Radar

Abstract

A radar system configured to determine a relative yaw ψ between first and second objects, 100, 102, each of which is provided with a radar device. One radar device comprises at least one antenna, and

Description

Technical Field This invention relates to radar systems and methods configured to determine a relative yaw between first and second objects. Particularly, though not exclusively, the present invention is concerned with determining the relative yaw between an aerial vehicle such as a UAV and a landing deck on a ship or vessel. Background Art Radar systems are used in various fields, including for air traffic control (ATC) purposes. For decades, such radar systems have been used to locate and identify objects in a geographic region, and typically for the location and identification of aircraft in a particular airspace. Such radar systems generally operate using electromagnetic radiation, particularly radio frequency (RF) electromagnetic signals. While some radar systems rely on reflections from otherwise-passive objects in the vicinity of the transmitter (for ranging to terrain features, for example), in some systems radar may be used to assist one object to position itself relative to another. A radar transmitter on one object may transmit radar signals which may be received by a radar receiver on the other object. Those skilled in the art will appreciate that the relative position between two objects (e.g. UAV and landing deck) in three-dimensional space may be defined in a spherical coordinate system by the distance, elevation angle, and azimuth angle. Using radar techniques, known in the art perse, the distance, elevation angle, and azimuth angle between the aerial vehicle and its target can be determined - for example, using a phase array antenna. For example, a radar system may be used for positioning of an aerial vehicle (e.g. an uncrewed aerial vehicle or 'UAV') relative to a landing deck on a ship or vessel, or for an aerial vehicle to track a ground vehicle. Resilient localisation for uncrewed aerial systems (UAS) is vital if they are to complete their mission when satellite navigation systems are temporarily unavailable, occluded by buiIdings, or have been actively blocked. Using conventional radar systems, known in the art perse, it may be possible to determine the distance, elevation angle, and azimuth angle between two objects (e.g. a UAV and a ship). Some such techniques may rely on synchronization between radar devices at each of the objects. The Applicant has previously presented an advantageous technique to achieve synchronization between two frequency-modulated continuous-wave (FMCW) radar devices in WO2023228152A1, the contents of which are incorporated herein by reference. The Applicant has appreciated, however, that while the distance, elevation angle, and azimuth angle (however so determined) may be sufficient to know the relative position of the two objects, there are scenarios where an additional parameter - the relative yaw between the two objects - may be critical. As an exemplary scenario, a UAV in the air may seek to land on a landing deck of a ship, where the ship is located on the surface of the sea. The UAV may be able to determine the distance, elevation angle, and azimuth angle to the landing deck, however the ship could be oriented at any angle on the sea surface plane, i.e. its degree of yaw is unknown. As the ship can move dynamically, its yaw is a highly relevant parameter for determining the trajectory of the ship and, by extension, the landing deck. Thus the relative 'twist' of the two objects is important, but conventional radar systems for positioning do not typically provide for a mechanism for determining the yaw. While such conventional radar systems may allow for the position of an object to be determined, its orientation is may not be. The present invention seeks to provide improvements to radar localisation arrangement for determining yaw between two objects such as an aerial vehicle (e.g. UAV) and a movable target (e.g. ship landing deck). Summary of the Invention In accordance with a first aspect, embodiments of the present invention provide a radar system configured to determine a relative yaw between first and second objects, the system comprising first and second radar devices wherein one of the radar devices is configured to be installed on the first object and the other of the radar devices is configured to be installed on the second object, wherein: a) the first radar device comprises at least one antenna; b) the second radar device comprises at least first and second antennas; c) wherein the system is configured such that when the first and second radar devices are positioned in a predetermined alignment orientation relative to one another: i) the antenna of the first radar device is co-polarised with the first antenna of the second radar device; and ii) the antenna of the first radar device is at least partially crosspolarised with the second antenna of the second radar device by a first angular offset; and d) wherein the system is further configured to determine data indicative of the relative yaw from relative powers of radar signals received across respective antenna-antenna interfaces between the antenna of the first radar device and each antenna of the second radar device. The first aspect of the invention extends to a method of determining a relative yaw between first and second objects, the method comprising: a) receiving radar signals across respective antenna-antenna interfaces between an antenna of a first radar device and each of first and second antennas of a second radar device, wherein when the first and second radar devices are positioned in a predetermined alignment orientation relative to one another: i) the antenna of the first radar device is co-polarised with the first antenna of the second radar device; ii) the antenna of the first radar device is at least partially crosspolarised with the second antenna of the second radar device by a first angular offset; and b) comparing respective signal powers of the received radar signals to determine data indicative of the relative yaw. The first aspect of the invention also extends to a non-transitory computer-readable medium comprising instructions which, when executed by a processor, cause the processor to carry out a method of determining a relative yaw between first and second objects, the method comprising: a) receiving radar signals across respective antenna-antenna interfaces between an antenna of a first radar device and each of first and second antennas of a second radar device, wherein when the first and second radar devices are positioned in a predetermined alignment orientation relative to one another: i) the antenna of the first radar device is co-polarised with the first antenna of the second radar device; ii) the antenna of the first radar device is at least partially crosspolarised with the second antenna of the second radar device by a first angular offset; and b) comparing respective signal powers of the received radar signals to determine data indicative of the relative yaw. The first aspect of the invention further extends to a computer software product comprising instructions which, when executed by a processor, cause the processor to carry out a method of determining a relative yaw between first and second objects, the method comprising: a) receiving radar signals across respective antenna-antenna interfaces between an antenna of a first radar device and each of first and second antennas of a second radar device, wherein when the first and second radar devices are positioned in a predetermined alignment orientation relative to one another: i) the antenna of the first radar device is co-polarised with the first antenna of the second radar device; ii) the antenna of the first radar device is at least partially crosspolarised with the second antenna of the second radar device by a first angular offset; and b) comparing respective signal powers of the received radar signals to determine data indicative of the relative yaw. Thus it will be appreciated that embodiments of the present invention provide an improved radar system which leverages polarisation to provide information regarding the relative yaw of the two objects. As there are at least two antenna-antenna interfaces (i.e. transmitter-receiver antenna pairs) between the two devices with an angular offset between the two, one transmitter-receiver pair will yield a stronger signal power than the other transmitter-receiver antenna pair. The antenna-antenna interface with the greater degree of co-polarisation, i.e. angular alignment, will yield a stronger signal power at the receiver. A further advantage of the present invention is that the yaw may be determined without requiring any moving parts. The antennas (or antenna arrays) can be provided in a low size, low weight, and low power package suitable for battery power. Further advantageously, radar is largely unaffected by poor visibility, lighting, and bad weather, unlike camera-based localisation. The principles of the present invention may be achieved with different configurations in terms of the transmission and reception roles of the two radar devices, as outlined in further detail below. Regardless of whether the different polarisations are as a result of multiple transmissions with different polarisations being received by a given receiver and / or multiple receptions with different polarisations being received from a given transmitter, it is the relative signal powers of the received signals that are ultimately used to determine the relative yaw. In a first configuration, used in a set of embodiments, the multiple antennas of the second radar device may each be used to transmit radar signals, with the antenna of the first radar device receiving each of those transmissions which will each have a respective polarity as a result of the transmit antennas of the second radar device being angled with respect to one another and to the receive antenna of the first radar device. In this configuration, there are multiple differently polarised transmissions that can be received by a single receiver. In general, these differently polarised transmissions will be transmitted at different times to prevent merging of the different polarisations. This may result in overall slower performance (since it takes longer to perform the radar transmission step) but may be advantageous where the radar receiver is being dedicated to the detection of elevation and azimuth angles, as described in more detail later. In a second configuration, used in another set of embodiments, the multiple antennas of the second radar device may each be used to receive radar signals transmitted by the antenna of the first radar device. Each of those received transmissions which will each have a respective polarity as a result of the receive antennas of the second radar device being angled with respect to one another and to the transmit antenna of the first radar device. Thus, in this configuration, there are multiple differently polarised receptions received from a single transmitter. In this case, there is no need for multiple time-separated radar transmissions, which may yield faster performance. A combination of these configurations may be used, in which there are multiple differently polarised transmissions (from differently oriented transmit antennas) and multiple differently polarised receptions (from differently oriented receive antennas). One or both of the radar devices may be radar transceivers, i.e. they may each (or both) transmit and receive radar signals. Either radar device may be installed, or may be configured to be installed, on either object. However, in some embodiments, the first radar device is installed or is configured to be installed on the first object, and wherein the second radar device is installed or is configured to be installed on the second object. As outlined above, either of the radar devices may be the transmitter or the receiver, and in some embodiments one or both radar devices may respectively comprise a radar transceiver. In some embodiments, the second radar device is configured to transmit radar signals using the antennas of the second radar device, and wherein the first radar device is configured to receive the transmitted radar signals using the antenna of the first radar device. This corresponds to the first configuration mentioned above in which multiple differently polarised transmissions from the second radar device are received by the antenna of the first radar device. This may enable the determination of the elevation angle. In some such embodiments, the first radar device comprises a vertically aligned pair of antennas, wherein the first radar device is configured to receive the transmitted radar signals using the antenna of the first radar device, and wherein the radar system is configured to determine an elevation angle of the first object relative to the second object from a relative phase difference between corresponding transmitted radar signals received at each antenna of the vertically aligned pair of antennas; optionally wherein each antenna of the vertically aligned pair of antennas is connected to a corresponding waveguide having substantially the same length and / or substantially the same number of bends. This configuration may also enable the determination of the azimuth angle. In some potentially overlapping embodiments, the first radar device comprises a horizontally aligned pair of antennas, wherein the first radar device is configured to receive the transmitted radar signals using the antenna of the first radar device, and wherein the radar system is configured to determine an azimuth angle of the first object relative to the second object from a relative phase difference between corresponding transmitted radar signals received at each antenna of the horizontally aligned pair of antennas; optionally wherein each antenna of the horizontally aligned pair of antennas is connected to a corresponding waveguide having substantially the same length and / or substantially the same number of bends. The waveguides, where provided, may be any suitable type of waveguide known in the art perse. However, in some embodiments, the waveguides may each respectively comprise a substrate integrated waveguide or a coplanar waveguide (CPWG). Whether the first or second configuration is being used (or a combination of these), the range or distance between the objects may also be determined using the radar system. Thus, in some further potentially overlapping embodiments, the first radar device is configured to receive the transmitted radar signals using the antenna of the first radar device, and wherein the radar system is configured to determine a distance between the first object and the second object. The radar system may, in some such embodiments, be configured to determine the distance between the first object and the second object based on the time-of-flight of the radar signals. In some potentially overlapping embodiments, the radar devices may be frequency-modulated continuous-wave (FMCW) radar devices, wherein the radar system determines the distance between the first object and the second object based on a frequency distance between transmitted and received FMCW radar signals. The radar devices may be configured to synchronize with one another and may do so using a self-synchronization procedure. An example of such a self-synchronization procedure has been described previously by the Applicant in WO2023228152A1, the contents of which are incorporated herein by reference. Thus the radar system may, in a particular set of embodiments, determine the distance and bearing (i.e. the azimuth and elevation angles) between the first and second objects, as well as the relative yaw. The system may, at least in some embodiments where the first radar device comprises a vertically aligned pair of antennas and / or a horizontally aligned pair of antennas, be configured such that when the first and second radar devices are positioned in the predetermined alignment orientation relative to one another, each antenna of said vertically aligned pair of antennas and / or horizontally aligned pair of antennas of the first radar device is co-polarised with the first antenna of the second radar device. Thus the antennas of the first radar device used for determining bearing may each be angularly aligned with one another (but may be laterally aligned relative to one another to enable measurement of the elevation angle and / or azimuth angle, as appropriate). In some embodiments, the first radar device is configured to transmit radar signals using the antenna of the first radar device, and wherein the second radar device is configured to receive said transmitted radar signals using each antenna of the second radar device. This corresponds to the second configuration mentioned above in which multiple differently polarised receptions at the second radar device are received from the antenna of the first radar device. In some embodiments, the first object comprises an aerial vehicle. In some such embodiments, the aerial vehicle comprises a drone and / or an uncrewed aerial vehicle (UAV). In some embodiments, the second object comprises a movable target. In a set of such embodiments, the movable target comprises a landing deck on a ship or vessel. In an alternative set of embodiments, the movable target comprises a ground vehicle. The number of antennas and the angular offset(s) between may be selected to provide a desired range of yaw values that can be resolved by the radar system. The angular offsets may be selected such that the orientations of the antennas are evenly distributed. For example, where two antennas are provided, these may be oriented at 90° to one another; whereas where three antennas are provided, these may be oriented at 60° to one another. In general, in some embodiments, at least one of the first and second radar devices comprises N antennas, wherein the N antennas are rotated by 180° / N with respect to one another. However, in other embodiments, the antennas may not be evenly distributed. The provision of additional antennas improves the ability to resolve the relative yaw. In some embodiments, the second radar device comprises a third antenna, wherein the system is configured such that when the first and second radar devices are positioned in the predetermined alignment orientation relative to one another: iii) the antenna of the first radar device is at least partially cross-polarised with the third antenna of the second radar device by a second angular offset different to the first angular offset. In some potentially overlapping embodiments, the first angular offset is between approximately 40° and 80°, optionally between approximately 50° and 70°, further optionally approximately 60°, yet further optionally wherein the first angular offset is 60°. In some alternative embodiments, the first angular offset is between approximately -100° and -140°, optionally between approximately -110° and -130°, further optionally approximately -120°, yet further optionally wherein the first angular offset is -120°. In some further potentially overlapping embodiments, the second angular offset is between approximately 100° and 140°, optionally between approximately 110° and 130°, further optionally approximately 120°, yet further optionally wherein the second angular offset is 120°. In some alternative embodiments, the second angular offset is between approximately -40° and -80°, optionally between approximately -50° and -70°, further optionally approximately -60°, yet further optionally wherein the second angular offset is -60°. The antenna patches may be rotationally symmetric such that angular offsets separated by 180° are functionally equivalent. As such, angular rotations with a positive value of degrees X° may be functionally equivalent to an angular offset equal to that value minus 180° (i.e. X-180°), e.g. an offset of 60° may be equivalent to an angular offset of -120°; an offset of 120° may be equivalent to an angular offset of -60°; an offset of 45° may be equivalent to an angular offset of -135°; and so on. In some embodiments, the second radar device further comprises a fourth antenna, wherein the system is further configured such that when the first and second radar devices are positioned in the predetermined alignment orientation relative to one another: iv) the antenna of the first radar device is at least partially cross-polarised with the fourth antenna of the second radar device by a third angular offset different to the first and second angular offsets. In some potentially overlapping embodiments, the first angular offset is between approximately 25° and 65°, optionally between approximately 35° and 55°, further optionally approximately 45°, yet further optionally wherein the first angular offset is 45°. In some alternative embodiments, the first angular offset is between approximately -155° and -115°, optionally between approximately -145° and -125°, further optionally approximately -135°, yet further optionally wherein the first angular offset is -135°. In some further potentially overlapping embodiments, the second angular offset is between approximately 115° and 155°, optionally between approximately 125° and 145°, further optionally approximately 135°, yet further optionally wherein the second angular offset is 135°. In some alternative embodiments, the second angular offset is between approximately -65° and -25°, optionally between approximately -55° and -35°, further optionally approximately -45°, yet further optionally wherein the second angular offset is -45°. In some yet further potentially overlapping embodiments, the third angular offset is between approximately 70° and 110°, optionally between approximately 80° and 100°, further optionally approximately 90°, yet further optionally wherein the third angular offset is 90°. In some alternative embodiments, the third angular offset is between approximately -110° and -70°, optionally between approximately -100° and -80°, further optionally approximately -90°, yet further optionally wherein the third angular offset is -90°. In some embodiments, one or more of the antennas respectively comprises a patch antenna, optionally wherein each antenna of the respectively comprises a patch antenna. The determination of the data indicative of the relative yaw may, in some embodiments, be performed by a processing unit. Thus, in some embodiments, the radar system comprises a processing unit configured to determine the data indicative of the relative yaw from relative powers of radar signals received across respective antenna-antenna interfaces between the antenna of the first radar device and each antenna of the second radar device. Such a processing unit may be any suitable type of processing unit, including one or more of: a central processing unit (CPU), graphical processing unit (GPU), a microprocessor, an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a reduced instruction set computer (RISC), or other similar type of processing unit or means known in the art perse. Either the first object or the second object may comprise or carry the processing unit. The first radar device or the second radar device may comprise the processing unit. The determination of the relative yaw may be carried out by the object to which it is of interest. For example, where the first object is a UAV and the second object is a ship, and the UAV intends to land on a landing deck aboard that ship, then the relative yaw may be determined by the UAV as part of its landing planning process. However, this is not necessarily the case. In the same scenario, the ship may be the one to make the determination of relative yaw, for example as part of an air traffic control (ATC) process. The first and second objects may, in some embodiments, be configured to communicate via a communications channel (e.g. an RF-based communications channel), and the determined data indicative of the relative yaw may be communicated from one object to the other via said communications channel. Thus, in some embodiments, the radar device - which may have one or multiple receive antennas - of the first object (e.g. a drone or UAV) receives the radar signals and uses a processing unit on that first object (which may be within the corresponding radar device itself) to determine the data indicative of the relative yaw. In some potentially overlapping embodiments, the determination of the relative yaw may be carried out by the second object, e.g. a ship, vessel, or ground vehicle. In such embodiments, the radar device - which may have one or multiple receive antennas - of the second object (e.g. a ship, vessel, or ground vehicle) receives the radar signals and uses a processing unit on that second object (which may be within the corresponding radar device itself) to determine the data indicative of the relative yaw. These two approaches could be combined, in which both the first and second objects each have a respective processing unit configured to determine respective data indicative of the relative yaw. The respective data determined by the first object and / or the second object may be shared with the other object, e.g. using a communications channel such as the communications channel described hereinabove. When viewed from a second aspect, embodiments of the present invention provide a radar system configured to determine a relative yaw between a first object and a second object, the system comprising at least a radar transmitter and a radar receiver, wherein: the radar transmitter comprises a radar transmitter antenna arrangement including at least one antenna; the radar receiver comprises a radar receiver antenna arrangement including at least one antenna; at least one of the antenna arrangements includes at least two antennas, wherein the at least two antennas are angled with respect to one another; and the relative powers of signals received at each of the receive antenna(s) from each of the transmit antenna(s) are compared to determine data indicative of the relative yaw. The second aspect of the invention extends to a method of determining a relative yaw between first and second objects, the method comprising: a) receiving radar signals across respective antenna-antenna interfaces between a radar transmitter antenna arrangement including at least one antenna and a radar receiver antenna arrangement including at least one antenna, wherein at least one of the antenna arrangements includes at least two antennas, and wherein the at least two antennas are angled with respect to one another; and comparing the relative powers of signals received at each of the receive antenna(s) from each of the transmit antenna(s) to determine data indicative of the relative yaw. The second aspect of the invention also extends to a non-transitory computer-readable medium comprising instructions which, when executed by a processor, cause the processor to carry out a method of determining a relative yaw between first and second objects, the method comprising: a) receiving radar signals across respective antenna-antenna interfaces between a radar transmitter antenna arrangement including at least one antenna and a radar receiver antenna arrangement including at least one antenna, wherein at least one of the antenna arrangements includes at least two antennas, and wherein the at least two antennas are angled with respect to one another; and comparing the relative powers of signals received at each of the receive antenna(s) from each of the transmit antenna(s) to determine data indicative of the relative yaw. The second aspect of the invention further extends to a computer software product comprising instructions which, when executed by a processor, cause the processor to carry out a method of determining a relative yaw between first and second objects, the method comprising: a) receiving radar signals across respective antenna-antenna interfaces between a radar transmitter antenna arrangement including at least one antenna and a radar receiver antenna arrangement including at least one antenna, wherein at least one of the antenna arrangements includes at least two antennas, and wherein the at least two antennas are angled with respect to one another; and comparing the relative powers of signals received at each of the receive antenna(s) from each of the transmit antenna(s) to determine data indicative of the relative yaw. In some embodiments, at least one of the antenna arrangements includes at least three antennas, and wherein the at least three antennas are angled with respect to one another. In some embodiments, the radar transmitter comprises two or more transmit antennas. In some such embodiments, the radar transmitter comprises three or more transmit antennas. In some embodiments, the radar transmitter comprises P transmit antennas, wherein the P transmit antennas are rotated by 180° / P with respect to one another. However, in other embodiments, the transmit antennas may not be evenly distributed. In some potentially overlapping embodiments, the radar receiver comprises two or more receive antennas. In some such embodiments, the radar receiver comprises three or more receive antennas. In some potentially overlapping embodiments, the radar receiver comprises Q. receive antennas, wherein the Q receive antennas are rotated by 180° / Q with respect to one another. However, in other embodiments, the receive antennas may not be evenly distributed. It will be appreciated that the optional features described hereinabove in respect of embodiments of the any aspect of the invention apply equally, where technically appropriate, to the other aspects of the invention outlined herein. Where technically appropriate, embodiments of the invention may be combined. Embodiments are described herein as comprising certain features / elements. The disclosure also extends to separate embodiments consisting or consisting essentially of said features / elements. Technical references such as patents and applications are incorporated herein by reference. Any embodiments specifically and explicitly recited herein may form the basis of a disclaimer either alone or in combination with one or more further embodiments. Where one antenna is said to be rotated with respect to another so as to provide an angular offset, those rotations may be in the clockwise direction or in the counterclockwise direction. Typically, a convention will be chosen such that, for example, positive values of angular rotations are clockwise and negative values of angular rotations are counterclockwise (or vice versa). The term "relative powers" as used in respect of the radar signals should be understood to extend to other corresponding metrics such as the signal strength or amplitudes of those radar signals. In the context of this specification, the term "approximately" is defined as ± 10%. In the context of this specification "comprising" is to be interpreted as "including". Aspects of the invention comprising certain elements are also intended to extend to alternative embodiments "consisting" or "consisting essentially" of the relevant elements. Brief Description of the Drawings Certain embodiments of the present invention will now be described with reference to the accompanying drawings, in which: Fig. 1 is an illustrative example of a radar localisation scenario involving a UAV and a ship; Fig. 2 is a diagram illustrating the distance and elevation and azimuth angles between the two objects; Fig. 3 is a diagram illustrating relative yaw; Fig. 4 is a schematic diagram illustrating radar antenna alignment for use in a radar system in accordance with an embodiment of the invention; Fig. 5 is a further schematic diagram illustrating separated transmit and receive antennas; Fig. 6 is a graph illustrating relative signal power levels at a radar receiver device with a receive antenna that receives three differently polarised radar signals from three transmit antennas; and Fig. 7 is a schematic diagram illustrating a radar system with antennas arranged in accordance with a further embodiment of the invention. Detailed Description Certain exemplary embodiments are described herein which relate to a radar system. It will be appreciated that the radar system and its various components - as well as systems and components it interacts with - are complex technical systems, and so the illustrations and descriptions provided herein are simplified for ease of reference. It will be appreciated that this description provides examples for reference purposes, and the scope of the invention is defined by the claims. Fig. 1 is an illustrative example of a radar localisation scenario involving two objects, in this case a UAV 100 and a ship 102. In this scenario, the ship 102 is floating in the sea 104. The UAV 100 is flying in the sky above the sea 104 and intends to land on a landing deck 106 of the ship 102. In order to plan the manoeuvres required to land the UAV 100 on the landing deck 106 of the ship 102, the distance and bearing to the landing deck 106 of the ship 102 are needed. To determine these, the UAV 100 is provided with a first radar device 110, and the ship 102 is provided with a second radar device 112. These radar devices 110,112 exchange RF radar signals (i.e. electromagnetic signals) which can be used for the determination of distance 'r', elevation angle '0', and azimuth angle '(p', which can be understood with further reference to Fig. 2. In addition, however, the radar system enables the relative yaw 'ip' between the objects, which can be understood with further reference to Fig. 3. The different measurements can be obtained due to the antenna arrangements within the radar devices 110,112 - this will be explained in more detail below with reference to Figs. 4 to 6. Fig. 2 is a diagram illustrating the distance r, the elevation angle 0, and the azimuth angle <p between the two objects. The distance and bearing of the UAV 100 relative to the ship 102 can be expressed in a spherical coordinate tuple r, 0, ¢. For simplicity, the ship 102 is taken as the origin. As such, the distance r is the radial Euclidian distance from that origin to the UAV 100. The elevation 0 is the angle from the reference plane 200 (in the above scenario, broadly equivalent the surface of the sea) direction to the radial line segment that joins the points of the origin (the ship 102) and the UAV 100. The azimuth 4» is the angle measured from the azimuth reference direction to the orthogonal projection of the radial line segment that joins the points of the origin (the ship 102) and the UAV 100 on the reference plane 200. It will of course be appreciated that while the use of spherical coordinates is preferable for convenience, this coordinate system is merely exemplary, and a different coordinate system could be used, for example where the origin is based on some fixed point in space or centred on the UAV 100. Even if a different coordinate system were used (e.g. a cartesian coordinate system), the concepts of the distance r and the elevation and azimuth angles 0, cp would nevertheless be applicable in terms of describing the distance and bearing between the objects in a three-dimensional space. Fig. 3 is a diagram illustrating relative yaw ip. It can be seen from Fig. 2 that the instantaneous position of the ship 102 relative to the UAV 100 can be determined in terms of the distance r, the elevation angle 0, and the azimuth angle ¢. However, the ship 102 can be in any orientation in the reference plane 200, and this orientation is not captured within the tuple r, 0, ¢. In other words, the ship 102 can pivot in-plane around its position without affecting the values of the tuple r, 0, ¢. The relative yaw or 'twist' is denoted 'ip' and serves as a further parameter which can be determined using a radar system in accordance with embodiments of the present invention. Knowledge of the relative yaw ip is important for certain scenarios, for example when planning landing manoeuvres for the UAV 100 to land on the landing deck 106 of the ship 102. The relative yaw can be used to determine the trajectory of the ship 102 such that its time-varying position can be accounted for when planning the landing manoeuvres. Fig. 4 is a schematic diagram illustrating radar antenna alignment for use in a radar system in accordance with an embodiment of the invention. In particular, Fig. 4 shows a single printed circuit board (PCB) 400 which has both a transmit antenna array 402 and a receive antenna array 404. Strictly, only one object needs a transmit antenna arrangement and the other object needs a receive antenna arrangement, however for ease of describing the antennas and their relative alignments, it is first easiest to consider a transceiver that has both types of antenna arrangements. In practice, both objects may have such a transceiver, i.e. both objects may be supplied with a radar device having both a transmit antenna arrangement and a receive antenna arrangement. Fig. 5 is a further schematic diagram illustrating the devices where the transmit antenna array 402 and the receive antenna array 404 are provided in physically separate devices -one of these may be supplied on the UAV 100 and the other on the ship 102. The 'receive side' is the side which will determine the relative yaw <p. The receive side may be the object 'interested' in the relative yaw ip - this might be the UAV 100 (if it is determining the relative yaw ip itself) or might be the ship 102 (if it is determining the relative yaw ip and then communicating this to the UAV 100, e.g. as part of an ATC process, via a suitable communications channel between the UAV 100 and the ship 102). The transmit antenna array 402 comprises three transmit antenna patches 406a-c, which are angled with respect to one another. The first transmit antenna patch 406a is considered to have a rotation of 0°. Relative to the first transmit antenna patch 406a, the second transmit antenna patch 406b is rotated by 60°, providing a first angular offset of 60°. Relative to the first transmit antenna patch 406a, the third transmit antenna patch 406c is rotated by 120°, providing a second angular offset of 120°. The three transmit antenna patches 406a-c are - in this exemplary embodiment - provided in a triangular formation, in this case an equilateral triangle. Thus the angular offsets are equally spaced by an angle equal to 180° divided by the number ('N') of antennas, in this case 3, i.e. 180° / 3 = 60°. Lines that bisect ('bisectors') each of the transmit antenna patches 406a-c meet at a point (together forming a 'Y' shape) with an angle of 120° between adjacent bisectors (i.e. the available 360° divided equally by 3). It will be appreciated that the antenna patches could have a different layout, however. For example, the in-plane positions of the second and third transmit antenna patches 406b, 406c could be transposed The receive antenna array 404 comprises four receive antenna patches, made up of a vertically aligned pair of patches 408a-b, and a horizontally aligned pair of patches 410a-b. Each of these receive antenna patches 408a-b, 410a-b are oriented at 0°, i.e. they are: co-polar with the first transmit antenna patch 406a; cross-polar with the second transmit antenna patch 406b with a first angular offset of 60°; and cross-polar with the third transmit antenna patch 406c with a second angular offset of 120°. The patches are The vertically aligned pair of patches 408a-b are positioned in-plane such that they share a horizontal position (in the 'x-direction') but have different vertical positions (in the 'y-direction'). This vertically aligned pair of patches 408a-b can be used to measure the elevation angle 0. As the patches 408a-b have different vertical positions, there will generally be a phase difference in radar transmission received at each of these vertically aligned patches 408a-b. The elevation angle 0 can be extracted from that phase difference across the vertically aligned patches 408a-b. Each of the vertically aligned pair of patches 408a-b is connected to further receiver electronics 414 via a respective waveguide 416 (e.g. a substrate integrated waveguide, coplanar waveguide (CPWG), or other such waveguide known in the art perse), and these waveguides 416 may be optimised to be substantially equal in length and to have the same number of bends in each path so that the phase difference in the paths to / from each antenna 408a-b is minimised, thus minimising any error in elevation angle 0 determination. Conversely, the horizontally aligned pair of patches 410a-b are positioned in-plane such that they share a vertical position (in the 'y-direction') but have different horizontal positions (in the 'x-direction'). This horizontally aligned pair of patches 410a-b can be used to measure the azimuth angle ¢. As the patches 410a-b have different horizontal positions, there will generally be a phase difference in radar transmission received at each of these horizontally aligned patches 410a-b. The azimuth angle 4> can be extracted from that phase difference across the horizontally aligned patches 410a-b. As with the vertically aligned pair of patches 408a-b, each of the horizontally aligned pair of patches 410a-b is connected to further receiver electronics via a respective waveguides 418 (e.g. CPWG, substrate integrated waveguides, or other such waveguides known in the art perse) which may be optimised to be substantially equal in length and to have the same number of bends in each path so that the phase difference in the paths to / from each antenna 410a-b is minimised, thus minimising any error in azimuth angle 4> determination. In order to measure the elevation angle 0 azimuth angle $ from phase differences at patch pairs 408a-b, 410a-b on the receive side, it is highly beneficial to have equal length waveguides 416, 418 (e.g. CPWGs) for a given patch pair 408a-b, 410a-b and ideally bends too. Additionally, matching waveguide lengths on the transmit side is good practice, though not as critical. When losses are similar between radar and antenna, for each transmit antenna, the power levels can be compared at the receiver without dealing with the complication of differing waveguide losses between the transmit antennas. The range r between the UAV 100 and the ship 102 can be determined using standard radar techniques, known in the art perse. This may, for example, be achieved using the time-of-flight of received radar signals at one or more of the antennas of the receive antenna array 404, or by utilising an FMCW scheme in which the range r can be determined from a difference in frequency between transmitted and received radar signals. The different alignments of the antennas in the transmit antenna array 402 and receive antenna array 404 yields differing levels of co- or cross-polarity between transmit-receive pairs of antennas. When both radar devices are aligned in a particular way as shown in Fig. 5, the first transmit antenna patch 406a is - at this moment in time - co-polar with all of the antenna patches 408a-b, 410a-b of the receive antenna array 404 (as they are all oriented the same way). Meanwhile, the second transmit antenna patch 406b is 60° crosspolar with the antenna patches 408a-b, 410a-b of the receive antenna array 404; and the third transmit antenna patch 406c is 120° cross-polar with the antenna patches 408a-b, 410a-b of the receive antenna array 404. The transmit antenna array 402 transmits three radar signals 412a-c, one from each of the transmit antenna patches 406a-c. In order to prevent merging of the different polarities, a radar signal is only transmitted from one transmit antenna patch 406a-c at a time, i.e. the transmissions are time-division multiplexed. Owing to the different angular alignment of each of the transmit antenna patches 406a-c, the corresponding transmitted radar signals 412a-c each have a different respective polarity. During normal operations (i.e. at run time), the two radar devices may not necessarily be aligned as shown in Fig. 5 because there may be a relative yaw ip (or 'twist') between the objects to which the radar devices are affixed, e.g. the UAV 100 and ship 102. As the receive antenna array 404 receives the differently polarised radar signals 412a-c, the relative power levels of those received signals 412a-c will vary depending on the degree of co- or cross-polarity of the interface between the relevant transmit and receive antennas. This is illustrated in Fig. 6, which is a graph illustrating relative signal power levels at a radar receiver device with a receive antenna that receives three differently polarised radar signals 412a-c from three transmit antennas 406a-c in the system shown in Fig. 5. Each plot on the graph of Fig. 6 shows the relative power level (in decibels, dB) as a function of the relative yaw ¢) (in degrees, °). A first plot represents the received signal 412a from the first transmit antenna patch 406a, which is co-polar with the receive antennas 408a-b, 410a-b when the devices are in the predetermined alignment orientation shown in Figs. 4 and 5. A second plot represents the received signal 412b from the second transmit antenna patch 406b, which is 60° cross-polar with the receive antennas 408a-b, 410a-b when the devices are in the predetermined alignment orientation shown in Figs. 4 and 5. A third plot represents the received signal 412c from the third transmit antenna patch 406c, which is 120° (equivalent to -60°) cross-polar with the receive antennas 408a-b, 410a-b when the devices are in the predetermined alignment orientation shown in Figs. 4 and 5. As can be seen in Fig. 6, as the relative yaw ¢) varies (i.e. as the ship 102 twists with respect to the UAV 100), the respective power levels of the received differently polarised transmitted radar signals 412a-c varies. When the two radar devices are aligned, i.e. when the first transmit antenna patch 406a is coaligned with the receive antenna patches with an angular offset of 0° (or, equivalently, 180°), it is at maximum relative power, i.e. at 0 dB, while the signals 412b, 412c from the other two transmit antennas 406b, 406c are each down by approximately 5 dB. When the two radar devices are angularly offset at +60° (or, equivalently, -120°), the second transmit antenna patch 406b instead is coaligned with the receive antenna patches. As such, the transmitted signal 412b from that patch 406b is at maximum relative power, i.e. at 0 dB, while the signals 412a, 412c from the other two transmit antennas 406a, 406c are each down by approximately 5 dB. Conversely, when the two radar devices are angularly offset at -60° (or, equivalently, +120°), the third transmit antenna patch 406c is coaligned with the receive antenna patches. In that scenario, it is the transmitted signal 412c from that patch 406c that is at maximum relative power, i.e. at 0 dB, while the signals 412a, 412b from the other two transmit antennas 406a, 406b are each down by approximately 5 dB. The relative power level of each signal 412a-c drops to its lowest value when the corresponding transmit antenna patch 406a-c is at 90° to - and thus completely cross-polar with - the receive antenna. For the first transmit antenna patch 406a this occurs at a relative yaw ip of +90°. Meanwhile, for the second transmit antenna patch 406b this occurs at a relative yaw ip of 30° and -150°. Finally, for the third transmit antenna patch 406c this occurs at a relative yaw ip of -30° and 150°. At intermediate degrees of relative yaw ip between these extremes, the relative signal powers vary accordingly, according to a cosine-based relationship. At an unknown relative yaw ip, the relative signal powers of each of the received signals 412a-c can be measured and compared to determine the relative yaw ip. The relative yaw ip can be resolved with two possible solutions, separated by ±180°. For example, based on readings of the relative signal powers, the system may determine that the relative yaw ip is either 75° or -105°. This determination and the relevant calculations may be made by a suitable processing arrangement, which may form part of the radar device supplied on either object (e.g. on the UAV 100 or on the ship 102) or part of some other electronic device (which again, may be provided on either object). Fig. 7 is a schematic diagram illustrating a radar system with antennas arranged in accordance with a further embodiment of the invention. Here two objects 700, 702 are each provided with a radar device. For example, one object 700 may be a UAV and the other object 702 may be a ship. The first object 700 is provided with a single radar transmit antenna 704 and four radar receive antennas 706a-d. The four radar receive antennas 706a-d are angularly oriented relative to one another in 45° intervals, such that: the first receive antenna 706a is oriented at 0°; the second receive antenna 706b is oriented at 45°; the third receive antenna 706c is oriented at 90°; and the fourth receive antenna 706d is oriented at 135°. The transmit antenna 706 is oriented at 0°. Similarly, the second object 702 is provided with a single radar transmit antenna 708 and four radar receive antennas 710a-d. The four radar receive antennas 710a-d are angularly oriented relative to one another in 45° intervals, such that: the first receive antenna 710a is oriented at 0°; the second receive antenna 710b is oriented at 45°; the third receive antenna 710c is oriented at 90°; and the fourth receive antenna 710d is oriented at 135°. The transmit antenna 708 is oriented at 0°. In the embodiments described above in respect of Figs. 4 to 6, there were a number of differently polarised radar transmissions. By contrast, in the embodiment of Fig. 7, there is only a single radar transmission 714, 716 from the respective radar transmit antennas 704, 708. However, as the receive antennas 706a-d, 710a-d are oriented with angular offsets, they each receive differently polarised received signals. In effect, the receiving elements are positioned so that a polarised incident wave will result in a varying signal amplitude per channel. Similar to the case described previously with reference to the graph of Fig. 6, the relative power levels of the transmitted signals 714, 716 as received by each of the respective receive antennas 706a-d, 710a-d will depend on the degree of alignment between the transmit antenna 704, 708 in one device and the relevant receive antenna 706a-d, 710a-d in the other device. By measuring and comparing the relative signal powers, the relative yaw ¢) may be determined. In this embodiment, both objects 700, 702 are able to determine the relative yaw ip. They may communicate their determined values for ip to one another to improve accuracy, redundancy, and / or robustness. It should be noted that this is also true with the earlier described embodiments - if both objects (such as the UAV 100 and ship 102) were each object provided with means to receive differently polarised transmissions from the other object, they could each determine the relative yaw <p and, if appropriate, communicate their determined values with one another. While the embodiments described above refer to the applicability of the radar system to a UAV and a ship, the radar system described herein may be readily applied in other applications. For example, rather than a ship, the UAV may seek to track a ground vehicle such as a car, truck, van, lorry, or similar. Similarly, rather than a UAV, some other form of object, aerial vehicle, aircraft (e.g. an aeroplane, helicopter, or such like) may be the intended use case for the radar device. Thus it will be appreciated that embodiments of the present invention provide an 5 improved radar system and corresponding method for localising one object relative to another that can determine a relative yaw or twist between those objects. This provides significant benefits, particularly though not exclusively, to radar systems for use with aerial vehicles and movable targets, e.g. UAVs or drones and ships or ground vehicles. By leveraging the degree of co-polarisation (or cross-polarisation) between antennas on the 10 different objects, the relative yaw can be determined. This may be achieved using the same antenna arrays used for detection of azimuth and elevation angles.

Claims

1. A radar system configured to determine a relative yaw between first and second objects, the system comprising first and second radar devices wherein one of the radar devices is configured to be installed on the first object and the other of the radar devices is configured to be installed on the second object, wherein:a) the first radar device comprises at least one antenna;b) the second radar device comprises at least first and second antennas;c) wherein the system is configured such that when the first and second radar devices are positioned in a predetermined alignment orientation relative to one another:i) the antenna of the first radar device is co-polarised with the first antenna of the second radar device; andii) the antenna of the first radar device is at least partially crosspolarised with the second antenna of the second radar device by a first angular offset; andd) wherein the system is further configured to determine data indicative of the relative yaw from relative powers of radar signals received across respective antenna-antenna interfaces between the antenna of the first radar device and each antenna of the second radar device.

2. The radar system as claimed in claim 1, wherein the first radar device is installed or is configured to be installed on the first object, and wherein the second radar device is installed or is configured to be installed on the second object.

3. The radar system as claimed in claim 1 or 2, wherein the second radar device is configured to transmit radar signals using the antennas of the second radar device, and wherein the first radar device is configured to receive the transmitted radar signals using the antenna of the first radar device.

4. The radar system as claimed in claim 3, wherein the first radar device comprises a vertically aligned pair of antennas, wherein the first radar device is configured to receive the transmitted radar signals using the antenna of the first radar device, and wherein theradar system is configured to determine an elevation angle of the first object relative to the second object from a relative phase difference between corresponding transmitted radar signals received at each antenna of the vertically aligned pair of antennas;optionally wherein each antenna of the vertically aligned pair of antennas is connected to a corresponding waveguide having substantially the same length and / or substantially the same number of bends.

5. The radar system as claimed in claim 3 or 4, wherein the first radar device comprises a horizontally aligned pair of antennas, wherein the first radar device is configured to receive the transmitted radar signals using the antenna of the first radar device, and wherein the radar system is configured to determine an azimuth angle of the first object relative to the second object from a relative phase difference between corresponding transmitted radar signals received at each antenna of the horizontally aligned pair of antennas;optionally wherein each antenna of the horizontally aligned pair of antennas is connected to a corresponding waveguide having substantially the same length and / or substantially the same number of bends.

6. The radar system as claimed in claim 4 or 5, wherein the system is configured such that when the first and second radar devices are positioned in the predetermined alignment orientation relative to one another, each antenna of said vertically aligned pair of antennas and / or horizontally aligned pair of antennas of the first radar device is copolarised with the first antenna of the second radar device.

7. The radar system as claimed in claim 1 or 2, wherein the first radar device is configured to transmit radar signals using the antenna of the first radar device, and wherein the second radar device is configured to receive said transmitted radar signals using each antenna of the second radar device.

8. The radar system as claimed in any preceding claim, wherein the first object comprises an aerial vehicle, optionally wherein the aerial vehicle comprises a drone and / or an uncrewed aerial vehicle (UAV).

9. The radar system as claimed in any preceding claim, wherein the second object comprises a movable target, optionally wherein the movable target comprises a landing deck on a ship or vessel.

10. The radar system as claimed in any of claims 1 to 8, wherein the second object comprises a movable target, wherein the movable target comprises a ground vehicle.

11. The radar system as claimed in any preceding claim, wherein the first angular offset is between approximately 40° and 80°, optionally between approximately 50° and 70°, further optionally approximately 60°, yet further optionally wherein the first angular offset is 60°; orwherein the first angular offset is between approximately -100° and -140°, optionally between approximately -110° and -130°, further optionally approximately -120°, yet further optionally wherein the first angular offset is -120°.

12. The radar system as claimed in any preceding claim, wherein the second radar device comprises a third antenna, wherein the system is configured such that when the first and second radar devices are positioned in the predetermined alignment orientation relative to one another:iii) the antenna of the first radar device is at least partially cross-polarised with the third antenna of the second radar device by a second angular offset different to the first angular offset.

13. The radar system as claimed in claim 12, wherein the second angular offset is between approximately 100° and 140°, optionally between approximately 110° and 130°, further optionally approximately 120°, yet further optionally wherein the second angular offset is 120°; orwherein the second angular offset is between approximately -40° and -80°, optionally between approximately -50° and -70°, further optionally approximately -60°, yet further optionally wherein the second angular offset is -60°.

14. The radar system as claimed in any of claims 1 to 10, wherein the first angular offset is between approximately 25° and 65°, optionally between approximately 35° and55°, further optionally approximately 45°, yet further optionally wherein the first angular offset is 45°.

15. The radar system as claimed in claim 12 or claim 14 when dependent on claim 12, wherein the second angular offset is between approximately 115° and 155°, optionally between approximately 125° and 145°, further optionally approximately 135°, yet further optionally wherein the second angular offset is 135°.

16. The radar system as claimed in claim 12 or any of claims 13 to 15 when dependent on claim 12, wherein the second radar device further comprises a fourth antenna, wherein the system is further configured such that when the first and second radar devices are positioned in the predetermined alignment orientation relative to one another:iv) the antenna of the first radar device is at least partially cross-polarised with the fourth antenna of the second radar device by a third angular offset different to the first and second angular offsets.

17. The radar system as claimed in claim 18, wherein the third angular offset is between approximately 70° and 110°, optionally between approximately 80° and 100°, further optionally approximately 90°, yet further optionally wherein the third angular offset is 90°.

18. The radar system as claimed in any preceding claim, wherein at least one of the first and second radar devices comprises N antennas, wherein the N antennas are rotated by 180° / N with respect to one another.

19. The radar system as claimed in any preceding claim, wherein one or more of the antennas respectively comprises a patch antenna, optionally wherein each antenna of the respectively comprises a patch antenna.

20. A method of determining a relative yaw between first and second objects, the method comprising:a) receiving radar signals across respective antenna-antenna interfaces between an antenna of a first radar device and each of first and second antennasof a second radar device, wherein when the first and second radar devices are positioned in a predetermined alignment orientation relative to one another:i) the antenna of the first radar device is co-polarised with the first antenna of the second radar device;ii) the antenna of the first radar device is at least partially crosspolarised with the second antenna of the second radar device by a first angular offset; andb) comparing respective signal powers of the received radar signals to determine data indicative of the relative yaw.

21. The method as claimed in claim 20, further comprising receiving radar signals across a respective interface between the antenna of the first radar device and a third antenna of the second radar device, wherein when the first and second radar devices are positioned in a predetermined alignment orientation relative to one another:iii) the antenna of the first radar device is at least partially cross-polarised with the third antenna of the second radar device by a second angular offset different to the first angular offset.

22. The method as claimed in claim 20 or 21, wherein the first object comprises an aerial vehicle, optionally wherein the aerial vehicle comprises a drone and / or an uncrewed aerial vehicle (UAV).

23. The method as claimed in any of claims 20 to 22, wherein the second object comprises a movable target, optionally wherein the movable target comprises a landing deck on a ship or vessel, or wherein the movable target comprises a ground vehicle.

24. The method as claimed in any of claims 20 to 23, carried out using the radar system as claimed in any of claims 1 to 19.

25. A computer software product or a non-transitory computer-readable medium comprising instructions which, when executed by a processor, cause the processor to carry out the method of any of claims 20 to 24.31

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