solve the problem of accurate measurement of the installation position of the array element antenna of the interferometer under the condition of complex configuration, the present application provides a complex configuration interferometer antenna array measurement and control method based on multi-coordinate conversion, which uses multi-coordinate system conversion to obtain the position and direction of the array element antenna for different configurations, thereby improving the direction finding accuracy of the interferometer direction finding system.

[0007] The technical scheme adopted by the present application is as follows: A complex configuration interferometer antenna array measurement and control method based on multi-coordinate conversion, comprising: performing phase consistency test on the array element antennas of the interferometer antenna array, and counting the equivalent phase centers of a plurality of array element antennas in the same coordinate system; The equivalent phase centers are combined with the array element antennas of different configurations, and the position and direction of the array element antennas are obtained through the transfer matrix between multiple coordinate systems.

[0008] Further, the phase consistency test is performed on the array element antennas of the interferometer antenna array, and the equivalent phase centers of the array element antennas in the same coordinate system are counted, including: performing the phase consistency test on the array element antennas of the interferometer antenna array in a microwave darkroom, dividing different frequency bands according to the antenna characteristics, and counting the equivalent phase centers of the array element antennas in the same coordinate system.

[0009] Further, when the same coordinate system is the antenna electrical coordinate system, the equivalent phase centers of the array element antennas in the antenna electrical coordinate system in each frequency band include: (1) wherein, n the number of array element antennas is N, m the number of divided frequency bands is M, D the antenna electrical coordinate system is X.

[0010] Further, the configurations of the array element antennas include fixed array element antennas and unfolded array element antennas, the fixed array element antennas are directly installed on a bearing platform, and the unfolded array element antennas are installed on the bearing platform through unfolding arms and movable mechanisms, and the installation position and installation angle of the movable mechanisms are measured through the reference mirrors of the movable mechanisms.

[0011] Further, the equivalent phase centers are combined with the array element antennas of different configurations, and the position and direction of the array element antennas are obtained through the transfer matrix between multiple coordinate systems, including: for the fixed array element antennas, calculating the transfer matrix from the electrical coordinate system to the bearing platform coordinate system, and calculating the vector and coordinates of the origin of the electrical coordinate system in the bearing platform coordinate system.

[0012] Further, for the fixed array element antennas, the transfer matrix from the electrical coordinate system to the bearing platform coordinate system is calculated, and the vector and coordinates of the origin of the electrical coordinate system in the bearing platform coordinate system are calculated, including: calculating the transfer matrix from the electrical coordinate system of the fixed array element antennas to the bearing platform coordinate system : (2) wherein, the transfer matrix from the reference mirror coordinate system of the fixed array element antennas to the bearing platform coordinate system is T, the transfer matrix from the electrical coordinate system of the fixed array element antennas to the reference mirror coordinate system is T; calculating the vector of the origin of the electrical coordinate system of the fixed array element antennas in the bearing platform coordinate system: (3) in, Let be the coordinate vector of a point in the electrical coordinate system of the fixed array antenna in the coordinate system of the supporting platform. The translation parameters are those from the origin of the reference mirror coordinate system to the coordinate system of the bearing platform. Let be the coordinate vector of a point in the reference mirror coordinate system, which can be obtained by the following formula: (4) in, These are the translation parameters from the origin of the electrical coordinate system of the fixed array antenna to the coordinate system of the reference mirror. This represents the coordinate vector of a point in a fixed array antenna in the electrical coordinate system. Combining equations (3) and (4), we have: (5) make Find the coordinates of the origin of the electrical coordinate system of the fixed array element antenna in the coordinate system of the supporting platform: (6) in, This is the transfer matrix from the coordinate system of the fixed array element antenna reference mirror to the coordinate system of the carrier platform. These are the translation parameters from the coordinate system of the fixed array element antenna reference mirror to the coordinate system of the supporting platform. These are the translation parameters from the electrical coordinate system of the fixed array element antenna to the coordinate system of the reference mirror.

[0013] Furthermore, for array element antennas of different configurations, the position and orientation of the array element antennas are obtained by step-by-step transformation through transfer matrices between multiple coordinate systems, in conjunction with the equivalent phase center, including: For deployable array antennas, the installation position of the movable mechanism in the coordinate system of the supporting platform is obtained through coordinate system transformation; Calculate the spatial position of the array element antenna in the deployed state within the coordinate system of the movable mechanism installation; The measured and theoretical coordinate values ​​of a point in the electrical coordinate system of the array element antenna are calculated in the coordinate system of the supporting platform, thereby obtaining the installation angle error and position error of the array element antenna.

[0014] Furthermore, obtaining the installation position of the movable mechanism in the coordinate system of the bearing platform through coordinate system transformation includes: (7) in, The installation position of the moving mechanism in the platform coordinate system. For the reference mirror coordinate system of the support platform J Translation from coordinate system S of the bearing platform to coordinate system S. For the reference mirror coordinate system of the moving mechanism J2 To the reference mirror coordinate system of the bearing platform J A translation of 1, Install coordinate system G from the reference mirror coordinate system of the moving mechanism. J2 Translation amount; C SJ1 From the coordinate system S of the bearing platform to the coordinate system of the bearing platform reference mirror J The transition matrix of 1, C J1J2 For the reference mirror coordinate system of the support platform J 1 to the reference mirror coordinate system of the moving mechanism J2 The transition matrix, C J2G For the reference mirror coordinate system of the moving mechanism J2 The transfer matrix for the coordinate system G installed on the moving mechanism.

[0015] Furthermore, the calculation of the spatial position of the array element antenna in the deployed state within the coordinate system of the movable mechanism includes: (8) in, This refers to the spatial position of the array element antenna in its deployed state within the coordinate system of the movable mechanism. For the reference mirror coordinate system of the support arm J 3. The translation of the coordinate system G of the moving mechanism. Coordinate system of the array element antenna reference mirror J 4. Support Arm Reference Mirror Coordinate System J A translation of 3, For the array element antenna electrical coordinate system D To the coordinate system of the array element antenna reference mirror J Translation of 4; C GJ3 Install coordinate system G from the reference mirror coordinate system of the support arm to the moving mechanism. J The transition matrix of 3, C J3J4 For the reference mirror coordinate system of the support arm J 3-element antenna reference mirror coordinate system J The transition matrix of 4, C J4D Coordinate system of the array element antenna reference mirror J 4-element antenna electrical coordinate system D The transition matrix.

[0016] Furthermore, the measured coordinates and theoretical coordinates of a point in the electrical coordinate system of the array element antenna are compared with those in the coordinate system of the supporting platform to obtain the installation angle error and position error of the array element antenna, including: Combining equations (7) and (8), and substituting them step by step, we can obtain a point in the electrical coordinate system of a certain array element antenna. Coordinate values ​​in the platform coordinate system : (9) If the coordinate of the origin of the electrical coordinate system of an array element antenna in the coordinate system of the bearing platform is to be obtained, let , then: (10) The coordinate measurement value of the origin of the electrical coordinate system of an array element antenna in the coordinate system of the bearing platform is calculated by formula (10) , and the transfer matrix measurement value of the electrical coordinate system of an array element antenna to the coordinate system of the bearing platform is calculated : (11) According to the theoretical model, the theoretical value of the coordinate of the origin of the electrical coordinate system of an array element antenna in the coordinate system of the bearing platform is , and the theoretical value of the transfer matrix of the electrical coordinate system of an array element antenna to the coordinate system of the bearing platform is C SD ; The installation angle and position error of an array element antenna are calculated: (12) Therefore, formula (12) is used to judge whether the installation precision of an array element antenna meets the requirements.

[0017] The beneficial effects of the present application are: The present application uses the transfer matrix between multiple coordinate systems to gradually convert and obtain the relatively accurate spatial position of an array element antenna, can solve the problem of testing the phase center position of fixed and unfolded array element antennas in a complex configuration interferometer antenna array, improve the array model precision of the interferometer antenna array, and further improve the direction finding precision of the system. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a fixed and unfolded array element antenna composition block diagram of embodiment 1 of the present application.

[0019] Figure 2 is a complex configuration interferometer antenna array measurement and control method flow chart of embodiment 1 of the present application.

[0020] Figure 3 is an interferometer antenna array configuration schematic diagram of embodiment 2 of the present application. DETAILED DESCRIPTION

[0021] In order to make the technical features, objectives and effects of the present application clearer, the specific embodiments of the present application are described. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application, that is, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0022] Embodiment 1 The present embodiment provides a complex configuration interferometer antenna array measurement and control method based on multi-coordinate conversion, comprising: performing phase consistency test on the array element antennas of the interferometer antenna array, and counting the equivalent phase centers of a plurality of array element antennas in the same coordinate system; for array element antennas of different configurations, combining the equivalent phase centers, and gradually converting through the transfer matrix between a plurality of coordinate systems to obtain the position and direction of the array element antennas.

[0023] The present method mainly uses multi-coordinate conversion to perform precision measurement on fixed and unfolded interferometer array element antennas, wherein the compositions of the fixed and unfolded array element antennas are as shown in Figure 1 .

[0024] Specifically, as shown in Figure 2 , the present method can be implemented by the following steps: Step 1: phase consistency and phase center test between multiple groups of array element antennas; Step 2: installation and installation precision test of fixed array element antennas; Step 3: installation and installation precision test of unfolded array element antenna mechanism; Step 4: unfolding test and unfolding precision test of unfolded array element antennas; Step 5: repeat steps 2-4 to complete the installation and test of all array element antennas.

[0025] Preferably, in step 1, the phase consistency test of the array element antennas of the interferometer antenna array is carried out in a microwave darkroom, and different frequency bands are divided according to the antenna characteristics, and the equivalent phase centers of a plurality of array element antennas in the same coordinate system are counted. If the same coordinate system is an antenna electrical coordinate system, the equivalent phase centers of a plurality of array element antennas in the antenna electrical coordinate system in each frequency band are: (1) wherein, n is the number of array element antennas, m is the number of divided frequency bands, D is the antenna electrical coordinate system.

[0026] It should be noted that the configuration of the array antenna includes a fixed array antenna and an unfolded array antenna. The fixed array antenna is usually directly installed on the bearing platform, and the unfolded array antenna is installed on the bearing platform through an unfolding arm and a movable mechanism, and the installation position and the installation angle of the movable mechanism are measured through a reference mirror of the movable mechanism itself.

[0027] Preferably, in step two, for the fixed array antenna, the transfer matrix of the electrical coordinate system to the bearing platform coordinate system is calculated first, and then the vector and the coordinates of the origin of the electrical coordinate system in the bearing platform coordinate system are calculated, which specifically includes: calculating the transfer matrix of the electrical coordinate system of the fixed array antenna to the bearing platform coordinate system (2) wherein, is the transfer matrix of the reference mirror coordinate system of the fixed array antenna to the bearing platform coordinate system, is the transfer matrix of the electrical coordinate system of the fixed array antenna to the reference mirror coordinate system.

[0028] calculating the vector of the origin of the electrical coordinate system of the fixed array antenna in the bearing platform coordinate system: (3) wherein, is the coordinate vector of a certain point of the fixed array antenna in the electrical coordinate system in the bearing platform coordinate system, is the translation parameter of the origin of the reference mirror coordinate system to the bearing platform coordinate system, is the coordinate vector of the certain point in the reference mirror coordinate system, which is obtained by the following formula: (4) wherein, is the translation parameter of the origin of the electrical coordinate system of the fixed array antenna to the reference mirror coordinate system, is the coordinate vector of the certain point of the fixed array antenna in the electrical coordinate system.

[0029] in combination with formula (3) and formula (4), we have: (5) let , the coordinates of the origin of the electrical coordinate system of the fixed array antenna in the bearing platform coordinate system are obtained: (6) wherein, is the transfer matrix of the reference mirror coordinate system of the fixed array antenna to the bearing platform coordinate system, is the translation parameter of the reference mirror coordinate system of the fixed array antenna to the bearing platform coordinate system, ​The translation parameter of the electrical coordinate system of the fixed array antenna to the reference mirror coordinate system.

[0030] Preferably, in step three, for the unfolded array antenna mechanism, the active mechanism installation position in the bearing platform coordinate system is obtained through coordinate system conversion, specifically including: (7) Wherein, is the active mechanism installation position in the bearing platform coordinate system, is the bearing platform reference mirror coordinate system J 1 to the translation amount of the bearing platform coordinate system S, is the active mechanism reference mirror coordinate system J2 to the translation amount of the bearing platform reference mirror coordinate system J 1, is the translation amount of the active mechanism installation coordinate system G to the active mechanism reference mirror coordinate system J2 C. SJ1 is the translation matrix of the bearing platform coordinate system S to the bearing platform reference mirror coordinate system J 1, C J1J2 is the translation matrix of the bearing platform reference mirror coordinate system J 1 to the active mechanism reference mirror coordinate system J2 C. J2G is the translation matrix of the active mechanism reference mirror coordinate system J2 to the active mechanism installation coordinate system G.

[0031] Preferably, in step four, for the unfolded array antenna, first calculate the spatial position of the array antenna in the unfolded state in the active mechanism installation coordinate system, and then calculate the coordinate measurement value and the coordinate theoretical value of a point coordinate in the array antenna electrical coordinate system in the bearing platform coordinate system, and then obtain the installation angle error and the position error of the array antenna. The specific implementation process is as follows.

[0032] Calculating the spatial position of the array antenna in the unfolded state in the active mechanism installation coordinate system includes: (8) Wherein, is the spatial position of the array antenna in the unfolded state in the active mechanism installation coordinate system, is the support arm reference mirror coordinate system J 3 to the translation amount of the active mechanism installation coordinate system G, is the array antenna reference mirror coordinate system J 4 to the translation amount of the support arm reference mirror coordinate system J 3, is the array antenna electrical coordinate system D to the array antenna reference mirror coordinate system J C.translation amount of 4; C GJ3 Install coordinate system G for active mechanism to support arm reference mirror coordinate system J transfer matrix of 3, C J3J4 Install coordinate system G for support arm reference mirror coordinate system J 3 to array element antenna reference mirror coordinate system J transfer matrix of 4, C J4D Install coordinate system G for array element antenna reference mirror coordinate system J 4 to array element antenna electrical coordinate system D transfer matrix of.

[0033] Combined with formula (7) and formula (8), the coordinates of a certain point in a certain array element antenna electrical coordinate system are calculated step by step. The coordinate value of the coordinate in the bearing platform coordinate system : (9) If the coordinates of the origin of a certain array element antenna electrical coordinate system in the bearing platform coordinate system are calculated, let , then: (10) The coordinate measurement value of the origin of a certain array element antenna electrical coordinate system in the bearing platform coordinate system is calculated using formula (10) , and the transfer matrix measurement value of a certain array element antenna electrical coordinate system to the bearing platform coordinate system is calculated : (11) According to the theoretical model, the theoretical value of the coordinates of the origin of a certain array element antenna electrical coordinate system in the bearing platform coordinate system is , and the theoretical value of the transfer matrix of a certain array element antenna electrical coordinate system to the bearing platform coordinate system is C SD .

[0034] The installation angle and position error of a certain array element antenna are calculated: (12) Therefore, formula (12) is used to judge whether the installation accuracy of a certain array element antenna meets the requirements.

[0035] Example 2 This embodiment is based on example 1: This embodiment provides a complex configuration interferometer antenna array measurement and control method based on multi-coordinate conversion, wherein the interferometer antenna array is a cross interferometer array, a one-dimensional layout design using three array element antennas, the longest baseline is 10 meters, the shortest baseline is 4 meters, and five array element antennas are divided into two installation modes, wherein the No. 3 array element antenna is a fixed installation, and the remaining four antennas are unfolded array element antennas, as shown in Figure 3 .

[0036] According to the theoretical model, the theoretical relationship between the electrical coordinate system of the No. 3 array element antenna and the bearing platform coordinate system is shown in Table 1.

[0037] Table 1 is the theoretical value of the electrical coordinate system of the No. 3 array element antenna and the bearing platform coordinate system

[0038] According to the installation precision test of the fixed array element antenna by the method, according to the test data of the No. 3 array element antenna, the relationship between the electrical coordinate system of the fixed array element antenna and the bearing platform coordinate system is shown in Table 2.

[0039] Table 2 is the measured value of the electrical coordinate system of the No. 3 array element antenna and the bearing platform coordinate system

[0040] According to the theoretical model, the theoretical relationship between the electrical coordinate system of the No. 1 array element antenna and the bearing platform coordinate system is shown in Table 3 and Table 4.

[0041] Table 3 is the transfer matrix and center coordinate theoretical value of the electrical coordinate system of the No. 1 array element antenna to the bearing platform coordinate system

[0042] Table 4 is the transfer matrix and center coordinate theoretical value of the electrical coordinate system of the No. 2 array element antenna to the bearing platform coordinate system

[0043] According to the installation precision test of the unfolded array element antenna by the method, according to the installation and unfolding test data of the unfolded array element antenna, the relationship between the electrical coordinate system of the unfolded array element antenna and the bearing platform coordinate system is shown in Table 5 and Table 6.

[0044] Table 5 is the transfer matrix and center coordinate measured value of the electrical coordinate system of the No. 1 array element antenna to the bearing platform coordinate system

[0045] Table 6 is the transfer matrix and center coordinate measured value of the electrical coordinate system of the No. 2 array element antenna to the bearing platform coordinate system

[0046] According to formula (12), the installation position error of the No. 1, No. 2 and No. 3 array element antennas is:

[0047] The test results show that according to the method, the spatial position of the complex long baseline interferometer antenna can be obtained more accurately, and the array model precision of the interferometer antenna can be improved.

[0048] Embodiment 3 This embodiment is based on Embodiment 1: This embodiment provides a computer device, comprising a memory and a processor, the memory stores a computer program, and the processor implements the method for measuring and controlling a complex configuration interferometer antenna array based on multi-coordinate conversion of Embodiment 1 when executing the computer program. The computer program can be in the form of source code, object code, an executable file, or some intermediate form, etc.

[0049] Embodiment 4 This embodiment is based on Embodiment 1: This embodiment provides a computer readable storage medium, which stores a computer program, and the computer program implements the method for measuring and controlling a complex configuration interferometer antenna array based on multi-coordinate conversion of Embodiment 1 when executed by a processor. The computer program can be in the form of source code, object code, an executable file, or some intermediate form, etc. The storage medium includes any entity or device capable of carrying computer program code, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc. It should be noted that the content included in the storage medium can be appropriately added or reduced according to the requirements of legislation and patent practice in the jurisdiction, for example, in some jurisdictions, according to legislation and patent practice, the storage medium does not include electrical carrier signals and telecommunication signals.

[0050] It should be noted that, for the foregoing method embodiments, in order to facilitate description, they are expressed as a series of action combinations, but those skilled in the art should know that the present application is not limited to the order of the actions described, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should know that the embodiments described in the specification all belong to preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

Claims

1. A method for measuring and controlling an antenna array of a complex configuration interferometer based on multi-coordinate conversion, characterized in that, include: Phase consistency tests were performed on the element antennas of the interferometer antenna array, and the equivalent phase centers of multiple element antennas in the same coordinate system were statistically analyzed. For array element antennas with different configurations, the position and direction of the array element antennas can be obtained by combining the equivalent phase center and transforming step by step through the transfer matrix between multiple coordinate systems.

2. The method according to claim 1, wherein, The phase consistency test of the array element antennas of the interferometer antenna array and the statistical analysis of the equivalent phase centers of multiple array element antennas in the same coordinate system include: conducting phase consistency tests on the array element antennas of the interferometer antenna array in a microwave anechoic chamber, dividing different frequency bands according to antenna characteristics, and statistically analyzing the equivalent phase centers of multiple array element antennas in each frequency band in the same coordinate system.

3. The method according to claim 2, wherein, When the same coordinate system is the antenna electrical coordinate system, the equivalent phase centers of multiple array element antennas in each frequency band under the antenna electrical coordinate system include: (1) wherein, n is the number of antenna elements, m is the number of divided frequency bands, D is the antenna electrical coordinate system.

4. The method of claim 1, wherein, The configuration of the array element antenna includes a fixed array element antenna and a deployable array element antenna. The fixed array element antenna is directly mounted on the support platform, while the deployable array element antenna is mounted on the support platform through a deployable arm and a movable mechanism. The installation position and installation angle of the movable mechanism are measured by the reference mirror of the movable mechanism itself.

5. The method according to claim 4, wherein, The method for obtaining the position and orientation of array element antennas with different configurations by combining the equivalent phase center and transforming them step by step through the transfer matrix between multiple coordinate systems includes: for fixed array element antennas, calculating the transfer matrix from the electrical coordinate system to the carrier platform coordinate system, and calculating the vector and coordinates of the origin of the electrical coordinate system in the carrier platform coordinate system.

6. The method according to claim 5, wherein, For fixed array element antennas, the calculation of the transfer matrix from the electrical coordinate system to the carrier platform coordinate system, and the calculation of the vector and coordinates of the origin of the electrical coordinate system in the carrier platform coordinate system, including: Computing a transfer matrix of an electrical coordinate system of a stationary array antenna to a bearing platform coordinate system : (2) wherein, is a transfer matrix of the fixed array antenna reference mirror coordinate system to the carrier platform coordinate system, is a transfer matrix of the fixed array antenna electrical coordinate system to the reference mirror coordinate system; Calculate the vector of the origin of the electrical coordinate system of the fixed array antenna in the coordinate system of the supporting platform: (3) wherein, is the coordinate vector of a point in the fixed array antenna coordinate system in the coordinate system of the carrier platform, is the translation parameter from the origin of the reference mirror coordinate system to the coordinate system of the carrier platform, is the coordinate vector of the point in the reference mirror coordinate system, which is obtained from the following equation: (4) wherein, is a translation parameter from the origin of the electrical coordinate system of the fixed array antenna to the coordinate system of the reference mirror, is a coordinate vector of a certain point of the fixed array antenna in the electrical coordinate system; Combining equations (3) and (4), we have: (5) Let , find the coordinates of the origin of the electrical coordinate system of the fixed array antenna under the coordinate system of the bearing platform: (6) wherein, is a transfer matrix of the fixed array antenna reference mirror coordinate system to the carrier platform coordinate system, is a translation parameter of the fixed array antenna reference mirror coordinate system to the carrier platform coordinate system, is a translation parameter of the fixed array antenna electrical coordinate system to the reference mirror coordinate system.

7. The method according to claim 4, wherein, The method involves obtaining the position and orientation of array element antennas with different configurations by combining the equivalent phase center and performing step-by-step transformations between multiple coordinate systems using transfer matrices. For deployable array antennas, the installation position of the movable mechanism in the coordinate system of the supporting platform is obtained through coordinate system transformation; Calculate the spatial position of the array element antenna in the deployed state within the coordinate system of the movable mechanism installation; The measured and theoretical coordinate values ​​of a point in the electrical coordinate system of the array element antenna are calculated in the coordinate system of the supporting platform, thereby obtaining the installation angle error and position error of the array element antenna.

8. The method according to claim 7, wherein, The process of obtaining the installation position of the movable mechanism in the coordinate system of the bearing platform through coordinate system transformation includes: (7) in, The installation position of the moving mechanism in the platform coordinate system. For the reference mirror coordinate system of the support platform J Translation from coordinate system S of the bearing platform to coordinate system S. For the reference mirror coordinate system of the moving mechanism J2 To the reference mirror coordinate system of the bearing platform J A translation of 1, Install coordinate system G from the reference mirror coordinate system of the moving mechanism. J2 Translation amount; C SJ1 From the coordinate system S of the bearing platform to the coordinate system of the bearing platform reference mirror J The transition matrix of 1, C J1J2 For the reference mirror coordinate system of the support platform J 1 to the reference mirror coordinate system of the moving mechanism J2 The transition matrix, C J2G For the reference mirror coordinate system of the moving mechanism J2 The transfer matrix for the coordinate system G installed on the moving mechanism.

9. The method according to claim 8, wherein, The calculation of the spatial position of the array element antenna in the deployed state within the coordinate system of the movable mechanism includes: (8) wherein, is the spatial position of the array antenna in the deployed state in the active mechanism mounting coordinate system, is the support arm reference mirror coordinate system J 3 is the translation of the active mechanism mounting coordinate system G, is the array antenna reference mirror coordinate system J 4 is the support arm reference mirror coordinate system J 3 is the translation of 3, is the array antenna electrical coordinate system D is the translation of the array antenna reference mirror coordinate system J 4 to the array antenna electrical coordinate system; C GJ3 is the translation matrix of the active mechanism mounting coordinate system G to the support arm reference mirror coordinate system J 3, C J3J4 is the translation matrix of the support arm reference mirror coordinate system J 3 to the array antenna reference mirror coordinate system J 4, C J4D is the translation matrix of the array antenna reference mirror coordinate system J 4 to the array antenna electrical coordinate system D .

10. The method according to claim 9, wherein, The calculation of the coordinates of a point in the electrical coordinate system of the array element antenna and the measured and theoretical coordinates in the coordinate system of the supporting platform is used to obtain the installation angle error and position error of the array element antenna, including: Combining formula (7) and formula (8), the coordinates of a certain point in the antenna coordinate system of a certain array element are calculated step by step The coordinate value of the coordinate in the bearing platform coordinate system : (9) If the coordinates of an array element antenna in the bearing platform coordinate system are to be found, let then: (10) The coordinate measurement value of the antenna element antenna electric coordinate system origin in the bearing platform coordinate system is calculated by using formula (10) The transfer matrix measurement value of the antenna element antenna electric coordinate system to the bearing platform coordinate system is calculated : (11) According to the theoretical model, the coordinate theoretical value of the origin of the antenna electrical coordinate system of a certain array element in the bearing platform coordinate system is , and the transfer matrix theoretical value of the antenna electrical coordinate system of a certain array element to the bearing platform coordinate system is C SD . Calculate the installation angle and position error of a certain array element antenna: (12) Therefore, equation (12) can be used to evaluate whether the installation accuracy of a certain array element antenna meets the requirements.

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