Method and system for estimating a radar calibration matrix

Abstract

A method and system for estimating a radar calibration matrix are provided. According to the method, an initial calibration matrix is received and radar detections are obtained from an external environment of a radar sensor via the radar sensor. A plurality of beam vectors is determined from the radar detections, and a correction matrix is estimated based on the plurality of beam vectors. The initial calibration matrix and the correction matrix are combined to estimate a refined radar calibration matrix for use as a calibration matrix when applying the radar sensor.

Description

Technical Field

[0001] This disclosure relates to methods and systems for estimating radar calibration matrices. Background Technology

[0002] Radar sensors are commonly used in modern vehicles for driver assistance systems and to facilitate autonomous driving. In addition to distance and Doppler measurements of objects within the vehicle's environment, angle lookup (AF) for such objects is a crucial step in radar signal processing. To perform these measurements correctly, the radar sensor needs to be calibrated. Typically, a so-called calibration matrix is ​​estimated, which is used to calibrate any raw response of the radar sensor (e.g., for subsequent angle lookups).

[0003] Offline radar sensor calibration can also be performed in an anechoic chamber. However, this offline calibration is time-consuming. Typically, the radar sensor to be calibrated must be positioned at a so-called "far-field distance" relative to the calibration target, requiring an anechoic chamber of a certain size. Furthermore, after being installed in a vehicle, such as outside the dashboard of a car and surrounded by other parts of the vehicle, the characteristics of the radar sensor may be affected, making the results of offline calibration potentially unreliable for radar sensors installed in a vehicle.

[0004] Furthermore, estimating the calibration matrix can rely on “block” schemes, such as matrix inversion or singular value decomposition (SVD), which are typically applied to the computation of the calibration matrix as a linear transformation matrix. However, such block schemes cannot be broken down into small computational subtasks suitable for so-called online calibration, i.e., calibration based on radar detection results after the radar sensor has been installed in its intended environment (e.g., in a vehicle with limited computing power). Therefore, iterative estimation methods for the radar calibration matrix have been developed, known as the “rank-1 update method” (described in detail below), which is based on the individual beam vectors provided by the radar detection results. Although this iterative method has lower complexity, it tends to be unstable and converges slowly or not at all.

[0005] Therefore, there is a need to provide a method suitable for embedded systems for reliably estimating radar calibration matrices with low computational workload. Summary of the Invention

[0006] This disclosure provides methods implemented by a computer, computer systems, and non-transitory computer-readable media. Embodiments are shown in the specification and accompanying drawings.

[0007] In one aspect, this disclosure relates to a computer-implemented method for estimating a radar calibration matrix, the method comprising the following steps performed by computer hardware components (in other words: performed by computer hardware components): receiving an initial calibration matrix; acquiring radar detection results from the external environment of the radar sensor via the radar sensor; determining a plurality of beam vectors obtained based on the radar detection results; estimating a correction matrix based on the plurality of beam vectors; and combining the initial calibration matrix and the correction matrix to estimate a refined radar calibration matrix used as a calibration matrix when the radar sensor is applied.

[0008] The starting point of this method is an initial calibration matrix, which can be determined, for example, via a single measurement at a predetermined azimuth angle relative to the radar sensor (e.g., at zero degrees). To determine the initial calibration matrix, partial calibration can be utilized, such as a factory-based partial calibration based on measurements taken in a chamber. For example, a single measurement of a single calibration target set at a known angle would be sufficient to calculate the diagonal initial calibration matrix.

[0009] The radar sensor can be mounted in the vehicle. In this case, the radar sensor can be configured to monitor the vehicle's environment. For example, a calibration matrix can be estimated based on beam vectors representing all available radar detection results at a specific point in time; alternatively, if the radar sensor is mounted in the vehicle, the calibration matrix can be estimated based on online measurements. The initial calibration matrix is ​​then modified by the calibration matrix. Furthermore, combining the initial calibration matrix and the calibration matrix can include adding the initial calibration matrix and the calibration matrix.

[0010] Multiple beam vectors can include beam vectors obtained from radar detection results; the number of such beam vectors can be at least as large as the number of antennas or detection elements of the radar sensor. Furthermore, individual beam vectors among the multiple beam vectors can be obtained for different azimuth angles. That is, for each of the multiple azimuth angles, the multiple beam vectors can include a single beam vector. The corresponding azimuth angle can be defined relative to the aiming line direction of the radar sensor.

[0011] Multiple antenna elements can be assigned to a radar sensor, representing not only multiple "real" physical antennas belonging to the radar sensor, but also multiple virtual antennas for which corresponding beam vectors can be defined. Typically, the components of the beam vector are based on the Fourier transform of the radar detection results as raw data received by the corresponding real or virtual antennas.

[0012] To estimate the calibration matrix, a system of equations can typically be solved, for example, by using known mathematical methods, such as least squares estimation. Since the method according to this disclosure relies on estimating the calibration matrix, rather than, for example, matrix inversion or singular value decomposition, the method can be iterative and can be divided into subtasks with reduced computational effort.

[0013] Furthermore, using multiple beam vectors to estimate the correction matrix increases the robustness and reliability of the method compared to the known (simple) rank-one update method, which estimates the correction matrix based on only a single beam vector. If the steps of the method according to this disclosure are performed iteratively, excellent convergence can be achieved compared to the simple rank-one update method. Moreover, the calibration accuracy achieved by the method according to this disclosure is comparable to or even better than that achieved by applying known methods based on, for example, matrix inversion or singular value decomposition (SVD), which, however, requires a high computational workload.

[0014] According to the implementation method, the corresponding adjustment matrix can be estimated based on one of a plurality of beam vectors, and the correction matrix can be estimated by averaging the adjustment matrices of the plurality of beam vectors. In other words, the adjustment matrix is ​​first estimated for each beam vector in a manner similar to the known rank-one update method, and then the average of all adjustment matrices is estimated to provide the correction matrix.

[0015] Therefore, the estimation process for each adjustment matrix can be parallelized. Thus, this method may still have low computational complexity and requires a low computational workload similar to known rank-one update methods. Furthermore, averaging the adjustment matrices can further stabilize the estimation process, especially if the estimation process is performed iteratively.

[0016] To calculate the average, a subset of available beam vectors can be selected, such that the selected beam vectors are linearly independent. The number of beam vectors in the subset can be equal to or greater than the number of antenna array elements in the radar sensor. Antenna array elements can be real array elements or virtual array elements. In the case of virtual array elements, the number of antenna array elements can be greater than the number of actual antenna array elements present in the radar sensor.

[0017] The computational workload of this method can be reduced by selecting a subset of beam vectors for averaging. However, the linear independence of the selected beam vectors is a condition for selection, so as not to degrade stability when estimating the correction matrix. Setting the minimum number of beam vectors to be the number of real or virtual antenna array elements may be an appropriate condition for reliably implementing this method.

[0018] According to another embodiment, the multiple beam vectors can cover a predetermined azimuth range relative to the radar sensor. As mentioned above, the azimuth can be defined relative to the aiming line direction of the radar sensor. In this case, the multiple beam vectors can be referred to as an angle-dependent primitive array manifold because they smoothly cover a certain range of azimuth angles.

[0019] Furthermore, the entire angular range usable by the radar sensor can be covered by multiple beam vectors, for example, at equal angular intervals or in the form of a box. Such an angular range can range from -45 degrees to +45 degrees, or even from -90 degrees to +90 degrees. By covering a large angular range via multiple beam vectors, the reliability of the method can be further improved.

[0020] A grid of equidistant nodes can be defined for the electrical angle related to the azimuth, and each beam vector among multiple beam vectors can be assigned to one of the equidistant nodes in the grid for the electrical angle. The electrical angle can also be represented as a spatial frequency and can be given as the sine of the azimuth (e.g., relative to the direction of the radar sensor's line of sight). Directly associating multiple beam vectors with an equidistant grid for the electrical angle, rather than the azimuth angle, can further improve the accuracy of the method.

[0021] The azimuth angle can also be determined for each beam vector based on the range change rate estimated from radar detection results. That is, the true ground value of the azimuth angle for each beam vector can be directly obtained from the radar detection results. Therefore, associating beam vectors with their corresponding azimuth angles does not require a complete angle lookup process. The term range change rate refers to, for example, the radial velocity of the detected object relative to the radar sensor.

[0022] According to another embodiment, the steps of estimating the calibration matrix and combining the initial calibration matrix and the calibration matrix can be performed iteratively until the deviation between the refined calibration matrix and the previous refinement estimated in the previous iteration step is less than a predetermined value. That is, the refined calibration matrix estimated in a particular iteration step can be used as the initial calibration matrix for the next iteration step.

[0023] Iterative estimation of the correction matrix and its repeated combination with the corresponding previous calibration matrix can lead to improved convergence and thus improved calibration accuracy. Furthermore, convergence and calibration accuracy can be further enhanced if the averaging of the adjustment matrix over a single beam vector can be used to estimate the corresponding correction matrix in each iteration step.

[0024] The initial calibration matrix can be the first calibration matrix used in the iterative estimation, and can be determined, for example, by measurements taken in a calibration chamber and / or at zero azimuth and zero elevation. For example, the measurements can include a single measurement at a predetermined azimuth and / or elevation angle. In this way, the initial calibration matrix can include only diagonal elements, thereby reducing the computational workload compared to the full calibration method according to the prior art, which is performed in a calibration chamber over the entire range of azimuth. Furthermore, the initial calibration matrix can be stored in a database on a vehicle where radar sensors can be mounted.

[0025] According to another embodiment, the range or distance relative to a radar sensor can be determined for each of a plurality of radar detection results. To determine multiple beam vectors, each of the plurality of radar detection results can be used only if the range or distance of that detection result (i.e., the range or distance of the corresponding detection result under consideration) is greater than a predetermined range or distance. Therefore, detection results from far-field targets can be selected for use only in determining beam vectors, because in this embodiment, the detection results are filtered according to distance.

[0026] For each radar detection result among multiple radar detection results, it can be determined whether the corresponding radar detection result is related to a single scattering center, and therefore radar detection results determined not to be related to a single scattering center can be ignored. Thus, it can be determined that multiple beam vectors can be associated with those detection results originating from a single scattering center. As a result, multiple beam vectors can be unaffected by multiple scattering of the emitted radar waves, which can improve the reliability of calibration.

[0027] In another aspect, this disclosure relates to a computer system comprising a plurality of computer hardware components configured to perform one or all of the steps of the computer-implemented methods described herein.

[0028] A computer system may include multiple computer hardware components (e.g., a processor, such as a processing unit or processing network, at least one memory, such as a memory cell or memory network, and at least one non-transitory data storage device). It should be understood that additional computer hardware components may be provided and used to perform the steps of the computer-implemented methods within the computer system. The non-transitory data storage and / or memory cell may include computer programs that instruct the computer, for example, to use the processing unit and at least one memory cell to perform multiple or all of the steps or aspects of the computer-implemented methods described herein.

[0029] According to another aspect, the computer system also includes radar sensors configured to acquire the detection results of the plurality of radars.

[0030] In another respect, the present invention relates to a vehicle comprising a computer system as described herein.

[0031] As used herein, the terms processing means and processing units may refer to, or include, an application-specific integrated circuit (ASIC); electronic circuitry; combinational logic circuitry; field-programmable gate arrays (FPGAs); processors (shared, dedicated, or grouped) that execute code; other suitable components that provide the functions described herein; or combinations of some or all of the foregoing, such as in a system-on-a-chip. Processing means and processing units may include memory (shared, dedicated, or grouped) storing code executed by the processor.

[0032] On the other hand, this disclosure relates to a non-transitory computer-readable medium comprising instructions for performing multiple or all of the steps or aspects of the computer-implemented methods described herein. The computer-readable medium may be configured as: an optical medium, such as an optical disc (CD) or digital versatile disc (DVD); a magnetic medium, such as a hard disk drive (HDD); a solid-state drive (SSD); a read-only memory (ROM); flash memory; etc. Furthermore, the computer-readable medium may be configured as data storage accessible via a data connection such as an Internet connection. The computer-readable medium may, for example, be an online database or cloud storage.

[0033] This disclosure also relates to a computer program for instructing a computer to perform one or all of the steps or aspects of the computer-implemented methods described herein. Attached Figure Description

[0034] This document describes exemplary embodiments and functions of the present disclosure in conjunction with the following schematically illustrated figures:

[0035] Figure 1 A vehicle is shown, which includes a computer system for performing the method according to this disclosure.

[0036] Figure 2 This illustrates a calibration process for radar sensors based on existing technology.

[0037] Figure 3A and Figure 3B The steps for estimating the radar calibration matrix are shown.

[0038] Figure 4 The diagram shows a comparison between calibration results provided by the method according to this disclosure and calculation results provided by known methods, based on chamber data.

[0039] Figure 5 The diagram illustrates a comparison between calibration results provided by the method according to this disclosure and calibration results provided by known methods, based on online data.

[0040] Figure 6A and Figure 6B This shows a comparison of the estimated azimuth error when the calibration results are applied to the angle lookup process.

[0041] Figure 7 Flowcharts are shown illustrating methods for estimating radar calibration matrices according to various embodiments.

[0042] Figure 8 The diagram illustrates calibration matrix estimation systems according to various implementations, and...

[0043] Figure 9 A computer system having multiple computer hardware components is shown, the multiple computer hardware components being configured to implement steps of a computer-implemented method for estimating a radar calibration matrix. Detailed Implementation

[0044] Figure 1 A vehicle 10 including a computer system 11 is depicted, the computer system 11 being used to execute a method for estimating a calibration matrix for a radar sensor 13. The computer system 11 includes a radar sensor 13 and a processing unit 15, the processing unit 15 being connected to the radar sensor 13 and configured to receive radar detection results and analyze these radar detection results according to the steps of the method.

[0045] Regarding radar sensor 13, a line-of-sight direction 17 is defined. Radar sensor 13 includes an instrument field of view 19, which is defined by the spatial angles in which radar sensor 13 can monitor its external environment (i.e., the environment of vehicle 10).

[0046] Radar sensor 13 is configured to emit radar waves and provide radar detection results originating from radar waves reflected from target objects 21, 23. Target objects 21, 23 include moving objects 21, such as other vehicles, and stationary objects 23, such as buildings. Furthermore, target objects 21, 23 can be considered as a single scattering center or not a single scattering center. For each of target objects 21, 23, a corresponding azimuth angle or angle of arrival θ1, θ2 is defined relative to the aiming line direction 17 of radar sensor 13. The angles of arrival θ1, θ2 can be determined based on radar detection results, for example, by angle lookup based on the rate of change of range (or from the Doppler frequency shift), as is known in the art.

[0047] In order to provide appropriate results, such as the distance, rate of change of distance, and azimuth of targets 21 and 23, radar sensor 13 must be calibrated. Figure 2A calibration process according to the prior art, performed, for example, in an anechoic chamber, is illustrated. That is, offline calibration is typically applied to radar sensor 13, which uses a dedicated target or calibration object 25. The calibration object 25 needs to be positioned at a so-called "far-field distance" relative to radar sensor 13. Therefore, the anechoic chamber must have certain dimensions to accommodate the positioning of the calibration object 25 at the far-field distance.

[0048] During offline calibration, measurements need to be taken at equal angular intervals between the aiming line direction 17 of the radar sensor 13 and the calibration object 25, i.e., the radar detection results. Therefore, as shown by arrow 27, the calibration object 25 moves relative to the radar sensor 13 in a circle, i.e., at a constant distance. Alternatively, the radar sensor 13 can rotate relative to the calibration object 25, as shown by arrow 29. In both cases, the movement of the calibration object 25 or the rotation of the radar sensor 13 must be achieved such that the entire instrument field of view 19 of the radar sensor 13 is covered in equally spaced angular steps (see...). Figure 1 ).

[0049] like Figure 2 The offline calibration shown implicitly provides equal or uniform weighting of the radar detection results with respect to the azimuth angle. Therefore, corresponding equations can be established for each sampling angle. This yields a set of equations that can be solved using known mathematical methods (e.g., least squares estimation), thereby calculating the calibration matrix C of the radar sensor 13.

[0050] However, when radar sensor 13 is mounted on a vehicle (e.g., outside the panel of vehicle 10, see...), Figure 1 Furthermore, being surrounded by other components of the vehicle, the antenna array characteristics of radar sensor 13 may be affected and altered relative to the offline conditions under which calibration is performed in the anechoic chamber. Therefore, calibration results may not be entirely reliable after radar sensor 13 is mounted on the vehicle. Moreover, offline calibration of radar sensor 13 performed in the anechoic chamber is expensive and time-consuming.

[0051] To overcome the drawbacks of offline calibration, calibration can be performed based on data from vehicle 10 and radar sensor 13 (see...). Figure 1Online calibration of radar reflections in a "scene" within an environment is performed. For this online calibration, radar detection results from "far-field" target objects 21 and 23 are selected. Based on the radar detection results, a range or distance can be obtained for each of the target objects 21 and 23, and for online calibration, target objects 21 and 23 whose corresponding distances are greater than a predetermined distance are selected. That is, available radar reflections can be easily filtered with respect to this distance, and conversely, radar detection results for the corresponding objects 21 and 23 that are too close to the vehicle 10 and radar sensor 13 are ignored because their distances relative to radar sensor 13 are less than the predetermined distances.

[0052] Furthermore, a single scattering body test can be performed on the radar detection results. That is, for each of the multiple radar detection results from the "scene" surrounding radar sensor 13, it is determined whether the corresponding radar detection result is related to a single scattering center. Single scattering body testing is known in the art and is described, for example, in EP 3 454 081 A1 or EP 3144 696 A1. If it is determined that the radar detection is not related to a single scattering center, the corresponding radar detection result is ignored from the online calibration.

[0053] The result of radar calibration is usually expressed by a radar calibration matrix C that satisfies the following formula:

[0054]

[0055]

[0056] X is the original array manifold, which includes multiple beam vectors, and it is assumed that it can be used to determine the radar calibration matrix. That is, multiple beam vectors x are obtained from the original radar detection results. i For example, it can be obtained through Fourier transform. Figure 3A The diagram shows multiple beam vectors constituting the original array manifold X, where a single beam vector is denoted by 31. The number of components of each beam vector corresponds to the number of real or virtual antennas included in the radar sensor 13.

[0057] In equation (1), A(θ) represents the matrix of the nominal or ideal steering or beam vectors, which depends on the azimuth angle θ. These ideal beam vectors a i One of the beam vectors in 1,37 Figure 3B The image is shown relative to radar sensor 13. This represents a diagonal matrix used only for normalization.

[0058] If the original array manifold X or multiple beam vectors are available, then the system of equations must be solved as indicated in equation (1) to determine the calibration matrix C. As further proposed in the second line of equation (1), this system of equations can be solved simultaneously by matrix inversion or singular value decomposition (SVD), i.e., in the "least squares" sense, and X + =X H (XX H ) -1 However, these methods, namely those based on matrix inversion or SVD, cannot be broken down into small computational subtasks. Therefore, they are not suitable for estimating radar calibration matrices based on online calibration data.

[0059] To estimate the radar calibration matrix based on online calibration data, a so-called rank-one update method has been developed, which relies on specific azimuth angles θ. i exist Figure 3A The single beam vector x shown in the figure i 31.

[0060] Typically, the goal of the method and rank-one update method disclosed herein is to find the ideal calibration matrix C that satisfies the following formula. ideal :

[0061]

[0062] As a prerequisite, it is assumed that the initial calibration matrix C0 is available, which is determined beforehand, i.e., via measurements taken in the calibration chamber at a zero azimuth angle θ. That is, this initial calibration matrix C0 consists only of diagonal elements.

[0063] Based on a single beam vector x i 31. The addition matrix or adjustment matrix C is estimated through the following process. add 33 (see) Figure 3A ):

[0064] initialization:

[0065]

[0066] And based on x i and To calculate as follows:

[0067]

[0068]

[0069] By using the previous calibration matrix C old (or the initial calibration matrix C0, for i=1) and the adjustment matrix C add Adding 33 together yields the updated calibration matrix C.new :

[0070]

[0071] Then, repeat the aforementioned steps, i.e., update C. old :

[0072]

[0073] And repeat the steps according to equations (4) to (6), for example, for a predetermined number of iterations, to provide the final result:

[0074]

[0075] However, the equation (4) describes a single beam vector x i The simple rank-one update method does not converge properly in many cases.

[0076] To overcome this problem, a cumulative rank-one update method according to this disclosure is provided. This cumulative method relies on all available beam vectors x. i (instead of a single beam vector x) i That is, such as Figure 3A The multiple beam vectors x shown i 31 is used as the input to this method. Multiple beam vectors 31 can be considered as the collected or reconstructed original array manifold X. Figure 3A In this representation, the manifold X is depicted relative to the azimuth angle θ. Instead of a regular grid or regular box used to represent the azimuth angle θ of the beam vector 31 of the array manifold X, a regular grid or regular box of the electric angle or spatial frequency u can be used, given as u = sin(θ). Such a representation facilitates the following methodological steps.

[0077] According to the accumulation method, all beam vectors x of the original array manifold X are used. i 31. Update the initial calibration matrix C old For each beam vector 31, based on beam vector x i The adjustment matrix for estimating a beam vector in 31 is obtained as described above according to formula (4):

[0078]

[0079] This is Figure 3A As shown in the figure, for L beam vectors x i The beam vectors in 31 describe L adjustment matrices. L is the available beam vector x of the array manifold X. i The number of L adjustment matrices C is as follows. add,i Take the average to obtain the correction matrix C add:

[0080]

[0081] Here, a uniform average is applied. Alternatively, a weighted average can also be used in this estimation method.

[0082] exist Figure 3A In the mean correction matrix C add Represented by 35. To update the initial calibration matrix C old The average correction matrix C from equation (10) add It is added to the initial or previous calibration matrix C using the same additive method as the simple rank-one update method described above. old :

[0083]

[0084] Furthermore, the above steps are repeated. More than one beam vector x is used. i The accumulation method of 31 converges as shown below to achieve the desired goal:

[0085]

[0086] To evaluate the quality of the corresponding calibration results, i.e., the estimated calibration matrix, the so-called subspace angle is considered. It is defined as the ideal or nominal beam vector a i 37 and the calibrated beam vector Cx i The angle between; for a specific (azimuth) angle θ i The calibrated beam vector Cx i Represented by 39 (see) Figure 3B The calibrated beam vector is the result of the calibration matrix and the result of applying the calibration matrix to the azimuth angle θ. i beam vector x i The product of 31. Vectors 37 and 39 are depicted relative to radar sensor 13. Therefore, the subspace angle... It is determined by applying the arccosine of the result of dividing the inner product of vectors 37 and 39 by the absolute values ​​of vectors 37 and 39, which is known in the art (also known as a measure of collinearity between vectors).

[0087] exist Figure 4 and Figure 5 In the context of calibration matrices obtained through different calibration methods, the subspace angles are expressed in degrees. The azimuth angle, expressed in degrees, is depicted in the corresponding left figure. The azimuth angle covers a range from -45° to +45°, providing 91 equally spaced corner boxes. That is, the original array manifold X comprises 91 beam vectors x. i 31.

[0088] exist Figure 4 and Figure 5 In the left figure, the subspace angle has been determined by the calibration matrix estimated via single-chamber measurements 41, 51, by matrix inversion methods 43, 53, by SVD-based methods 45, 55, and by the cumulative rank-one update methods 47, 57 according to this disclosure. Single-chamber measurements 41, 51 are performed with zero azimuth (θ = 0°) and zero elevation, such that the corresponding calibration matrix includes only diagonal elements. This calibration matrix (i.e., based on the chamber measurement at θ = 0) is also used as the initial calibration matrix for the cumulative rank-one update methods 47, 57 (i.e., C in the first iteration). old ).

[0089] exist Figure 4 and Figure 5 In the corresponding right figure, the subspace angle is depicted relative to the number of iterations performed according to the accumulation method of this disclosure. The root mean square (RMS) of the subspace angles is constant, as the results obtained when using other calibration methods (i.e., single-chamber measurements 41, 51, matrix inversion-based methods 43, 53, and SVD-based methods 45, 55) do not change with iterations of the cumulative rank-one update method, and thus the RMS of the subspace angles provided by these methods are constant, as can be identified in the figure.

[0090] for Figure 4 Raw radar detection results from chamber measurements or chamber data were used to determine the beam vector x. i , and for Figure 5 Online data assigned to one of the 91 corner boxes was used. As mentioned above, the iteration started with the initial calibration matrix from single-chamber measurements 41 and 51, and the root mean square of the subspace angle decreased from one iteration to the next, i.e., after 50 iterations, it decreased from an initial value of 8.96 degrees to a final value of 7.01 degrees. Figure 4 The final value decreased from 8.74 degrees to 6.65 degrees after 50 iterations.

[0091] This demonstrates that the calibration accuracy of the accumulation method according to this disclosure is comparable to or even better than that of the calibration matrix provided by the SVD-based method, and in all cases, it is better than that of the calibration matrix provided by the matrix inversion-based method. This can also be achieved through... Figure 4 and Figure 5The subspace angle curves are identified by the graphs on their respective left sides. For calibration matrices provided by SVD-based methods 45 and 55 and by cumulative rank-one update methods 47 and 57 after 50 iterations, the curves are very close to each other. However, for calibration matrices provided by single-chamber measurements 41 and 51 and by matrix inversion-based methods 43 and 53, the curves show much larger deviations. Nevertheless, the cumulative methods offer computational advantages over matrix inversion and SVD operations (as described above). A summary of the results for the root mean square and azimuth errors of the subspace angles is provided in Table 1 below.

[0092] exist Figure 4 and Figure 5 The calibration matrices for the subspace angles and their root mean squares are shown and have also been applied to angle lookup to check the performance of each calibration matrix. Figure 6A and Figure 6B In this context, the estimated azimuth error, expressed in degrees relative to the azimuth, is described for this angle lookup process using different calibration matrices.

[0093] For the left figure, these calibration matrices are estimated based on chamber data, such as for Figure 4 The results are shown, and for the right figure, the calibration matrices are as follows: Figure 5 The results shown are based on online calibration data. Results for an ideal calibration matrix providing zero azimuth error are also shown and are represented by 60 and 70, respectively. Furthermore, the estimated azimuth error for angle lookup is shown for the corresponding calibration matrices estimated using single-chamber measurements 61, 71, chamber measurements and matrix inversion 63, online data and matrix inversion 73, chamber data and SVD 65, online data and SVD 75, chamber data and accumulation method 67, and online data and accumulation method 77.

[0094] As can be appreciated, when the obtained calibration matrix is ​​applied to angle lookup, the accumulation method according to this disclosure provides a considerably small azimuth error, i.e., within a range comparable to or even slightly smaller than that of the SVD method, while the corresponding calibration matrices based on matrix inversion and single-chamber measurements at zero degrees provide larger azimuth errors. Therefore, overall calibration accuracy can be improved by the accumulation method according to this disclosure.

[0095] The corresponding root mean square of the subspace angle (see) Figure 4 and Figure 5The results for the estimated azimuth error are summarized in Table 1 below, i.e., along the line for the angular range from -45 degrees to +45 degrees. Furthermore, results based on chamber data for the angular range from -60 degrees to +60 degrees are also shown. These additional results demonstrate lower root mean square subspace angles and lower estimated azimuth errors for the cumulative method according to this disclosure compared to all other methods, and even to the SVD method.

[0096] Table 1

[0097]

[0098] Figure 7 A flowchart illustrating a method for estimating a radar calibration matrix according to various embodiments is shown at 700. At 702, an initial calibration matrix can be received. At 704, radar detection results can be acquired from the external environment of the radar sensor via the radar sensor. At 706, multiple beam vectors that can be obtained based on the radar detection results can be determined. At 708, a correction matrix can be estimated based on the multiple beam vectors. At 710, the initial calibration matrix and the correction matrix can be combined to estimate a refined radar calibration matrix used as the calibration matrix when applying the radar sensor.

[0099] According to various implementation methods, it is possible to determine whether each radar detection result among multiple radar detection results is related to a single scattering center.

[0100] According to various implementation methods, the corresponding adjustment matrix can be estimated based on one of a plurality of beam vectors, and the correction matrix can be estimated by calculating the average of the adjustment matrices of the beam vectors.

[0101] According to various implementation methods, a subset of available beam vectors can be selected to calculate the average, such that the selected beam vectors are linearly independent.

[0102] According to various implementation methods, the number of beam vectors in the subset can be equal to or greater than the number of antenna receiving units of the radar sensor.

[0103] According to various implementations, multiple beam vectors can cover a predetermined (azimuth) angular range relative to the radar sensor.

[0104] According to various implementations, a grid of equidistant nodes can be defined for electrical angles related to azimuth, and each of the multiple beam vectors can be assigned to one of the equidistant nodes in the grid for electrical angles.

[0105] According to various implementation methods, the corresponding azimuth angle for each beam vector can be determined based on the range change rate estimated from (stationary) radar detection.

[0106] According to various embodiments, the steps of estimating the correction matrix and combining the initial calibration matrix and the correction matrix can be performed iteratively until the deviation between the refined calibration matrix and the previous refined calibration matrix estimated in the previous iteration step is less than a predetermined value.

[0107] According to various implementations, the initial calibration matrix can be determined via (single) measurement results, such as in the calibration chamber and / or at zero azimuth and zero elevation.

[0108] According to various implementation methods, the distance relative to the radar sensor can be determined for each radar detection result among multiple radar detection results, and each radar detection result among multiple radar detection results can be used to determine multiple beam vectors only when the distance of the detection result is greater than a predetermined distance.

[0109] According to various implementation methods, it is possible to determine whether each radar detection result among multiple radar detection results is related to a single scattering center, and radar detection results determined not to be related to a single scattering center can be disregarded.

[0110] Each of steps 702, 704, 706, 708, and 710, as well as the further steps described above, can be performed by computer hardware components.

[0111] Figure 8 A calibration matrix estimation system 800 according to various embodiments is shown. System 800 can be implemented in processing unit 15 (see...). Figure 1 The system 800 can be implemented in a matrix receiving circuit 802, a radar detection circuit 804, a beam vector determination circuit 806, a correction matrix estimation circuit 808, and a combination circuit 810.

[0112] The initial matrix receiving circuit 802 can be configured to receive an initial calibration matrix. The radar detection circuit 804 can be configured to acquire radar detection results from the environment of the radar sensor via the radar sensor. The beam vector determination circuit 806 can be configured to determine multiple beam vectors that can be obtained from the radar detection results. The correction matrix estimation circuit 808 can be configured to estimate a correction matrix based on the multiple beam vectors. The combination circuit 810 can be configured to combine the initial calibration matrix and the correction matrix to estimate a refined radar calibration matrix.

[0113] The initial matrix receiving circuit 802, radar detection circuit 804, beam vector determination circuit 806, correction matrix estimation circuit 808, and combination circuit 810 can be interconnected, for example, via an electrical connection 812 such as a cable or computer bus or via any other suitable electrical connection to exchange electrical signals.

[0114] "Circuit" can be understood as any type of logical implementation entity, which can be a dedicated circuit or a processor that executes a program stored in memory, firmware, or any combination thereof.

[0115] Figure 9 A computer system 900 is depicted having multiple computer hardware components configured to perform steps of a computer-implemented method for estimating a radar calibration matrix according to various embodiments. The computer system 900 corresponds to... Figure 1 The computer system 11 shown may include a processor 902, a memory 904, and a non-transitory data storage unit 906. Radar sensor 13 (see...) Figure 1 ) can be provided as part of computer system 900 (e.g. Figure 9 (as shown), or it can be provided outside the computer system 900. The processor 902, memory 904, and non-transitory data storage unit 906 can be the processing unit 15 (see...). Figure 1 ) components.

[0116] Processor 902 can execute instructions provided in memory 904. Non-transitory data storage unit 906 can store computer programs, including instructions that can be transferred to memory 804 and then executed by processor 902. Radar sensor 13 can be used to acquire radar sensor data, based on which the range change rate can be obtained.

[0117] The processor 902, memory 904, and non-transitory data storage unit 906 can be connected to each other, for example, via electrical connection 910 (e.g., cable or computer bus) or via any other suitable electrical connection to exchange electrical signals. The radar sensor 13 can be connected to the computer system 900, for example, via an external interface, or can be provided as part of the computer system (in other words: inside the computer system, for example, via electrical connection 910).

[0118] The terms “connection” or “link” are intended to include direct “connection” (e.g., via a physical link) or direct “link” as well as indirect “connection” or indirect “link” (e.g., via a logical link).

[0119] It should be understood that the above description of one of the methods can similarly apply to system 800 and / or computer system 900.

[0120] List of reference numerals

[0121] 10 vehicles

[0122] 11 Computer Systems

[0123] 13 Radar Sensors

[0124] 15 processing units

[0125] 17. Direction of the aiming line

[0126] 19 Instrument Field of View

[0127] 21. Move the target object

[0128] 23. Static target object

[0129] 25 Calibration Objects

[0130] 27 arrows

[0131] 29 arrows

[0132] 31 Beam Vector

[0133] 33 Adjusting the matrix

[0134] 35. Correction Matrix

[0135] 37 Ideal Beam Vector

[0136] 39. Calibrate beam vector Cx i

[0137] 41. Subspace angles and RMS of the calibration matrix based on chamber measurements and chamber data.

[0138] 43. Subspace angles and RMS of the calibration matrix based on matrix inversion and chamber data.

[0139] 45. Subspace angles and RMS of the calibration matrix based on SVD and chamber data

[0140] 47. Subspace angles and RMS of the calibration matrix based on the accumulation method and chamber data.

[0141] 51. Subspace angles and RMS of the calibration matrix based on chamber measurements and online data.

[0142] 53. Subspace angles and RMS of the calibration matrix based on matrix inversion and online data.

[0143] 55. Subspace angles and RMS of the calibration matrix based on SVD and online data.

[0144] 57. Based on the cumulative method, the subspace angles and RMS of the calibration matrix of online data.

[0145] 60 Ideal calibration matrix orientation error

[0146] 61. Azimuth error of the calibration matrix based on chamber measurements and chamber data.

[0147] 63. Azimuth error of the calibration matrix based on matrix inversion and chamber data.

[0148] 65. Azimuth error of the calibration matrix based on SVD and chamber data

[0149] 67. Azimuth error of the calibration matrix based on the cumulative method and chamber data.

[0150] 70 Ideal calibration matrix orientation error

[0151] 71. Azimuth error of the calibration matrix based on chamber measurements and online data

[0152] 73. Azimuth error of calibration matrix based on matrix inversion and online data.

[0153] 75. Azimuth error of the calibration matrix based on SVD and online data

[0154] 77. Azimuth error of calibration matrix based on cumulative method and online data

[0155] 700 shows a flowchart of a method for estimating the radar calibration matrix.

[0156] 702 Steps for receiving the initial calibration matrix

[0157] 704 Steps for acquiring radar detection results from the external environment of the radar sensor via the radar sensor

[0158] 706. Steps for determining multiple beam vectors obtained from radar detection results

[0159] 708 Steps for estimating the correction matrix based on multiple beam vectors

[0160] 710 The step of combining the initial calibration matrix and the correction matrix to estimate the refined radar calibration matrix

[0161] 800 Calibration Matrix Determination System

[0162] 802 Initial Matrix Receiver Circuit

[0163] 804 Radar Detection Circuit

[0164] 806 Beam Vector Determination Circuit

[0165] 808 Correction Matrix Estimation Circuit

[0166] 810 Combinational Circuit

[0167] 812 connection

[0168] 900 Computer systems according to various implementation methods

[0169] 902 processor

[0170] 904 memory

[0171] 906 Non-Temporary Data Storage Department

[0172] 910 connection

Claims

1. A computer-implemented method for estimating a radar calibration matrix, the method comprising the following steps: Receive (702) initial calibration matrix, Multiple radar detection results of the external environment obtained from the radar sensor (13) (704) are obtained from the radar sensor (13). Determine (706) multiple beam vectors (31) obtained from the radar detection results. Based on the multiple beam vectors (31), the correction matrix (35) is estimated (708), and The initial calibration matrix (710) and the correction matrix (35) are combined to estimate the refined radar calibration matrix used as the calibration matrix when applying the radar sensor (13). in, For each of the plurality of beam vectors, the corresponding adjustment matrix (33) is estimated based on the corresponding beam vector (31). The correction matrix (35) is estimated by averaging the adjustment matrix (33) of the plurality of beam vectors (31). The plurality of beam vectors (31) cover a predetermined azimuth range relative to the radar sensor (13). For the electric angle related to the azimuth angle, a grid of equidistant nodes is defined, and Each of the plurality of beam vectors (31) is assigned to one of the equidistant nodes of the grid for the electric angle.

2. The method according to claim 1, wherein, To calculate the average, a subset of the available beam vectors (31) is selected such that the selected beam vectors (31) are linearly independent.

3. The method according to claim 2, wherein, The number of beam vectors (31) in the subset is equal to or greater than the number of antenna array elements of the radar sensor (13).

4. The method according to claim 1, wherein, Based on the range change rate estimated from the radar detection results, the corresponding azimuth angle is determined for each beam vector (31).

5. The method according to claim 1, wherein, The steps of estimating the correction matrix (35) and combining the initial calibration matrix and the correction matrix (35) are performed iteratively until the deviation between the refined radar calibration matrix and the previous refined radar calibration matrix estimated in the previous iteration step is less than a predetermined value.

6. The method according to claim 1, wherein, The initial calibration matrix was determined by measurements taken in the calibration chamber at zero azimuth and zero elevation angles.

7. The method according to claim 1, wherein, For each of the multiple radar detection results, determine the distance relative to the radar sensor (13), and Each radar detection result among the multiple radar detection results is used to determine the multiple beam vectors only when the distance of the radar detection result is greater than a predetermined distance (31).

8. The method according to claim 1, wherein, For each radar detection result among the multiple radar detection results, determine whether the corresponding radar detection result is related to a single scattering center, and Radar detection results that are determined not to be associated with a single scattering center are not considered.

9. A computer system (11, 900) comprising a plurality of computer hardware components configured to perform the steps of a computer-implemented method according to at least one of claims 1 to 8.

10. A vehicle (10) comprising the computer system (11, 900) according to claim 9.

11. The vehicle (10) according to claim 10, the vehicle further comprising a radar sensor (13) configured to acquire the results of the plurality of radar detections.

12. A non-transitory computer-readable medium comprising instructions for performing a computer-implemented method according to at least one of claims 1 to 8.

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