Method for measuring an antenna pattern of an antenna on a first flying object by means of a second flying object

Abstract

The invention relates to a method for measuring an antenna pattern (AP) of an antenna (1) on a first flying object (RSS) by means of a second flying object (MES), wherein the first flying object (RSS) moves in orbit along a first elliptical path (EB1) around a celestial body (100) and the second flying object (MES) moves in orbit along a second elliptical path (E2) around the celestial body (100), wherein during the movement of the first and second flying objects (RSS, MES), the antenna (1) emits antenna radiation along a main beam direction (HS) and / or receives antenna radiation from the second flying object (MES), wherein the main beam direction (HS) has a predetermined lateral viewing angle (θoff), which is an angle of rotation equal to or unequal to zero about the direction of movement of the first flying object (RSS) relative to the direction to the centre (M) of the celestial body (100), wherein signal values (SV) of the antenna (1) are obtained by means of the second flying object (MES) and at least a part of the antenna pattern (AP) is determined therefrom. In the method according to the invention, the first elliptical path (EB1) and the second elliptical path (EB2) are adjusted relative to each other in such a way that the signal values (SV) obtained during one revolution belong to a fixed predetermined azimuth angle (ξcut) and different polar angles (ψ) with respect to the antenna (1), wherein the predetermined azimuth angle (ξcut) represents an angle of rotation about the main beam direction (HS) and the different polar angles (ψ) represent angles of inclination relative to the main beam direction (HS).

Description

[0001]P2972PC00 German Aerospace Center e. V. Königswinterer Str.522-524 53227 Bonn ____________________________________________________________________ Method for measuring an antenna pattern of an antenna on a first flying object using a second flying object ____________________________________________________________________ Description The invention relates to a method for measuring an antenna pattern of an antenna on a first flying object using a second flying object. In the context of remote sensing of a celestial body (such as the Earth's surface) using a radar system, it is necessary to have precise knowledge of the corresponding antenna pattern of the radar antenna used. For this purpose, the antenna pattern must be measured.This also applies to communications and navigation systems and generally to systems in space that operate with antenna signals in the radar wave frequency range or in another frequency range. It is known from the state of the art to determine the antenna pattern of an antenna on the ground before the antenna is deployed in orbit. However, this poses the problem that the antenna pattern of the antenna in orbit can change compared to the state before the antenna was deployed into orbit P2972PC00 and continues to change over time thereafter, so that the antenna pattern should be re-measured at regular intervals even while the antenna is in orbit. To determine the antenna pattern of a radar antenna in orbit, it is known to measure signal values ​​of the antenna pattern based on calibration targets with a known structure and position on the Earth's surface.However, this procedure is very complex, and only antenna patterns in predetermined directions can be recorded. A comprehensive measurement of the antenna pattern in all spatial directions is not possible. The object of the invention is to measure an antenna pattern of an antenna in orbit in a novel way. This object is achieved by the method according to patent claim 1. Further developments of the invention are defined in the dependent claims. The method according to the invention serves to measure an antenna pattern of an antenna on a first flying object by means of a second flying object. In a preferred embodiment, the antenna is a radar antenna; however, the antenna pattern of another antenna can also be measured.The first flying object moves in orbit along a first elliptical path around a celestial body, whereas the second flying object moves in orbit along a second elliptical path around the celestial body. Preferably, the first flying object and the second flying object are satellites. The celestial body can be any celestial body in space. Preferably, the celestial body is a planet, and in particular the Earth. While the first and second flying objects move in orbit, the antenna emits antenna radiation along a main beam direction and / or receives antenna radiation from the second flying object along the main beam direction.The main beam direction, which corresponds to the direction of the antenna's greatest transmission and / or reception power, has a predetermined lateral viewing angle, which is a rotation angle equal to or unequal to zero around the direction of movement of the first flying object (RSS) relative to the direction toward the center of the celestial body. Antennas with a main beam direction tilted to the side in the direction of flight are used in particular in SAR radar systems (SAR = Synthetic Aperture Radar). Accordingly, in a preferred embodiment, the antenna is a SAR antenna. Signal values ​​of the antenna are obtained using the second flying object, and from this, at least part of the antenna pattern and preferably the complete antenna pattern are determined.According to the invention, the first elliptical orbit and the second elliptical orbit are adjusted relative to one another in such a way that the signal values ​​obtained during one orbit, in which the first flying object and the second flying object orbit the celestial body once, correspond to a fixed, predetermined azimuth angle and different polar angles with respect to the antenna, i.e. with respect to a local coordinate system of the antenna. The predetermined azimuth angle is an angle of rotation about the main beam direction, whereas the different polar angles represent angles of inclination with respect to the main beam direction, wherein the angle of inclination can also be zero. The above formulation, according to which the first elliptical orbit and the second elliptical orbit are adjusted relative to one another, is to be understood broadly. In particular, only the first elliptical orbit or only the second elliptical orbit can be changed for this purpose.Likewise, both the first and second elliptical orbits can be changed for this purpose. Preferably, only the second elliptical orbit is changed. The method according to the invention is based on the finding that, by appropriately selecting the parameters for the orbits of two flying objects flying in formation, the signal values ​​of a corresponding antenna pattern in the direction of the polar angle can be recorded at a fixed azimuth angle. By changing the P2972PC00 parameters of at least one orbit, corresponding signal values ​​can be obtained for different predetermined azimuth angles, and the antenna pattern can thus be determined at any position.In a preferred embodiment of the method according to the invention, the setting of the first elliptical orbit and the second elliptical orbit relative to one another is changed after a predetermined number of orbits, and preferably after one orbit, in order to thereby vary the predetermined azimuth angle for at least the next orbit. With this variant of the invention, a comprehensive measurement of the antenna pattern for a multitude of azimuth angles can be achieved. In a further preferred embodiment, the first elliptical orbit and the second elliptical orbit are ellipses with semi-major axes of the same length and the same focal point, at which the center of the celestial body is located, during the orbit. The eccentricity of the ellipse of the second elliptical orbit is changed by the amount of an eccentricity difference compared to the eccentricity of the ellipse of the first elliptical orbit.Furthermore, the inclination of the ellipse of the second elliptical orbit is changed by the amount of an inclination difference compared to the inclination of the ellipse of the first elliptical orbit. Furthermore, the angle of the ascending node of the ellipse of the second elliptical orbit is changed by the amount of an angular difference compared to the angle of the ascending node of the ellipse of the first elliptical orbit. The above quantities of eccentricity, inclination, and the angle of the ascending node are well known to those skilled in the art as Keplerian orbital elements. In particular, the inclination describes the angle of inclination of an elliptical orbit relative to the equatorial plane of the celestial body, whereas the angle of the ascending node represents the angle of the intersection point of the corresponding elliptical orbit toward the northern hemisphere with a predetermined reference direction in the equatorial plane.P2972PC00 In order to take into account the coupling of the differences in the orbit elements eccentricity, inclination, and ascending nodes when calculating the first and / or second elliptical orbit, in a preferred variant of the invention, the position of the second flying object on the second elliptical orbit is adjusted by the amount of a phase difference with which an offset of the position of the second flying object in the direction of movement of the first flying object is compensated at a central orbit position of the first flying object, wherein the central orbit position is the position of the first flying object closest to the celestial body or the position furthest away from the celestial body. A variant of this compensation is explained in more detail in the detailed description.In a further embodiment of the method according to the invention, the inclination difference and the phase difference contain a correction to ensure that the main beam direction runs through the second flying object at the central trajectory position of the first flying object. A variant of this correction is explained in more detail in the detailed description. In a further, particularly preferred embodiment, the above angular difference of the ascending nodes is predetermined, wherein the eccentricity difference and / or the inclination difference are determined as a function of the predetermined angular difference of the ascending nodes. In a preferred embodiment of the method according to the invention, the eccentricity difference is determined based on the following equation:. where Δe is the eccentricity difference, where i RSS is the inclination of the ellipse of the first elliptical orbit, where e RSSis the eccentricity of the ellipse of the first elliptical orbit, where ΔΩ is the given angular difference of the ascending nodes, P2972PC00 where θ off is the given side view angle, where ξ = ξ cut + ξ off holds, where ξ cut is the given azimuth angle and ξ off an azimuth offset angle is equal to or unequal to zero, where an azimuth offset angle unequal to zero represents the rotation of the antenna about its main beam direction relative to a given normal position. The given normal position is preferably the position in which the antenna is used during operation for remote sensing of the surface of the celestial body. The eccentricity difference is given by ∆e = e MES - e RSS and the angle difference of the ascending nodes is ∆Ω = Ω MES - Ω RSS , where e MES is the eccentricity of the ellipse of the second elliptical orbit, where Ω RSSis the angle of the ascending node of the first elliptic orbit, where Ω MES is the angle of the ascending node of the second elliptical orbit. In a further preferred embodiment, the inclination difference is determined based on the following equation: Δi = ( −1 ) ⋅ asin� tan θoff⋅Δe1∓(eRSS+Δe)�, where Δi is the inclination difference and Δi = i MES − i RSS applies, where i MES is the inclination of the ellipse of the second elliptical orbit, where the minus sign in front of (e RSS + Δe) applies if ξ ≤ 0, where the plus sign in front of (e RSS+ Δe) applies if ξ > 0. In a further preferred embodiment of the method according to the invention, the angular difference of the ascending nodes is specified such that when the second flying object moves relative to the first flying object, the minimum distance between the first flying object and the second flying object assumes a predetermined value. Preferably, the secondary condition is met that the absolute value of the angle, which is made up of the predetermined azimuth angle and a P2972PC00 azimuth offset angle equal to or unequal to zero, does not exceed a predetermined maximum value and does not fall below a predetermined minimum value, wherein an azimuth offset angle unequal to zero represents the rotation of the antenna about its main beam direction relative to a predetermined normal position.As mentioned above, the normal position is preferably the position in which remote sensing of the surface of the celestial body is carried out during operation of the antenna. In a further preferred variant, the azimuth offset angle is changed after a predetermined number of orbits without changing the setting of the first elliptical orbit and the second elliptical orbit relative to one another, wherein the azimuth offset angle is changed in such a way that the predetermined azimuth angle is varied. In other words, the same orbits of the first and second elliptical orbits can be used to measure the antenna pattern for several predetermined azimuth angles, which saves on orbit maneuvers, since the same orbits can be flown several times in succession. In extreme cases, the same orbits can be used to measure all different predetermined azimuth angles.In a further preferred embodiment, the antenna radiation of the antenna is frequency-modulated and preferably linearly frequency-modulated. In this way, the frequency dependence of the antenna pattern can also be measured. The method according to the invention can be used to measure different antenna patterns. In particular, a transmission pattern and / or a reception pattern and / or a two-way pattern can be measured as the antenna pattern. When measuring a transmission pattern, the signal strength of antenna radiation emitted by the antenna of the first flying object is measured by means of the second flying object (i.e., a measuring device located thereon). When measuring a reception pattern, the P2972PC00 antenna detects the signal strength of received antenna radiation emitted by the second flying object (i.e., an antenna located thereon).When measuring a two-way pattern, the signal strength of antenna radiation is recorded. This radiation is emitted by the antenna, reflected by a reflector on the second flying object, and then received again by the antenna. As an alternative to a reflector, a so-called transponder can also be used. This is a receiving / transmitting device on the second flying object, which receives the radiation emitted by the first flying object and then, after a defined modification, sends it back. In addition to the method described above, the invention relates to a system for measuring an antenna pattern of an antenna on a first flying object using a second flying object. The system is set up for operation in which the method according to the invention or one or more preferred variants of the method according to the invention are carried out. The components described above, i.e.the first flying object, the second flying object and the antenna, part of this system. Exemplary embodiments of the invention are described in detail below with reference to the attached figures. They show: Fig. 1 a schematic representation of a first flying object and a second flying object according to an embodiment of the invention; Fig. 2 a schematic representation which illustrates which different orbits can result from differences in individual orbit parameters of the flying objects from Fig. 1; P2972PC00 Fig. 3A and Fig. 3B perspective views which illustrate the antenna pattern of the radar antenna of the first flying object and the relative position of the second flying object with respect to the antenna pattern, wherein Fig. 3A shows the antenna system A which is designed for an azimuth offset angle ξ. offof zero is equal to the antenna system Ar rotated around the main beam direction and where Fig.3B shows the rotated antenna system Ar with respect to the antenna system A for an azimuth offset angle ξ offnot equal to zero. Fig. 4 shows a perspective view analogous to Fig. 3A, wherein the position of the second flying object is described by an azimuthal angle and an elevation angle; Fig. 5 is a representation which, in the left-hand part, shows the change in baselines for a known standard helix configuration of two flying objects in orbit around the Earth in the antenna coordinate system and which, in the right-hand part, illustrates for a local coordinate system how the two components of the cross-track baseline of a helix add up to an overall cross-track baseline according to an embodiment of the invention. Figs. 6 and 7 are perspective representations of the elliptical trajectories of the first flying object and the second flying object, wherein parameters of the trajectories are highlighted; Fig. 8 and 9 are diagrams which show variants for calculating and correcting the elliptical trajectory of the second flying object.P2972PC00 An embodiment of the invention is described below based on the measurement of a two-way antenna pattern of a radar antenna on a first flying object in the form of a satellite. Nevertheless, the invention can also be used to measure a transmitting antenna pattern of the radar antenna or a receiving antenna pattern of the radar antenna. Likewise, the antenna pattern of an antenna that operates in a different frequency range than radar waves can also be measured. Fig. 1 shows a schematic representation of the measurement of the two-way antenna pattern. The first flying object is a satellite RSS (Radio Signal Satellite), which is shown schematically in plan view and comprises a flat radar antenna 1 in the form of a transmitting and receiving antenna and a solar panel 2. The two-way antenna pattern of the radar antenna 1 is measured in the embodiment described here.For this survey, a second flying object MES (MES = Measurement Satellite) is used, which is also a satellite and moves in formation with the satellite RSS around the corresponding celestial body, which in the embodiment described here is the Earth, as explained in more detail below. The satellite MES comprises a spherical reflector 3, which is connected to another unit comprising a corresponding solar panel 4 and control nozzles 5. The radar radiation emitted by the radar antenna 1 is reflected by the spherical reflector 3 and then received again by the radar antenna 1, whereby signal values ​​SV are obtained which, depending on the current relative position of the satellite MES to the satellite RSS, correspond to different azimuth angles and polar angles in the antenna coordinate system of the radar antenna 1, as explained in more detail below.The path of the radar radiation and its reflection by the spherical reflector 3 is only indicated schematically in Fig. 1 by the long double arrow. The short double arrows indicate that a spherical reflector reflects the same signal strength in all directions. P2972PC00 Fig. 2 once again illustrates, by way of example, elliptical orbits on which the two satellites RSS and MES can move around the Earth, with each of the three representations showing the baseline components resulting from the difference in an orbit parameter. The essence of the invention lies in a suitable selection of the parameters of the elliptical orbit of the satellite MES relative to the elliptical orbit of the satellite RSS, so that the two-way antenna pattern of the radar antenna 1 can be measured simply and efficiently. Fig. 2 contains three representations with different elliptical orbits for the satellite RSS and the satellite MES.The elliptical orbit of the RSS satellite is designated EB1, and the elliptical orbit of the MES satellite is designated EB2. The satellites move in the direction indicated by arrow P around the Earth 100, at whose center M lies the origin of a Cartesian inertial coordinate system with the x-axis. I , y I and z I The focal point of both elliptical orbits EB1 and EB2 is also located at the center point M. Fig. 2 shows various positions of the satellites RSS and MES, resulting in different baselines B along , B rad and B crossThese baselines are explained in more detail below. The left-hand illustration in Fig. 2 shows the case in which there is a difference Δe between the eccentricities of the two elliptical orbits EB1 and EB2, but the orbits move in the same plane. The middle illustration in Fig. 2 shows the case in which the inclinations of the ellipses differ by the value Δi, where in a known manner the inclination is given by the inclination of the corresponding ellipse with respect to the equatorial plane of the Earth 100. The right-hand illustration in Fig. 2 shows the case in which the known angles of the ascending node of the two ellipses differ from each other by ΔΩ. The angle of the ascending node describes the rotation of the corresponding ellipse with respect to a reference direction which is located in the equatorial plane of the Earth 100.P2972PC00 Before the invention is described in more detail, the relevant coordinate systems will first be explained, which are relevant to the antenna pattern to be measured. Fig. 3A shows a perspective view of antenna 1 with the corresponding antenna pattern AP in the antenna coordinate system A. The origin of the antenna coordinate system is designated AC. The axes x and y are defined by the x-axis. A , y A and z A represents the Cartesian antenna coordinate system A. The main beam direction HS of antenna 1 runs along the z A -axis. For example, in Fig. 3A, the satellite MES with its reflector 3 is indicated by a point on its relative motion (represented by line LI) around the satellite RSS during a measurement at a certain fixed azimuth angle. In coordinate system A, the position of the satellite MES is represented by the corresponding coordinates B. A a longalong the x A -axis, B A c ross along the y A -axis and B A r ad along the z A -axis. These coordinates are also referred to as the baseline, a term commonly used to describe the distance between two antennas in satellite systems. The baseline coordinates can be uniquely converted into spherical coordinates, which are given by the distance d r , the polar angle ψ and the azimuth angle ξ. This conversion is given in the first three lines of equation (1) below. Fig. 3B shows a perspective view which differs from Fig. 3A in that the antenna 1 is rotated, resulting in a rotated antenna coordinate system Ar, where the rotation corresponds to an azimuth offset angle ξ offnot equal to zero around the main beam direction HS of the antenna 1 and where the axes of the rotated antenna coordinate system Ar are shown in relation to the axes of the antenna system A. Analogous to Fig. 3A, Fig. 3B also indicates the satellite MES with its reflector 3 on its relative movement (represented by the line LI) around the satellite RSS during a measurement at a certain fixed azimuth angle. P2972PC00 In the following, the antenna pattern AP is considered as a two-dimensional pattern described by the polar angle ψ and the azimuth angle ξ, where the quantity d ris a parameter that is available for each ξ- ψ combination from the measurement geometry. The antenna pattern is thus sufficiently measured when there are enough signal values ​​for the corresponding azimuth and polar angles, so that the pattern is sufficiently well covered. Fig. 4 shows a representation analogous to Fig. 3A, where the position of the satellite MES or its reflector 3 is now represented by the angles θ el or θ az The angle θ el is referred to as the elevation angle and the angle θ az as an azimuthal angle, which is to be distinguished from the above-mentioned azimuthal angle ξ. Only then does a unique relation exist between the above baseline coordinates B A a long , B A c ross and B A r ad and the angles θ el and θ az, if the order of rotations is uniquely defined. This order of rotations is given in the following by the vector that enters the z A -direction, first by the angle θ el around the x A -axis and then the resulting vector is rotated by the angle θ az around the y A -axis. The last two lines of the following equation (1) show the relationship between the baseline coordinates and θ az and θ el .tan(ξ) = [ BA 90° along sin(θ BA alo a ) = ng z dr⋅cos θel P2972PC00 The local coordinate system L of the satellite RSS is defined by the orthogonal vectors in the following equation (2), where r I R SS or v I R SSrepresents the position or speed of the satellite RSS in the inertial coordinate system of the Earth according to Fig. 2. In equation (2), a circumflex denotes unit vectors and r I R SS and v I R SS represent absolute values. The transformation of the difference between the position vector r I M ES of the satellite MES and the position vector r I R SS of the satellite RSS in the inertial system I into the local coordinate system L of the satellite RSS provides the vector B L , ie the baseline vector in the local system L. In equation (2) L D I a rotation matrix that represents the transformation. The respective coordinate system is represented by a superscript index. The RSS satellite can change its attitude using a known control system by altering its yaw angle α, its pitch angle β, and its roll angle γ. This corresponds to a rotation of the baseline vector ^^^^ L from the local coordinate system L of the satellite into the so-called body system B. This rotation can be represented mathematically as follows:^^^^B = BDL ⋅ ^^^^L (3) In the following it is assumed that α = β = γ = 0°, so that B B = B L Furthermore, a satellite RSS is assumed, whose radar antenna 1 is looking obliquely at the Earth's surface, which results in a side view angle θ off This angle describes a rotation around the x B -axis of the above-mentioned body system, P2972PC00, which transforms the baseline vector into the rotated antenna system Ar. In other words, the side view angle θ describes offthe rotation of the main beam direction of radar antenna 1 of the RSS satellite with respect to the direction of the Earth's center. For a side view angle |θ off | ≤ 90°, a positive side view angle θoff leads to a system looking to the right in the direction of flight and a negative side view angle θ off leads to a system looking to the left in the direction of flight. The baseline vector in the coordinate system Ar, which takes the side view angle into account, can be represented as follows: 1 0 0 ^^^^Ar =�0 cos θoff − sin θ off� ⋅ ^^^^B = Ar DB ⋅ ^^^^B 0+ sin θoff cos θoffIn addition, a rotation of the antenna by the azimuth offset angle ξ off around the z A -axis must be taken into account. This means that the following relationship applies: From the coordinates B A a long , B A c ross and B A r adthe polar angle ψ, the azimuth angle ξ and the azimuthal angle θ az and the elevation angle θ elcan be calculated using equation (1) above. The aim of the method described here is to arrange the orbit of the satellite MES relative to the orbit of the satellite RSS in such a way that the azimuth angle remains fixed during one orbit and the polar angle is varied along the azimuth angle, creating a section through the antenna pattern that includes the main beam direction HS. By appropriately changing the azimuth angle and thus the section during a later orbit, signal values ​​for corresponding polar angles for a different azimuth angle can then be recorded P2972PC00. This allows the entire antenna pattern to be traversed, so that a measurement of the antenna pattern across all azimuth angles can be achieved.The key finding of the invention is that the parameters of the elliptical orbits of the MES satellite can indeed be selected such that the antenna pattern can be fully measured over corresponding sections with different azimuth angles. The derivation leading to the orbit parameters is explained below, so that the antenna pattern of radar antenna 1 of the RSS satellite can be measured using the MES satellite. The starting point for this derivation is the well-known helical orbit flown by two satellites of the well-known TanDEM-X mission. The closest point to Earth of both satellite orbits is at the latitude argument u = 90°, which corresponds to a Kepler orbit parameter argument of perigee (closest point to Earth) ω = 90°.During one orbit around the Earth, the MES satellite completely orbits the RSS satellite in all three dimensions of the RSS satellite's local coordinate system. The baseline coordinates B. L along and B L rad from the above equation (2) can be approximately described as follows: BL rad,Δe (u) ≈ BLrad,Δe,max BL along,Δe (u) ≈ BLalong,Δe,max ∙ cos u ≈ −2 ∙ a ∙ ∆e ∙ cos u (6)The closest point to Earth, ω, for both satellites MES and RSS lies at the latitude argument u = 90°. The quantity a corresponds to the length of the semi-major axis, which is identical for both satellites. The quantity ∆e = eMES - e RSS denotes the eccentricity difference between the eccentricity e MES the elliptical orbit of the satellite MES and the eccentricity e RSSof the elliptical orbit of the satellite RSS. The subscripts Δe in equation (6) indicate that the eccentricity difference generates the two baselines. The absolute values ​​of the radial baseline B L r ad,Δe,max (ie the baseline in the direction of the center of the Earth) are at u = ± 90° and the absolute P2972PC00 maxima of the so-called Along-Track Baseline B L along,Δe,max (ie the baseline in the direction of flight of the satellite RSS) lie at the equator. The so-called cross-track baseline B L c ross,∆Ω from the following equation (7) (ie the baseline perpendicular to the orbital plane of the satellite RSS) is determined by a difference in the angle of the ascending node ΔΩ = Ω MES – Ω RSS between the elliptical orbits of the satellites MES and RSS. This difference leads to the absolute maximum B Lcross,ΔΩ,maxthis cross-track baseline is located at the equator, whereas baseline B L c ross,ΔΩ at u = ± 90° (ie at the point closest to and farthest from Earth) takes the value 0. In the subscripts of the following equation (7), the difference ΔΩ in the angle of the ascending node has been added to indicate that this cross-track baseline is caused by this. i RSS is the inclination of the elliptical orbit of the satellite RSS. The helix shape described above, which results from the differences Δe and ΔΩ, is referred to below as the standard helix. In order to generate the sections through the antenna pattern AP described above, running through the main beam direction HS of the radar antenna 1, a central orbit position COP must be present as shown in Fig. 3, at which the satellite RSS is at the point closest to or farthest from Earth, and B Ac ross = B A a long = 0 and B A r ad positive and significantly greater than zero. This is because the central sections with the different azimuth angles are supposed to intersect at this central orbit position. For the standard helix with α = β = γ = 0° and with angles of θ off and ξ off of zero (ie B A = B L ) the central orbit position COP is at the closest point to Earth, u = 90°. This is further illustrated in the left diagram of Fig. 5, which shows the course of the baseline coordinates described above in P2972PC00 in the antenna system A, which here is the same as the local coordinate system L of the satellite RSS, as a function of the latitude argument. The central orbit position COP is also shown in both diagrams of Fig. 5. As can be seen in the left diagram of Fig. 5, the coordinate B A c rossmaximum at the equator (u = 0°) and zero at u = 90°. Therefore, B A a long = B L a long at u = 90° must also be zero, so that the nearest Earth points of the satellites RSS and MES must also be at u = 90°. This is set by choosing the perigee argument ω to 90°. In the embodiment described here, a system is considered in which a side view angle θ off non-zero, ie, where the antenna can also look to the side, as is the case with SAR radar systems, for example. In such a constellation, the standard helix described above cannot be used, since B L ≠ B A From Fig.6 it can be seen how the side view angle θ off for a side-looking system can be taken into account by applying a difference Δi = i MES - i RSSis introduced by the inclinations of the elliptical orbit EB2 of the satellite MES relative to the elliptical orbit EB1 of the satellite RSS, thereby adding an additional contribution to the cross-track baseline. EQ describes the equatorial plane. In Fig. 6 and also in the further exemplary embodiments, a right-facing radar antenna on the satellite RSS is assumed, ie, an antenna whose main beam direction HS, viewed in the direction of flight of the satellite RSS, is to the right of the axis z pointing to the Earth's center. L Fig.6 shows the positions of the satellites MES and RSS at the point closest to Earth. Furthermore, α = β = γ = 0° (ie B B = B L ). The choice of Ω is arbitrary, but for clarity, it was set to 90°. Important for the invention is the angle difference of the ascending nodes ΔΩ. The inclination difference Δi, illustrated in Fig. 6, produces a maximum B Lcross,Δi,max of this component of the cross-track baseline at u = 90° and a minimum for this component of the baseline in the equatorial plane EQ (see right diagram of Fig. 5). The size B L cross,Δi,max can be derived from Fig.6 and results in the following equation (8). P2972PC00 The Cross-Track Baseline B L c ross,Δi (u), which is caused by the inclination difference Δi, can be approximated by a sine function in equation (8). Bc L r oss,Δi ( u ) ≈ Bc L ross,Δi,max ∙ sin u ≈ a ∙ ( 1 ∓ (eRSS + Δe) ) ∙ sin Δ i ∙ sin u (8)The upper minus sign in the above equation (8) applies for an azimuth angle ξ ≤ 0° and the lower plus sign in the above equation (8) applies for an azimuth angle ξ > 0. For a positive eccentricity difference Δe (ie eMES > eRSS), the maximum radial baseline B L r ad,Δe,maxpositive at u = 90°. Therefore, it is necessary that the baseline B L cross,Δi,max is positive there, so that the satellite MES is in the main beam direction of the Earth-facing radar antenna of the satellite RSS. From Fig. 6, the equation (9) below can be derived, from which the required ratio Δi / Δe results (see equations (14) and (15) below). tan(θ BB L O ff) = cross,Δi,max Bcross,Δi,maxB B ≈ BL rad,Δe,max rad,Δe,max (9)The assumption was made that α = β = γ = 0 (ie B B = B L ). In case α, β and γ deviate significantly from zero, B B in equation (9) above. Otherwise, B Lbe used. A helix that only has an inclination difference Δi and an eccentricity difference Δe is not safe, because the orbits of the two satellites cross at the equator. To obtain a safe helix configuration, therefore, a difference ΔΩ in the angle of the ascending node must also be present. A contribution B caused by this difference L c ross,ΔΩ to the cross-track baseline is shown in the right diagram of Fig. 5 in the local coordinate system L. The sum B L c ross of the two cross-track baseline components, i.e. B L c ross,ΔΩ and B L c ross,Δi , is also shown in this diagram, as is the single component B L c ross,Δi . P2972PC00 In case the above equation (9) is satisfied, the transformation to B A , i.e. the transformation into the antenna coordinate system, using the azimuth offset angle θ off(with α = β = γ = ξ off = 0°) to a cross-track baseline B A c ross , which is zero at u = 90° and has its maximum at the equator, as is the case for the cross-track baseline of the standard helix configuration (see left diagram of Fig. 5 in the antenna system). The geometry of a corresponding helix with an angle difference ΔΩ is shown in Fig. 7. For clarification, this figure contains a detailed view D1 of a rectangular section A1 at the equator and a detailed view D2 of a rectangular section A2 at the point closest to Earth. From the detailed view D1, the quantity B L cross,ΔΩ,max from the first line of equation (10) below. The second line of the following equation is a further approximation for a small inclination difference Δi, which is also contained in the first part of equation (7) above. Due to the two cross-track components, an additional small baseline ΔB L at the central orbital position COP. In Fig.7, this is at the closest point to Earth u=90°. Its along-track component ΔB L a long is required further below in equation (18) and can be derived from the upper section A2 of Fig.7, resulting in the following equation (11): where the upper sign before (e RSS +∆e) is valid for ξ ≤ 0° and the lower sign in front of e MESis valid for ξ > 0°. P2972PC00 The following describes the derivation of the parameters Δe and Δi, which in the embodiment described here are set for a given azimuth angle ξ. This azimuth angle remains constant during one orbit of the satellites MES and RSS around the Earth at 100°. During one orbit, signal values ​​of the antenna pattern AP are measured, with each signal value corresponding to a different polar angle Ψ of the antenna pattern. The parameter ΔΩ represents an input value for the derivation. How this parameter can be set is explained below. Assuming α ≈ β ≈ γ ≈ ξ off ≈ 0°, the azimuth angle ξ can be calculated based on the first line of equation (1) as a function of the components of the baseline B LThe following equation (12) is obtained by using the sum of the contributions of the parameters ΔΩ and Δi for the cross-track component B L c ross (u), which are defined in equations (7) and (8). The along-track component and the radial component are defined in equation (6) above. The above equation (9) applies to the central orbit position COP. In Fig. 6, this is the closest point to Earth, u = 90°. It is also used approximately for the surrounding area. The angle θ off can be expressed by the following equation (13): By B L c ross,∆i (u) in equation (12) is replaced by equation (13), the quantity B L r ad (u) can be eliminated. After inserting equation (7) and equation (8), the equation can then be solved for Δe as follows: P2972PC00 Δe ≈ −sin iRSS⋅�1−e2RSS�⋅sin ΔΩ⋅cos θoff2 ⋅tan ξ This equation calculates the parameter Δe for a given azimuth angle ξ, so that the satellite MES at the central orbit position COP in the direction of the angle θ off of the radar antenna 1 of the satellite RSS. The corresponding parameter Δi is obtained from equation (13) by using the expressions for B L r ad (u) and B L c ross,∆i (u) from equations (6) and (8) respectively. Δi ≈ (−1) ⋅ asin�tan θoff⋅Δe1∓(eRSS+ ^^^^ ^^^^)� (15) The upper sign in front of (e RSS +∆e) applies for ξ ≤ 0°, whereas the lower sign in front of (e RSS+∆e) is valid for ξ > 0°. According to the above equation (14), Δe becomes very large for azimuth angles near 0°, resulting in a highly elliptical orbit of the satellite MES with a large altitude variation. On the other hand, azimuth angles near ±90° result in a very small Δe and thus in almost identical elliptical orbits EB1 and EB2 with respect to the radial baseline and the along-track baseline. Accordingly, in a preferred embodiment of the invention, the radar antenna 1 is mechanically rotated around the main beam direction HS by the azimuth offset angle ξ off rotated if the specified azimuth angle ξ is close to 0° or ±90°. The section through the antenna pattern AP, for which the corresponding signal values ​​are determined, is thus described by the following equation: Here, ξ cut the azimuth angle of the section in the rotated antenna system Ar (see Fig.3B; ξ corresponds to ξ cut in Fig.3A for ξ cut= 0°). The appropriate choice of threshold values ​​above which the radar antenna is tilted by the angle ξ off as the azimuth angle ξ approaches 0° or ±90°, is within the scope of P2972PC00 expert action. Furthermore, it can be shown that a rotation by the azimuth offset angle ξ off by adjusting the angles α, β and γ. A suitable value for the angle difference ΔΩ can be determined depending on a desired minimum distance between the satellite RSS and the satellite MES, ie based on B min , as well as a desired maximum amount ξ maxof the azimuth angle ξ contained in the above equation (14). In a preferred embodiment, the angle difference ΔΩ is specified based on the first line of the following equation (17). In the second line of this equation, depending on ΔΩ and a desired maximum distance between the satellite RSS and the satellite MES, ie based on B max , a required minimum amount ξ min for the azimuth angles. The third line in equation (17) represents an additional constraint for positive azimuth angles ξ, which is derived from equation (14) above to allow a negative eccentricity e MES A negative eccentricity for an ellipse is not possible, ie the eccentricity difference Δe must be ≥ -e RSS The additional restriction means that positive azimuth angles ξ cannot be below ξ pos,min may lie. The values ​​of ξ min , ξ max and ξ pos,min specify which values ​​for ξ and ξ off for a ξ cut These values ​​are used in the following equations for the entire range of values ​​of ξ cut specified. P2972PC00 0° < ξ cut ≤ max�ξ min , ξ pos,min � und The additional small baseline ∆B L a long from equation (11) produces an azimuthal angle θ az , which deviates slightly from zero at the central orbit position COP. In the embodiment described here, this deviation is compensated for by a small phase shift of the satellite MES by a time offset Δτ. The time offset Δτ is as follows: The size of v s,MESis the speed of the satellite MES at the central orbit position COP. Fig.8 illustrates once again the determination of the above quantities ΔΩ, Δe, Δi and Δτ. For clarity, the equations mentioned above are only generally replaced in Fig.8 by a corresponding function f ( ∙ ) Due to the approximations described above in the derivation of Δe, Δi, and Δτ, the following small deviations occur at the central orbit position COP. Firstly, the along-track baseline B A a longin antenna system A is not exactly zero, and secondly, the satellite MES is not positioned exactly in the main beam direction of the radar antenna 1 of the satellite RSS. This is corrected in the embodiment described here with the numerical adjustment shown in Fig. 9. For this purpose, the orbits of the satellites RRS and MES are first simulated based on the above-mentioned parameters ΔΩ, Δe, Δi, and Δτ. Subsequently, the P2972PC00 Baseline B A C OP at the central orbit position COP in the coordinate system A (antenna) is calculated from the simulated orbits. Finally, the quantities ∆τ res and ∆i res calculated using equation (19) below. The upper sign before (e RSS +∆e) applies for ξ ≤ 0°, whereas the lower sign in front of (e RSS +∆e) is valid for ξ > 0°. With the resulting values ​​∆τ res and ∆i resthe values ​​of Δτ and Δi are then corrected. The above steps are repeated iteratively until a certain threshold criterion is reached. This threshold criterion is defined, for example, such that the values ​​of Δτ and Δi change by less than a threshold value compared to the last iteration. The elliptical orbit of the satellite MES is then commanded or set using the final values ​​of Δτ and Δi determined during the iteration, as well as the values ​​of ΔΩ and Δe described above. The method according to the invention was tested by the inventors using simulations, and it has been shown that the parameters selected within the scope of the invention mean that the corresponding antenna pattern of a satellite can be fully measured using another satellite. The embodiments of the invention described above have a number of advantages. In particular, the orbits orThe orbits of a second satellite moving relative to a first satellite are chosen in such a way that, during one orbit, the signal values ​​of the antenna pattern of the radar antenna of the first satellite can be recorded for a given azimuth angle in the direction of the polar angle in the coordinate system of the radar antenna. By varying the orbits of the second satellite accordingly, the corresponding signal values ​​in the direction of the polar angle can be determined for a large number of different azimuth angles and the entire antenna pattern of the radar antenna can therefore be measured. A further advantage is that the measurement can be extended to all polar angles and the antenna pattern on the back of the antenna or the first satellite can therefore also be measured. A further advantage is that electronically controlled antenna patterns in which the main beam direction differs from the direction of the e.g. A-axis of the antenna system by an elevation angle θel,electronic and / or an azimuthal angle θaz,electronic. The electronic control of the main beam direction away from the z A -Axis of the antenna system can be adjusted by modifying the side view angle θ off in the calculation of the orbit parameters and / or by modifying the attitude angles of the first flying object, ie the yaw angle α, pitch angle β and roll angle γ. A further advantage is that with electronic antenna control, where the main beam direction depends on the direction of the z A -axis of the antenna system by an elevation angle θel,electronic and / or an azimuthal angle θaz,electronic, the main beam direction is equal to the direction of the z A-axis of the antenna system can be maintained in the calculation of the orbit parameters of the two elliptical orbits. Due to the electronic antenna control, the sections then run with a constant azimuth angle ξ cut no longer by the electronically controlled main beam direction of the antenna. However, by quickly switching between multiple antenna patterns, all of these antenna patterns can be measured consecutively in the same orbit. P2972PC00 A further advantage is that the measurement of the antenna pattern takes place entirely in space, thus eliminating all interference from the atmosphere, ionosphere, ground clutter, multipath effects, ambiguities, and volume scattering. In particular, this allows not only the measurement of the amplitude pattern but also a measurement of the phase diagram and an exact polarimetric measurement of the antenna pattern.

Claims

P2972PC00 Patent claims 1. Method for measuring an antenna pattern (AP) of an antenna (1) on a first flying object (RSS) by means of a second flying object (MES), wherein the first flying object (RSS) moves in orbit along a first elliptical path (EB1) around a celestial body (100) and the second flying object (MES) moves in orbit on a second elliptical path (EB2) around the celestial body (100), wherein during the movement of the first and second flying object (RSS, MES) the antenna (1) emits antenna radiation along a main beam direction (HS) and / or receives it from the second flying object (MES), wherein the main beam direction (HS) has a predetermined side view angle (θ off), which is a rotation angle equal to or unequal to zero around the direction of movement of the first flying object (RSS) with respect to the direction to the center (M) of the celestial body (100), wherein by means of the second flying object (MES) signal values ​​(SV) of the antenna (1) are obtained and from this at least a part of the antenna diagram (AP) is determined, wherein the first elliptical path (EB1) and the second elliptical path (EB2) are adjusted relative to one another in such a way that the obtained signal values ​​(SV) during one orbit in which the first flying object (RSS) and the second flying object (MES) orbit the celestial body (100) once, to a fixed predetermined azimuth angle (ξ cut ) and different polar angles (ψ) with respect to the antenna (1), wherein the predetermined azimuth angle (ξ cut) represents a rotation angle about the main beam direction (HS) and the different polar angles (ψ) represent angles of inclination relative to the main beam direction (HS).

2. Method according to claim 1, characterized in that the setting of the first elliptical path and the second elliptical path (EB2) relative to each other is changed after a predetermined number of revolutions in order to P2972PC00 thereby the specified azimuth angle (ξ cut ) for at least the next orbit.

3. Method according to claim 1 or 2, characterized in that the first elliptical orbit (EB1) and the second elliptical orbit (EB2) during the orbit represent ellipses with major semi-axes (a) of the same length and the same focal point at which the center (M) of the celestial body (100) is located, wherein the eccentricity (e MES) of the ellipse of the second elliptical orbit (EB2) by the amount of an eccentricity difference (Δe) compared to the eccentricity (e RSS ) of the ellipse of the first elliptical orbit (EB1) is changed and the inclination (i MES ) of the second elliptical orbit (EB2) by the amount of an inclination difference (Δi) compared to the inclination (i RSS ) of the first elliptical path (EB1) is changed and the angle (Ω MES ) of the ascending node of the second elliptical orbit (EB2) by the amount of an angle difference (ΔΩ) compared to the angle (Ω RSS) of the ascending node of the first elliptical orbit (EB1) is changed.

4. Method according to one of the preceding claims, characterized in that the position of the second flying object (MES) on the second elliptical orbit (EB2) is adjusted by the amount of a phase difference (Δτ) in order to compensate for an offset of the position of the second flying object (MES) in the direction of movement of the first flying object (RSS) at a central orbit position (COP) of the first flying object (RSS), wherein the central orbit position (COP) is the position of the first flying object (RSS) closest to the celestial body (100) or the position furthest away from the celestial body (100).

5. Method according to claim 3 and 4, characterized in that the inclination difference (Δi) and the phase difference (Δτ) contain a correction in order to at the central orbit position (COP) of the first flying object (RSS) P2972PC00 to ensure that the main beam direction (HS) of the antenna (1) passes through the second flying object (MES).

6. The method according to claim 3 or according to claim 4 or 5 in combination with claim 3, characterized in that the angular difference (ΔΩ) is predetermined and the eccentricity difference (Δe) and / or the inclination difference (Δi) are determined as a function of the predetermined angular difference (ΔΩ) of the ascending nodes.

7. The method according to claim 6, characterized in that the eccentricity difference (Δe) is determined based on the following equation: sin iRSS⋅θ1−e2RSS⋅sin ΔΩ⋅cos θoff2 ⋅tan ξ , where Δe is the eccentricity difference (Δe), where i RSS the inclination (i RSS ) of the ellipse of the first elliptical orbit (EB1), where e RSS the eccentricity (e RSS) of the ellipse of the first elliptical orbit (EB1), where ΔΩ is the given angular difference (ΔΩ) of the ascending nodes, where θ off the specified side viewing angle (θ off ), where ξ = ξ cut + ξ off holds, where ξ cut the specified azimuth angle (ξ cut ) and ξ off an azimuth offset angle�ξ off � is equal to zero or not equal to zero, where an azimuth offset angle (ξ off ) not equal to zero represents the rotation of the antenna (1) around its main beam direction (HS) relative to a given normal position, where for the eccentricity difference ∆e = e MES - e RSS and for the angle difference of the ascending nodes ∆Ω = Ω MES - Ω RSS applies, P2972PC00 where e MES is the eccentricity of the ellipse of the second elliptical orbit (EB2), where Ω RSSis the angle of the ascending node of the first elliptical orbit (EB1), where Ω MES is the angle of the ascending node of the second elliptical orbit (EB2).

8. The method according to claim 7, characterized in that the inclination difference (Δi ) is determined based on the following equation: Δi = (−1) ⋅ asin�tan θoff⋅Δe1∓(eRSS+Δe)�, where Δi is the inclination difference and Δi = i MES − i RSS applies, where i MES is the inclination of the ellipse of the second elliptical orbit (EB2), where e MES the eccentricity (e MES ) of the ellipse of the second elliptical orbit (EB2), where the minus sign in front of (e RSS + Δe) applies if ξ ≤ 0, where the plus sign in front of ( eRSS + Δe )applies if ξ > 0.

9. Method according to one of claims 6 to 8, characterized in that the angular difference (ΔΩ) of the ascending nodes is predetermined such that during the movement of the second flying object (MES) relative to the first flying object (RSS), the minimum distance between the first flying object (RSS) and the second flying object (MES) assumes a predetermined value, wherein preferably the secondary condition is met that the amount of the angle resulting from the predetermined azimuth angle (ξ cut ) and an azimuth offset angle (ξ off ) equal to zero or not equal to zero, does not exceed a predetermined maximum value and does not fall below a predetermined minimum value, whereby an azimuth offset angle (ξ off ) not equal to zero P2972PC00 represents the rotation of the antenna (1) about its main beam direction (HS) relative to a predetermined normal position.

10. Method according to one of claims 7 to 9, characterized in that after a predetermined number of revolutions, the azimuth offset angle ξ off � without changing the setting of the first elliptical orbit (EB1) and the second elliptical orbit (EB2) relative to each other, whereby the azimuth offset angle�ξ off � is changed in such a way that the specified azimuth angle (ξ cut) is varied.

11. Method according to one of the preceding claims, characterized in that the antenna radiation of the antenna (1) is frequency-modulated and preferably linearly frequency-modulated.

12. Method according to one of the preceding claims, characterized in that a transmission pattern and / or a reception pattern and / or a two-way pattern is measured as the antenna pattern (AP). 13.System for measuring an antenna pattern (AP) of an antenna (1) on a first flying object (RSS) by means of a second flying object (MES), wherein the system is set up for operation in which the first flying object (RSS) moves in orbit along a first elliptical path (EB1) around a celestial body (100) and the second flying object (MES) moves in orbit on a second elliptical path (EB2) around the celestial body (100), wherein during the movement of the first and second flying objects (RSS, MES) the antenna (1) emits antenna radiation along a main beam direction (HS) and / or receives it from the second flying object (MES), wherein the main beam direction (HS) has a predetermined lateral viewing angle (θ). off ) which is an angle of rotation equal to or unequal to zero around the direction of movement of the first flying object (RSS) with respect to the direction to the center (M) of the celestial body (100), wherein by means of the second flying object (MES) P2972PC00 signal values ​​(SV) of the antenna (1) are obtained and from this at least a part of the antenna diagram (AP) is determined, wherein the first elliptical path (EB1) and the second elliptical path (EB2) are adjusted relative to each other in such a way that the obtained signal values ​​(SV) during an orbit in which the first flying object (RSS) and the second flying object (MES) orbit the celestial body (100) once, to a fixed predetermined azimuth angle (ξ cut ) and different polar angles (ψ) with respect to the antenna (1), wherein the predetermined azimuth angle (ξ cut ) represents a rotation angle about the main beam direction (HS), and the different polar angles (ψ) represent angles of inclination relative to the main beam direction (HS).

14. System according to claim 13, characterized in that the system is configured to carry out a method according to one of claims 2 to 12.

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