Interferometric method and antenna arrangement for determining an incident direction of electromagnetic radiation

Abstract

The present invention relates to an antenna arrangement comprising a first antenna element, a second antenna element, a third antenna element, and a fourth antenna element, which are arranged non-coplanarly and configured to detect signals from an incident electromagnetic wave. The antenna arrangement comprises a processor configured to determine a direction of incidence of the electromagnetic wave using the detected signals.

Description

TECHNICAL FIELD OF THE INVENTION

[0001] The invention relates to an interferometric method and an antenna arrangement for determining a direction of incidence of electromagnetic radiation, in particular a non-coplanar antenna arrangement in three dimensions. BACKGROUND OF THE INVENTION

[0002] Known methods for determining the direction of incidence of electromagnetic radiation require a high computational effort to precisely determine the direction of incidence when using four or more antenna elements in an antenna array. With antenna arrays in two dimensions, the computational effort can be very large. Ambiguities due to a possible path difference between antenna elements cannot always be ruled out a priori, which may, for example, require checking several specific directions of incidence to determine the actual direction of incidence. Ambiguities must therefore be resolved during a direction estimation in order to unambiguously determine the directions of incidence.

[0003] In other words, the complexity of determining the direction of incidence of electromagnetic radiation, depending on the selected method and / or antenna arrangement, can lead to high computing demands on the radar seeker, for example, of a missile and / or associated systems, which are not compatible or only with difficulty compatible with other dimensioning requirements, such as volume, shape and / or weight, of the missile and / or associated systems. In the case of a missile, the necessary reduction in the complexity of determining the direction of incidence of electromagnetic radiation can, for example, require the antenna elements to be arranged in a plane, which can represent a significant restriction in the aerodynamic design of missiles, especially for comparatively small and / or complexly shaped missiles.

[0004] It would therefore be desirable to provide a method and a device which enables a precise and unambiguous determination of the direction of incidence of electromagnetic radiation with little computational effort, without compromising the optimal dimensioning of the system associated with the device.

[0005] Ly, PQC, Fast and unambiguous direction finding for digital radar intercept receivers, 2013, PhD thesis, discloses methods and antenna arrays for determining an angle of arrival (AOA) in the context of an application to electronic surveillance systems. According to Ly, the methods must be computationally fast and precise and implemented with large-area arrays with few channels to meet the requirements for the operation of such systems. Ly proposes an interferometric method for this purpose, whereby the method also aims to resolve ambiguities in determining the angle of arrival in a computationally efficient manner. The method uses collinear and coplanar antenna arrays, while antenna arrays with three dimensions and corresponding methods are not covered.

[0006] US 2006 / 081050 A1 discloses a complex system and method for resolving phase ambiguities of various arrays of signal transducers, including non-coplanar interferometer antennas on a side of an aircraft, in order to determine the direction of arrival of a signal received by the array and emitted by a source remote from the array.

[0007] US 6,195,043 B1 discloses an apparatus and method for determining the angles of incidence and the polarization states of incoming radio frequency (RF) signals of unknown polarization using five or more RF sensor antenna elements with different but known polarization orientations.

[0008] US 6,140,963 A discloses a method for resolving an angular ambiguity inherent in differential phase measurements of an electromagnetic signal source by an interferometric system of antenna elements. Three or more independent differential phase measurements are acquired between predetermined pairs of antenna elements. SUMMARY OF THE INVENTION

[0009] The invention is defined by the independent claims. The dependent claims define advantageous embodiments.

[0010] According to a first aspect of the invention, an antenna arrangement comprises a first antenna element, a second antenna element, a third antenna element, and a fourth antenna element arranged non-coplanarly and configured to detect signals from an incident electromagnetic wave; and a processor configured to determine an incident direction of the electromagnetic wave using the detected signals, as described below according to a second aspect or according to a third aspect.

[0011] According to a further development, the first antenna element and the second antenna element lie on a first axis of a coordinate system for determining the direction of incidence of the electromagnetic wave; the first antenna element and the fourth antenna element lie on a second axis of the coordinate system; and the first axis and the second axis are orthogonal to each other.

[0012] According to a further development, a distance of the second antenna element from the first antenna element and a distance of the fourth antenna element from the first antenna element are different.

[0013] According to a further development, the first antenna element is located at the origin of a coordinate system for determining the direction of incidence of the electromagnetic wave, and the second antenna element, the third antenna element, and the fourth antenna element in the coordinate system have coordinates which are each an integer multiple of a wavelength of the electromagnetic wave.

[0014] According to a further development, the integer multiples for each coordinate are less than 20 and preferably greater than 1.

[0015] According to a further development, the distances of the second, third and fourth antenna elements from the first antenna element are all different.

[0016] According to a second aspect of the invention, a method for determining an incident direction of an electromagnetic wave using the antenna arrangement described above comprises the following steps: determining a respective distance between a position of the first antenna element and a position of the second, third, and fourth antenna elements; determining possible ambiguities of a respective difference between a phase of the electromagnetic wave at the position of the first antenna element and a phase of the electromagnetic wave at the position of the second, third, and fourth antenna elements based on the determined respective distance; determining possible polar angles and possible azimuth angles for the incident direction of the electromagnetic wave, taking into account the possible ambiguities;Determining a tuple of the possible azimuth angles and the possible polar angles for which either a difference between two azimuth angles vanishes for a polar angle or a D between two polar angles vanishes for an azimuth angle.;

[0017] According to a further development, determining possible polar angles and possible azimuth angles for the direction of incidence of the electromagnetic wave, taking into account the possible ambiguities, comprises: determining the possible polar angles for the second antenna element; determining the possible azimuth angles for the third antenna element using the possible polar angles for the second antenna element; and determining the possible azimuth angles for the fourth antenna element using the possible polar angles for the second antenna element.

[0018] According to a further development, determining possible ambiguities further comprises: determining the possible ambiguities for the third antenna element with a determination that the third antenna element lies on a new axis of the coordinate system for determining the direction of incidence of the electromagnetic wave; determining possible polar angles and possible azimuth angles for the direction of incidence of the electromagnetic wave taking into account the possible ambiguities comprises: determining the possible polar angles for the third antenna element with respect to the new axis, and converting the possible polar angles for the third antenna element into polar angles in the original coordinate system for determining the direction of incidence of the electromagnetic wave or converting the possible polar angles for the second antenna element into polar angles with respect to the new axis of the coordinate system for determining the direction of incidence of the electromagnetic wave;and determining the tuple comprises: determining a difference between the possible polar angles for the second antenna element and the possible polar angles for the third antenna element, taking into account the possible azimuth angles for the third antenna element and / or the possible azimuth angles for the fourth antenna element;

[0019] According to a third aspect of the invention, a method for determining an incident direction of an electromagnetic wave using the antenna array described above comprises the following steps: ambiguously calculating polar angles based on a first antenna pair of the antenna array in a first coordinate system for the antenna array; ambiguously calculating azimuth angles for each possible polar angle, once based on a second antenna pair of the antenna array and once based on a third antenna pair of the antenna array, each antenna pair comprising a first antenna; for each possible polar angle, resolving the ambiguities in the azimuth angles by selecting an azimuth angle such that the distance between the azimuth angles calculated with the second antenna pair and the azimuth angles calculated with the third antenna pair is minimized;ambiguously calculating the polar angles based on the second antenna pair in a second coordinate system with a z-axis through the positions of the antennas of the second antenna pair; converting the previously determined tuples of azimuth and polar angle in the first coordinate system into polar angles in the second coordinate system; resolving the ambiguity of the polar angle by selecting the polar angle such that a distance between the polar angles determined with the first antenna pair and those determined with the second antenna pair is minimized; and selecting the thus selected polar angle in the first coordinate system and the corresponding previously determined azimuth angle in the first coordinate system as the direction of incidence.

[0020] According to a fourth third aspect of the invention, a missile comprises the antenna arrangement described above. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The invention is explained below with reference to the figures of the drawings. The figures show: Fig. 1 Definition of the azimuth angle ϕ and the polar angle ϑ with respect to an incident direction of an electromagnetic wave in a coordinate system with an orthogonal basis x, y and z. Fig. 2 exemplary non-coplanar antenna arrangement of four antenna elements in three dimensions according to an embodiment with an exemplary direction of incidence of an electromagnetic wave, wherein the coordinates of the antenna elements are specified by multiples of the wavelength of the electromagnetic wave. Fig. 3 Front view of an exemplary antenna arrangement with antenna elements arranged on a rotationally symmetric head of a body. Fig. 4 Side view of the exemplary antenna arrangement of Fig. 3. Fig. 5 Side view of a missile with an exemplary antenna arrangement. Fig. 6 Method for determining an incident direction of the electromagnetic wave according to an exemplary embodiment. Fig. 7 Method for determining an incident direction of the electromagnetic wave according to an exemplary embodiment.

[0022] The accompanying figures are intended to provide a further understanding of embodiments of the invention. They illustrate embodiments and, in conjunction with the description, serve to explain principles and concepts of the invention. Other embodiments and many of the noted advantages will become apparent upon review of the drawings. Elements of the drawings are not necessarily shown to scale relative to one another.

[0023] In the figures, the same reference symbols generally designate identical or functionally identical components, unless otherwise stated. DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0024] Fig. Figure 1 shows the definition of the azimuth angle ϕ and the polar angle ϑ with respect to the direction of incidence of an electromagnetic wave in a coordinate system with an orthogonal basis x, y and z. For the purpose of description and without loss of generality (oBdA), the direction of incidence of the electromagnetic wave can be expressed by the normalized vector d (φ, ϑ), with d(ϕ,ϑ)=(cos ϕ sin ϑsin ϕ sin ϑ cos ϑ)

[0025] The azimuth angle ϕ denotes the angle between the x-axis and the projection of the direction of incidence onto the xy-plane, while the polar angle ϑ denotes the angle between the z-axis and the direction of incidence, as in Fig. 1 shown.

[0026] Fig. Figure 2 shows an exemplary non-coplanar antenna array of four antenna elements in three dimensions according to an embodiment with an exemplary direction of incidence of an electromagnetic wave, where the coordinates of the antenna elements are specified as multiples of the wavelength of the electromagnetic wave. For radar applications, a range of wavelengths can be used. For example, a range of wavelengths around the wavelength.

[0027] As with reference to Fig. 2 shows the positions of the antenna elements for the purpose of description and oBdA with A m where the subscript m ∈ {1,.., M} with M ∈ ℕ denotes the m-th antenna of a total of M antennas. In other words, the antenna array comprises M antenna elements. Furthermore, it is assumed that the first antenna element, hereinafter referred to as the reference antenna, is located at the origin, so that A1 = 0.

[0028] To determine the direction of incidence d (ϕ, ϑ), the phase differences ψ 1m between the antenna element m = 1 and the antenna elements m ∈ {2,.., M} = M \ {1}. The phase difference ψ 1m is the difference ψ m - ψ1 of the phase ψ m of the electromagnetic wave at the position of the antenna element m with m ∈ M \ {1} and the phase ψ1 of the electromagnetic wave at the position of the antenna element m = 1.

[0029] The path differences between the antenna element m = 1 and the antenna elements m ∈ M \ {1} can therefore be given by the expression λ2π(ψ1m+2πρm) where λ is the wavelength of the electromagnetic wave, e.g. in the range between 30 MHz and 300 GHz, and ρ mstands for the possible integer multiples of the wavelength that lie in the direction of the incident electromagnetic wave between the antenna element m = 1 and the antenna element m ∈ M \ {1}. With regard to the reference antenna, the following relations apply: ψ1m+2πρ1m=2πλ〈d(ϕ,ϑ)|Am〉 where m ∈ M \ {1} and 〈·|·〉 denotes the scalar product. The set of possible numbers ρ 1m represents the possible ambiguities at the wavelength λ due to the path difference between the reference antenna and the antenna element m ∈ M \ {1}. For the integers p 1m and with the reference antenna at the origin A1 = 0, the relationship ⌈−‖Am‖λ−ψ1m⌉≤ρ1m≤⌊‖Am‖λ−ψ1m⌋ where ⌈⋅⌉ and ⌊⋅⌋ denotes the rounding function and ||·|| the standard norm. P m denote from now on the set of possible integers ρ 1m which satisfies condition (4).

[0030] For those in the Fig. 2, in which the position A2 of the antenna element m = 2 lies on the z-axis of the scaled coordinate system, is 〈d(ϕ, ϑ) |A2〉 = A2) z cosϑ, where (A2) z denotes the z-component of the vector A2. Consequently, with relation (3), due to the ambiguities P2 for the possible angles ϑ with respect to the z-axis through the position A2 of the antenna element m = 2, the set ϑ12z:={ϑ=cos−1((ψ122π+ρ12)λ(A2)z);ρ12∈P2}

[0031] For the position A3 of the antenna element m = 3, the relation (3), the ambiguities P3 and using the angle α between the x-axis and the projection of the position A3 onto the xy-plane for the possible angles ϕ yields the set ϕ13:={ϕ=α+cos−1((ψ13+2πρ13)λ2π−(A3)zcos ϑsin ϑ(A3)x2+(A3)y2);ρ13∈P3}

[0032] Because the position A4 of the antenna element m = 4 on the x-axis of the Fig. 2 shown scaled coordinate system, the following applies to this antenna element: 〈d(ϕ, ϑ)|A4〉=A4) x cos ϕ sin ϑ, where (A4) x denotes the x-component of the vector A4. Consequently, with relation (3) and due to the ambiguities P4 for the possible angles ϕ, the set ϕ14x:={ϕ=cos−1((ψ14+2πρ14)(A4)x sin τλ2π);ρ14∈P4}

[0033] The possible angles ϕ can therefore be determined for all angles ϑ of the set ϑ12z both with relation (6) and relation (7). Since the true angle ϕ for the true angle ϑ in both sets ϕ 13 and ϕ14x must be included, the true angle ϕ must be the difference between an angle ϕ determined according to relation (6) and an angle ϕ determined according to relation (7) for an angle ϑ of the set ϑ12z disappear. Consequently, the true azimuth angle ϕ and the true polar angle ϑ can be determined, for example, by substituting ϑ12z⊗ϕ13⊗ϕ14x the triple (ϑ, ϕ, ϕ) is sought which has the minimal difference, in symbols e.g.: min(ϑ,ϕ,ϕ)∈ϑ12z⊗ϕ13⊗ϕ14x|ϕ∈ϕ13−ϕ∈ϕ14x| where |·| denotes the magnitude function. In other words, the direction for which the above-mentioned differences (angle differences) are minimal can be chosen, i.e., the direction from among several possible directions that best fits two phase differences measured at different antenna pairs. The ambiguity of the azimuth angle ϕ can be resolved first, followed by the ambiguity of the polar angle ϑ.

[0034] Alternatively or additionally, the true azimuth angle ϕ and the true polar angle ϑ can also be determined, for example, by placing the z-axis through the position A3 of the antenna element m = 3. With this advantageous choice, the relationship (3) results in the set ϑ13z:={ϑ=cos−1((ψ132π+ρ13)λ‖A3‖);ρ13∈P3}

[0035] Those from the crowd ϑ12z The angle ϑ with respect to the z-axis determined according to the relationship (5) through the position A2 of the antenna element m = 2 can be converted into the corresponding angle ϑ with respect to the z-axis through the position A3 of the antenna element m = 3. This can be done, for example, by determining the angle ϑ of the set ϑ12z and the angles ϕ of the set ϕ 13 and / or the quantity ϕ14x using the relationship (1) into unit direction vectors d(ϕ, ϑ)) and using the scalar product 〈d(ϕ, ϑ)|A3〉 = ||A3|| cosϑ. The true azimuth angle ϕ and the true polar angle ϑ can in turn be determined by, for example, the product set ϑ12z⊗ϑ13z⊗ϕ14x the triple (ϑ, ϑ, ϕ) is sought which has a minimal difference in the angles ϑ, in symbols e.g.: min(ϑ,ϑ,ϕ)∈ϑ12z⊗ϑ13z⊗ϕ14x|ϑ∈ϑ13z−cos−1〈d(ϕ∈ϕ14x,ϑ∈ϑ122)|A3 / ‖A3‖〉| Instead of the quantity ϕ14x can also be the set ϕ 13can be used to determine the minimum according to equation (10). In other words, the direction for which the above-mentioned differences (angle differences) are minimal can be chosen, i.e., the direction from among several possible directions that best matches two phase differences measured at different antenna pairs. The ambiguity of the azimuth angle ϕ can be resolved first, followed by the ambiguity of the polar angle ϑ.

[0036] The above methods can be applied to any arrangement of four antennas. Any arrangement corresponds to the case where the position A4 of the antenna element m = 4 lies in the xz-plane. For any arrangement, the set of possible angles ϕ is ϕ14:={ϕ=cos−1(((ψ14+2πρ14)λ2π−(A4)zcos ϑ)(A4)xsin ϑ); ρ14∈P4}

[0037] Instead of the quantities ϕ14x and ϕ 13 can also be the set ϕ 14to determine the minimum according to relation (8) and / or relation (10).

[0038] The methods described above can also be used to describe antenna arrays with more than four antenna elements. To reduce computational effort, it is advantageous for the positions of the antenna elements to lie on one axis of the coordinate system, or to be placed on it, as described above with reference to equations (9) and (10).

[0039] Fig. 3 shows a front view of an exemplary antenna arrangement 310 with antenna elements on a head of a body and outside the body, for example a missile 500 as in Fig. 5. The head of the body exhibits rotational symmetry without loss of generality (oBdA), meaning it can be circular when viewed from the front along a rotation axis x. The head of the body can also be elliptical, for example, when viewed from the front along the rotation axis x.

[0040] As in the Fig. 3, the antenna arrangement comprises a plurality M of antenna elements m with 1 ≤ m ≤ M. The plurality M can be an even or an odd integer, for example 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17 or 18, in particular 4 or more than 4. The antenna elements can be identical or different. For example, S antenna elements can be configured for transmitting, E antenna elements for receiving, and B antenna elements for bidirectionally transmitting and receiving electromagnetic radiation. The plurality M of antenna elements m can, for example, comprise 0, 2, 4, or 8 antenna elements for transmitting and 16, 14, 12, or 8 antenna elements for receiving, a total of 16 antenna elements each. The plurality M of antenna elements may also comprise 4 antenna elements for transmitting and 14 antenna elements for receiving, a total of 16 antenna elements, i.e. 2 antenna elements for transmitting and for receiving.Other combinations are also possible, in particular the case where all antenna elements are configured for transmitting and receiving, B = M. Antenna elements can differ at least in the direction of polarization and otherwise be identical.

[0041] The antenna elements for transmitting and the antenna elements for receiving can be arranged in successive groups on the body or the head of the body, e.g., 2 of the plurality S and 14 of the plurality E; or 4 of the plurality S and 12 of the plurality E; or 4 of the plurality S, 4 of the plurality E, 4 of the plurality S, 4 of the plurality E; or alternating 1 of the plurality S and 1 of the plurality E. The, for example, 16 antenna elements can also all be configured for transmitting and / or receiving. The configuration for transmitting can exclude the configuration for receiving, and vice versa. In the case of a pure receive arrangement, when all antenna elements are configured for receiving and no antenna element is configured for transmitting, the antenna arrangement can, for example, receive radar waves reflected from a target object that have been radiated by a transmitter onto the target object.

[0042] The antenna elements can be configured, in particular, to transmit and / or receive electromagnetic radiation for radar applications. The antenna elements can also be configured to transmit and / or receive in different frequency ranges.

[0043] The plurality M of antenna elements m can be rotationally symmetrical on a circle with radius r i, be arranged in a plane perpendicular to the rotation axis x of the head of, for example, the missile. The position of the antenna elements can be represented, for example, by a rotation angle ϕ(m) with 1 ≤ m ≤ M. The rotation angle φ(m) for the antenna element m can be given by the relationship φ(m) = (m - 1) × Δφ, with Δφ = 360° / M. For the plurality S and the plurality E, different rotation angles are possible, for example, such that the distances between the antenna elements are different and / or an integer multiple of a frequency of an incident electromagnetic wave, in particular in the range of radar waves. As in the Fig. 3, the radius r i smaller than a radius of the missile r a , if oBdA the case of concentric circles as the shape of the missile (outer, solid circle in Fig. 3) and the arrangement of the antenna elements (inner, dotted circle in Fig. 3). A radius d m / 2 of one, several, or all of the antenna elements m may be less than, equal to, or greater than the difference r a - r i the radii r a and r i The location of the antenna elements at the edge of the head of the body can, for example, enable an enlarged field of vision.

[0044] The antenna elements can be arranged arbitrarily in a non-coplanar array. The array preferably does not exhibit non-trivial symmetry. Symmetry of the array is an operation by which the positions of the antenna elements in the array are mapped onto themselves.

[0045] The array can be located anywhere on the body. Placement on the head of the body is not required. The antenna elements of the array can be arranged conformally or non-conformally, for example, on or near the torso and / or tail of a body.

[0046] Fig. 4 shows a side view of an exemplary antenna arrangement 410 with antenna elements mounted on a head of an external body, for example a missile 500 as in Fig. 5. The head of the body has a hyperbolic shape when viewed laterally along a y-axis that is orthogonal to an x-axis. The head of the body can also have the shape of a circle or a triangle, for example, when viewed laterally along a y-axis.

[0047] As with reference to Fig. 3, the antenna arrangement comprises a plurality M of antenna elements m with 1 ≤ m ≤ M. To simplify the description, in Fig. 4 illustrates an example with 9 antenna elements. Alternative solutions, which are all consistent with the example in Fig. 4 are combinable, and vice versa, are related to the Fig. 3 described in detail.

[0048] Each of the antenna elements m may comprise a radome (derived from the English "radar dome") with a housing 411 and a tip 412. The housing may have a diameter (cf. d m in Fig. 3) in the range of 5 to 30 mm, preferably 10 to 20 mm, more preferably 12 to 15 mm. The housing 411 may have a length l mfrom 30 to 150 mm, preferably 50 to 120 mm, more preferably 70 to 100 mm. The radome can be arranged completely or at least partially outside the head of the body in order to increase a volume of available space within the head of the body. Each of the antenna elements m can further comprise an antenna 413. The antenna 413 can be a helical antenna configured to transmit and / or receive circularly polarized electromagnetic radiation. Other antennas extended in one direction, e.g., in the x-direction, and configured to transmit and / or receive circularly polarized electromagnetic radiation are also possible. The antenna 413 can, for example, form a helix around a cylinder, a cone, an ellipsoid, etc. The antenna 413 can have a directional characteristic (not shown) that is rotationally symmetric in a radiation direction.

[0049] The antenna 413 may be arranged in the radome. In particular, the length of the antenna 413 may be less than the length l m of the radome so that the antenna 413 in the radome can be arranged completely outside the head of the body.

[0050] The shape and material of each individual radome of an antenna 413 can be independent of the shape and material of the body head to enable optimal performance of the antenna 413. Losses and / or distortions during transmission and reception of a radar signal can thus be minimized. The shape and material of the respective radomes can also be adapted to the configuration of the antenna 413 (transmit, receive, transmit, and receive).

[0051] Due to the shape of the antenna elements and the dimensions of the respective antenna 413, the antenna elements can be mounted on the head of a missile 500 as shown in Fig. 5, so that space is freed up inside the head or the missile as a whole for, for example, a second instrument for guiding the missile. The second instrument can be an optical seeker, such as a seeker for detecting electromagnetic radiation in the infrared frequency range. Antenna arrangements according to the present disclosure can thus enable the use of multiple seekers to improve missile guidance, while avoiding the need for a comprehensive change in the missile's shape.

[0052] Each antenna 413 can be configured to generate radiation with the same left- or right-handed circular polarization, regardless of the relative position and orientation of the antenna elements m. This allows a radiated and backscattered radar signal from each transmitting antenna to be received by each receiving antenna without polarization losses. Polarization losses here refer to losses caused by different polarizations.

[0053] Fig. 5 shows a side view of a missile 500 with an antenna assembly 510 and a fuselage 520. The fuselage 520 may include a single-stage, two-stage, or multi-stage propulsion module. One or more of the propulsion stages of the propulsion module may be jettisonable. The antenna assembly 510 may surround one or more submodules. The antenna assembly 510 may, for example, surround an active or passive radar, one or more effectors, a controller, and / or means for wireless communication. In particular, an antenna assembly 510 may include a plurality of antenna elements, as described with reference to Fig. 3 and Fig. 4 described in detail.

[0054] In the foregoing detailed description, various features have been combined into one or more examples for clarity of illustration. It should be understood, however, that the above description is merely illustrative and not restrictive in nature. It is intended to cover all alternatives, modifications, and equivalents of the various features and embodiments. Many other examples will be readily apparent to those skilled in the art based on their skill in the art in light of the above description.

[0055] The embodiments were chosen and described in order to best illustrate the principles underlying the invention and their possible practical applications. This will enable those skilled in the art to optimally modify and utilize the invention and its various embodiments with respect to the intended purpose. In the claims and the description, the terms "including" and "having" are used as neutral language terms for the corresponding term "comprising." Furthermore, the use of the terms "a," "an," and "an" is not intended to exclude a plurality of such described features and components. LIST OF REFERENCE SYMBOLS x10 antenna arrangement (x = 3, 4 or 5) 411 Housing of a radome of an antenna element m 412 tip of a radome of an antenna element m 413 Antenna of an antenna element m 500 missiles 520 Fuselage of the missile 500

Claims

[1] Antenna arrangement (310; 410; 510) comprising: a first antenna element, a second antenna element, a third antenna element, and a fourth antenna element arranged non-coplanarly and configured to detect signals from an incident electromagnetic wave; and a processor configured to determine a direction of incidence of the electromagnetic wave using the detected signals, wherein determining the direction of incidence comprises: Determining (6100) a respective distance between a position of the first antenna element and a position of the second, third and fourth antenna elements; Determining (6200) possible ambiguities of a respective difference between a phase of the electromagnetic wave at the position of the first antenna element and a phase of the electromagnetic wave at the position of the second, third and fourth antenna elements based on the determined respective distance; Determining (6300) possible polar angles and possible azimuth angles for the direction of incidence of the electromagnetic wave, taking into account possible ambiguities; and Determining (6400) a tuple of the possible azimuth angles and the possible polar angles for which either a difference between two azimuth angles vanishes for a polar angle or a difference between two polar angles vanishes for an azimuth angle. [2] Antenna arrangement (310; 410; 510) comprising: a first antenna element, a second antenna element, a third antenna element, and a fourth antenna element arranged non-coplanarly and configured to detect signals from an incident electromagnetic wave; and a processor configured to determine a direction of incidence of the electromagnetic wave using the detected signals, wherein determining the direction of incidence comprises: ambiguously calculating (7100) polar angles based on a first antenna pair of the antenna array (310; 410; 510) in a first coordinate system for the antenna array (310; 410; 510); ambiguously calculating (7200) azimuth angles for each possible polar angle, once based on a second antenna pair of the antenna arrangement (310; 410; 510) and once based on a third antenna pair of the antenna arrangement (310; 410; 510), each antenna pair comprising a first antenna; for each possible polar angle, resolving (7300) the ambiguities in the azimuth angles by choosing an azimuth angle such that the distance between the azimuth angles calculated with the second antenna pair and the azimuth angles calculated with the third antenna pair is minimized; ambiguously calculating (7400) the polar angles based on the second antenna pair in a second coordinate system having a z-axis through the positions of the antennas of the second antenna pair; Converting (7500) the previously determined tuples of azimuth and polar angle in the first coordinate system into polar angles in the second coordinate system; Resolving (7600) the polar angle ambiguity by selecting the polar angle such that a distance between the polar angles determined with the first antenna pair and the polar angles determined with the second antenna pair is minimized; and Selecting (7700) the polar angle thus selected in the first coordinate system and the corresponding previously determined azimuth angle in the first coordinate system as the direction of incidence. [3] Antenna arrangement (310; 410; 510) according to any one of claims 1 to 2, wherein the first antenna element and the second antenna element lie on a first axis of a coordinate system for determining the direction of incidence of the electromagnetic wave; the first antenna element and the fourth antenna element lie on a second axis of the coordinate system; and the first axis and the second axis are orthogonal to each other. [4] The antenna arrangement (310; 410; 510) according to any one of claims 1 to 3, wherein a distance of the second antenna element from the first antenna element and a distance of the fourth antenna element from the first antenna element are different. [5] Antenna arrangement (310; 410; 510) according to any one of claims 1 to 4, wherein the first antenna element is located at the origin of a coordinate system for determining the direction of incidence of the electromagnetic wave and the second antenna element, the third antenna element, and the fourth antenna element have coordinates in the coordinate system which are each an integer multiple of a wavelength of the electromagnetic wave. [6] Antenna arrangement (310; 410; 510) according to claim 5, wherein the integer multiples for each coordinate are less than 20 and preferably greater than 1. [7] The antenna arrangement (310; 410; 510) of any one of claims 1 to 6, wherein the distances of the second, third and fourth antenna elements from the first antenna element are all different. [8] A method (6000) for determining an incident direction of an electromagnetic wave using the antenna arrangement (310; 410; 510) according to any one of claims 1 and 3 to 6, comprising: Determining (6100) a respective distance between a position of the first antenna element and a position of the second, third and fourth antenna elements; Determining (6200) possible ambiguities of a respective difference between a phase of the electromagnetic wave at the position of the first antenna element and a phase of the electromagnetic wave at the position of the second, third and fourth antenna elements based on the determined respective distance; Determining (6300) possible polar angles and possible azimuth angles for the direction of incidence of the electromagnetic wave, taking into account possible ambiguities; and Determining (6400) a tuple of the possible azimuth angles and the possible polar angles for which either a difference between two azimuth angles vanishes for a polar angle or a difference between two polar angles vanishes for an azimuth angle. [9] The method (6000) of claim 8, wherein determining possible polar angles and possible azimuth angles for the direction of incidence of the electromagnetic wave, taking into account the possible ambiguities, comprises: Determining the possible polar angles for the second antenna element; Determining the possible azimuth angles for the third antenna element using the possible polar angles for the second antenna element; and Determining the possible azimuth angles for the fourth antenna element using the possible polar angles for the second antenna element. [10] The method (6000) of claim 8, wherein: determining possible ambiguities further comprises: determining the possible ambiguities for the third antenna element with a determination that the third antenna element lies on a new axis of the coordinate system for determining the direction of incidence of the electromagnetic wave; Determining possible polar angles and possible azimuth angles for the direction of incidence of the electromagnetic wave, taking into account the possible ambiguities, comprises: determining the possible polar angles for the third antenna element with respect to the new axis, and converting the possible polar angles for the third antenna element into polar angles in the original coordinate system for determining the direction of incidence of the electromagnetic wave or converting the possible polar angles for the second antenna element into polar angles with respect to the new axis of the coordinate system for determining the direction of incidence of the electromagnetic wave; and determining the tuple comprises: determining a difference between the possible polar angles for the second antenna element and the possible polar angles for the third antenna element, taking into account the possible azimuth angles for the third antenna element and / or the possible azimuth angles for the fourth antenna element. [11] A method (7000) for determining an incident direction of the electromagnetic wave using the antenna arrangement (310; 410; 510) according to any one of claims 2 to 7, comprising: ambiguously calculating (7100) polar angles based on a first antenna pair of the antenna array (310; 410; 510) in a first coordinate system for the antenna array (310; 410; 510); ambiguously calculating (7200) azimuth angles for each possible polar angle, once based on a second antenna pair of the antenna arrangement (310; 410; 510) and once based on a third antenna pair of the antenna arrangement (310; 410; 510), each antenna pair comprising a first antenna; for each possible polar angle, resolving (7300) the ambiguities in the azimuth angles by choosing an azimuth angle such that the distance between the azimuth angles calculated with the second antenna pair and the azimuth angles calculated with the third antenna pair is minimized; ambiguously calculating (7400) the polar angles based on the second antenna pair in a second coordinate system having a z-axis through the positions of the antennas of the second antenna pair; Converting (7500) the previously determined tuples of azimuth and polar angle in the first coordinate system into polar angles in the second coordinate system; Resolving (7600) the polar angle ambiguity by selecting the polar angle such that a distance between the polar angles determined with the first antenna pair and the polar angles determined with the second antenna pair is minimized; and Selecting (7700) the polar angle thus selected in the first coordinate system and the corresponding previously determined azimuth angle in the first coordinate system as the direction of incidence. [12] Missile (500), comprising: the antenna arrangement (510) according to any one of claims 1 to 7.

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