Patent Publication Number: US-2022236409-A1

Title: Ambiguity mitigation based on common field of view of radar systems

Description:
INTRODUCTION 
     The subject disclosure relates to ambiguity mitigation based on a common field of view of radar systems. 
     Vehicles (e.g., automobiles, trucks, construction equipment, automated factory equipment) employ sensors to perform semi-autonomous or autonomous operation. Exemplary sensors (e.g., camera, radar system, lidar system, inertial measurement unit, accelerometer) provide information about the vehicle and its surroundings. Exemplary semi-autonomous operations include adaptive cruise control (ACC) and collision avoidance. A radar system generally transmits a radio frequency (RF) signal and receives reflected energy as a result of the transmitted signal encountering one or more objects. Processing the reflected energy provides a point cloud with each point being associated with range, direction of arrival (DOA) (e.g., azimuth angle and elevation angle to the object), and Doppler (range rate). Rather than indicating a single range, DOA, and Doppler for the object, each point may be associated with two or more hypotheses for a range value, two or more hypotheses for a DOA value, and two or more hypotheses for a Doppler value. In order to perform detection using the point cloud, the ambiguity created by the hypotheses must first be resolved. Accordingly, it is desirable to provide ambiguity mitigation based on a common field of view of radar systems. 
     SUMMARY 
     In one exemplary embodiment, a method includes obtaining an initial point cloud for each of two or more radar systems that share a common field of view. Each initial point cloud results from processing reflected energy at each of the two or more radar systems and each point of the initial point cloud indicates one or more hypotheses for a range, a Doppler, and a direction of arrival (DOA) to an object that resulted in the reflected energy. The method also includes obtaining a point cloud from the initial point cloud for each of the two or more radar systems. Each point of the point cloud for each of the two or more radar systems has a same number of hypotheses for the range as other points of the point cloud, a same number of hypotheses for the Doppler as other points of the point cloud, and a same number of hypotheses for the DOA as other points of the point cloud. Ambiguity in the common field of view is resolved based on the point cloud for each of the two or more radar systems to obtain resolved and unresolved points in the common field of view. The resolved points indicate one value for the range, one value for the Doppler, and one value of the DOA. A radar image is obtained from each of the two or more radar systems based on the resolved and unresolved points in the common field of view, wherein the radar images are used to control an aspect of operation of a vehicle. 
     In addition to one or more of the features described herein, the obtaining the point cloud from the initial point cloud includes, for each initial point cloud, determining a number of hypotheses for the range, a number of hypotheses for the Doppler, and a number of hypotheses for the DOA of each point of each initial point cloud, outputting the initial point cloud as the point cloud based on the number of hypotheses for the range being a first number for every point, the number of hypotheses for the Doppler being a second number for every point, and the number of hypotheses for the DOA being a third number for every point, and processing the initial point cloud to obtain the point cloud based on the number of hypotheses for the range being less than the first number for at least one point, the number of hypotheses for the Doppler being less than the second number for at least one point, or the number of hypotheses for the DOA being less than the third number for at least one point. 
     In addition to one or more of the features described herein, the processing the initial point cloud includes generating a subset of the initial point cloud to include each point that has fewer than the first number of hypotheses for the range, the second number of hypotheses for the Doppler, and the third number of hypotheses for the DOA and using an ambiguity function to obtain a complete subset of the initial point cloud that includes the first number of hypotheses for the range, the second number of hypotheses for the Doppler, and the third number of hypotheses for the DOA for each point in the subset of the initial point cloud. 
     In addition to one or more of the features described herein, the processing the initial point cloud includes obtaining a Mahalanobis distance between each point in the subset of the initial point cloud and each hypothesis in the complete subset of the initial point cloud and, based on the Mahalanobis distance, identifying each point in the subset of the initial point cloud that is a hypothesis in the complete subset of the initial point cloud. 
     In addition to one or more of the features described herein, the processing the initial point cloud includes discarding each point in the subset of the initial point cloud that is the hypothesis in the complete subset of the initial point cloud from the complete subset of the initial point cloud and retaining a remainder of the complete subset of the initial point cloud to generate the point cloud. 
     In addition to one or more of the features described herein, the method also includes identifying each point in the point cloud of each of the two or more radar systems that is in the common field of view. 
     In addition to one or more of the features described herein, the resolving the ambiguity in the common field of view includes obtaining, using the points in the common field of view for one of the two or more radar systems and another of the two or more radar systems at a time, a Mahalanobis distance between each hypothesis set of each point in the common field of view for the one of the two or more radar systems and each hypothesis set of each point in the common field of view for the other of the two or more radar systems, the hypothesis set including one combination of one of the one or more hypotheses for the range, one of the one or more hypotheses for the Doppler, and one of the one or more hypotheses for the DOA. 
     In addition to one or more of the features described herein, the resolving the ambiguity in the common field of view includes identifying a pair of points that result in a lowest Mahalanobis distance and, based on the pair of points passing a gating condition, retaining only the hypothesis set of the pair of points that is associated with the lowest Mahalonobis distance as unambiguous. 
     In addition to one or more of the features described herein, checking the gating condition for the pair of points includes using each of the range, the Doppler, and the DOA of the hypothesis set of the pair of points. 
     In addition to one or more of the features described herein, one or more objects is identified based on the radar image of one or more of the two or more radar systems. 
     In another exemplary embodiment, a vehicle includes two or more radar systems. The vehicle also includes a controller to obtain an initial point cloud for each of two or more radar systems that share a common field of view. Each initial point cloud results from processing reflected energy at each of the two or more radar systems and each point of the initial point cloud indicates one or more hypotheses for a range, a Doppler, and a direction of arrival (DOA) to an object that resulted in the reflected energy. The controller obtains a point cloud from the initial point cloud for each of the two or more radar systems. Each point of the point cloud for each of the two or more radar systems has a same number of hypotheses for the range as other points of the point cloud, a same number of hypotheses for the Doppler as other points of the point cloud, and a same number of hypotheses for the DOA as other points of the point cloud. The controller resolves ambiguity in the common field of view based on the point cloud for each of the two or more radar systems to obtain resolved and unresolved points in the common field of view. The resolved points indicate one value for the range, one value for the Doppler, and one value of the DOA, and to obtain a radar image from each of the two or more radar systems based on the resolved and unresolved points in the common field of view. The radar images are used to control an aspect of operation of a vehicle. 
     In addition to one or more of the features described herein, for each initial point cloud, the controller obtains the point cloud by determining a number of hypotheses for the range, a number of hypotheses for the Doppler, and a number of hypotheses for the DOA of each point of each initial point cloud, outputting the initial point cloud as the point cloud based on the number of hypotheses for the range being a first number for every point, the number of hypotheses for the Doppler being a second number for every point, and the number of hypotheses for the DOA being a third number for every point, and processing the initial point cloud to obtain the point cloud based on the number of hypotheses for the range being less than the first number for at least one point, the number of hypotheses for the Doppler being less than the second number for at least one point, or the number of hypotheses for the DOA being less than the third number for at least one point. 
     In addition to one or more of the features described herein, the controller processes the initial point cloud by generating a subset of the initial point cloud to include each point that has fewer than the first number of hypotheses for the range, the second number of hypotheses for the Doppler, and the third number of hypotheses for the DOA and using an ambiguity function to obtain a complete subset of the initial point cloud that includes the first number of hypotheses for the range, the second number of hypotheses for the Doppler, and the third number of hypotheses for the DOA for each point in the subset of the initial point cloud. 
     In addition to one or more of the features described herein, the controller processes the initial point cloud by obtaining a Mahalanobis distance between each point in the subset of the initial point cloud and each hypothesis in the complete subset of the initial point cloud and, based on the Mahalanobis distance, identifying each point in the subset of the initial point cloud that is a hypothesis in the complete subset of the initial point cloud. 
     In addition to one or more of the features described herein, the controller processes the initial point cloud by discarding each point in the subset of the initial point cloud that is the hypothesis in the complete subset of the initial point cloud from the complete subset of the initial point cloud and retaining a remainder of the complete subset of the initial point cloud to generate the point cloud. 
     In addition to one or more of the features described herein, the controller identifies each point in the point cloud of each of the two or more radar systems that is in the common field of view. 
     In addition to one or more of the features described herein, the controller resolves the ambiguity in the common field of view by obtaining, using the points in the common field of view for one of the two or more radar systems and another of the two or more radar systems at a time, a Mahalanobis distance between each hypothesis set of each point in the common field of view for the one of the two or more radar systems and each hypothesis set of each point in the common field of view for the other of the two or more radar systems, the hypothesis set including one combination of one of the one or more hypotheses for the range, one of the one or more hypotheses for the Doppler, and one of the one or more hypotheses for the DOA. 
     In addition to one or more of the features described herein, the controller resolves the ambiguity in the common field of view by identifying a pair of points that result in a lowest Mahalanobis distance and, based on the pair of points passing a gating condition, retaining only the hypothesis set of the pair of points that is associated with the lowest Mahalonobis distance as unambiguous. 
     In addition to one or more of the features described herein, the controller checks the gating condition for the pair of points includes using each of the range, the Doppler, and the DOA of the hypothesis set of the pair of points. 
     In addition to one or more of the features described herein, the controller identifies one or more objects based on the radar image of one or more of the two or more radar systems. 
     The above features and advantages, and other features and advantages of the disclosure are readily apparent from the following detailed description when taken in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other features, advantages and details appear, by way of example only, in the following detailed description, the detailed description referring to the drawings in which: 
         FIG. 1  is a block diagram of a vehicle that includes ambiguity mitigation based on a common field of view of radar systems; 
         FIG. 2  is a process flow of a method of performing ambiguity mitigation based on a common field of view of radar systems according to one or more embodiments; 
         FIG. 3  indicates processes performed for a part of the process flow shown in  FIG. 2  for each radar system according to one or more embodiments; and 
         FIG. 4  indicates processes performed for another part of the process flow shown in  FIG. 2  for two or more radar systems according to one or more embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     The following description is merely exemplary in nature and is not intended to limit the present disclosure, its application or uses. It should be understood that throughout the drawings, corresponding reference numerals indicate like or corresponding parts and features. 
     As previously noted, processing reflected energy received by a radar system facilitates obtaining range, DOA, and Doppler to the object that resulted in the reflections. As also noted, the point cloud obtained by processing radar data may include ambiguity such that each point in the point cloud includes two or more hypotheses of range, DOA, and Doppler. The hypotheses in one or more domains (i.e., range, Doppler, DOA) may be a result of waveform parameters, the transmission regime, the antenna pattern, grating lobes, or elevated sidelobe levels. As such, a each point of a point cloud obtained by the same radar system is expected to have the same number of hypotheses in each domain. For example, each point of the point cloud for a given radar system may be expected to have two hypotheses for range, three hypotheses for Doppler, one hypothesis (i.e., no ambiguity) for DOA. Embodiments of the systems and methods detailed herein relate to ambiguity mitigation based on a common field of view of radar systems. When the field of view of two or more radar systems overlaps, ambiguity associated with points in the point clouds corresponding with the overlap region (i.e., common field of view) may be resolved through a selection of the best hypothesis. 
     In accordance with an exemplary embodiment,  FIG. 1  is a block diagram of a vehicle  100  that includes ambiguity mitigation based on a common field of view  125  of radar systems  110   a ,  110   b . The exemplary vehicle  100  shown in  FIG. 1  is an automobile  101 . Three radar systems  110   a ,  110   b ,  110   c  (generally referred to as  110 ) are shown with corresponding fields of view  115   a ,  115   b ,  115   c  (generally referred to as  115 ). As illustrated, the field of view (FOV)  115   a  corresponding with the radar system  110   a  and the FOV  115   b  corresponding with the radar system  110   b  share a common region indicated as the common FOV  125 . The FOV  115   c  of the radar system  110   c  does not have any portion in common with the fields of view  115   a ,  115   b  of the radar systems  110   a ,  110   b . In addition to the radar systems  110 , the vehicle  100  may include additional sensors  130  (e.g., cameras, lidar systems). The number of radar systems  110 , their locations around the vehicle  100 , and the number of radar systems  110  whose FOV  115  is part of one or more common FOV  125 , as well as the numbers and locations of the additional sensors  130 , are not intended to be limited by the exemplary illustration in  FIG. 1 . 
     The vehicle  100  includes a controller  120  that may obtain information from the radar systems  110  and additional sensors  130  to control aspects of operation of the vehicle  100 . The controller  120 , alone or in combination with processing circuitry of each radar system  110 , may also perform ambiguity mitigation according to one or more embodiments that are detailed herein. The controller  120  includes processing circuitry that may include an application specific integrated circuit (ASIC), an electronic circuit, a processor (shared, dedicated, or group) and memory that executes one or more software or firmware programs, a combinational logic circuit, and/or other suitable components that provide the described functionality. 
       FIG. 2  is a process flow of a method  200  of performing ambiguity mitigation based on a common field of view  125  of radar systems  110  according to one or more embodiments. The method  200  may be performed by the controller  120  of the vehicle  100  alone or in combination with processing circuitry that is part of the radar systems  110 . At block  210 , the processes at block  215  are performed at each of the radar systems  110  whose FOV  115  overlaps with a common FOV  125 . In general, the processes at block  215  are performed for every radar system  110  regardless of any overlap in its FOV  115 , but only radar systems  110  associated with one or more common FOV  125  are relevant to the discussion of one or more embodiments. A given radar system  110  may have a FOV  115  that overlaps with the fields of view  115  of two or more other radar systems  110 . Further, the radar systems  110  of a given vehicle  100  may have multiple common FOV  125 . The processes performed at blocks  210  and  220  apply to every radar system  110  whose FOV  115  overlaps with the FOV  115  of another radar system  110  (i.e., every radar system  110  associated with at least one common FOV  125 ). The processes at block  230  are performed in consideration of one common FOV  125  at a time, as further detailed. 
     At block  215 , for each radar system  110  whose FOV  115  is part of a common FOV  125 , the processes include obtaining and processing reflected energy. These processes are well-known and one exemplary embodiment of processing reflected energy is briefly outlined here. As previously noted, RF energy is transmitted and reflected energy is received at each of the radar systems  110 . Generally, two fast Fourier transforms (FFTs) are performed on the received reflected energy. The first FFT is along range and the second FFT is along Doppler, which corresponds with radial velocity. More specifically, the first (range) FFT is performed per transmit signal to implement a range match filter processing. The second (Doppler) FFT is performed per each range bin of the first FFT result for all the simultaneously transmitted signals to implement a Doppler match filter processing. 
     Following the FFTs, a range-Doppler map is obtained. In the case of a multi-input multi-output (MIMO) radar system  110  with multiple transmit elements and multiple receive elements, a range-Doppler map is obtained for each combination of transmit element and receive element. Each range-Doppler map indicates a set of range bins, a set of Doppler bins, and an intensity associated with each range bin and Doppler bin combination. A beamforming process is performed on the range-Doppler map estimate (i.e., to obtain direction of arrival (DOA)) for each bin direction. Following the beamforming, a range-Doppler-beam map is obtained. A detection process in done over the range-Doppler-beam map to obtain detections that are associated with objects. A detection is a point of the initial point cloud IPC and has a corresponding one or more hypotheses for range, Doppler, and DOA associated with it. 
     At block  210 , after the initial point cloud IPC is obtained for each radar system  110  according to block  215 , then, at block  220 , the processes at blocks  225  are performed individually for each radar system  110 . At block  225 , the processes include making sure all the points of the initial point cloud IPC have all the expected hypotheses. For a given radar system  110 , all the points of the initial point cloud IPC generally should have the same number of hypotheses. The number of hypotheses expected for each point in the initial point cloud may typically be different for each radar system  110  (e.g., six hypotheses for each point of IPC 1 , four hypotheses for each point of IPC 2 ). For example, every point of the initial point cloud IPC 1  may be expected to include two range hypotheses (R 1 , R 2 ), one Doppler hypothesis (D 1 ), and three DOA hypotheses (DOA 1 , DOA 2 , DOA 3 ). As a result, each point of the initial point cloud IPC 1  is expected to be associated with six combinations (i.e., six hypotheses (H 1  through H 6 )) shown in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Exemplary hypotheses H for points of an initial point cloud IPC. 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 H1 
                 R1-D1-DOA1 
               
               
                   
                 H2 
                 R1-D1-DOA2 
               
               
                   
                 H3 
                 R1-D1-DOA3 
               
               
                   
                 H4 
                 R2-D1-DOA1 
               
               
                   
                 H5 
                 R2-D1-DOA2 
               
               
                   
                 H6 
                 R2-D1-DOA3 
               
               
                   
                   
               
            
           
         
       
     
     Generally, an initial point cloud IPC may have the expected number of hypotheses for either every point or none of the points. For explanatory purposes, an initial point cloud IPC with a mix of points with and without the expected number of hypotheses is discussed with reference to  FIG. 3 . At block  225 , one or more points of the initial point cloud IPC 1  may be found not to have all the expected hypotheses (e.g., a point in IPC 1  has only one or two hypotheses instead of six). In this case, a check is done to determine if the point is not a point of the initial point cloud IPC 1  at all but, instead, is a hypothesis of another legitimate point of the initial point cloud IPC 1 . If, based on the check, the point is not found to be a hypothesis of another point, then the correct number of hypotheses may be obtained by using the known ambiguity function. The processes at block  225  are further detailed with reference to  FIG. 3 . 
     The output of block  220  is point clouds PC that result from ensuring that each initial point cloud IPC obtained at each radar system  110  has the complete set of hypotheses for each point. For a given radar system  110 , the input initial point cloud IPC and the output point cloud PC may be the same. This is true if each point of the initial point cloud IPC already has the expected number of hypotheses. At block  230 , resolving ambiguity for points in a common FOV  125  refers to selecting one of the hypotheses and discarding the rest prior to performing detection. This selection is further detailed with reference to  FIG. 4 . 
     As previously noted, different ones of the radar systems  110  may share different common FOV  125 . For example, a radar system  110  may have a FOV  115  with a portion that overlaps with the FOV  115  of a second radar system  110  (i.e., a first common FOV  125 ) and also a separate portion that overlaps with the FOV  115  of a third radar system  110  (i.e., a second common FOV  125 ). The processes at block  230  are performed separately for each different common FOV  125  (i.e., differently for the first common FOV  125  and for the second common FOV  125 ). Thus, points from point clouds PC of two or more radar systems  110  that are part of a given common FOV  125  are considered in turn at block  230 . Once at least some of the ambiguities are resolved at block  230 , additional known detection processes may be performed, at block  240 . 
     That is, each radar system  110  provides a point cloud. Based on the one or more embodiments discussed herein, some of the points of the point cloud (i.e., some of the points that are part of the common FOV  125 ) may unambiguously indicate range, Doppler, and DOA. The point cloud from each radar system  110  essentially provides an image of the field of view  115  corresponding with the radar system  110 . That image may be used to identify a type of object (e.g., person, another vehicle). The images indicated by the point clouds of radar systems  110  with a common FOV  125  may used to determine accuracy (e.g., the two radar systems  110  indicate different ranges for portions of the same person in their respective images). 
       FIG. 3  shows a process flow performed at block  225  ( FIG. 2 ) for each radar system  110  according to one or more embodiments. As previously noted, the processes at block  225  are performed for each radar system  110  individually and begin with the initial point cloud IPC. At block  310 , a check is first done of whether every point in the initial point cloud IPC of the given radar system  110  has a full set of hypotheses. If so, then the initial point cloud IPC is the point cloud PC for the radar system  110 , at block  315 . If every point of the initial point cloud IPC does not have the full set of hypotheses (i.e., the same number of range hypotheses, Doppler hypotheses, and DOA hypotheses as every other point), then the processes at block  320  are reached. As previously noted, generally a radar system  110  either provides an initial point cloud IPC that is a point cloud PC (i.e., all points have the expected number of hypotheses) or an initial point cloud IPC in which none of the points include the expected number of hypotheses. For explanatory purposes, a mix of these scenarios is addressed by the exemplary case discussed herein. 
     In the exemplary case of a given initial point cloud IPC obtained (at block  215 ) from a given radar system  110 , point P 1  has the expected number of hypotheses (e.g., three hypotheses H 1 , H 2 , H 3 ), point P 2  is found to have only two of the three expected hypotheses H 1  and H 2 , and points P 3  and P 4  each have only one value for range, Doppler, and DOA. At block  320 , the processes include using the ambiguity function to obtain additional hypotheses for the points with an incomplete (e.g., fewer than three) number of hypotheses. In the exemplary case, the ambiguity function is used to obtain hypothesis H 3  for point P 2  and all three hypotheses H 1 , H 2 , H 3  for points P 3  and P 4 . 
     At block  330 , obtaining a Mahalanobis distance d for some or all points in the initial point cloud IPC refers to obtaining the Mahalanobis distance d for every point in the initial point cloud IPC for the given radar system  110  that does not have the expected number of hypotheses, as shown in Table 2. The Mahalanobis distance d is given by: 
     
       
         
           
             
               
                 
                   dij 
                   = 
                   
                     
                       
                         
                           
                             
                               
                                 
                                    
                                   
                                     
                                       Pi 
                                       R 
                                     
                                     - 
                                     
                                       Pj 
                                       R 
                                     
                                   
                                    
                                 
                                 2 
                               
                               
                                 σ 
                                 R 
                                 2 
                               
                             
                             + 
                             
                               
                                 
                                    
                                   
                                     
                                       Pi 
                                       D 
                                     
                                     - 
                                     
                                       Pj 
                                       D 
                                     
                                   
                                    
                                 
                                 2 
                               
                               
                                 σ 
                                 D 
                                 2 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                    
                                   
                                     
                                       Pi 
                                       Az 
                                     
                                     - 
                                     
                                       Pj 
                                       Az 
                                     
                                   
                                    
                                 
                                 2 
                               
                               
                                 σ 
                                 AZ 
                                 2 
                               
                             
                             + 
                             
                               
                                 
                                    
                                   
                                     
                                       Pi 
                                       El 
                                     
                                     - 
                                     
                                       Pj 
                                       El 
                                     
                                   
                                    
                                 
                                 2 
                               
                               
                                 σ 
                                 El 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     In EQ. 1, R, D, Az, and El refer respectively to the range, Doppler, azimuth, and elevation that define the particular hypothesis. In addition, σ R , σD, σ Az , σ El  are an accuracy parameter associated, respectively, with range, Doppler, azimuth, and elevation for the given radar system  110 . That is, σ R , σ D , σ Az , σ El  are the same for every calculation of the Mahalanobis distance d pertaining to the same radar system  110 . As shown in Table 2, the index i indicates a point in the initial point cloud IPC that is not associated with hypotheses (e.g., points P 3  and P 4  in the example) or indicates a point and hypothesis for a point (e.g., point P 2 ) that has fewer than expected hypotheses. For simplicity, each of the points P 3  and P 4  may be regarded as having a single hypothesis or estimate for range, Doppler, and DOA. Also, in Table 2, the index j indicates a point and hypothesis associated with a complete set based on the ambiguity function (at block  320 ). Thus, for example, the Mahalanobis distance d 322  is between the point P 3  (i.e., i=3) and the second hypothesis of the second point (i.e., j=22). As another example, d 2243  is between the second hypothesis H 2  of the second point P 2  (i.e., i=22) and the third hypothesis H 3  of the fourth point P 4  (i.e., j=43), which is obtained at block  320  based on the ambiguity function. 
     As previously noted, Table 2 shows the Mahalanobis distances dij obtained between the points obtained without hypotheses or with an incomplete set of hypotheses (shown along the column in Table 2) and the full set of hypotheses based on the ambiguity function (shown along the row in Table 2). Points with the full set of hypotheses (e.g., point P 1 ) are not part of the processes at blocks  320  through  340 . 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Distances among points of an initial point cloud IPC. 
               
            
           
           
               
               
               
               
            
               
                   
                 P2 
                 P3 
                 P4 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 H1 
                 H2 
                 H3 
                 H1 
                 H2 
                 H3 
                 H1 
                 H2 
                 H3 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 P2 
                 H1 
                 — 
                 — 
                 — 
                 d2131 
                 d2132 
                 d2133 
                 d2141 
                 d2142 
                 d2143 
               
               
                   
                 H2 
                 — 
                 — 
                 — 
                 d2231 
                 d2232 
                 d2233 
                 d2241 
                 d2242 
                 d2243 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 P3 
                 d321 
                 d322 
                 d323 
                 — 
                 — 
                 — 
                 d341 
                 d342 
                 d343 
               
               
                 P4 
                 d421 
                 d422 
                 d423 
                 d431 
                 d432 
                 d433 
                 — 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     At block  340 , the processes include identifying points that are actually hypotheses rather than points. This may be based on examining the lowest distance value d, in turn, in Table 2, for example. In the exemplary case, based on the distance d 323  (i.e., i=3 for point P 3  and j=23 for hypothesis H 3  of point P 2 ) being the smallest value in Table 2, it may be determined that the point P 3  in the initial point cloud IPC is actually the third hypothesis of the point P 2 . In this case, point P 3  is removed as an independent point and used as the hypothesis H 3  of point P 2  in the resulting point cloud PC. As another example, none of the distances d 4   j  (distances in the last row of Table 2) may be below a threshold value or the lowest values. In this case, the point P 4  is retained as an independent point and the hypotheses H 1 , H 2 , H 3  determined (at block  320 ) by using the ambiguity function are retained as the hypotheses of point P 4  in the point cloud PC. 
     At block  350 , generating a point cloud PC refers to providing all the points from the initial point cloud IPC that remain after the processes at blocks  320 ,  330 , and  340 . As indicated in  FIG. 2 , the point cloud PC from each radar system  110  is provided for the processes at block  230 , which are further discussed with reference to  FIG. 4 . 
       FIG. 4  shows a process flow performed at block  230  ( FIG. 2 ) for two or more radar systems  110  according to one or more embodiments. As previously noted, the processes at block  230  are performed for each common FOV  125  and, thus, involve points from the point clouds PCs of at least two radar systems  110 . At block  410 , the processes include identifying points within the common FOV  125  in point clouds PC of two or more radar systems  110 . This identification may be based on the range and DOA values associated with the hypotheses of the points, for example. 
     In the exemplary case discussed herein for exemplary purposes, a first radar system  110  (e.g., radar system  110   a  in  FIG. 1 ) is assumed to have three points Pa, Pb, Pc that are part of the same common FOV  125  as two points Px, Py of a second radar system  110  (e.g., radar system  110   b  in  FIG. 1 ). If the example discussed with reference to  FIG. 3  were continued, the three points P 1 , P 2 , P 4 , with three hypotheses each, that result from the processes at block  225  would be one of the points of one of the radar systems  110  shown in Table 3. The points Pa, Pb, Pc of the first radar system  110  may each have two hypotheses H 1  and H 2 , while the points Px, Py of the second radar system  110  each have three hypotheses H 1 , H 2 , and H 3 . 
     At block  420 , the processes include obtaining a Mahalanobis distance d between points (within the common FOV  125 ) of a pair of radar systems  110 . In the exemplary case, the distances d are between points Pa, Pb, Pc of the first radar system  110  and points Px, Py of the second radar system  110 , as shown in Table 3. Specifically, the points Pa, Pb, Pc of the first radar system  110  and their corresponding hypotheses H 1  and H 2  are shown along the top, and the points Px, Py of the second radar system  110  and their corresponding hypotheses H 1 , H 2 , and H 3  are shown along the side. Each Mahalanobis distance dij, according to EQ. 1, is between a hypothesis (H 1 , H 2 , or H 3 ) of one of the points Px or Py and a hypothesis (H 1  or H 2 ) of one of the points Pa, Pb, Pc, or Pd. For example, dx 1   a   1  is the Mahalanobis distance between hypothesis H 1  of point Px (i.e., i=x 1 ) and hypothesis H 1  of point Pa (j=a 1 ). Similarly, dy 3   c   2  is the Mahalanobis distance between hypothesis H 3  of point Py (i.e., i=y 3 ) and hypothesis H 2  of point Pc (j=c 2 ). In EQ. 1, the worst-case values between the two radar systems  110  are selected for the accuracy parameters σ R , σ D , σ Az , σEl. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Distances between points in a common field of view. 
               
            
           
           
               
               
               
               
            
               
                   
                 Pa 
                 Pb 
                 Pc 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 H1 
                 H2 
                 H1 
                 H2 
                 H1 
                 H2 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Px 
                 H1 
                 dx1a1 
                 dx1a2 
                 dx1b1 
                 dx1b2 
                 dx1c1 
                 dx1c2 
               
               
                   
                 H2 
                 dx2a1 
                 dx2a2 
                 dx2b1 
                 dx2b2 
                 dx2cl 
                 dx2c2 
               
               
                   
                 H3 
                 dx3a1 
                 dx3a2 
                 dx3b1 
                 dx3b2 
                 dx3c1 
                 dx3c2 
               
               
                 Py 
                 H1 
                 dy1a1 
                 dy1a2 
                 dy1b1 
                 dy1b2 
                 dy1c1 
                 dy1c2 
               
               
                   
                 H2 
                 dy2a1 
                 dy2a2 
                 dy2b1 
                 dy2b2 
                 dy2c1 
                 dy2c2 
               
               
                   
                 H3 
                 dy3a1 
                 dy3a2 
                 dy3b1 
                 dy3b2 
                 dy3c1 
                 dy3c2 
               
               
                   
               
            
           
         
       
     
     At block  430 , the processes include selecting a hypothesis based on the Mahalanobis distance dij for one or more pairs of points. Candidate pairs may be selected and then checked, as detailed. The selection of a candidate pair may be the selection, in turn, of a Mahalanobis distance dij that is the lowest value, for example. Then a check (e.g., filtering, gating) may be done for the candidate pair to determine if the hypotheses of the two points in the pair may be selected as the same unambiguous hypothesis for that pair of points and other hypotheses for the pair of points may be eliminated. 
     For example, if the Mahalanobis distance dy 3   b   2  (i.e., i=y 3  and j=b 2 ) is the lowest, then hypothesis H 3  of point Py and hypothesis H 2  of point Pb are a candidate pair of points. In that case, a check is done of whether all of the following are true with i=y 3  and j=b 2 : 
       | Pi   R   −Pj   R | 2 &lt;σ R   2   [EQ. 2]
 
       | Pi   D   −Pj   D | 2 &lt;σ D   2   [EQ. 3]
 
       | Pi   Az   −Pj   Az | 2 &lt;σ Az   2   [EQ. 4]
 
       | Pi   El   −Pj   El | 2 &lt;σ El   2   [EQ. 5]
 
     The check represented by EQS. 2-5 ensures that the candidate pair of points have hypotheses that are similar in every domain (i.e., range, Doppler, and DOA). Since the candidate pair of points are associated with two different radar systems  110 , the accuracy parameters σ R , σ D , σ Az , σ El  are not the same for both points. The worst-case scenario (i.e., higher value of the accuracy parameter) is used in each domain. If the check is met, then the hypotheses (e.g., hypothesis H 3  of point Py and hypothesis H 2  of point Pb in the example) are deemed to represent one unambiguous point and the other hypotheses are discarded. 
     Thus, in the exemplary case, hypotheses H 1  and H 2  for point Py and hypothesis H 1  for point Pb may be discarded and points Py and Pb are considered resolved. Specifically, the range, Doppler, and DOA indicated by hypothesis H 3  of point Py is retained for the point cloud of the second radar system  110  and hypothesis H 2  of point Pb is retained for the point cloud of the first radar system  110 . Some pairs of points in the common FOV  125  may not qualify as a candidate pair or may not pass the check represented by EQS. 2-5. Those points remain unresolved. At block  440 , obtaining resolved and unresolved points in the common FOV  125  facilitates the further processing at block  240 . Specifically, resolving ambiguity for at least a subset of the points in the common FOV  125  improves the accuracy of any subsequent application of the point clouds of each radar system  110 . 
     While the above disclosure has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from its scope. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the disclosure without departing from the essential scope thereof. Therefore, it is intended that the present disclosure not be limited to the particular embodiments disclosed, but will include all embodiments falling within the scope thereof.