CN113934965A - Phased array antenna on-orbit correction and deformation evaluation method - Google Patents

Phased array antenna on-orbit correction and deformation evaluation method Download PDF

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CN113934965A
CN113934965A CN202111006850.9A CN202111006850A CN113934965A CN 113934965 A CN113934965 A CN 113934965A CN 202111006850 A CN202111006850 A CN 202111006850A CN 113934965 A CN113934965 A CN 113934965A
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赵宏伟
吴疆
李琳
王迪
瞿颜
李成国
李樊
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Xian Institute of Space Radio Technology
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Abstract

The invention relates to an on-orbit correction and deformation evaluation method of a phased array antenna, which comprises the following steps of firstly, carrying out ground structure and amplitude phase measurement on an integrated link of a beacon, an array surface and a channel of an active phased array antenna; then calculating to obtain the on-orbit compensation phase of each channel on the basis of ground amplitude-phase measurement data, and completing on-orbit correction of the electrical performance of the phased array antenna; secondly, acquiring the physical deformation length from the array antenna beacon to each array surface unit position according to the phase change value of each channel; thirdly, predicting possible position coordinates of each unit of the array surface after the on-orbit deformation through comparison calculation with the array antenna ground structure measurement data; and finally, the on-orbit evaluation of the array surface deformation is summarized as the optimization problem of the array surface unit position, a deformation optimization model and an optimization constraint condition are constructed to update the array element position, and the final array element position coordinate is obtained by solving on the basis of multiple iterative optimization, so that the on-orbit surface change evaluation is realized.

Description

Phased array antenna on-orbit correction and deformation evaluation method
Technical Field
The invention relates to an on-orbit correction and deformation evaluation method for a phased array antenna, and belongs to the field of design of satellite-borne array antennas.
Background
The satellite-borne SAR (synthetic aperture radar) active phased-array antenna has the characteristics of high gain, narrow beam, fast beam scanning, agile beam shape and the like, and meets the requirement of the performance of satellite-borne electronic information equipment. The novel satellite-borne SAR phased-array antenna has the advantages of large caliber, large number of single plates, large change of external temperature, large heat consumption of the single plates, flexible and light array surface, reliable expansion by adopting a truss mode and high precision requirement of the antenna profile. The in-orbit surface change of the satellite-borne array antenna is possibly caused by factors such as space environment and the like, for example, the thermal deformation of each single plate under the background condition of different temperatures (-190 ℃ -160 ℃), the error precision control of the in-orbit surface of a plurality of antenna single plates is not in place, and the deformation has important influence on the performance of the SAR phased array antenna. The large-scale array antenna surface error assessment and electrical property correction technical research is developed, the rigidity requirements on an antenna structure plate and an expansion system can be reduced, and the total weight reduction of a satellite-borne SAR effective load system and the breakthrough and updating of a phased array technology are realized.
In a traditional scheme for measuring deformation errors and correcting antenna performance of a large-scale array antenna, a spatial large-distance high-precision camera measurement and mechanical control calibration system is generally constructed, or a real-time sensor monitoring and signal processing correction system distributed on the surface of an array plane is utilized to complete analysis, measurement and structural dynamic compensation of antenna array plane deformation. These measurement and correction systems can realize real-time error monitoring and correction, but are limited to the installation accuracy of the measurement equipment to a great extent, and at the same time, the satellite load design cost and the system complexity are increased, and the weight limit requirements of the satellite platform often cannot be met.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method overcomes the defects of the prior art, and provides the phased array antenna on-track correction and deformation evaluation method, which combines the array surface deformation structural characteristics and the active channel amplitude-phase measurement by using the active link characteristics of the phased array to realize the functions of antenna electrical property correction and deformation error evaluation.
The technical scheme of the invention is as follows:
an on-orbit correction and deformation evaluation method for a phased array antenna comprises the following steps:
(1) constructing an integrated correction link by the beacon, the passive array surface and the active channel of the array antenna;
(2) finishing the surface accuracy correction and the mechanical structure measurement of a radiation front on the ground and recording a table A1;
(3) finishing the balance of the active channel and the amplitude-phase consistency check in a ground darkroom and respectively recording the forms as A2 and A3;
(4) sequentially changing different bit states of each channel phase shifter, and measuring and recording corresponding power level values of the synthesized electric field;
(5) obtaining phase calibration values of all channels by adopting an anti-noise interference active channel phase calibration method and recording a table;
(6) on the basis of ground amplitude-phase measurement data tables A2 and A3, calculating the on-orbit compensation phase of each channel to realize on-orbit electrical performance correction of the phased array antenna;
(7) obtaining the physical length change value from the array antenna beacon to each array surface unit position after the track deformation according to the phase change compensation value of each active channel;
(8) predicting possible coordinate positions of the elements of each front surface after the deformation of the rail through a ground structure measurement data table A1 and length change values from the beacon of the rail to the elements;
(9) and the array surface deformation evaluation is summarized as the optimization problem of the array surface unit position, and a deformation optimization model and an optimization constraint condition are constructed to update the array element position, so that the array element position value is obtained through multiple times of iterative optimization solution, and the on-orbit surface error evaluation of the array antenna is realized.
Further, the array antenna calibration in the step (1) adopts an external calibration method, so that the integrated calibration link comprises a beacon antenna, a passive array surface and an active channel.
Further, in the step (1), the array antenna beacon adopts a wide beam element antenna, and the erection height and the erection position meet the requirements of the far-field distance of the array antenna and certain beam coverage.
Further, the array antenna shape accuracy and mechanical structure measurement in the step (2) are realized by adopting a photogrammetric method on the ground.
Further, the active channel configuration and amplitude and phase consistency check in the step (3) is realized by adopting an REV rotation vector method.
Further, the different bit states of each channel phase shifter in the step (4) include four states of 0 °, 90 °, 180 ° and 270 °.
Further, in step (5), the active channel phase calibration method includes: suppose the amplitude and phase of the signals of the active channels 1 and 2 of the array antenna are respectively E1、φ1And E2、φ2The power of the superposition of the two signals is expressed as
Figure BDA0003237520200000031
Delta is the channel 2 phase shifter additive phase, at which time, the phase shifter phase shift value for channel 2 is changed,
when delta is pi/2, the signals are combined to form power
Figure BDA0003237520200000034
When delta is 3 pi/2, the signals are combined to form power
Figure BDA0003237520200000035
When delta is 0, the signal synthesized power is at the moment
Figure BDA0003237520200000036
When delta is pi, the signal synthesized power
Figure BDA0003237520200000037
Wherein epsilon2Is the average noise power of the channel;
therefore, after measuring the signal power levels in the four phase-shifting states, the phase difference between the two channels can be calculated as
Figure BDA0003237520200000032
Further, the on-track compensation phase calculation method for each channel in step (6) is as follows:
assume that for the active channel i corresponding to the mn-th cell in the array surface, the initial calibration and pre-calibration phase values at the ground are phi respectively0iAnd phi1iThe phase measurement of the on-track calibration is phi2iSo that the compensation phase value is delta phimn＝-φ0i+(φ2i-φ1i)。
Further, the calculation method for obtaining the position change information of the wavefront unit from the compensation phase of each channel in step (7) is as follows:
if the array antenna structure measurement information is completed on the ground, the beacon antenna is set to be (x)p,yp,zp) And the mn-th cell (x) in the array planemn,ymn,zmn) A distance of
Figure BDA0003237520200000033
When the array surface is deformed on track, the beacon antenna and the mn-th unit of the array surface
Figure BDA0003237520200000041
A distance of
Figure BDA0003237520200000042
Thus, the wavefront distortion causes the distance between the wavefront unit and the beacon to change to
Figure BDA0003237520200000043
Corresponding to a compensation phase of
Figure BDA0003237520200000044
Thereby obtaining the distance change between the beacon and the mn-th unit of the wavefront after the wavefront deformation
Figure BDA0003237520200000045
Further, the coordinate position of the deformed array element pre-evaluated in the step (8) is expressed as
Figure BDA0003237520200000046
Further, in the optimization problem of the positions of the array surface units in the step (9), a genetic algorithm can be adopted for solving the optimization model:
Figure BDA0003237520200000047
s.t.
Figure BDA0003237520200000048
Figure BDA0003237520200000049
Figure BDA00032375202000000410
Δφmn＝-φ0i+(φ2i-φ1i)
f(xmn,ymn,zmn)＝f0
wherein argmin represents the minimum value to be solved; f (x)mn,ymn,zmn)＝f0Other models are known that the wavefront satisfies after deformation of the rail structure.
Compared with the prior art, the invention has the beneficial effects that:
(1) compared with a camera or sensor measurement and mechanical calibration method, the method disclosed by the invention fully utilizes the active link characteristic of the active array antenna, combines the array surface deformation structural characteristic with the amplitude-phase characteristic of an active channel, realizes the electrical performance calibration and array surface deformation error evaluation of the antenna, does not need to additionally increase a large number of measurement and calibration equipment, and is beneficial to the reduction of satellite load cost and the weight reduction of a system;
(2) most of the related documents disclosed at present are the analysis and research of antenna structure to structure, electrical property to electrical property and structure to electrical property, the method of the invention innovatively provides a reverse comprehensive idea of antenna electrical property to structural parameters, and can provide design guidance basis for structural design, tolerance distribution, overall index decomposition and the like of an active array antenna;
(3) the method of the invention adopts an active channel phase correction technology which can effectively reduce or eliminate the influence of noise power on the channel to be corrected and improve the correction precision; only the power level of the combined signal needs to be measured, and the method has the characteristics of easiness in engineering realization and small calculation amount.
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FIG. 1 is a schematic diagram of the external calibration system;
FIG. 2 is a schematic diagram of an active channel correction algorithm;
FIG. 3 is a flow chart of channel compensation phase calculation;
FIG. 4 is a schematic diagram of the locations of the cells before and after orbital deformation of the array plane;
fig. 5 is an overall flow chart of the invention.
Detailed Description
The invention is further illustrated by the following examples.
In order to realize the on-orbit correction and deformation evaluation of the phased array, the method specifically comprises the following calculation steps:
(1) referring to the external calibration system composition scheme, an integrated calibration link is constructed by an array antenna beacon, a passive array surface and an active channel, the beacon erection meets a certain height and coverage range, and the system composition is shown in fig. 1.
(2) And (3) finishing the surface accuracy correction of the radiation front surface and the mechanical structure measurement on the ground by adopting a high-accuracy structure measurement method such as photogrammetry and recording a table A1.
(3) Active channel balancing and amplitude consistency check are completed in a ground darkroom by methods such as REV (rotating vector method) and the like, and the results are recorded as A2 and A3 respectively.
(4) And sequentially changing different bit states (comprising four states of 0 degree, 90 degrees, 180 degrees and 270 degrees) of each channel phase shifter through beam control software, and measuring and recording corresponding power level values of the synthesized electric field.
(5) And obtaining phase calibration values of all channels by adopting an active channel phase calibration technology resisting noise interference and recording a table. By using the thought of REV (rotation vector method), the amplitude and phase of the active channel 1 and 2 signals of the array antenna are respectively assumed to be E1、φ1And E2、φ2The power of the superposition of the two signals can be expressed as
Figure BDA0003237520200000061
Delta is the channel 2 phase shifter added phase. At this time, the phase shifter that changes channel 2 adds a phase shift value delta,
when delta is pi/2, the signals are combined to form power
Figure BDA0003237520200000068
When delta is 3 pi/2, the signals are combined to form power
Figure BDA0003237520200000069
When delta is 0, the signal synthesized power is at the moment
Figure BDA00032375202000000610
When delta is pi, the signal synthesized power
Figure BDA00032375202000000611
Wherein epsilon2Is the average noise power of the channel.
Therefore, based on the signal power measurement levels in the four phase-shifted states (as shown in FIG. 2), the phase difference between the two channels is calculated as
Figure BDA0003237520200000062
(6) On the basis of ground amplitude-phase measurement data tables A2 and A3, on-track compensation phases of all channels are calculated, and on-track electrical performance correction of the phased array antenna is achieved. The on-orbit compensation phase calculation process of each channel is shown in fig. 3, and for the active channel i corresponding to the mn-th unit in the array surface, the initial calibration and the pre-calibration phase values on the ground are respectively phi0iAnd phi1iThe phase measurement of the on-track calibration is phi2iThe obtained compensation phase value is delta phimn＝-φ0i+(φ2i-φ1i)。
(7) And obtaining the physical length change value from the array antenna beacon to each array surface unit position after the track deformation according to the phase change compensation value of each active channel. The calculation idea is that the position information of the array antenna structure, such as the position (x) of the beacon antenna, is measured according to the groundp,yp,zp) The mn-th element (x) in the beacon and the wavefrontmn,ymn,zmn) A distance of
Figure BDA0003237520200000063
Assuming that the amplitude-phase error of the channel is not considered and the position of the beacon antenna on the track is fixed, when the wavefront is deformed on the track, the beacon antenna and the mn-th unit of the wavefront
Figure BDA0003237520200000064
A distance of
Figure BDA0003237520200000065
Thus, the wavefront changesThe shape causes the array surface unit to vary from the beacon distance to
Figure BDA0003237520200000066
Corresponding to a compensation phase of
Figure BDA0003237520200000067
Because of delta phimn、RmnThe information is known, so that the distance between the beacon and the mn-th unit of the wavefront can be changed into
Figure BDA0003237520200000071
Fig. 4 is a schematic diagram showing the change in the positions of the respective units before and after deformation.
(8) The pre-estimated array surface deformed array element coordinate position set can be expressed as
Figure BDA0003237520200000072
(9) And the array surface deformation evaluation is summarized as the optimization problem of the array surface unit position, and the global optimal solution can be obtained by adopting optimization iterative algorithms such as a genetic algorithm and the like to solve the optimization problem, so that the evaluation of the unit position after the array surface deformation is realized. The model is summarized as follows.
Figure BDA0003237520200000073
s.t.
Figure BDA0003237520200000074
Figure BDA0003237520200000075
Figure BDA0003237520200000076
Δφmn＝-φ0i+(φ2i-φ1i)
f(xmn,ymn,zmn)＝f0
Wherein argmin represents the minimum value to be solved; f (x)mn,ymn,zmn)＝f0Other models are known that the wavefront satisfies after deformation of the rail structure.
The whole patent flow is shown in fig. 5.
The invention discloses an on-orbit correction and deformation evaluation method for a phased array antenna. Firstly, carrying out ground structure and amplitude phase measurement on an integrated link of an active phased array antenna beacon, a array surface and a channel; then calculating to obtain the on-orbit compensation phase of each channel on the basis of ground amplitude-phase measurement data, and completing on-orbit correction of the electrical performance of the phased array antenna; secondly, acquiring the physical deformation length from the array antenna beacon to each array surface unit position according to the phase change value of each channel; thirdly, predicting possible position coordinates of each unit of the array surface after the on-orbit deformation through comparison calculation with the array antenna ground structure measurement data; and finally, the on-orbit evaluation of the array surface deformation is summarized as the optimization problem of the array surface unit position, a deformation optimization model and an optimization constraint condition are constructed to update the array element position, and the final array element position coordinate is obtained by solving on the basis of multiple iterative optimization, so that the on-orbit surface change evaluation is realized.
Compared with a traditional camera measurement and mechanical control calibration system or a distributed real-time sensor monitoring and signal processing correction system, the method disclosed by the invention fully utilizes the active link characteristics of an active phased array antenna, provides a reverse comprehensive method for measuring the electrical property of the antenna to structural parameters, combines array surface deformation structure measurement with active channel phase correction, realizes the electrical property correction and array surface deformation error evaluation functions of the phased array antenna, and does not need to additionally increase a large amount of satellite system cost and payload weight; the active channel phase correction technology adopting anti-noise interference provides powerful technical support for realizing high-precision beam pointing and high gain of the array antenna, and is an important means for improving the performance of the active array antenna.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (11)

1.一种相控阵天线在轨校正与形变评估方法，其特征在于，包括以下步骤：1. a phased array antenna on-orbit correction and deformation evaluation method, is characterized in that, comprises the following steps: (1)将阵列天线的信标、无源阵面和有源通道构建一体化校正链路；(1) Construct an integrated correction link of the beacon, passive array and active channel of the array antenna; (2)在地面完成辐射阵面形面精度校正和机械结构测量并记录表格A1；(2) Complete the radiation front surface accuracy correction and mechanical structure measurement on the ground and record Form A1; (3)在地面暗室完成有源通道配平和幅相一致性检查并分别记录表格为A2和A3；(3) Complete the active channel trim and amplitude-phase consistency check in the ground anechoic chamber and record the forms as A2 and A3 respectively; (4)依次改变各个通道移相器的不同位态，测量并记录对应的合成电场功率电平值；(4) Change the different positions of the phase shifters of each channel in turn, measure and record the corresponding synthetic electric field power level value; (5)采用抗噪声干扰的有源通道相位校准方法得到各个通道的相位校准值并记录表格；(5) Adopt the active channel phase calibration method of anti-noise interference to obtain the phase calibration value of each channel and record the table; (6)在地面幅相测量数据表A2和A3的基础上，计算得到各个通道的在轨补偿相位，实现相控阵天线在轨电性能校正；(6) On the basis of the ground amplitude and phase measurement data tables A2 and A3, the on-orbit compensation phase of each channel is calculated to realize the on-orbit electrical performance correction of the phased array antenna; (7)根据各有源通道的相位变化补偿值，获得在轨形变后阵列天线信标到各个阵面单元位置的物理长度变化值；(7) According to the phase change compensation value of each active channel, obtain the physical length change value of the array antenna beacon to the position of each front unit after the rail deformation; (8)通过地面结构测量数据表A1和在轨信标到各个单元的长度变化值，预测在轨变形后各个阵面单元位置可能的坐标位置；(8) Through the ground structure measurement data table A1 and the length change value of the on-orbit beacon to each unit, predict the possible coordinate position of each front unit position after the on-orbit deformation; (9)将阵面形变评估归结为阵面单元位置的最优化问题，构建形变优化模型和优化约束条件对阵元位置进行更新，从而在多次迭代优化求解得到阵元位置值，实现阵列天线的在轨形面误差评估。(9) The evaluation of the array deformation is attributed to the optimization problem of the position of the array element, and the deformation optimization model and optimization constraints are constructed to update the position of the array element, so as to obtain the position value of the array element in multiple iterative optimization solutions, and realize the optimization of the array antenna. Error evaluation on the orbital surface. 2.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(1)中阵列天线校正采取外校准方法，使一体化校正链路包含信标天线、无源阵面和有源通道。2. a kind of phased array antenna on-orbit correction and deformation evaluation method according to claim 1, is characterized in that, in step (1), array antenna correction adopts external calibration method, makes integrated correction link comprise beacon antenna , passive arrays and active channels. 3.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(1)中阵列天线信标采取宽波束振子天线，架设高度和位置满足阵列天线远场距离和一定的波束覆盖要求。3. a kind of phased array antenna on-orbit correction and deformation evaluation method according to claim 1, is characterized in that, in step (1), array antenna beacon adopts wide beam vibrator antenna, and erection height and position satisfy array antenna far away. Field distance and certain beam coverage requirements. 4.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(2)中阵列天线形面精度和机械结构测量在地面采取摄影测量方法实现。4 . The method for on-orbit correction and deformation evaluation of a phased array antenna according to claim 1 , wherein in step (2), the measurement of the shape and surface accuracy of the array antenna and the measurement of the mechanical structure is realized by photogrammetry on the ground. 5 . 5.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(3)中有源通道配平和幅相一致性检查采取REV旋转矢量法实现。5 . The method for on-orbit correction and deformation evaluation of a phased array antenna according to claim 1 , wherein, in step (3), the active channel trim and amplitude-phase consistency check are implemented by the REV rotation vector method. 6 . 6.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(4)中各个通道移相器的不同位态包括0°、90°、180°和270°四个状态。6. a kind of phased array antenna on-orbit correction and deformation evaluation method according to claim 1 is characterized in that, in step (4), the different positions of each channel phase shifter comprise 0°, 90°, 180° and 270° four states. 7.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(5)中，有源通道相位校准方法为：假设阵列天线有源通道1、2信号的幅度和相位分别为E1、φ1和E2、φ2，两个信号叠加的功率表示为
Figure FDA0003237520190000021
Δ为通道2移相器附加相位，此时，改变通道2的移相器相移值，7. a kind of phased array antenna on-orbit correction and deformation evaluation method according to claim 1, is characterized in that, in step (5), active channel phase calibration method is: suppose array antenna active channel 1,2 The amplitude and phase of the signals are E 1 , φ 1 and E 2 , φ 2 respectively, and the power of the superposition of the two signals is expressed as
Figure FDA0003237520190000021
Δ is the additional phase of the phase shifter of channel 2. At this time, change the phase shift value of the phase shifter of channel 2, 当Δ＝π/2时，此时信号合成功率
Figure FDA0003237520190000022
When Δ=π/2, the signal combined power
Figure FDA0003237520190000022
 当Δ＝3π/2时，此时信号合成功率
Figure FDA0003237520190000023
When Δ=3π/2, the signal synthesis power at this time
Figure FDA0003237520190000023
 当Δ＝0时，此时信号合成功率
Figure FDA0003237520190000024
When Δ=0, the signal combined power
Figure FDA0003237520190000024
 当Δ＝π时，此时信号合成功率
Figure FDA0003237520190000025
When Δ=π, the signal combined power
Figure FDA0003237520190000025
 其中，ε2为通道的平均噪声功率；Among them, ε 2 is the average noise power of the channel; 因此，在四个移相态下的信号功率电平测量后，计算可得出两通道的相位差为Therefore, after measuring the signal power levels in the four phase-shifted states, the calculation results in that the phase difference of the two channels is
Figure FDA0003237520190000026
Figure FDA0003237520190000026
 8.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，骤(6)中各个通道的在轨补偿相位计算方法为：8. a kind of phased array antenna on-orbit correction and deformation evaluation method according to claim 1 is characterized in that, the on-orbit compensation phase calculation method of each channel in step (6) is: 假设对于阵面中第mn个单元对应的有源通道i，其在地面的初始校准和预校准的相位值分别为φ0i和φ1i，在轨校准的相位测量值为φ2i，因此补偿相位值为Δφmn＝-φ0i+(φ2i-φ1i)。Assuming that for the active channel i corresponding to the mnth unit in the array, its initial calibration and pre-calibration phase values on the ground are φ 0i and φ 1i respectively, and the phase measurement value of on-orbit calibration is φ 2i , so the compensated phase The value is Δφ mn = -φ 0i +(φ 2i -φ 1i ). 9.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(7)中由各个通道的补偿相位获得阵面单元位置变化信息的计算方法为：9. a kind of phased array antenna on-orbit correction and deformation evaluation method according to claim 1, is characterized in that, in step (7), the calculation method that obtains array element position variation information by the compensation phase of each channel is: 若在地面完成阵列天线结构测量信息，信标天线位置为(xp,yp,zp)，与阵面中第mn个单元(xmn,ymn,zmn)的距离为
Figure FDA0003237520190000031
If the array antenna structure measurement information is completed on the ground, the position of the beacon antenna is (x p , y p , z p ), and the distance from the mn-th element (x mn , y mn , z mn ) in the array is
Figure FDA0003237520190000031
 当阵面在轨发生变形时，信标天线与阵面第mn个单元
Figure FDA0003237520190000032
的距离为
Figure FDA0003237520190000033
When the array is deformed on-orbit, the beacon antenna is connected to the mnth unit of the array.
Figure FDA0003237520190000032
The distance is
Figure FDA0003237520190000033
 因此，阵面变形导致阵面单元与信标距离变化为
Figure FDA0003237520190000034
其对应的补偿相位为
Figure FDA0003237520190000035
Therefore, the front deformation causes the distance between the front unit and the beacon to change as
Figure FDA0003237520190000034
The corresponding compensation phase is
Figure FDA0003237520190000035
 由此得到阵面变形后信标与阵面第mn个单元的距离变化为
Figure FDA0003237520190000036
Thus, the distance change between the beacon and the mnth unit of the front after the deformation of the front is obtained as
Figure FDA0003237520190000036
 10.根据权利要求9所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(8)中预评估的变形后阵元坐标位置表示为
Figure FDA0003237520190000037
10. A kind of phased array antenna on-orbit correction and deformation evaluation method according to claim 9, is characterized in that, the coordinate position of array element after pre-evaluation in step (8) is expressed as
Figure FDA0003237520190000037
 11.根据权利要求1所述的一种相控阵天线在轨校正与形变评估方法，其特征在于，步骤(9)中阵面单元位置的最优化问题，求解该优化模型可采用遗传算法：11. a kind of phased array antenna on-orbit correction and deformation evaluation method according to claim 1, is characterized in that, in step (9), the optimization problem of front unit position, solves this optimization model and can adopt genetic algorithm:
Figure FDA0003237520190000041
Figure FDA0003237520190000041
 s.t.s.t.
Figure FDA0003237520190000042
Figure FDA0003237520190000042
Figure FDA0003237520190000043
Figure FDA0003237520190000043
Figure FDA0003237520190000044
Figure FDA0003237520190000044
 Δφmn＝-φ0i+(φ2i-φ1i)Δφ mn = -φ 0i +(φ 2i -φ 1i ) f(xmn,ymn,zmn)＝f0 f(x mn , y mn , z mn )=f 0 其中，argmin表示求解最小值；f(xmn,ymn,zmn)＝f0为阵面在轨结构变形后满足的已知其他模型。Among them, argmin represents the minimum value to be solved; f(x mn , y mn , z mn )=f 0 is the known other model that the front satisfies after the deformation of the orbit structure.
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