Patent Publication Number: US-2022236400-A1

Title: Methods and System for Determining an Angle of a Detection

Description:
CROSS-REFERENCE OF RELATED APPLICATIONS 
     This application claims priority to European Patent Application Number 21153435.9, filed Jan. 26, 2021, the disclosure of which is hereby incorporated by reference in its entirety herein. 
     BACKGROUND 
     Detections measured by radars contain the range rate. The range rate may be used to determine estimates for an angle of a detection. However, commonly used methods may not allow determination of a unique angle, but there may be ambiguities. 
     Accordingly, there is a need to provide improved angle estimation based on range rate. 
     SUMMARY 
     The present disclosure relates to methods and systems for determining an angle of a detection. The present disclosure provides a computer implemented method, a computer system, a vehicle, and a non-transitory computer readable medium according to the independent claims. Embodiments are given in the subclaims, the description, and the drawings. 
     In one aspect, the present disclosure is directed at a computer implemented method for determining an angle of a detection, the method comprising the following steps performed (in other words: carried out) by computer hardware components: acquiring a range rate of the detection; determining a pair of candidate angles of the detection based on the range rate; acquiring a beamvector of the detection; determining a correlation between the beamvector and a reference vector; and determining the angle of the detection based on the pair of candidate angles and based on the correlation. 
     In other words, a method for disambiguation of angles calculated from range rate may be provided. 
     The method may process radar signals from multiple antennas by calculating the angle of detection (from the combined plane) from the range rate of stationary detections. 
     However, it will be understood that the method may be applied to non-stationary targets, for example, if the actual object velocity vector is known from another source of information (for example from an external sensor). 
     Given an object (detection) that moves with a velocity vector 
     
       
         
           
               
             
               ( 
               
                 
                   
                     
                       v 
                       
                         obj 
                         , 
                         x 
                       
                     
                   
                 
                 
                   
                     
                       v 
                       
                         obj 
                         , 
                         y 
                       
                     
                   
                 
               
               ) 
             
             ⁢ 
             
                 
             
           
         
       
     
     and the radar&#39;s motion vector 
     
       
         
           
             
               ( 
               
                 
                   
                     
                       v 
                       x 
                     
                   
                 
                 
                   
                     
                       v 
                       y 
                     
                   
                 
               
               ) 
             
             , 
           
         
       
     
     the radar may observe the detection from an angle θ and may measure the relative radial velocity component {dot over (r)}, i.e., the relative motion vector projected to the radial vector between the radar and the detection (at the angle θ). 
     The relative motion vector is 
     
       
         
           
             
               ( 
               
                 
                   
                     
                       v 
                       
                         obj 
                         , 
                         x 
                       
                     
                   
                 
                 
                   
                     
                       v 
                       
                         obj 
                         , 
                         y 
                       
                     
                   
                 
               
               ) 
             
             - 
             
               
                 ( 
                 
                   
                     
                       
                         v 
                         x 
                       
                     
                   
                   
                     
                       
                         v 
                         y 
                       
                     
                   
                 
                 ) 
               
               . 
             
           
         
       
     
     The radial vector is 
     
       
         
           
             
               ( 
               
                 
                   
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                 
                 
                   
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                 
               
               ) 
             
             · 
             
               ( 
               
                 
                   
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                 
                 
                   
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                 
               
               ) 
             
             · 
             
               [ 
               
                 
                   ( 
                   
                     
                       
                         
                           v 
                           
                             obj 
                             , 
                             x 
                           
                         
                       
                     
                     
                       
                         
                           v 
                           
                             obj 
                             , 
                             y 
                           
                         
                       
                     
                   
                   ) 
                 
                 - 
                 
                   ( 
                   
                     
                       
                         
                           v 
                           x 
                         
                       
                     
                     
                       
                         
                           v 
                           y 
                         
                       
                     
                   
                   ) 
                 
               
               ] 
             
           
         
       
     
     The projection is thus 
     which equals the range rate 
     
       
         
           
             
               r 
               . 
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         cos 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         sin 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                     
                   
                 
                 ) 
               
               · 
               
                 [ 
                 
                   
                     ( 
                     
                       
                         
                           
                             v 
                             
                               obj 
                               , 
                               x 
                             
                           
                         
                       
                       
                         
                           
                             v 
                             
                               obj 
                               , 
                               y 
                             
                           
                         
                       
                     
                     ) 
                   
                   - 
                   
                     ( 
                     
                       
                         
                           
                             v 
                             x 
                           
                         
                       
                       
                         
                           
                             v 
                             y 
                           
                         
                       
                     
                     ) 
                   
                 
                 ] 
               
             
           
         
       
     
     The classification of detections into stationary/moving (i.e., non-stationary) may be done by using a classical radar angle finding (wherein in most of the practical cases, this angle (which may be the angle of a detection that is calculated by a classical angle finding method) may be available and may be calculated by, e.g., an FFT), and/or by getting this information from an outside module or sensor (as described in more detail below), and/or by using an angle provided by another sensor (e.g., another radar, or a camera, or a lidar sensor, or any other kind of suitable sensor). 
     This classification may only be necessary if the detection&#39;s/object&#39;s motion vector is not known. In case the velocity vector is known, the formulas for the projection and for the range rate as described herein may be used without any restrictions and without this classification. 
     In another aspect, a fully stationary environment may be assumed. However, every non-stationary detection may result in a wrong angle measurement. 
     Commonly used angle finding methods assume a good calibration matrix C. However, it may not be possible to obtain a good calibration matrix if the method is still in the process of creating the calibration matrix (e.g. while driving). If an angle from a classical angle finding should be cross-checked for accuracy with angle from range rate, it cannot be assumed that the angle from classical angle finding is precise enough to allow disambiguation. In contrast thereto, the method, according to various embodiments, allows disambiguation. According to various embodiments, off-line calibration may be carried out at least for a respective reference position. 
     Compared to commonly used angle finding methods (which at least require a Fourier transform), the method, according to various embodiments, is less time consuming by determining the correlation coefficient. 
     According to another aspect, the detection comprises a radar detection. According to another aspect, the detection comprises a radar detection of a stationary object. 
     According to another aspect, the pair of candidate angles comprises two angles which are located symmetrically around a pre-determined axis. The pre-determined axis may be the x-direction (for example, defined by the forward moving direction of vehicle on which a (radar) sensor is mounted). 
     According to another aspect, the reference vector comprises data based on a reflection point originating from the pre-determined axis. 
     According to another aspect, the beamvector comprises sensor data of a plurality of antennas provided in an antenna array. According to another aspect, the antenna array is provided in a plane. There may be provided antenna arrays in more than one plane. Each antenna may belong to one or more antenna arrays. 
     According to another aspect, the correlation is based on a product of the beamvector and the reference vector. The product may be a dot product. The correlation may be or may include a correlation coefficient. 
     According to another aspect, the correlation is determined further based on a calibration matrix. The calibration matrix may be determined by solving the following equation for C: C·bv=λ·a, where by is the measured beamvector, λ is a complex scaling factor, and a is the (ideal) beamvector. 
     According to another aspect, the computer implemented method further comprises the following step carried out by the computer hardware components: multiplying the calibration matrix with the reference vector. It has been found that, by multiplying the calibration matrix with the reference vector, the calibration matrix does not need to be multiplied with every test vector. 
     In another aspect, the present disclosure is directed at a computer system, said computer system comprising a plurality of computer hardware components configured to carry out several or all steps of the computer implemented method described herein. 
     The computer system may comprise a plurality of computer hardware components (for example a processor, for example processing unit or processing network, at least one memory, for example memory unit or memory network, and at least one non-transitory data storage). It will be understood that further computer hardware components may be provided and used for carrying out steps of the computer implemented method in the computer system. The non-transitory data storage and/or the memory unit may comprise a computer program for instructing the computer to perform several or all steps or aspects of the computer implemented method described herein, for example, using the processing unit and the at least one memory unit. 
     According to another aspect, the computer system further comprises: a radar sensor configured to acquire radar measurements; wherein computer system is configured to determine the range rate based on the radar measurements; and wherein computer system is configured to determine the beamvector based on the radar measurements. 
     According to another aspect, the radar sensor comprises a plurality of antennas (for example an antenna array). 
     In another aspect, the present disclosure is directed at a vehicle, comprising: the computer system as described herein; and the radar sensor. 
     In another aspect, the present disclosure is directed at a non-transitory computer readable medium comprising instructions for carrying out several or all steps or aspects of the computer implemented method described herein. The computer readable medium may be configured as: an optical medium, such as a compact disc (CD) or a digital versatile disk (DVD); a magnetic medium, such as a hard disk drive (HDD); a solid state drive (SSD); a read only memory (ROM), such as a flash memory; or the like. Furthermore, the computer readable medium may be configured as a data storage that is accessible via a data connection, such as an internet connection. The computer readable medium may, for example, be an online data repository or a cloud storage. 
     The present disclosure is also directed at a computer program for instructing a computer to perform several or all steps or aspects of the computer implemented method described herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments and functions of the present disclosure are described herein in conjunction with the following drawings, showing schematically: 
         FIG. 1  an illustration of a radar scenario according to various embodiments; 
         FIG. 2  an illustration of a complex plane; 
         FIG. 3  an illustration of an array of antennas; 
         FIG. 4  a graph wherein the angle of an ideal test detection is plotted against the phase of the correlation coefficient; 
         FIG. 5  an illustration of azimuth and elevation measurement; 
         FIG. 6  a flow diagram illustrating a method for determining an angle of a detection according to various embodiments; 
         FIG. 7  an angle determination system according to various embodiments; and 
         FIG. 8  a computer system with a plurality of computer hardware components configured to carry out steps of a computer implemented method for determining an angle of a detection according to various embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Detections measured by radars may contain the range rate, which may be the radial component of the velocity of the object that caused the detection. The velocity may be relative to the radar, and the radial component may be directed from the object to the radar. 
     The range rate {dot over (r)} of detections enables estimation of the angle of the detection θ if yaw rate ω and speed v veh  of the ego vehicle are known (at the center of gravity) and the sensor mounting position relative to the center of gravity, L, is known: 
         {dot over (r)} =cos(θ+θ M )( v   x   det   −v   x )+sin(θ+θ M )( v   y   det   −v   y )  (1)
 
       with 
         v   x   =−ω·L   y   +v   x   veh  and  v   y   =ω·L   x   +v   y   veh    
     wherein v x  and v y  are the velocity components of the radar sensor&#39;s motion over the ground, and wherein v x   det  and v y   det  are the velocity of a detection. For stationary detections, v x   det =0 and v y   det =0. The velocity may be provided by another source of information (for example from an external sensor). 
     There are several ways for determining whether a detection is related to a stationary object. This determination is only necessary if the detection&#39;s/object&#39;s velocity is not known; in case the velocity vector is known, the formulas for the projection and for the range rate as described herein may be used without any restrictions, and then the determination whether a detection is related to a stationary object may not be necessary. 
     For example, it may be determined whether a detection is related to a stationary object by carrying out a check against the ego velocity in combination with a threshold. In that case, the regular signal processing to calculate the angle of a detection may be executed. 
     Another option for determining whether a detection is related to a stationary object may be to use outside information, e.g., from a tracker or from another sensor. 
     The x-axis may be oriented longitudinally in parallel through the longitudinal axis of the ego vehicle. The y-axis may be oriented in parallel to the lateral axis of the ego vehicle. 
     θ M  is the angle of mounting the radar in the car, i.e., the angle between the ego vehicle&#39;s longitudinal axis and the line that is perpendicular to the radar antenna surface may also be desired to be known. 
     Given those values and the measured range rate P of a detection, the detection&#39;s angle θ can be calculated by solving (1) for θ. 
     θ is the angle in sensor coordinates, and θ veh =θ+θ M  is the angle in vehicle coordinates. 
     The radar may also output the estimated angle of a detection that is determined by other methods not related to and independent of range rate (“classical angle finding methods”). 
     However, the advantages of calculating the angle from the range rate according to various embodiments are, amongst others:
         It can be more accurate than classical angle finding methods (depends on the accuracy of the ego velocity measurement).   Classical angle finding methods require an intrinsic calibration of each individual sensor type. Calculating angle from range rate does not require such calibration.   If the antenna disambiguation, as described below, is applied, then an antenna calibration matrix may be applied to the reference angle only but not to the beamvectors for each detection.       

     The determination of the angle of a detection from range rate as described above may not have a unique solution. 
     The reason may be that two stationary detections which are located symmetrically to the x axis, i.e., their angles are θ veh  and −θ veh , have the same range rate P. Disambiguation of the two potential angles ±θ veh  is thus necessary to calculate the angle of a detection from range rate. 
       FIG. 1  shows an illustration  100  of a radar scenario according to various embodiments. A car  102  may define a forward axis x ( 104 ) and a lateral axis y ( 106 ). A radar sensor  108  (which may also be referred to just as “radar”) is provided on the car  102 . Potential detections  110  and  112  may lead to the same range rate detected by the radar sensor  108 . The potential detections  110  and  112  may be symmetrical with respect to an axis  114  that may coincide with the x direction  104 . A sensor Field-of-View (FoV)  116  is illustrated by dashed lines. 
     According to various embodiments, the beamvector of the detection whose angle is to be estimated (dis-ambiguated), b test ∈   n , may be compared to a beamvector b ref  ∈   n  from a reflection point that originates from the symmetry axis, θ ref   veh =0°. n may be the number of antenna elements. Comparison may be done by calculating and evaluating the correlation coefficient (between b test  and b ref ). b ref  may be an ideal (calibrated) beamvector used as a reference, i.e., it is pre-calculated and not measured. b ref  may be the ideal beamvector for the forward (or backward) direction in the vehicle coordinate system. It may be calculated by knowing the reference angle that is to be tested against, and the ideal antenna response from a signal impinging from that angle is known. For example, for the 0° reference angle, each antenna element may have a complex value with a constant length (e.g. 1) and an angle of 0°. 
     b ref  may be calculated, given the reference angle in sensor coordinates θ, according to 
     
       
         
           
             
               b 
               ref 
             
             = 
             
               
                 E 
                 0 
               
               · 
               
                 
                   ( 
                   
                     
                       
                         1 
                       
                     
                     
                       
                         
                           exp 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   i 
                                 
                                 · 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   λ 
                                 
                               
                               ⁢ 
                               
                                 sin 
                                 ⁡ 
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 z 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         
                           exp 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   i 
                                 
                                 · 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   λ 
                                 
                               
                               ⁢ 
                               
                                 sin 
                                 ⁡ 
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 z 
                                 3 
                               
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         ⋮ 
                       
                     
                     
                       
                         
                           exp 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   - 
                                   i 
                                 
                                 · 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     π 
                                   
                                   λ 
                                 
                               
                               ⁢ 
                               
                                 sin 
                                 ⁡ 
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 z 
                                 4 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   ) 
                 
                 . 
               
             
           
         
       
     
     The value E 0  may represent a magnitude of the electromagnetic wave. Since only the phase information may be important, it may be set to any value, e.g., 1. The first component of b ref  may be normalized to 1, per convention. z i  may be the geometrical position of antenna i along the z axis. The z axis may be on the antenna array plane, and the first antenna may be on the origin of the z axis. The plane where the angle θ is measured may be perpendicular to the antenna array plane and parallel to the z axis. A may be the wavelength of the electromagnetic waves of the radar. The term 
     
       
         
           
             
               2 
               ⁢ 
               π 
             
             λ 
           
         
       
     
     may be the spatial frequency of the electromagnetic waves. When the electromagnetic wave impinges on the antenna array at an angle θ, the term sin(θ) may represent the projection of the spatial frequency on the antenna array plane. 
     If two angles (e.g. azimuth and elevation) should be measured instead of only one angle, the equation for f b ref  may be extended. In this case, it may be calculated according to, for example, Adolfo Di Serio et al., 2D-MIMO Radar: A Method for Array Performance Assessment and Design of a Planar Antenna Array, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, Page 3. 
     The ideal beamvector may be perturbed using the calibration matrix to make it match with the practical sensor properties. 
     If the detection originates from an angle (in sensor coordinates) larger than the angle of the reference beamvector, the phase of the correlation coefficient c is positive, and, otherwise, it may be negative: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           c 
                           = 
                           
                             
                               b 
                               ref 
                               H 
                             
                             · 
                             
                               b 
                               test 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             
                               ( 
                               
                                 
                                   
                                     b 
                                     ¯ 
                                   
                                   
                                     ref 
                                     , 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     b 
                                     ¯ 
                                   
                                   
                                     ref 
                                     , 
                                     2 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 … 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     b 
                                     ¯ 
                                   
                                   
                                     ref 
                                     , 
                                     n 
                                   
                                 
                               
                               ) 
                             
                             · 
                             
                               ( 
                               
                                 
                                   
                                     
                                       b 
                                       
                                         test 
                                         , 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       b 
                                       
                                         test 
                                         , 
                                         2 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       b 
                                       
                                         test 
                                         , 
                                         n 
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             
                               
                                 
                                   b 
                                   ¯ 
                                 
                                 
                                   ref 
                                   , 
                                   1 
                                 
                               
                               · 
                               
                                 b 
                                 
                                   test 
                                   , 
                                   1 
                                 
                               
                             
                             + 
                             
                               
                                 
                                   b 
                                   ¯ 
                                 
                                 
                                   ref 
                                   , 
                                   2 
                                 
                               
                               · 
                               
                                 b 
                                 
                                   test 
                                   , 
                                   2 
                                 
                               
                             
                             + 
                             … 
                             + 
                             
                               
                                 
                                   b 
                                   ¯ 
                                 
                                 
                                   ref 
                                   , 
                                   n 
                                 
                               
                               · 
                               
                                 b 
                                 
                                   test 
                                   , 
                                   n 
                                 
                               
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     The complex contribution of one element i (i.e., for one antenna i) to the correlation coefficient is  b   ref,i ·b test,i , and its phase (angle) may be the difference between the phases of b ref,i  and b test,i . 
       FIG. 2  shows an illustration  200  of a complex plane with a real axis  202  and an imaginary axis  204 . The vectors b ref,i    206 , b ref,i    208 , and b test,i .  210  are shown. The angle  212  between the phases of b ref,i    206  and b test,i    208  is also illustrated. 
     A pre-condition is that the phases of the elements of the beam vectors be normalized, such that the phase of the first antenna may be 0. 
     As a consequence, the first summand in (1) may be omitted. Since the first elements  b   ref,1  and b test,i  may have zero phase due to normalization, their product may not change the phase of the correlation coefficient and may be omitted: 
       phase( c )=   b     ref,2   ·b   test,2   + . . . + b     ref,n   ·b   test,n    
       FIG. 3  shows an illustration  300  of an array of antennas with an integer number n of antennas. A first antenna  302 , a second antenna  304 , an i-th antenna  306 , and an n-th antenna  308  are shown. 
     Detections under a reference angle  314  are illustrated (indicated by reference sign  312  for the first antenna  302 , reference sign  320  for the second antenna  304 , reference sign  324  for the i-th antenna, and reference sign  328  for the n-th antenna  308 ). Detections under a test angle  318  are illustrated (indicated by reference sign  316  for the first antenna  302 , reference sign  322  for the second antenna  304 , reference sign  326  for the i-th antenna, and reference sign  330  for the n-th antenna  308 ). 
     Dotted lines  332  and  334  denote the same phase of the incoming electromagnetic wave received by the n antenna elements  302 ,  304 ,  306 , and  308 . 
     The angles are provided with respect to a reference direction  310 , for example, a forward direction of a vehicle on which the array of antennas is mounted. 
     As can be seen in  FIG. 3 , the phase difference of the reference and the test signal impinging to antenna i ( 306 ) is positive if θ test   veh &gt;θ ref   veh . 
     Thus, each term  b   ref,i ·b test,i  in (1) may have a positive phase contribution for θ test   veh &gt;θ ref   veh  and a negative phase contribution otherwise. Consequently, the sign of the phase of the correlation coefficient c indicates from which side a detection would come from, i.e., it allows disambiguation (taking into account that θ ref   veh =0°). 
       FIG. 4  shows a graph  400 , wherein the angle  402  of an ideal test detection is plotted against the phase  404  of the correlation coefficient resulting from a comparison to a test vector of θ ref   veh =0°, according to (1). The angle of the detection (x-axis) is plotted in sensor coordinates, and the longitudinal axis of the vehicle, θ ref   veh =0°, corresponds to ˜59° in sensor coordinates (as indicated by vertical line  406 ) due to the sensor being mounted into the vehicle with a rotation of −59° (corner sensor). 
     As can be seen from the resulting curve  408 , the sign of the phase of the correlation coefficient shows whether the detection comes from one side or the other side of the vehicle&#39;s longitudinal axis, thus allowing disambiguation. 
     In the following, a solution for antennas located on multiple planes (e.g. for measuring both azimuth and elevation) will be described. 
     In general, to measure an angle θ xy  that is parallel to the plane spanned by the x and the y axis, the antenna elements may be as well located on a plane P that is parallel to the plane spanned by the x and the y axis. Such a plane that is parallel to the plane spanned by the x and the y axis is henceforth called xy plane. This definition is valid also for combinations of dimensions other than xy (for example, for a xz plane spanned by the x and the z axis). 
     This means that if an azimuth angle θ xy  and an elevation angle θ xz  are to be measured, antenna elements may exist on an xz plane. 
     This poses a problem for measuring an angle θ xy  (azimuth) because the phase of the electromagnetic beam at an antenna element is governed by both θ xy  and θ xz  (elevation). To separate the combined influence, in order to measure an angle θ ab  of an ab plane (a, b being dimensions, e.g., x, z), only antenna elements may be used that lie on the same ab plane (wherein antenna elements that physically lie on different ab planes may be virtually placed such that they lie on the same ab plane, albeit while possibly introducing a measurement error). Combining elements across different ab planes (i.e., leaving a single ab plane) may introduce an unwanted coupling between the angles of the two dimensions. 
     As a consequence, the correlation coefficient (1) may only be calculated using antenna elements that lie on the same ab plane (if θ ab  is the angle to be estimated from the range rate). 
     Antenna elements lying on other planes may be combined into groups, where each group contains only elements from the same ab plane. Then, for each group, the beamvectors may be normalized to the first element of a group. 
       FIG. 5  shows an illustration  500  of azimuth and elevation measurement with artificial noise of 25 dB SNR. For  FIG. 5 , an antenna configuration was assumed where azimuth and elevation are measured. Two sub-arrays have been simulated, and the phase of the correlation coefficient has been calculated according to (1). Additionally, white noise has been added to the antenna signals resulting in an SNR of 25 dB. The phase of correlation coefficient is illustrated on a vertical axis  504  and the angle on a horizontal axis  502 . The resulting curve  508  for a first subarray and the resulting curve  510  for a second subarray are shown. 
     As can be seen from  FIG. 5 , the disambiguation of the angle is still possible, except for a very small range of angles (less than +/−0.1°) around the longitudinal axis of the vehicle, i.e., the axis defined by θ ref   veh =0°, corresponding to ˜59° in sensor coordinates (as illustrated by the vertical line  506 ). This is due to the sensor being mounted into the vehicle with a rotation of −59° (corner sensor). 
     According to various embodiments, multiplications with the calibration matrix may be provided efficiently, as will be described in the following. 
     The test beamvector results from applying the sensor-specific calibration matrix C to the raw measured beamvector b test,raw  are: 
     
       
      
       b 
       test 
       =C·b 
       test,raw  
      
     
     This may be done for each individual beam vector to be tested. 
     Thus, the correlation coefficient is: 
         c=b   ref   H ·( C·b   test,raw )
 
     According to various embodiments, speed may be improved by applying the calibration matrix to the reference beam vector 
         c =( b   ref   H   ·C )· b   test,raw  
 
     and pre-calculating b ref   H ·C once. Thus, the raw test beam vector may not need to be multiplied with C, thereby saving execution time for each vector (detection) to be tested. 
       FIG. 6  shows a flow diagram  600  illustrating a method for determining an angle of a detection according to various embodiments. At  602 , a range rate of the detection may be acquired. At  604 , a pair of candidate angles of the detection based on the range rate may be determined. At  606 , a beamvector of the detection may be acquired. At  608 , a correlation between the beamvector and a reference vector may be determined. At  610 , the angle of the detection may be determined based on the pair of candidate angles and based on the correlation. 
     According to various embodiments, the detection may include or may be a radar detection. 
     According to various embodiments, the detection may include or may be a radar detection of a stationary object. 
     According to various embodiments, the detection may include or may be a radar detection of a non-stationary object. 
     According to various embodiments, the pair of candidate angles may include or may be two angles which are located symmetrically around a pre-determined axis. 
     According to various embodiments, the reference vector may include or may be data based on a reflection point originating from the pre-determined axis. 
     According to various embodiments, the beamvector may include or may be sensor data of a plurality of antennas provided in an antenna array. 
     According to various embodiments, the antenna array may be provided in a plane. 
     According to various embodiments, the correlation may be based on a product of the beamvector and the reference vector. 
     According to various embodiments, the correlation may be determined further based on a calibration matrix. 
     According to various embodiments, the calibration matrix may be multiplied with the reference vector. 
     Each of the steps  602 ,  604 ,  606 ,  608 , and  610  and the further steps described above may be performed by computer hardware components. 
       FIG. 7  shows an angle determination system  700  according to various embodiments. The angle determination system  700  may determine an angle of a detection and may include a range rate acquiring circuit  702 , a candidate determination circuit  704 , a beamvector acquiring circuit  706 , a correlation determination circuit  708 , and an angle determination circuit  710 . 
     The range rate acquiring circuit  702  may be configured to acquire a range rate of the detection. The candidate determination circuit  704  may be configured to determine a pair of candidate angles of the detection based on the range rate. The beamvector acquiring circuit  706  may be configured to acquire a beamvector of the detection. The correlation determination circuit  708  may be configured to determine a correlation between the beamvector and a reference vector. The angle determination circuit  710  may be configured to determine the angle of the detection based on the pair of candidate angles and based on the correlation. 
     The range rate acquiring circuit  702 , the candidate determination circuit  704 , the beamvector acquiring circuit  706 , the correlation determination circuit  708 , and the angle determination circuit  710  may be coupled with each other, e.g., via an electrical connection  712 , such as, e.g., a cable or a computer bus or via any other suitable electrical connection to exchange electrical signals. 
     A “circuit” may be understood as any kind of a logic implementing entity, which may be special purpose circuitry or a processor executing a program stored in a memory, firmware, or any combination thereof. 
       FIG. 8  shows a computer system  800  with a plurality of computer hardware components configured to carry out steps of a computer implemented method for determining an angle of a detection according to various embodiments. The computer system  800  may include a processor  802 , a memory  804 , and a non-transitory data storage  806 . A radar sensor  808  may be provided as part of the computer system  800  (as illustrated in  FIG. 8 ) or may be provided external to the computer system  800 . 
     The processor  802  may carry out instructions provided in the memory  804 . The non-transitory data storage  806  may store a computer program that includes the instructions that may be transferred to the memory  804  and then executed by the processor  802 . The radar sensor  808  may be used for acquiring radar sensor data that may be used to acquire a range rate. 
     The processor  802 , the memory  804 , and the non-transitory data storage  806  may be coupled with each other, e.g., via an electrical connection  810 , such as, e.g., a cable or a computer bus or via any other suitable electrical connection to exchange electrical signals. The radar sensor  808  may be coupled to the computer system  800 , for example, via an external interface, or may be provided as part of the computer system (in other words: internal to the computer system, for example, coupled via the electrical connection  810 ). 
     The terms “coupling” or “connection” are intended to include a direct “coupling” (for example via a physical link) or direct “connection” as well as an indirect “coupling” or indirect “connection” (for example via a logical link), respectively. 
     What has been described for one of the methods above may analogously hold true for the angle determination system  700  and/or for the computer system  800 .