Procedure for creating a reference radar map

Abstract

The invention relates to a method for creating a reference radar map (10), wherein the reference radar map (10) is configured to be compared with radar information (11) generated by means of at least one radar sensor (3) of the vehicle (F) in order to determine the position of the vehicle (F).

Description

The invention relates to a method for creating a reference radar map and to a system for determining the position of a vehicle based on a reference radar map.Methods for determining the position of a vehicle are already known. For example, it is known to determine the position of a vehicle by means of a GPS sensor and based on GPS information provided by satellites.DE 102014223363 A1 discloses a method and a device for locating a motor vehicle in a stationary reference map.DE 102018127059 B4 describes a method for checking at least one environment detection sensor of a vehicle.Paper WALD STEFAN [et al.]: ATRIUM: Test Environment for Automotive Radars. In: IEEE MTT-S International Conference on Microwaves for Intelligent Mobility (ICMMIM), 2020. S. 1-4. ISBN 978-1-7281-6756-5 discloses a method for testing radar sensors.The publications ANSYS, Inc.: Avxcelerate sensors. 2023 (866.267.9724). 5 S. Company Publication) and ANSYS, Inc.: ANSYS® HFSS SBR+. 2018 (866.267.9724). 2 S. Company publication show sensor simulation methods for different sensor types.The problem here is that such a position determination is relatively inaccurate.Proceeding from this, it is an object of the invention to specify a method for creating a reference radar map, by means of which a localization of the vehicle is made possible, specifically by comparing the created reference radar map with the radar information which is provided by a radar sensor of the vehicle whose position is to be determined.The object is achieved by a method having the features of independent claim 1. Preferred embodiments are the subject matter of the dependent claims. A system for determining the position of a vehicle is the subject matter of independent claim 13.According to a first aspect, a method for creating a reference radar map is disclosed. The created reference radar map is configured to be compared with radar information generated by at least one radar sensor of the vehicle, in order to thereby determine the position of the vehicle. The method comprises the following steps:First, a geodata map is received that contains geodata of objects located on the surface of the earth. For example, the map is a three-dimensional map in which the objects are contained three-dimensionally, i.e. with their length, width and height. The map can be, for example, an OpenDrive map (in the xodr format) or an OpenStrMap map that contains the geometry of surrounding objects in three-dimensional form. The geodata of the geodata map contains, at least in part, height information relating to the objects, for example the height of a house, a traffic sign, etc. In addition, gradations in the roadway region can preferably be taken from the map, for example a curb provided on the edge side on the roadway.Based on the geodata map, virtual radar detections are calculated by means of a ray tracing method, which is carried out from discrete spatial points in the geodata map. The ray tracing method determines which back reflections from objects contained in the geodata map in the surrounding area of the respective spatial point to this spatial point arise. In particular, it is determined which objects are visible from a discrete spatial point in the map by a radar sensor having a radar lobe with a predefined opening angle in the elevation direction, and whether and with which amplitude back reflections from the visible objects back to the discrete spatial point occur.Finally, a reference radar map is generated based on the generated virtual radar detections. This is effected, for example, in such a way that the calculated virtual radar detections are entered in a raster map, namely in the raster of the raster map which is assigned to the location at which the respective reflection of the radar signal has taken place.The technical advantage of the method is that a reference radar map can be generated by means of the described method from digital maps which are available with high precision and in regularly updated form, which reference radar map can be used in the vehicle to be compared with radar information which is generated by a radar sensor of the vehicle itself, so that the current position of the vehicle in the reference radar map and thus the actual real position of the vehicle (for example in the UTM, UTMRF / MGRS, CH1903, Gaussian Krueger, GK, NAC, W3W or WGS coordinate system) can be determined with high precision by means of the comparison.According to one embodiment, drivable areas are determined in the geodata map and the discrete spatial points are selected on these drivable areas. Thus, for example, roads, roads and / or other trafficable areas can be recorded in the geodata map and identified as such. Since a vehicle will most likely move along these roads, roads, and / or other drivable areas, it is advantageous for reasons of computing efficiency to limit the ray tracing method to these areas. Preferably, the discrete spatial points are selected along a central longitudinal axis of a drivable roadway, since vehicles usually move along this central longitudinal axis. The discrete spatial points in the geodata map are thus located where, in reality, the environment is detected by means of a radar sensor of the vehicle.According to one exemplary embodiment, the geodata map is filtered for objects that can be detected by a radar sensor installed on the vehicle side, as a result of which a filtered geodata map is produced. The filtered geodata map thus contains a reduced data record, in particular a reduced number of objects, since objects that cannot be detected or are not required by a radar sensor, for example road markings, non-reflecting objects or movable objects such as, for example, motor vehicles or bicycles, are removed from the geodata map. The filtered geodata map is used to create the reference radar map. The reference radar map is thus created with a geodata map that is reduced to the essential elements relevant for the radar detections.According to one exemplary embodiment, ray tracing takes place at the discrete spatial points in each case in a plurality of different spatial directions in order to determine which objects of the geodata map lying in the different spatial directions lead to back reflections to the respective spatial point. In other words, starting from the discrete spatial points, the ray tracing method (ray tracing method) is carried out with different azimuth angles in order to take into account objects at which back reflections take place in the horizontal plane in front of and laterally next to the respective spatial point.According to one exemplary embodiment, a virtual radar lobe with a predefined vertical opening angle (radar lobe opening angle in elevation direction) is used in each case at the discrete spatial points. In the case of a plurality of objects arranged one behind the other in the direction of the emission direction of the virtual radar lobe or an object with a height contouring, the proportional back reflections which arise by reflection of a proportion of the virtual radar lobe on the respective object are determined. Reflections which arise at a plurality of objects or object sections arranged one behind the other can thus be determined and detected in the reference radar map.According to the invention, the amount of the back-reflected portion of the virtual radar beam is determined depending on the height of the object at which back-reflection takes place. The higher the object, the larger the reflection surface at which the radar radiation can be reflected back. In the case of a plurality of objects arranged one behind the other, the proportion is determined on the basis of their height ratio. This makes it possible to ascertain the amplitude of the virtual radar detections and to enter it into the reference radar map.According to the invention, in the case of a plurality of objects arranged one behind the other in the direction of the virtual radar beam or an object with object regions of different height, the objects or the object regions are sorted according to their height. The amount of the reflected-back portion of the virtual radar beam of a second object or of a second object region which, starting from the discrete spatial point at which the virtual radar beam is emitted, lies behind a first object or of a first object region is determined by subtracting the amount of the reflected-back portion of the virtual radar beam of the second object or of the second object region from the amount of the reflected-back portion of the virtual radar beam of the first object or of the first object region. In other words, it is initially assumed that the reflection takes place only on the higher, second object, and the portion of the virtual radar beam reflected back on this second object is determined. Subsequently, the portion of the virtual radar beam reflected back at the first object or the first object region, which is / is arranged in front of the second object or the second object region, is determined. The portion of the virtual radar beam that is actually reflected back at the second object or the second object region is determined by subtracting the portion of the virtual radar beam that is reflected back at the first object or the first object region from the portion of the virtual radar beam that is reflected back and was assumed for the entire second object or the entire second object region without being occluded by the first object or the first object region.According to one exemplary embodiment, an object that is completely hidden by other objects is determined on the basis of the respective discrete spatial point. If such an object exists, this is not taken into account in the ray tracing method. As a result, the ray tracing method can be limited to the objects at which reflections can occur at all.According to one exemplary embodiment, roadway boundaries are determined by jumps in height between a first region of the geodata map, which represents a drivable region, and a second region of the geodata map, and these jumps in height are taken into account when creating the reference radar map. As a result, curbstones or similar objects which serve for the roadway boundary but are not classified as such in the geodata map can be recognized and used as potentially reflecting objects when creating the reference radar map.According to one exemplary embodiment, the objects contained in the geodata map are at least partially provided with object information. The object information is, for example, classification information which indicates the class into which the object is to be semantically classified (e.g. trafficable area, guardrail, traffic island, lane marking, etc.). The object information is used for filtering the geodata map in order to reduce the information content of the geodata map. The ray tracing method can thus only be applied to the objects on which a back reflection can actually take place. Road markings, for example, at which no back reflection occurs are therefore removed from the geodata map. The same applies, for example, to objects that are too far away from the trafficable regions of the geodata map and are therefore of no interest, since these are also not to be detected by the radar sensor of the vehicle.According to one exemplary embodiment, the objects contained in the geodata map are assigned at least partially reflection information which is a measure of the reflectivity of the respective object for radar beams. The reflectivity of the object can thus be taken into account in the determination of the amplitude of the back reflection which arises at the respective object.According to one exemplary embodiment, the reference radar map is a map with a discrete grid, into which the artificial radar detections generated by means of the ray tracing method are entered. The entry into a respective grid takes place depending on the location at which the respective back reflection takes place.According to one exemplary embodiment, the method is carried out offline in a computing unit remote from the vehicle. In this case, the reference radar map is received via a data interface of the vehicle and used for determining the position of the vehicle.Alternatively, the method is carried out online by a computing unit of the vehicle, the position of which is to be determined by means of the reference radar map. Preferably, a reference radar map is calculated only for a limited area around the current position of the vehicle. As a result, a reference radar map can be calculated in situ on the vehicle side and this can be used for determining the position of the vehicle.According to a further aspect, a computer program is disclosed. The computer program comprises instructions which, when the method is executed by a computer unit, cause the computer unit to execute the method according to one of the preceding exemplary embodiments.In yet another aspect, a system for determining the position of a vehicle is disclosed. The system includes an interface for receiving a geodata map containing geodata of objects located on the surface of the earth, and a radar sensor for ascertaining radar information of the environment of the vehicle. The system is configured to perform the following steps:receiving a geodata map containing geodata of objects located on the surface of the earth, the geodata containing elevation information relating to the objects at least in part;determining virtual radar detections based on the geodata map by means of a ray tracing method, which is carried out from discrete spatial points in the geodata map, wherein the ray tracing method determines which objects contained in the geodata map in the surrounding area of the respective spatial point lead to back reflections to this spatial point;creating a reference radar map based on the generated virtual radar detections;determining the position of the vehicle by comparing the radar information with the reference radar map.The terms "approximately", "substantially" or "about" mean, for the purposes of the invention, deviations from the exact value in each case by + / - 10%, preferably by + / - 5%, and / or deviations in the form of changes which are insignificant for the function.Developments, advantages and possible applications of the invention also result from the following description of exemplary embodiments and from the figures. All features described and / or graphically depicted are fundamentally the subject matter of the invention, either alone or in any combination, independently of their summary in the claims or their reference back. The contents of the claims are also made part of the description.The invention is explained in more detail below on the basis of the figures using exemplary embodiments. The following are shown: FIG. 1 shows, by way of example, a schematic illustration of a vehicle having a system for determining the position of the vehicle on the basis of a reference radar map; FIG. 2 shows, by way of example, a section from a geodata map which shows a circular traffic with a plurality of roads branching off from it; FIG. 3 shows, by way of example, a schematic illustration of the ray tracing method which is carried out at a plurality of discrete spatial points along the roadway; FIG. 4 shows, by way of example, a schematic lateral sectional illustration of a virtual radar lobe which impinges on a plurality of objects which are contained in the geodata map and the height- and distance-dependent division of the amplitude of the back reflection onto the respective objects; FIG. 5 shows, by way of example, a reference radar map, ascertained by means of the ray tracing method, for the section of the geodata map according to FIG. 2 ; FIG. 6 shows, by way of example, radar information which is generated by a radar sensor installed on the vehicle side with respect to the section of the geodata map according to FIG. 2 ; and FIG. 7 is a block diagram illustrating the steps of a method for creating a reference radar map, by way of example.FIG. 1 shows, by way of example and schematically, a vehicle F which has a system 1 for determining the position of the vehicle F on the basis of a comparison of a reference radar map 10 with radar information 11 which has been generated by means of at least one radar sensor 3 of the vehicle F. The vehicle F comprises a computing unit 4 which is designed to compare a reference radar map 10, which was generated on the basis of data from a geodata map 12, with radar information 11 which was generated by means of a radar sensor 3 of the vehicle F itself, and to determine the position of the vehicle via the comparison. In particular, a more accurate position determination can be carried out by means of the comparison than is possible by means of a GPS position determination.In order to receive the geodata map 12 or the reference radar map 10 (provided that this has been calculated by an external computing unit independent of the vehicle F), the vehicle F has an interface 2. The interface 2 can be a wireless data interface via which the geodata map 12 or the reference radar map 10 can be received.FIG. 2 shows a section of a geodata map 12 in the area of a circular traffic with a plurality of entering and / or branching roads.The geodata map 12 used to create the reference radar map 10 is a digital map by means of which a spatial position is assigned to objects located on the surface of the earth. In addition to the extension of the respective objects in the two spatial directions in a horizontal plane (x-y direction), the geodata map 12 also contains height information (z direction) relating to the objects. In particular, the geodata map 12 can be a digital map which reproduces the objects via discrete spatial points in three-dimensional space, so that an object is reproduced by means of a multiplicity of discrete points with its actual height contour. By way of example, the following maps can be used as the geodata map 12: OpenDRIVE (.xodr maps); OpenStrMap.The geodata map 12 can have object information assigned to the objects, by means of which the respective object can be classified. For example, areas (roads, etc.) that can be traveled by vehicles can be classified as "drivable" or as "road", so that these are taken into account in particular for creating the reference radar map 10. In addition, objects which project upward from the ground surface or roadway plane, for example curbstones, guardrails, buildings, trees, etc., on which radar radiation is reflected, can be classified as such in the reference radar map 10.Based on the object information, filtering of the geodata map 12 can take place, so that a filtered geodata map 12 is produced. In particular, those objects that cannot be detected by a radar sensor 3 of the vehicle F can be excluded from the geodata map 12. These are, for example, road markings which are located on the roadway and do not project, or project only very slightly, with respect to the roadway surface.The geodata map 12 can also contain further object information which is advantageous for creating the reference radar map 10. This is, for example, information about the radar beam reflectivity of an object, i.e. how strongly radar radiation is reflected at the respective object.The geodata map 12 can be processed, for example, by a machine-learning system, in particular an artificial neural network, in order to modify the geodata map 12 for the generation of the reference radar map 10. By means of the machine-learning system, for example, classification of the objects, semantic segmentation and / or filtering of the reference radar map 10 with respect to relevant objects in the environment of the trafficable areas or roads can take place.FIG. 3 schematically illustrates the determination of virtual radar reflections based on the geodata map 12. This is preferably a raster map, wherein the individual fields of the raster map are each assigned information which indicates the probability with which radar reflection takes place at the geographical position assigned to this field.As indicated in FIG. 3, the virtual radar reflections are determined iteratively at discrete positions P, P', P" on the roadway of a drivable region of the geodata map 12 or the filtered geodata map 12. The ray tracing method uses, for example, a virtual radar lobe 5 having a predefined opening angle in the elevation direction, as is illustrated in FIG. 3.The ray tracing method determines whether one or more objects are located in the geodata map 12 or the filtered geodata map 12 on which a radar radiation is reflected, starting from the position P, P', P". Preferably, only a defined region is considered, i.e. for example a region which is at a specific radial distance from the position P, P', P". If such an object exists, a reflection is mapped in the reference radar map at the location where the object is located in the geodata map 12. Preferably, in addition, information is stored in the reference radar map as to how high the reflection is at this location. This can be done, for example, on the basis of the contour of the object (e.g. a planar object or corner which reflects more strongly than an object with a diffuse surface) and / or on the basis of the information contained in the geodata map 12 regarding the reflectivity of the object.At the respective positions P, P', P", the ray tracing method is applied in different spatial directions, as is indicated by the fan-like lines in FIG. 3. The ray tracing method can be applied, for example, starting from the central axis of the respective roadway on both sides at a plurality of discrete detection angles. As a result, the opening angle of the detection range of a radar sensor is simulated in azimuth, in order to be able to simulate reflections running obliquely to the direction of travel of the vehicle (for example as a result of curbstones, guardrails or buildings).As can be seen in FIG. 3, the ray tracing method is iteratively carried out at a plurality of positions P, P', P" at different points in time. As a result, the surrounding area contained on the geodata map 12 in the environment of the roadway can be processed step by step using the ray tracing method and virtual radar reflections along the roadway can be determined. This corresponds to the radar detection of the environment by means of a radar sensor which is installed on the front side of the vehicle.The positions P, P', P" can have a definable height with respect to the road surface, which corresponds to the installation height of the radar sensor 3 on the vehicle F. As a result, the ray tracing method can be carried out from positions which correspond to the actual height of the radar sensor 3, as a result of which the ray tracing method is adapted to the actual vehicle-side detection situation.FIG. 4 shows, by way of example and schematically, a lateral illustration of the radar lobe 5 which is emitted from a position P in the direction of a plurality of objects O 1, O 2, O 3. The position P is a spatial point in the geodata map 12 and the objects O 1, O 2, O 3 are entries of this geodata map 12, i.e. the scenario shown in FIG. 4 shows a step of the ray tracing method for generating virtual radar detections and the creation of the reference radar map 10 based thereon.In the exemplary embodiment according to FIG. 4, the radar radiation of the radar lobe 5 impinges on a first object O 1 and a second object O 2, whereas the third object O 3 is concealed by the second object O 2, i.e. the radar radiation of the radar lobe 5 does not impinge on the third object O 3 and therefore does not generate any back reflection at the third object O 3.In order to take account of scenarios of this type which can arise in the geodata map 12 starting from the position P, it is first determined for each beam direction of the radar lobe 5 which objects are in visual connection from the respective position P and thus have to be taken into account at all in the ray tracing method. In the exemplary embodiment shown in FIG. 4, the third object O 3 would thus be ignored and only the first and second objects O 1, O 2 would be considered further.Subsequently, it is determined based on the aperture angle α of the radar lobe 5 which portion of the radar radiation impinges on the respective object O 1, O 2 and is thus reflected by the latter.In the case where a reflection takes place on a plurality of different objects, i.e. the radar radiation is distributed proportionally to a plurality of objects, firstly the objects can be sorted. This sorting can be carried out, for example, according to the distance thereof from the respective position P. Subsequently, it is determined based on the height of the objects which portion of the radar beam is reflected by the respective object. For example, when distributing the radar radiation over a plurality of objects, it is possible to proceed in such a way that it is first determined which portion A ges would be reflected on the highest object, in the exemplary embodiment shown the second object O2, if there were no partial masking by a further object O1 (A ges= A 1+ A 2), then the portion A 1 of the reflected radiation of a further object lying between the position P and the object, which causes masking (in the exemplary embodiment shown the object O1), is determined, and finally, by subtracting the component A 1 from the component A ges the component A 2 is determined which is actually reflected at the second object O2.As described above, the reflectivity of the respective object with respect to radar radiation can be taken into account in the calculation of the reflected component, provided that this information is present in the geodata map 12 or can be derived therefrom.As described above in connection with FIG. 3, the ray tracing method is carried out iteratively along the roadway on which a vehicle F can move, specifically in each case for different azimuth angles at a defined position and at further positions along the roadway.The virtual radar detections determined by the ray tracing method, i.e. the locations at which radar reflections result and preferably also the amplitude of these radar reflections, are then entered into a raster map. This raster map provided with the virtual radar detections forms the reference radar map 10; FIG. 5 shows, by way of example, the reference radar map 10, which results from the processing of the geodata map 12 according to FIG. 2 by means of the above-described ray tracing method. It can be seen that object contours such as road boundaries, traffic islands, guardrails, etc., which result due to the virtual radar detections, are contained in the reference radar map 10.FIG. 6 shows radar information 11 by way of example, which can be detected by a vehicle F by means of its radar sensor 3 when said vehicle is moving on the driving paths of the environment shown in FIG. 2. The comparison of FIGS. 5 and 6 shows a considerable congruence of the generated virtual radar detections with the radar information 11 detectable in reality by means of the radar sensor 3 of the vehicle F. The vehicle can be located very exactly via the radar information 11 currently detectable in the vehicle in each case and the comparison of this radar information 11 with the reference radar map 10.The generation of the reference radar map 10 can be carried out remotely from the vehicle F, for example in a stationary computer unit. The generated reference radar map 10 can then be transmitted to the vehicle F in order to be able to carry out the localization of the vehicle F on the basis thereof by comparing the reference radar map 10 with the currently detected radar information.Alternatively, the reference radar map 10 can be generated by the vehicle F itself, namely by a computing unit 4 of the vehicle which creates the reference radar map 10 on the basis of a geodata map 12 by means of the above-described ray tracing method.FIG. 7 is a schematic block diagram illustrating the steps of the method for creating a reference radar map 10.First, a geodata map is received that contains geodata of objects located on the surface of the earth. The geodata at least partially contains height information regarding the objects (S 10).Virtual radar detections are then determined based on the geodata map by means of a ray tracing method. The ray tracing method is performed from discrete spatial points in the geodata map. The ray tracing method is used to determine which back reflections from objects contained in the geodata map in the surrounding area of the respective spatial point to this spatial point arise (S 11).Finally, a reference radar map is created based on the generated virtual radar detections (S 12).The invention has been described above with reference to exemplary embodiments. It is to be understood that numerous changes and modifications are possible without thereby departing from the scope of protection defined by the claims.List of reference characters1 System 2 Interface 3 Radar sensor 4 Computing unit 5 Radar lobe 10 Reference radar map 11 Radar information 12 Geodata map α Vertical opening angle of the radar lobe F Vehicle O 1, O 2, O 3 Object

Claims

Method for creating a reference radar map (10), wherein the reference radar map (10) is configured to be compared with radar information (11) generated by means of at least one radar sensor (3) of the vehicle (F) in order to thereby determine the position of the vehicle (F), wherein the method comprises the following steps: - receiving a geodata map (12) containing geodata of objects (O1, O2, O3) located on the surface of the earth, wherein the geodata at least partially contain height information about the objects (O1, O2, O3) (S10); - determining virtual radar detections based on the geodata map (12) by means of a ray tracing method, which reflection is carried out from discrete spatial points in the geodata map (12), wherein the ray tracing method is used to determine which reflections are produced (S11) from objects (O1, O2) which are contained in the geodata map (12) in the surrounding region of the respective spatial point, wherein the amount of the back-reflected portion of the virtual radar beam is determined as a function of the height of the object (O1, O2) at which a reflection takes place, and wherein, in the case of a plurality of objects (O1, O2, O3) arranged one behind the other in the direction of the virtual radar beam or an object having object regions of different height, the objects (O1, O2 are sorted, O3) or the object regions take place according to their height and the amount of the back-reflected portion of the virtual radar beam of a second object (O2) or of a second object region which, starting from the discrete spatial point at which the virtual radar beam is emitted, lies behind a first object (O1) or a first object region is determined in that the amount of the back-reflected portion of the virtual radar beam of the second object (O2) or of the second object region is subtracted from the amount of the back-reflected portion of the virtual radar beam of the first object (O1) or of the first object region; - creating a reference radar map (10) on the basis of the generated virtual radar detections (S12).Method according to Claim 1, characterized in that drivable regions are determined in the geodata map (12) and the discrete spatial points on these drivable regions are selected.Method according to Claim 1 or 2, characterized in that the geodata map (12) is filtered for objects (O1, O2, O3) which can be detected by a radar sensor (3) installed on the vehicle side, as a result of which a filtered geodata map (12) is produced, and in that the filtered geodata map is used to generate the reference radar map (10).Method according to one of the preceding claims, characterized in that ray tracing in a plurality of different spatial directions is carried out in each case at the discrete spatial points in order to determine which objects (O1, O2, O3) of the geodata map (12) lying in the different spatial directions lead to back reflections to the respective spatial point.Method according to one of the preceding claims, characterized in that a virtual radar lobe (5) with a predetermined vertical aperture angle (α) is used in each case at the discrete points in space, and in that, in the case of a plurality of objects (O1, O2, O3) arranged one behind the other in the emission direction of the virtual radar lobe or an object with a height contouring, the proportional back reflections which arise as a result of reflection of a proportion of the virtual radar lobe (5) on the respective object are determined.Method according to Claim 5, characterized in that, starting from the respective discrete spatial point, an object (O3) which is completely concealed by other objects (O1, O2) is determined and is ignored in the ray tracing method.Method according to one of the preceding claims, characterized in that roadway boundaries are determined by jumps in height between a first region of the geodata map (12), which represents a drivable region, and a second region of the geodata map (12), and these jumps in height are taken into account when creating the reference radar map (10).Method according to one of the preceding claims, characterized in that the objects (O1, O2, O3) contained in the geodata map (12) are at least partially provided with object information and the object information is used for filtering the geodata map (12) in order to reduce the information content of the geodata map (12).Method according to one of the preceding claims, characterized in that the objects (O1, O2, O3) contained in the geodata map (12) are assigned at least partially reflection information which is a measure of the reflectivity of the respective object (O1, O2, O3) for radar beams.Method according to one of the preceding claims, characterized in that the reference radar map (10) is a map with a discrete grid, into which the artificial radar detections generated by means of the ray tracing method are entered.Method according to one of the preceding claims, characterized in that the method is carried out offline in a computing unit remote from the vehicle (F) or in that the method is carried out online by a computing unit (4) of the vehicle (F) whose position is to be determined by means of the reference radar map (10).A computer program comprising instructions which, when the method is executed by a computer unit, cause the computer unit to execute the method according to one of the preceding claims.System for determining the position of a vehicle (F), which system has an interface (2) for receiving a geodata map (12) which contains geodata of objects located on the earth surface, and a radar sensor (3) for ascertaining radar information relating to the environment of the vehicle (F), the system (1) being configured to carry out the following steps: - receiving a geodata map (12) which contains geodata of objects located on the earth surface (O1, O2, O3), the geodata containing at least partially height information relating to the objects (O1, O2, O3); - by means of a computing unit (4) of the system (1), ascertaining virtual radar detections on the basis of the geodata map (12) by means of a ray tracing method, which objects (O1, O2, O3) contained in the geodata map (12) in the surrounding region of the respective spatial point lead to back reflections to this spatial point, wherein the amount of the back-reflected portion of the virtual radar beam is determined as a function of the height of the object (O1, O2) at which back reflection takes place, and wherein in the case of a plurality of objects (O1, O2, O3) arranged one behind the other in the direction of the virtual radar beam or an object with object regions of different height, a sorting of the objects (O1, O2, is determined by means of the ray tracing method, O3) or the object regions take place according to their height and the amount of the back-reflected portion of the virtual radar beam of a second object (02) or of a second object region which, starting from the discrete spatial point at which the virtual radar beam is emitted, lies behind a first object (O1) or a first object region is determined in that the amount of the back-reflected portion of the virtual radar beam of the second object (O2) or of the second object region is subtracted from the amount of the back-reflected portion of the virtual radar beam of the first object (O1) or of the first object region; - creating a reference radar map (10) on the basis of the generated virtual radar detections; determining the position of the vehicle (F) by comparing the radar information (11) with the reference radar map (10).

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