Alignment detection for vehicle radar transceivers

Abstract

This disclosure focuses on the pitch angle (φ p ) and roll angle (φ r The present invention relates to a measurement system (12) for measuring the alignment of a vehicle radar transceiver (3), the measurement system having a The measurement system (12) is configured to: - transmit a radar signal (5); - receive a reflected radar signal (6) reflected by at least one target object (7); and - determine by the reflected radar signal (6) a measured azimuth angle (θ) of each target object (7) relative to a reference plane (R). det ) and the measured elevation angle (ψ det The measurement system (12) is adapted to measure a measurement angle (θ) such that: - assuming that each target object (7) and the radar transceiver (3) are positioned in a common plane (P) at a distance (d) from the ground surface (G), and - the equation is satisfied: det , ψ det ) to determine the pitch angle (α p ) and roll angle (α r ) is further adapted to estimate

Description

[Technical Field]

[0001] The present disclosure relates to measuring the alignment of a vehicle radar transceiver, where alignment is defined by the pitch, yaw and roll angles of the radar transceiver relative to a fixed coordinate system. [Background technology]

[0002] Today, vehicles may be equipped with one or more radar transceivers to detect reflections from surrounding objects to implement safety features such as collision avoidance and autonomous / assisted driving. These radar transceivers must obtain the azimuth angle, which is the angle in the direction of the target, the distance to the object, and the relative velocity between the vehicle and the object. They may also need to report the elevation angle to the target.

[0003] In most vehicle radar applications, it is important to measure the azimuth angle with a relatively high degree of accuracy. The angular accuracy of a radar system depends on fundamental parameters such as the number of receive channels, component tolerances, assembly accuracy, and installation conditions.

[0004] The proper radar transceiver orientation when mounted on a vehicle is given when its x- and y-axes subtend in a plane parallel to the vehicle's x-y plane, with its x-axis pointing along the specified mounting aiming direction. Complete 3D misalignment is three times the angle that a radar sensor or radar transceiver must be rotated to bring it from its proper orientation to its actual misaligned orientation. The first rotation is about its z-axis and is called yaw; the second rotation is about its y-axis and is called pitch; and the third rotation is about its x-axis and is called roll.

[0005] In order to transform target coordinates from the radar transceiver coordinate system to the vehicle coordinate system, it is important to know the complete position and orientation of the radar transceiver coordinate system in the vehicle coordinate system. Due to mounting tolerances or due to the impact of an accident, the radar sensor may also be misaligned in pitch and / or roll angles. In this case, if the pitch and roll misalignment are not known, a correct transformation of the radar target into another coordinate system (e.g., the vehicle coordinate system) is not possible. Furthermore, if the pitch and roll misalignment are not known, a correct estimation of the yaw misalignment is not possible.

[0006] Radar transceivers can also be affected by various vehicle components, such as different types of bumpers and front and rear vehicle geometries. Radar transceivers are also affected by variations during manufacturing and assembly. Therefore, sensor systems require calibration to produce accurate sensor output signals. This calibration is often performed during manufacturing in the factory, which is time-consuming and increases costs. Optimal calibration parameters can also change over time, which requires recalibration, which can be inconvenient. Summary of the Invention [Problem to be solved by the invention]

[0007] It is an object of the present disclosure to present an alternative, less complex method and system for detecting the alignment and possible misalignment of radar transceivers.

[0008] This object is achieved by a measurement system for measuring the alignment of a vehicle radar transceiver, the alignment being determined by a pitch angle φ of the radar transceiver relative to a fixed coordinate system. p and roll angle φ rThe measurement system includes a radar system, which includes a radar transceiver and a control unit. The measurement system transmits a radar signal, receives a reflected radar signal reflected by at least one target object, and determines a measured azimuth angle θ of each target object relative to a reference plane R based on the reflected radar signal. det and the measured elevation angle ψ det The measurement system is adapted to measure the measurement angle θ, assuming that each target object and the radar transceiver are positioned in a common plane P at a distance d from the ground surface G, such that the following equation is satisfied: det , ψ det using the pitch angle α of the radar transceiver relative to the fixed coordinate system p and roll angle α r is further adapted to estimate

[0009]

number

[0010] This is the pitch angle α of the radar transceiver relative to a fixed coordinate system. p and roll angle α r This means that an accurate estimate of the pitch angle α can be obtained in a relatively simple manner. This estimate is based on the assumption that each target object and the radar transceiver are positioned in a common plane, and the pitch angle α p and roll angle α r is the measurement azimuth angle θ det and the measured elevation angle ψ det It is based on the inventor's insight into how the technology impacts the [Means for solving the problem]

[0011] According to some aspects, the measurement system is adapted to satisfy the equation by using a nonlinear least squares fit.

[0012] According to some aspects, the measurement system is adapted to satisfy the equation using Bayesian estimation.

[0013] This means that well-known methods can be used to make the desired estimates, although of course many other numerical methods are applicable.

[0014] This object is also achieved by a method and a vehicle with the above mentioned advantages. [Brief explanation of the drawings]

[0015] The present disclosure will now be described in more detail with reference to the accompanying drawings. [Figure 1] FIG. 1 is a schematic top view of a vehicle and a measurement system. [Figure 2] 1 shows a schematic side view of a radar transceiver and a target object. [Figure 3] 1 shows a schematic perspective view of a radar transceiver in a coordinate system. [Figure 4] 1 shows a first schematic view of a radar transceiver in a coordinate system; [Figure 5] 2 shows a second schematic view of a radar transceiver in a coordinate system. [Figure 6] 3 shows a third schematic view of a radar transceiver in a coordinate system. [Figure 7] 1 shows a schematic side perspective view of a target object for a radar transceiver. [Figure 8A] 1 illustrates azimuth cuts for different measurement azimuth angles. [Figure 8B] 1 illustrates azimuth cuts for different measurement azimuth angles. [Figure 8C] 1 illustrates azimuth cuts for different measurement azimuth angles. [Figure 8D] 1 illustrates azimuth cuts for different measurement azimuth angles. [Figure 9] 1 is a graphical representation showing how measured azimuth and elevation angles relate to each other for a particular misalignment. [Figure 10] This paper illustrates nonlinear parameter optimization for a cross-traffic scenario without installation errors. [Figure 11] This paper illustrates nonlinear parameter optimization for a cross-traffic scenario without installation errors. [Figure 12] This paper illustrates nonlinear parameter optimization for a cross-traffic scenario with installation errors. [Figure 13] This paper illustrates nonlinear parameter optimization for cross-traffic scenarios with mounting errors. [Figure 14] We illustrate Bayesian estimation for a cross-traffic scenario with mounting errors. [Figure 15] We illustrate Bayesian estimation for a cross-traffic scenario with mounting errors. [Figure 16] We illustrate Bayesian estimation for a cross-traffic scenario with mounting errors. [Figure 17] We illustrate Bayesian estimation for a cross-traffic scenario with mounting errors. [Figure 18] We illustrate Bayesian estimation for a cross-traffic scenario with mounting errors. [Figure 19] We illustrate Bayesian estimation for a cross-traffic scenario with mounting errors. [Figure 20] 1 illustrates a control unit diagrammatically. [Figure 21] 1 illustrates an exemplary computer program product. [Figure 22] 1 shows a flowchart of a method according to the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0016] Aspects of the present disclosure will now be described more fully with reference to the accompanying drawings. However, the different devices and methods disclosed herein may be embodied in many different forms and should not be construed as limited to the aspects set forth herein. Like numbers in the drawings refer to like elements throughout.

[0017] The terminology used herein is for the purpose of describing aspects of the present disclosure only and is not intended to be limiting of the present disclosure. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

[0018] 1 shows a top view of a vehicle 1 equipped with a radar system 2, which comprises a vehicle radar transceiver 3 and a control unit 4. The radar transceiver 3 has a particular field of view (FOV) 9 and a front face 11 that includes a radar aperture.

[0019] According to some embodiments, the radar transceiver 3 is positioned behind or inside a bumper 8 which acts as a radome for the radar transceiver 3 .

[0020] FIG. 1 further shows a measurement system 12 for measuring the alignment of the vehicle radar transceiver 3, which is defined as the pitch angle φ of the radar transceiver 3 relative to a fixed coordinate system x, y, z, as shown in FIGS. 3 to 6. p , yaw angle φ y and roll angle φ r FIG. 3 shows a schematic perspective view of the radar transceiver 3 in the coordinate system x, y, z, and FIGS. 4 to 6 show the pitch angle φ of the radar transceiver 3. p , yaw angle φ y and roll angle φ r 1 shows a schematic diagram of a radar transceiver 3 with a front face 11 of the radar transceiver 3 in a coordinate system x, y, z illustrating

[0021] Measurement system 12 includes a radar system 2, which includes a radar transceiver 3 and a control unit 4. According to some embodiments, measurement system 12 further includes at least one target object 7, for example, if a target object 7 is included in a given test setup.

[0022] Referring also to FIG. 2 , the measurement system 12 transmits a radar signal 5, receives a reflected radar signal 6 reflected by a target object 7, and determines a measured azimuth angle θ of the target object 7 relative to a reference plane R based on the reflected radar signal 6. det and the measured elevation angle ψ det is adapted to measure

[0023] To this end, the radar transceiver 3 is adapted to transmit a radar signal 5 and receive a reflected radar signal 6 reflected by a target object 7. The control unit 4 is adapted to control the radar transceiver 3, e.g., the transmission timing, the transmission frequency content, as well as the actual transmission time waveform. According to some embodiments, the control unit 4 is also adapted to perform signal processing to extract target data related to the detected target object, e.g., a 2D FFT to obtain a range-Doppler matrix in a previously known manner. According to some embodiments, the control unit 4 is connected to an external computing device 20.

[0024] According to the present disclosure, the measurement system 12 assumes that the target object 7 and the radar transceiver 3 are positioned in a common plane P at a distance d from the ground surface G, and calculates the measurement angle θ such that the following equation is satisfied: det , ψ det using the pitch angle α of the radar transceiver 3 relative to the fixed coordinate system x, y, z p and roll angle α r It is further adapted to estimate

[0025]

number

[0026] This is the pitch angle α of the radar transceiver 3 relative to the fixed coordinate system x, y, z. p and roll angle α r This means that an accurate estimate of can be obtained in a relatively simple way.

[0027] According to some embodiments, the measurement system 12 includes a target object 7 that is determined to be in motion.

[0028] The present disclosure relates to a pitch angle α p and roll angle α r is the measurement azimuth angle θ det and the measured elevation angle ψ det Based on inventor's insight into how the technology impacts

[0029] This is illustrated in Figure 7, where φ p There is a certain error due to pitch misalignment such that the measured azimuth angle θ of the target objects 71, 72, 73, 74 is ≠ 0. det1 , θ det2 , θ det3 , θ det4 Depending on the measured elevation angle ψ det The target objects 71, 72, 73, 74 and the radar transceiver 3 are assumed to lie in a common plane P.

[0030] 8A-8D illustrate this when the target objects 71, 72, 73, and 74 are measured at different azimuth angles θ 1det , θ 2det , θ 3det , θ 4det This is illustrated by showing the corresponding azimuthal cuts for

[0031] FIG. 8A shows the first measurement azimuth angle θ det1 and the first measurement elevation angle ψ det1 2 shows the case where a first target object 71 is present.

[0032] FIG. 8B shows the second measurement azimuth angle θ det2 and the second measurement elevation angle ψ det2 2 shows the case where a second target object 72 is present.

[0033] FIG. 8C shows the third measurement azimuth angle θ det3 and the third measurement elevation angle ψ det3 4 shows the case where a third target object 73 is present.

[0034] FIG. 8D shows the fourth measurement azimuth angle θ 4det and the fourth measurement elevation angle ψ det4 4 shows the case where a fourth target object 74 is present.

[0035] Due to the pitch misalignment separating the common plane P from the reference plane R, the larger the measured azimuth angle relative to the pointing direction B, the smaller the measured elevation angle.

[0036] Figure 9 shows the p =-6.5° pitch misalignment and φ r 4.0°) provides a graphical representation of how the measured azimuth angle and the measured elevation angle relate to each other for a roll misalignment of θ = -4.0°. For example, det The target object 7' detected at =0.0° is approximately

[0037]

number

[0038] and the measured elevation angle ψ det The target object 7” detected at =0.0° is approximately

[0039]

number

[0040] This becomes:

[0041] As a result, the measured azimuth angle θ det and the measured elevation angle ψ det At least one measured azimuth angle θ is obtained using different measurements for det and at least one measured elevation angle ψ det These angle values ​​φ satisfy the above equation (1) for p , φ r By finding , the pitch and roll alignment errors can be measured. Typically, multiple detections are used.

[0042] According to some embodiments, the aiming direction B is in the reference plane R.

[0043] Pitch misalignment angle φ p and roll misalignment angle φ r Different numerical methods can be used to solve for , and examples of using different numerical methods are disclosed below.

[0044] 10-13, measurement system 12 is adapted to satisfy the equation by using a nonlinear least-squares fit with nonlinear parameter optimization. In the illustrated example, there is a cross-traffic scenario with five vehicles intersecting, and radar transceiver 3 is mounted behind bumper 8.

[0045] Figure 10 shows the results when there is no installation error, i.e., when the pitch misalignment is φ p =0° and the roll misalignment is φ r = 0° and the resulting calculated pitch misalignment is φ p = 0.42° and the resulting calculated roll misalignment is φ r = -0.11°. The dotted line relates to the expected value of the nonlinear parameter optimization, and the solid line relates to the result, both as a function of azimuth and elevation angles.

[0046] Figure 11 illustrates estimated parameter values ​​plotted as a function of iteration number of the parameter optimization described above with reference to Figure 10. The x-axis shows the iteration number and the y-axis shows the estimated parameter values.

[0047] Figure 12 shows the pitch misalignment p =-6.5°, and the roll misalignment is φ r =-4.0°, and the resulting calculated pitch misalignment is φ p= -5.84° and the resulting calculated roll misalignment is φ r =-3.68°. The dotted line relates to the expected value of the nonlinear parameter optimization and the solid line relates to the result, both as a function of azimuth and elevation angles.

[0048] Figure 13 illustrates estimated parameter values ​​plotted as a function of iteration number of the parameter optimization described above with reference to Figure 12. The x-axis shows the iteration number and the y-axis shows the estimated parameter values.

[0049] 14-19, the measurement system 12 is adapted to satisfy the equation by using Bayesian estimation. In the illustrated example, there is a cross-traffic scenario with five vehicles intersecting, and the radar transceiver 3 is mounted behind the bumper 8.

[0050] Figures 14-19 visualize the mechanism of Bayesian inference, where observations of detected target objects are used to refine knowledge about parameters present in the form of distributions. The prior parameter distribution is updated with each observation to a posterior parameter distribution. As more observations of detected target objects are observed, the posterior distribution becomes sharper over time. In each left-hand diagram, the x-axis represents the azimuth angle, and the y-axis represents the elevation angle relative to the observation. In each right-hand diagram, the x-axis represents the pitch misalignment angle of the radar transceiver, and the y-axis represents the roll misalignment angle of the radar transceiver.

[0051] In Figures 14 to 16, there is no installation error, that is, φ p = 0° pitch misalignment and φ r = 0° roll misalignment.

[0052] In Figure 14, for observation 0, no observations of the detected target object have been captured, and therefore the pitch and roll distributions are the initial distributions. The resulting calculated pitch misalignment is φ p=0° and the resulting calculated roll misalignment is φ r =0°.

[0053] Figure 15 shows the posterior distribution after 50 observations, and the resulting calculated pitch misalignment, φ p = 1.93° and the resulting calculated roll misalignment is φ r =-0.79°.

[0054] Figure 16 shows the posterior distribution after 500 observations. The resulting calculated pitch misalignment is φ p = 0.38° and the resulting calculated roll misalignment is φ r =-0.15°.

[0055] The results are very accurate, and as a result, the parameter pitch misalignment angle φ p and roll misalignment angle φ r An estimate of can be measured.

[0056] In Figures 17 to 19, there is an installation error, and p =-6.5° pitch misalignment and φ r There is a roll misalignment of -4°.

[0057] In Figure 17, for observation 0, no observations of the detected target object have been captured, and therefore the pitch and roll distributions are the initial distributions. The resulting calculated pitch misalignment is φ p =0° and the resulting calculated roll misalignment is φ r =0°.

[0058] Figure 18 shows the posterior distribution after 50 observations. The resulting calculated pitch misalignment is φ p = -6.15° and the resulting calculated roll misalignment is φ r=-3.13°.

[0059] Figure 19 shows the posterior distribution after 500 observations. The resulting calculated pitch misalignment is φ p = -5.89° and the resulting calculated roll misalignment is φ r =-3.57°. The result is very accurate, and as a result, the parameter pitch misalignment angle φ p and roll misalignment angle φ r An estimate of can be measured.

[0060] Although only one implementation of each of the numerical methods described above is provided, it will be appreciated that there are many other ways of implementing these methods.

[0061] Furthermore, the above-mentioned numerical method can be applied to the pitch misalignment angle φ p and roll misalignment angle φ r This is merely an example of how to derive σ, and many other such numerical methods are of course conceivable and obvious to one skilled in the art.

[0062] According to some aspects, the pitch misalignment angle φ p and roll misalignment angle φ r Once the measured pitch misalignment angle φ is measured, these can be stored in memory and used by the control unit 4, which calculates the measured pitch misalignment angle φ. p and roll misalignment angle φ r is adapted to compensate for subsequent detection of the target object such that

[0063] As will be described in more detail below, in accordance with some aspects, a control unit and a computer program are used to control the pitch angle φ p and roll angle φ r The most likely misalignment value can be measured.

[0064] 20 schematically illustrates, in terms of some functional units, components of a control unit 70, according to one embodiment, which correspond to the illustrated control unit 4. The processing circuitry 71 is provided using any combination of one or more suitable central processing units (CPUs), multiprocessors, microcontrollers, digital signal processors (DSPs), dedicated hardware accelerators, etc., capable of executing software instructions stored in a computer program product, for example, as in the form of a storage medium 72. The processing circuitry 71 may further be provided as at least one application specific integrated circuit (ASIC) or field programmable gate array (FPGA).

[0065] In particular, processing circuitry 71 is configured to cause control unit 70 to perform a series of operations or steps. These operations or steps are described above in connection with the various measurement systems 12 and methods. For example, storage medium 72 can store a set of operations, and processing circuitry 71 can be configured to retrieve the set of operations from storage medium 72 and cause control unit 70 to perform the set of operations. The set of operations can be provided as a set of executable instructions. As a result, processing circuitry 71 is configured to perform the methods and operations disclosed herein.

[0066] Storage medium 72 may also comprise persistent storage, which may be, for example, any one or combination of magnetic memory, optical memory, solid state memory, or even remotely attached memory.

[0067] The control unit 70 may further comprise a communication interface 73 for communicating with at least one other unit. The interface 73 may therefore comprise one or more transmitters and receivers with analog and digital components and a suitable number of ports for wired or wireless communication.

[0068] Processing circuitry 71 is adapted to control the overall operation of control unit 70, for example, by sending data and control signals to external units and storage medium 72, receiving data and reports from external units, and retrieving data and instructions from storage medium 72. Other components and associated functions of control unit 70 have been omitted so as not to obscure the concepts presented herein.

[0069] FIG. 21 illustrates a computer program product 81 including computer-executable instructions 82 disposed on a computer-readable medium 83 for performing any of the methods disclosed herein.

[0070] Referring to FIG. 22, the present disclosure also relates to a method for measuring the alignment of a vehicle radar transceiver 3, the alignment being determined by a pitch angle φ of the radar transceiver 3 relative to a fixed coordinate system x, y, z. p and roll angle φ r The method includes transmitting a radar signal 5 (S100), receiving a reflected radar signal 6 (S200) reflected by at least one target object 7, and using the reflected radar signal 6 to determine a measured azimuth angle θ of each target object 7 relative to a reference plane R. det and the measured elevation angle ψ det and measuring S300.

[0071] The method further comprises assuming S400 that each target object 7 and radar transceiver 3 are positioned in a common plane P at a distance h from the ground surface G, and determining the measured angle θ such that the following equation is satisfied: det , ψ detusing the pitch angle α of the radar transceiver 3 relative to the fixed coordinate system x, y, z p and roll angle α r The method includes estimating S500.

[0072]

number

[0073] According to some embodiments, the method includes using a target object 7 that is determined to be in motion.

[0074] According to some embodiments, the method includes S510 satisfying the equation by using a nonlinear least squares fit.

[0075] According to some aspects, the method includes satisfying S520 the equation by using Bayesian estimation.

[0076] The present disclosure is not limited to the described embodiments, but may be freely modified within the scope of the appended claims. For example, the radar transceiver may be of any suitable type and, according to some aspects, may comprise suitable devices such as an antenna, a transmitter, a receiver, a control unit, etc.

[0077] The control unit 4 may be configured by one unit or by two or more distributed sub-units. According to some embodiments, the control unit 4 may be adapted to perform one or more of the steps described as being performed by the measurement system 12.

[0078] The present disclosure may be applied to any suitable radar transceiver or transceivers included in the radar system 2.

[0079] The present disclosure is useful, for example, when the radar transceiver 3 is not accessible to the person performing the alignment test, for example, to place an inclinometer on the radar transceiver 3. Thus, the person performing the alignment test needs a way to know that the radar transceiver 3 is aligned on the vehicle within tolerances agreed upon by the radar manufacturer, and this is provided by the present disclosure.

[0080] According to some embodiments, the alignment of the radar transceiver 3 is directed to the alignment of an antenna 21 included in the radar transceiver 3, which is adapted to transmit radar signals and receive reflected radar signals in a known manner. According to some embodiments, the radar transceiver 3 is an integrated unit, and any adjustment or misalignment of the radar transceiver 3 directly affects the antenna 21 included in the radar transceiver 3.

[0081] It should be noted that when we say that each target object 7 and radar transceiver 3 are positioned in a common plane P at a distance h from the ground surface G, this is an assumption. This does not necessarily mean that this is the case in practice.

Claims

1. A method for measuring the alignment of a vehicle radar transceiver (3), said alignment being determined by the pitch angle (φ) of said radar transceiver (3) relative to a fixed coordinate system (x, y, z). ｐ ) and roll angle (φ ｒ ) wherein the method is defined by Transmitting (S100) a radar signal (5); Receiving (S200) a reflected radar signal (6) reflected by at least one target object (7); The reflected radar signal (6) is used to determine the measured azimuth angle (θ) of each target object (7) relative to a reference plane (R). ｄｅｔ ) and the measured elevation angle (ψ ｄｅｔ ) (S300), The method comprises: Assuming (S400) that each target object (7) and the radar transceiver (3) are positioned in a common plane (P) at a distance (h) from the ground surface (G); The measured angle (θ ｄｅｔ , ψ ｄｅｔ ) to determine the pitch angle (α) of the radar transceiver (3) relative to a fixed coordinate system (x, y, z). ｐ ) and the roll angle (α ｒ estimating (S500) [Equation 1]

2. 2. The method of claim 1, wherein the method includes using a target object (7) that is determined to be moving.

3. The method of claim 1 or 2, wherein the method includes satisfying (S510) the equation by using a non-linear least squares fit.

4. The method of claim 1 or 2, wherein the method comprises satisfying (S520) the equation by using Bayesian estimation.

5. A metrology system (12) for measuring the alignment of a vehicle radar transceiver (3), said alignment being determined by the pitch angle (φ) of said radar transceiver (3) relative to a fixed coordinate system (x, y, z). ｐ ) and roll angle (φ ｒ ) wherein the measurement system (12) comprises a radar system (2), the radar system (2) comprises the radar transceiver (3) and a control unit (4), and the measurement system (12) comprises: - transmitting a radar signal (5), - receiving a reflected radar signal (6) reflected by at least one target object (7); and - The reflected radar signal (6) determines the measured azimuth angle (θ) of each target object (7) relative to a reference plane (R). ｄｅｔ ) and the measured elevation angle (ψ ｄｅｔ ) and The measurement system (12) - each target object (7) and said radar transceiver (3) are assumed to be positioned in a common plane (P) at a distance (d) from the ground surface (G); and The measured angle (θ ｄｅｔ , ψ ｄｅｔ ) to determine the pitch angle (α) of the radar transceiver (3) relative to a fixed coordinate system (x, y, z). ｐ ) and the roll angle (α ｒ ) [Equation 2]

6. The measurement system of claim 5, wherein the measurement system (12) includes a target object (7) determined to be moving.

7. The metrology system of claim 5, wherein the metrology system (12) is adapted to satisfy the equation by using a nonlinear least squares fit.

8. The metrology system of claim 5 , wherein the metrology system (12) is adapted to satisfy the equation using Bayesian estimation.

9. A vehicle (1) comprising a measurement system (12) according to any one of claims 5 to 8.

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