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CN113486550B - A method for determining triplet feed coefficients in hardware-in-the-loop radio frequency simulation - Google Patents

A method for determining triplet feed coefficients in hardware-in-the-loop radio frequency simulation Download PDF

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CN113486550B
CN113486550B CN202110701578.XA CN202110701578A CN113486550B CN 113486550 B CN113486550 B CN 113486550B CN 202110701578 A CN202110701578 A CN 202110701578A CN 113486550 B CN113486550 B CN 113486550B
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唐波
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Abstract

本发明提供一种半实物射频仿真中的三元组馈电系数确定方法，属于半实物射频仿真技术领域。所述方法包括：对仿真场景建立数学坐标系；根据建立的仿真场景的数学坐标系，建立仿真中导引头天线口面上的场蕴含的方位信息等效性方程；根据建立的位信息等效性方程，推导出三元组仿真的非线性插值方程，以代替幅度重心公式；根据推导出的三元组仿真的非线性插值方程，确定半实物射频仿真三元组的馈电系数。采用本发明，能够精确和快速地确定半实物射频仿真中三元组的馈电系数。

Figure 202110701578

The invention provides a method for determining a triad feed coefficient in a semi-physical radio frequency simulation, and belongs to the technical field of semi-physical radio frequency simulation. The method includes: establishing a mathematical coordinate system for the simulation scene; according to the established mathematical coordinate system of the simulation scene, establishing an equivalence equation of azimuth information contained in the field on the antenna surface of the seeker antenna in the simulation; according to the established position information, etc. Based on the effectiveness equation, the nonlinear interpolation equation of triplet simulation is derived to replace the formula of amplitude center of gravity; according to the derived nonlinear interpolation equation of triplet simulation, the feeding coefficient of triplet for half-in-the-loop RF simulation is determined. By adopting the invention, the feeding coefficient of the triplet in the semi-physical radio frequency simulation can be accurately and quickly determined.

Figure 202110701578

Description

Triplet feed coefficient determination method in semi-physical radio frequency simulation
Technical Field
The invention relates to the technical field of semi-physical radio frequency simulation, in particular to a method for determining a triplet feed coefficient in semi-physical radio frequency simulation.
Background
In recent years, simulation and test are indispensable links in the development process of modern electronic systems. The field test can obtain the most realistic relevant performance parameters of the electronic system to be tested, and find out some possible problems, and has the highest experimental value. However, the outfield test is generally complicated, involves many aspects, and is thus expensive. In order to better improve the cost performance, a semi-physical radio frequency simulation is often required to be carried out in a microwave darkroom before an external field test is carried out on an electronic system such as a guide head. The semi-physical radio frequency simulation is also called physical in-loop simulation, namely, in a simulation loop, the seeker to be tested exists in physical form and in actual working state. The semi-physical radio frequency simulation has the simulation physical introduced into the simulation loop, so that the simulation result is very similar to the outfield test. However, the cost is greatly reduced. Therefore, the method has higher cost performance. Therefore, the semi-physical radio frequency simulation plays an important role in the research and development of electronic systems such as a guide head, and the semi-physical radio frequency simulation system has become an essential research and development equipment in some countries.
The semi-physical radio frequency simulation system is generally composed of a radiation array, a turntable, a computer control system and the like. In a microwave darkroom, there is a relatively large antenna array on which a plurality of radiating elements are arranged in order. The outer edge of the array surface is generally circular, regular hexagonal or rectangular, etc. The antennas are generally aligned in a regular pattern, and adjacent antennas are generally triangular. The whole antenna array surface faces one turntable, and electronic systems such as a guide head to be tested and the like can be arranged on the turntable. When the semi-physical radio frequency simulation experiment is carried out, every adjacent three radiating units can form a triplet so as to simulate the echo of the point target to be simulated in the triplet triangle. This Triple (TUA) structure was proposed earlier by boeing, and has been adopted by semi-physical radio frequency simulation laboratories in various countries and regions of the world. The three radiating elements of the triplet generally form a regular triangle. The rationality is that better unit utilization can be obtained. The three radiating units can feed simultaneously, electromagnetic waves radiated by the three radiating units are overlapped at the guide head, and the energy flow direction of a composite field at the guide head is exactly the same as the echo energy flow direction of a target of a point to be simulated in real environment space at the guide head. The energy flow direction of the synthesized field is a function of the feed amplitude of the three radiating elements, so that the synthesized electromagnetic energy flow direction can be adjusted and changed by adjusting the feed amplitude of the three radiating elements, thereby achieving the purpose of simulating echoes of point targets in different directions at different moments. On the basis, the simulation of the radio frequency environment under the whole ballistic motion is realized.
In triplet simulation, there is always an important problem, namely the triplet near field effect. Because there is an important formula in the feed coefficient calculation of the triplet, the amplitude center of gravity formula. The formula may represent the direction of the point target at the simulation as a linear combination of the directions of the three radiating elements of the triplet. This is in and out of the actual simulated non-punctuation direction, which is the triplet near field error. The existing method for solving the triplet near field error generally comprises an iteration method and a fitting method. The simulated angle error is obtained by experimental measurements or strict electromagnetic calculations, with which the change of the feed coefficient (which is proportional to the feed amplitude) is driven, so that the simulated angle error is reduced to an acceptable level by iteration, which is used because no strict analytical function expression between the feed coefficient and the simulated direction is obtained. In addition, existing triplet near field correction techniques do not take into account the effects of seeker spin.
Thus, the disadvantages of the prior art are mainly: the feed coefficient of the triplet in the semi-physical radio frequency simulation cannot be rapidly determined, and the universality is poor.
Disclosure of Invention
The embodiment of the invention provides a method for determining the feed coefficient of a triplet in semi-physical radio frequency simulation, which can accurately and rapidly determine the feed coefficient of the triplet in the semi-physical radio frequency simulation. The technical scheme is as follows:
the embodiment of the invention provides a method for determining a triplet feed coefficient in semi-physical radio frequency simulation, which comprises the following steps:
establishing a mathematical coordinate system for the simulation scene;
establishing an azimuth information equivalence equation contained in a field on the port surface of the guide head antenna in simulation according to the established mathematical coordinate system of the simulation scene;
deducing a nonlinear interpolation equation of the triplet simulation according to the established bit information equivalence equation to replace an amplitude gravity center formula;
and determining the feed coefficient of the semi-physical radio frequency simulation triplet according to the derived nonlinear interpolation equation of the triplet simulation.
Further, the establishing a mathematical coordinate system for the simulation scene includes:
establishing an xyz rectangular coordinate system by taking the center point of the antenna port surface of the seeker as a coordinate origin O, wherein two orthogonal base line directions of the antenna array of the seeker are respectively the x direction and the y direction by taking the antenna port surface of the seeker as the xy surface, and the ith spoke in the tripletThe coordinates of the shooting unit are (x i ,y i ,z i )，z i >>x i ,y i I=1, 2,3, the coordinates of the point object are (x, y, z), z>>x, y, the offset angle of the point target and the ith radiating element in the triplet with respect to the z-axis in the x-direction and the y-direction is:
Figure BDA0003129918970000031
Figure BDA0003129918970000032
Figure BDA0003129918970000033
Figure BDA0003129918970000034
wherein, psi is x 、ψ y The offset angles, ψ, of the point target in the x-direction and y-direction, respectively, relative to the z-axis xi 、ψ yi The offset angles of the ith radiating element of the triplet in the x-direction and the y-direction relative to the z-axis respectively, asin (·) representing an arcsine function;
the position of the turntable is taken as an origin, and the directions of the x axis and the y axis are respectively psi x Shaft, psi y The direction of the axis and takes the central point P of the triplet as a pole, and is parallel to the psi x The direction is the polar axis direction, and the polar angle of the ith radiation unit in the triplet is denoted as alpha i The polar angle of the point target is alpha, and the polar diameter is psi r Triplet edge length opening angle is psi l The angular domain distance from each radiation unit to the P point is
Figure BDA0003129918970000035
Further, the establishing the azimuth information equivalence equation of the field on the opening surface of the guide head antenna in the simulation according to the established mathematical coordinate system of the simulation scene comprises the following steps:
assuming four antenna units on the aperture surface of the seeker, the seeker has different equivalent phase center points, wherein two antenna units form an interferometer in the x direction, the other two antenna units form an interferometer in the y direction, and the interference base line lengths in the x direction and the y direction are L respectively x 、L y ；
Calibrating the phase of each radiation unit of the triplet according to the distance from each radiation unit to the original point O, so that the fields of each radiation unit at the point O are in phase;
if the antennas 2 and 4 are in the x direction, the radiation fields of the three radiation units of the triplets received by the antennas 2 and 4 are respectively:
Figure BDA0003129918970000036
wherein A is a constant coefficient, j in exp (·) is an imaginary unit, s 2 、s 4 Representing the radiation fields of three radiation units of the triplets received by the antennas 2 and 4, C i The feed coefficient of the ith radiating element, k is the wave vector, k is the wave number, r i0 Vector line segment from the ith radiation unit of the triplet to the origin point O, r ij Vector line segments from the ith element to the jth antenna of the triplet;
the radiation fields of the point targets received by the antennas 2 and 4 are respectively:
Figure BDA0003129918970000041
Figure BDA0003129918970000042
wherein s is t2 、s t4 Radiation fields r representing the point targets received by the antennas 2, 4, respectively t0 Vector line segment from point target to point of origin O, r tj For the point target to the j th dayVector line segments of the line;
according to the fact that the azimuth information is contained in the phase information, and the phase information of the field on the antenna port surface of the receiving antenna in the simulation environment is equal to the phase information of the antenna port surface field in the actual environment, the method comprises the following steps of:
Figure BDA0003129918970000043
wherein arg (. Cndot.) represents the principal value of the argument.
Further, deriving a non-linear interpolation equation of the triplet simulation according to the established bit information equivalence equation to replace the amplitude barycenter equation comprises:
for a pair of
Figure BDA0003129918970000044
Solving to obtain a nonlinear interpolation equation:
Figure BDA0003129918970000045
by using the approximation of sin function under small angle, the method obtains
Figure BDA0003129918970000046
Expression in polar coordinate system:
Figure BDA0003129918970000047
and similarly, obtaining:
Figure BDA0003129918970000048
further, the determining the feed coefficient of the semi-physical radio frequency simulation triplet according to the derived nonlinear interpolation equation of the triplet simulation comprises:
according to
Figure BDA0003129918970000049
Is->
Figure BDA00031299189700000410
Obtaining an analytic expression of the feed coefficient;
and according to the analysis expression of the feeding coefficient, the feeding coefficient of the semi-physical radio frequency simulation triplet avoiding the near field error of the triplet is obtained.
Further, the analytical expression of the feed coefficient is:
Figure BDA0003129918970000051
further, after determining the feed coefficient of the semi-physical radio frequency simulation triplet according to the derived triplet simulated nonlinear interpolation equation, the method further comprises:
and determining the optimal estimation of the analysis expression result of the feed coefficient when the spin gesture of the seeker is unknown, and obtaining the optimal estimation value of the feed coefficient when the spin gesture of the seeker is unknown.
Further, the determining the optimal estimation of the analysis expression result of the feed coefficient when the spin gesture of the seeker is unknown, and obtaining the optimal estimation value of the feed coefficient when the spin gesture of the seeker is unknown includes:
let L x ＝L y Record kL x /2＝kL y And (2) carrying out mathematical expectation on random distribution of spin postures of the seeker by using the analysis expression result of the feed coefficient to obtain that the spin postures of the seeker are in [0,2 pi ]]C when uniformly distributed in i Is a mathematical expectation of:
Figure BDA0003129918970000052
wherein Γ is a shorthand symbol,
Figure BDA0003129918970000053
is algebraic quantityExpressed as:
Figure BDA0003129918970000054
wherein,,
Figure BDA0003129918970000055
the best estimate of the feed coefficient when the seeker spin attitude is unknown is represented.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
1. when the gesture of the seeker is known, the feeding coefficient avoiding the triplet near field error can be obtained;
2. when the gesture of the seeker is unknown, an optimal feed coefficient estimated value can be obtained;
3. the method for improving the three-tuple feed coefficient in the semi-physical radio frequency simulation provides a quicker and more effective three-tuple feed coefficient method for better improving the semi-physical radio frequency simulation precision, and can accurately and quickly determine the feed coefficient of the three-tuple in the semi-physical radio frequency simulation.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for determining a triplet feed coefficient in semi-physical radio frequency simulation according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a simulation scene coordinate provided in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a two-dimensional angular domain coordinate system according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a director head plane antenna according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, an embodiment of the present invention provides a method for determining a triplet feed coefficient in a semi-physical radio frequency simulation, including:
s101, establishing a mathematical coordinate system for a simulation scene;
s102, establishing an azimuth information equivalence equation contained in a field on the port surface of a pilot head antenna in simulation according to a mathematical coordinate system of the established simulation scene;
s103, deducing a nonlinear interpolation equation of the triplet simulation according to the established bit information equivalence equation to replace an amplitude gravity center formula;
s104, determining the feed coefficient of the semi-physical radio frequency simulation triplet according to the deduced nonlinear interpolation equation of the triplet simulation.
The method for determining the triple feed coefficient in the semi-physical radio frequency simulation establishes a mathematical coordinate system for a simulation scene; establishing an azimuth information equivalence equation contained in a field on the port surface of the guide head antenna in simulation according to the established mathematical coordinate system of the simulation scene; deducing a nonlinear interpolation equation of the triplet simulation according to the established bit information equivalence equation to replace an amplitude gravity center formula; and determining the feed coefficient of the semi-physical radio frequency simulation triplet according to the derived nonlinear interpolation equation of the triplet simulation. Therefore, the feeding coefficient of the triplet in the semi-physical radio frequency simulation can be accurately and rapidly determined, and the obtained feeding coefficient is the feeding coefficient avoiding the near field error of the triplet, so that the influence of the near field error of the triplet can be overcome, and the accuracy requirement of the semi-physical radio frequency simulation test can be met.
In a specific embodiment of the method for determining a triplet feed coefficient in a semi-physical radio frequency simulation, the establishing a mathematical coordinate system for a simulation scene further includes:
establishing an xyz rectangular coordinate system by taking the center point of the antenna port surface of the seeker as a coordinate origin O, wherein two orthogonal bases of the antenna array of the seeker are taken as xy surfaces by taking the antenna port surface of the seekerThe line directions are the x direction and the y direction respectively, and the coordinate of the ith radiating element in the triplet is (x i ,y i ,z i )，z i >>x i ,y i I=1, 2,3, the coordinates of the point object are (x, y, z), z>>x, y, the offset angle of the point target and the ith radiating element in the triplet with respect to the z-axis in the x-direction and the y-direction is:
Figure BDA0003129918970000061
Figure BDA0003129918970000071
Figure BDA0003129918970000072
Figure BDA0003129918970000073
wherein, psi is x 、ψ y The offset angles, ψ, of the point target in the x-direction and y-direction, respectively, relative to the z-axis x 、ψ y The direction in which the point target is located is indicated as shown in fig. 2; psi phi type xi 、ψ yi Offset angles, ψ, of the ith radiating element of the triplet in x-direction, y-direction, respectively, relative to the z-axis xi 、ψ yi Indicating the direction in which each radiating element of the triplet is located, asin (·) representing an arcsine function;
let psi be examined x 、ψ y The plane of the angle domain takes the position of the turntable as the origin and takes the directions of the x axis and the y axis as psi respectively x Shaft, psi y The direction of the axis and takes the central point P of the triplet as a pole, and is parallel to the psi x The direction is the polar axis direction, and the polar angle of the ith radiation unit in the triplet is denoted as alpha i The polar angle of the point target is alpha, and the polar diameter is psi r Triplet edge length opening angle is psi l The angular domain distance from each radiation unit to the P point is
Figure BDA0003129918970000074
As shown in fig. 3.
In a specific embodiment of the method for determining a triplet feed coefficient in semi-physical radio frequency simulation, further, the establishing an azimuth information equivalence equation of field implications on an antenna port surface of a pilot head in simulation according to an established mathematical coordinate system of a simulation scene includes:
assuming four antenna units on the aperture surface of the seeker, the seeker has different equivalent phase center points, wherein two antenna units form an interferometer in the x direction, the other two antenna units form an interferometer in the y direction, and the interference base line lengths in the x direction and the y direction are L respectively x 、L y As shown in fig. 4;
calibrating the phase of each radiation unit of the triplet according to the distance from each radiation unit to the original point O, so that the fields (specifically, radiation fields) of each radiation unit at the point O are in phase; wherein each radiation unit in the triplet is in the far field of the caliber of the seeker;
if the antennas 2 and 4 are in the x direction, the radiation fields of the three radiation units of the triplets received by the antennas 2 and 4 are respectively:
Figure BDA0003129918970000075
Figure BDA0003129918970000076
wherein A is a constant coefficient, j in exp (·) is an imaginary unit, s 2 、s 4 Representing the radiation fields of three radiation units of the triplets received by the antennas 2 and 4, C i The feed coefficient of the ith radiating element (which is proportional to the feed amplitude), k is the wave vector, k is the wave number, r i0 Vector line segment from the ith radiation unit of the triplet to the origin point O, r ij Vector line segment from the ith element to the jth antenna of the triplet；
The radiation fields of the point targets received by the antennas 2 and 4 are respectively:
Figure BDA0003129918970000081
Figure BDA0003129918970000082
wherein s is t2 、s t4 Radiation fields r representing the point targets received by the antennas 2, 4, respectively t0 Vector line segment from point target to point of origin O, r tj Vector line segment from point target to j-th antenna;
according to the fact that the azimuth information is contained in the phase information, and the phase information of the field on the antenna port surface of the receiving antenna in the simulation environment is equal to the phase information of the antenna port surface field in the actual environment, the method comprises the following steps of:
Figure BDA0003129918970000083
wherein arg (. Cndot.) represents the principal value of the argument.
In a specific embodiment of the foregoing method for determining a triplet feed coefficient in a semi-physical radio frequency simulation, further, deriving a nonlinear interpolation equation of the triplet simulation according to the established bit information equivalence equation, to replace the amplitude barycenter equation includes:
for formula (9):
Figure BDA0003129918970000084
solving to obtain a nonlinear interpolation equation:
Figure BDA0003129918970000085
by using the approximation of sin function under small angle, the method obtains
Figure BDA0003129918970000086
The expression under the polar coordinate system of fig. 3:
Figure BDA0003129918970000087
and similarly, obtaining:
Figure BDA0003129918970000088
wherein the small angle is an angle smaller than a preset threshold.
In a specific embodiment of the foregoing method for determining a feeding coefficient of a triplet in a semi-physical radio frequency simulation, further, determining a feeding coefficient of a semi-physical radio frequency simulation triplet according to a derived nonlinear interpolation equation of the triplet simulation includes:
from equations (11) and (12), the analytical expression for the feed coefficient is obtained as:
Figure BDA0003129918970000091
parameters k, L x .L y ,ψ s ,ψ r ,α,α i Substituting into the formula (13), the feed coefficient of the triplet in the semi-physical radio frequency simulation, which avoids the near field error of the triplet, can be obtained.
In a specific embodiment of the method for determining a triplet feed coefficient in a semi-physical radio frequency simulation, further, after determining a feed coefficient of a semi-physical radio frequency simulation triplet according to a derived nonlinear interpolation equation of the triplet simulation, the method further includes:
determining the seeker spin attitude is unknown (i.e., α i Unknown) and obtaining an optimal estimated value of the feed coefficient when the spin attitude of the seeker is unknown, wherein the method specifically comprises the following steps of:
let L x ＝L y Record kL x /2＝kL y Using the result of equation (13) to make mathematical expectation on random distribution of the spin gesture of the seeker, the spin gesture of the seeker is obtained when [0,2 pi ]]C when uniformly distributed in i Is a mathematical expectation of:
Figure BDA0003129918970000092
wherein Γ is a shorthand symbol,
Figure BDA0003129918970000093
the number of generations, expressed as:
Figure BDA0003129918970000094
parameters k, L x .L y ,ψ s ,ψ r ,α-α i Substituting into the blocks (14) and (15) to calculate to obtain the spin gesture of the seeker as [0,2 pi ]]C when uniformly distributed in i Mathematical expectation of (a)
Figure BDA0003129918970000095
Namely: the best estimate of the feed coefficient when the seeker spin attitude is unknown.
In the present embodiment, although alpha, alpha i Is unknown, but alpha-alpha i Is known and unchanged.
In the present embodiment, when the seeker posture is unknown, the optimum feed coefficient estimation value can be obtained according to the equations (14), (15).
In summary, aiming at the problems of more iteration times, poor universality and the like, the embodiment of the invention provides a method for determining the triplet feed coefficient in semi-physical radio frequency simulation, which at least has the following advantages:
1. when the gesture of the seeker is known, the feeding coefficient avoiding the triplet near field error can be obtained;
2. when the gesture of the seeker is unknown, an optimal feed coefficient estimated value can be obtained;
3. the method for improving the three-tuple feed coefficient in the semi-physical radio frequency simulation provides a quicker and more effective three-tuple feed coefficient method for better improving the semi-physical radio frequency simulation precision, and can accurately and quickly determine the feed coefficient of the three-tuple in the semi-physical radio frequency simulation.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims (6)

1.一种半实物射频仿真中的三元组馈电系数确定方法，其特征在于，包括：1. a method for determining triplet feed coefficients in a hardware-in-the-loop radio frequency simulation, is characterized in that, comprising: 对仿真场景建立数学坐标系；Establish a mathematical coordinate system for the simulation scene; 根据建立的仿真场景的数学坐标系，建立仿真中导引头天线口面上的场蕴含的方位信息等效性方程；According to the established mathematical coordinate system of the simulation scene, the equivalence equation of the azimuth information contained in the field on the seeker antenna surface in the simulation is established; 根据建立的位信息等效性方程，推导出三元组仿真的非线性插值方程，以代替幅度重心公式；Based on the established equivalence equation of bit information, a nonlinear interpolation equation for triplet simulation is derived to replace the amplitude center of gravity formula; 根据推导出的三元组仿真的非线性插值方程，确定半实物射频仿真三元组的馈电系数；According to the derived non-linear interpolation equation of triplet simulation, determine the feeding coefficient of triplet for hardware-in-the-loop RF simulation; 其中，所述对仿真场景建立数学坐标系包括：Wherein, the establishment of a mathematical coordinate system for the simulation scene includes: 以导引头的天线口面中心点为坐标原点O，建立xyz直角坐标系，其中，以导引头的天线口面为xy面，导引头天线阵列的两个正交的基线方向分别为x方向和y方向，三元组中第i个辐射单元的坐标为(xi,yi,zi)，zi>>xi,yi，i＝1,2,3，点目标的坐标为(x,y,z)，z>>x,y，则点目标及三元组中第i个辐射单元在x方向、y方向上相对于z轴的偏移角度为：Taking the center point of the seeker’s antenna mouth as the coordinate origin O, an xyz rectangular coordinate system is established, where the seeker’s antenna mouth is the xy plane, and the two orthogonal baseline directions of the seeker’s antenna array are respectively In the x direction and y direction, the coordinates of the i-th radiation unit in the triplet are (x i , y i , z i ), z i >> x i , y i , i=1, 2, 3, the coordinates of the point target The coordinates are (x, y, z), z>>x, y, then the offset angle of the point target and the i-th radiation unit in the triplet in the x direction and y direction relative to the z axis is:
Figure FDA0004269880670000011
Figure FDA0004269880670000011
Figure FDA0004269880670000012
Figure FDA0004269880670000012
Figure FDA0004269880670000013
Figure FDA0004269880670000013
Figure FDA0004269880670000014
Figure FDA0004269880670000014
 其中，ψx、ψy分别为点目标在x方向、y方向上相对于z轴的偏移角度，ψxi、ψyi分别为三元组的第i个辐射单元在x方向、y方向上相对于z轴的偏移角度，asin(·)表示反正弦函数；Among them, ψ x , ψ y are the offset angles of the point target in the x-direction and y-direction relative to the z-axis, respectively, ψ xi , ψ yi are the i-th radiation unit of the triplet in the x-direction and y-direction Relative to the offset angle of the z-axis, asin(·) represents the arc sine function; 以转台位置为原点，以x、y轴方向分别为ψx轴、ψy轴的方向，并以三元组的中心点P为极点，平行于ψx方向为极轴方向，记三元组中第i个辐射单元的极角为αi，点目标的极角为α，极径为ψr，三元组边长张角为ψl，各辐射单元到P点的角域距离为
Figure FDA0004269880670000021
Take the position of the turntable as the origin, take the directions of the x and y axes as the directions of the ψ x- axis and ψ y- axis respectively, and take the center point P of the triplet as the pole, and take the direction of the polar axis parallel to the ψx direction as the direction of the triplet. The polar angle of the i-th radiating unit is α i , the polar angle of the point target is α, the polar radius is ψ r , the side length of the triad is ψ l , and the angular domain distance from each radiating unit to point P is
Figure FDA0004269880670000021
 其中，所述根据建立的仿真场景的数学坐标系，建立仿真中导引头天线口面上的场蕴含的方位信息等效性方程包括：Wherein, according to the mathematical coordinate system of the established simulation scene, the establishment of the orientation information equivalence equation contained in the field on the seeker antenna mouth surface in the simulation includes: 假设导引头口径面上有四个天线单元，具有不同的等效相位中心点，其中两幅天线单元在x方向上构成一幅干涉仪，另外两幅天线单元在y方向上构成一幅干涉仪，x方向、y方向上的干涉基线长度分别为Lx、Ly；Assuming that there are four antenna elements on the seeker aperture surface with different equivalent phase centers, two of the antenna elements form an interferometer in the x direction, and the other two antenna elements form an interferometer in the y direction instrument, the lengths of the interference baselines in the x direction and the y direction are L x and L y respectively; 将三元组各辐射单元的相位依各辐射单元到原点O点的距离进行校准，使得各辐射单元在O点的场同相位；Calibrate the phase of each radiating unit of the triplet according to the distance from each radiating unit to the origin point O, so that the field of each radiating unit at the O point has the same phase; 若天线2和天线4在x方向上，则天线2和天线4接收到的三元组三个辐射单元的辐射场分别为：If antenna 2 and antenna 4 are in the x direction, the radiation fields of the three radiating elements received by antenna 2 and antenna 4 are respectively:
Figure FDA0004269880670000022
Figure FDA0004269880670000022
 其中，A为常数系数，exp(·)里的j为虚数单位，s2、s4分别表示天线2、天线4接收到的三元组三个辐射单元的辐射场，Ci为第i个辐射单元的馈电系数，k为波矢量，k为波数，ri0为三元组第i个辐射单元到原点O点的矢量线段，rij为三元组第i个单元到第j个天线的矢量线段；Among them, A is a constant coefficient, j in exp(·) is an imaginary number unit, s 2 and s 4 respectively represent the radiation fields of the three radiating elements received by antenna 2 and antenna 4, and C i is the i-th The feeding coefficient of the radiating element, k is the wave vector, k is the wave number, r i0 is the vector line segment from the i-th radiating element of the triplet to the origin O, r ij is the i-th element of the triplet to the j-th antenna The vector line segment of 天线2和天线4接收到的点目标的辐射场分别为：The radiation fields of the point targets received by antenna 2 and antenna 4 are respectively:
Figure FDA0004269880670000023
Figure FDA0004269880670000023
Figure FDA0004269880670000024
Figure FDA0004269880670000024
 其中，st2、st4分别表示天线2、天线4接收到的点目标的辐射场，rt0为点目标到原点O点的矢量线段，rtj为点目标到第j个天线的矢量线段；Among them, st2 and st4 respectively represent the radiation field of the point target received by antenna 2 and antenna 4, r t0 is the vector line segment from the point target to the origin point O, and rtj is the vector line segment from the point target to the jth antenna; 根据方位信息蕴含在相位信息中，且仿真环境下的接收天线口面上的场的相位信息等于实际环境下的天线口面场的相位信息，得到：According to the azimuth information contained in the phase information, and the phase information of the field on the face of the receiving antenna in the simulation environment is equal to the phase information of the field on the face of the antenna in the actual environment, we get:
Figure FDA0004269880670000031
Figure FDA0004269880670000031
 其中，arg(·)表示辐角主值。Among them, arg( ) represents the main value of argument. 2.根据权利要求1所述的半实物射频仿真中的三元组馈电系数确定方法，其特征在于，所述根据建立的位信息等效性方程，推导出三元组仿真的非线性插值方程，以代替幅度重心公式包括：2. the method for determining triplet feed coefficient in the hardware-in-the-loop radio frequency simulation according to claim 1, is characterized in that, described according to the bit information equivalence equation of establishment, derives the non-linear interpolation value of triplet simulation Equations, instead of magnitude centroid formulas include: 对
Figure FDA0004269880670000032
进行求解，得到非线性插值方程：right
Figure FDA0004269880670000032
Solve to obtain the nonlinear interpolation equation:
Figure FDA0004269880670000033
Figure FDA0004269880670000033
 利用sin函数在小角度下的近似性，得到
Figure FDA0004269880670000034
在极坐标系下的表达式：Using the approximation of the sin function at small angles, we get
Figure FDA0004269880670000034
Expression in polar coordinates:
Figure FDA0004269880670000035
Figure FDA0004269880670000035
 同理，得到：Similarly, get:
Figure FDA0004269880670000036
Figure FDA0004269880670000036
 3.根据权利要求2所述的半实物射频仿真中的三元组馈电系数确定方法，其特征在于，所述根据推导出的三元组仿真的非线性插值方程，确定半实物射频仿真三元组的馈电系数包括：3. according to the method for determining the triad feed coefficient in the half-in-the-loop radio frequency simulation according to claim 2, it is characterized in that, described according to the non-linear interpolation equation of the triple group simulation of derivation, determine half-in-the-loop radio frequency simulation three The tuple of feed coefficients includes: 根据
Figure FDA0004269880670000037
及/>
Figure FDA0004269880670000038
得到馈电系数的解析表达式；according to
Figure FDA0004269880670000037
and />
Figure FDA0004269880670000038
The analytical expression of the feed coefficient is obtained; 根据得到的馈电系数的解析表达式，得到避免了三元组近场误差的半实物射频仿真三元组的馈电系数。According to the obtained analytical expression of the feed coefficient, the feed coefficient of the semi-physical RF simulation triplet that avoids the near-field error of the triplet is obtained. 4.根据权利要求3所述的半实物射频仿真中的三元组馈电系数确定方法，其特征在于，馈电系数的解析表达式为：4. the method for determining triplet feed coefficient in the hardware-in-the-loop radio frequency simulation according to claim 3, is characterized in that, the analytical expression of feed coefficient is:
Figure FDA0004269880670000041
Figure FDA0004269880670000041
 5.根据权利要求4所述的半实物射频仿真中的三元组馈电系数确定方法，其特征在于，在根据推导出的三元组仿真的非线性插值方程，确定半实物射频仿真三元组的馈电系数之后，所述方法还包括：5. the method for determining triplet feed coefficients in the half-in-the-loop radio frequency simulation according to claim 4 is characterized in that, according to the non-linear interpolation equation of the triplet simulation of derivation, determine the triplet of half-in-the-loop radio frequency simulation After the feed coefficients of the set, the method further includes: 确定导引头自旋姿态未知时所述馈电系数的解析表达式结果的最佳估计，得到导引头自旋姿态未知时馈电系数的最佳估计值。The best estimate of the analytical expression result of the feed coefficient is determined when the spin attitude of the seeker is unknown, and the best estimate value of the feed coefficient is obtained when the spin attitude of the seeker is unknown. 6.根据权利要求5所述的半实物射频仿真中的三元组馈电系数确定方法，其特征在于，所述确定导引头自旋姿态未知时所述馈电系数的解析表达式结果的最佳估计，得到导引头自旋姿态未知时馈电系数的最佳估计值包括：6. the method for determining the triplet feed coefficient in the hardware-in-the-loop radio frequency simulation according to claim 5, is characterized in that, the analytical expression result of the feed coefficient when the described determination seeker spin attitude is unknown The best estimate, to get the best estimate of the feed coefficient when the spin attitude of the seeker is unknown includes: 令Lx＝Ly，记kLx/2＝kLy/2＝Γ，利用所述馈电系数的解析表达式结果对导引头自旋姿态的随机分布做数学期望，得到当导引头的自旋姿态在[0,2π]内均匀分布时的Ci的数学期望：Let L x =L y , record kL x /2=kL y /2=Γ, use the result of the analytical expression of the feed coefficient to make a mathematical expectation on the random distribution of the spin attitude of the seeker, and obtain when the seeker The mathematical expectation of C i when the spin attitude of is uniformly distributed in [0,2π]:
Figure FDA0004269880670000042
Figure FDA0004269880670000042
 其中，Γ为简记符号，
Figure FDA0004269880670000043
为代数量，表示为：Among them, Γ is a shorthand symbol,
Figure FDA0004269880670000043
is an algebraic quantity, expressed as:
Figure FDA0004269880670000044
Figure FDA0004269880670000044
 其中，
Figure FDA0004269880670000045
表示导引头自旋姿态未知时馈电系数的最佳估计值。in,
Figure FDA0004269880670000045
Indicates the best estimate of the feed coefficient when the spin attitude of the seeker is unknown.
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