Detection of obstructed radar sensors

Abstract

The present disclosure relates to a method for detecting obstruction of a radar sensor (105) by processing a radar signal (115, 116, 117) received by the radar sensor (105). The method comprises obtaining (S1) the radar signal (115, 116, 117), determining (S2) a range-Doppler representation (300) of the radar signal such that received radar signal energy (311) is represented as a function of range (d0-d13) and relative velocity (v0-v7), determining (S4) predetermined azimuth angles (θ1, θ2, θ3) of the radar sensor (105), and calculating (S31) a relative velocity (v0, v3, v5) for each predetermined azimuth angle (θ1, θ2, θ3). The method further comprises obtaining (S5) a first distribution (301) and at least one other distribution (302, 303) of received energy (311) relative to range in the range-Doppler representation (300) for a first azimuth angle (θ1) and at least one other azimuth angle (θ2, θ3), generating (S7) a similarity measure of the distributions, and detecting (S8) an obstruction of the radar sensor (105) if the similarity measure satisfies a similarity criterion.

Description

Summary of the Invention

[0001] The present disclosure relates to a method for detecting blockage of a radar sensor by processing a radar signal received by the radar sensor.

[0002] Many vehicle radar systems include a radar transceiver arranged to generate a radar signal that is transmitted, reflected, and received using the respective antennas making up the radar system. The radar signal may, for example, be in the form of an FMCW (Frequency Modulated Continuous Wave) signal.

[0003] It's sometimes difficult to distinguish between situations where a radar sensor is blocked by an obstruction and situations where there are few or no reflective objects in the environment. This is at least partially due to the fact that even when the radar transceiver is operating normally, strong reflections are often received from locations close to the radar transceiver. Therefore, when a blocking object is added near the radar transceiver, the received signal does not change significantly compared to normal operating conditions, but reflections from objects farther away are not detected.

[0004] US 10042041 discloses a radar system wherein the radar system is indicated when the radar detector is at least partially blocked. The method described requires a change in the motion state of the radar system, for example from moving to standing.

[0005] US10054672 discloses a radar system in which spots in the average range-Doppler plot are used to indicate that the radar detector is unobstructed. Such spots consist of cyclic discontinuities in the detected amplitude.

[0006] However, it is desirable to provide a faster, more stable and reliable method for determining whether a radar detector is obstructed, and this forms an object of the present disclosure.

[0007] This object is achieved by a method for detecting obstruction of a radar sensor by processing a radar signal received by the radar sensor. The method includes obtaining a radar signal and determining a range-Doppler representation of the radar signal by processing the obtained radar signal such that received radar signal energy is represented as a function of range and relative velocity. Furthermore, the method includes determining predetermined azimuth angles of the radar sensor, wherein each predetermined azimuth angle corresponds to a respective relative velocity, and calculating the relative velocity for each predetermined azimuth angle. The method also includes obtaining a first distribution of received energy versus distance in the range-Doppler representation for a first azimuth angle, and obtaining at least one other distribution of received energy versus distance in the range-Doppler representation for at least one other azimuth angle different from the first azimuth angle. The method also includes generating a similarity metric by comparing the first distribution of detected energy versus distance with the at least one other distribution of detected energy versus distance; and detecting obstruction of the radar sensor if the similarity metric satisfies a similarity criterion.

[0008] In this way, two cases can be distinguished:

[0009] (1) The radar sensor is blocked

[0010] (2) The radar sensor does not detect anything because there are no objects to detect, so it is called a desert situation.

[0011] This distinction can be made in an uncomplicated, fast, efficient, and reliable manner, avoiding radar sensors being unnecessarily determined to be blocked. The present disclosure provides this distinction even with relatively low Doppler resolution.

[0012] According to some aspects, the range-Doppler representation is a matrix comprising matrix indices, where each matrix index corresponds to a range and a relative velocity.

[0013] This means that the generally known range-Doppler matrix representation can be used.

[0014] According to some aspects, the first azimuth angle corresponds to a first velocity, the first velocity being zero relative velocity.

[0015] In this way, the present disclosure is also applicable to cases where there is no moving radar sensor.

[0016] According to some aspects, each azimuth angle is determined relative to a reference line and an azimuth bearing.

[0017] In this way, a reliable and well-defined corner is provided.

[0018] According to some aspects, each distribution of detected energy versus range is obtained by integrating at least a portion of the range-Doppler representation over time or over multiple radar sensor scans.

[0019] In this way, a more reliable distinction is obtained.

[0020] According to some aspects, the first speed and / or at least one other speed is adjusted based on yaw rate and / or vehicle speed as it changes over time or between radar sensor scans.

[0021] In this way, a more reliable distinction is obtained.

[0022] According to some aspects, each velocity is related to a relative motion of the radar sensor with respect to an object in a field of view of the radar sensor.

[0023] According to some aspects, the similarity measure includes any of the following:

[0024] - Difference between means

[0025] - Difference between variances

[0026] -Bhattacharyya distance

[0027] -Kullback-Leibler Divergence

[0028] -Mahalanobis vector distance.

[0029] In other words, there are many well-known methods for obtaining similarity measures.

[0030] According to some aspects, the similarity criterion comprises a predetermined threshold.

[0031] The object is also achieved by a radar system associated with the above-mentioned advantages. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The present disclosure will now be described in more detail with reference to the accompanying drawings, in which:

[0033] Figure 1 shows a schematic top view of a vehicle having a radar transceiver;

[0034] Figure 2 A radar signal frame is schematically shown;

[0035] Figure 3 The range-Doppler matrix is ​​shown;

[0036] Figure 4 Three integral curves in the occlusion scenario are shown;

[0037] Figure 5 Three integral curves in the unblocked scene are shown;

[0038] Figure 6 is a flow chart illustrating a method;

[0039] Figure 7 A control unit is schematically shown; and

[0040] Figure 8 An exemplary computer program product is shown. DETAILED DESCRIPTION

[0041] Various aspects of the present disclosure will now be described more fully below with reference to the accompanying drawings. However, the various devices, systems, computer programs, and methods disclosed herein may be implemented in many different forms and should not be construed as limited to the aspects set forth herein. Throughout the text, like reference numerals refer to like elements in the accompanying drawings.

[0042] The terms used herein are only used to describe aspects of the present disclosure and are not intended to limit the present invention.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.

[0043] Figure 1 Vehicle 100 is shown traveling on road 101 in forward direction 102. Vehicle 100 includes a radar system 140, which in turn includes a control unit 120, a radar transceiver unit 110 having a radar sensor 105. According to some aspects, transceiver unit 110 is constituted by an FMCW (Frequency Modulated Continuous Wave) transceiver adapted to transmit radar signals and receive corresponding reflected radar signals 115, 116, 117 that have been reflected by corresponding objects 150, 160, 170.

[0044] In this embodiment, there is a first reflected radar signal 115 reflected from a first object 150 at a first azimuth angle θ1, a second radar signal 116 reflected from a second object 160 at a second azimuth angle θ2, and a third radar signal 117 reflected from a third object 170 at a third azimuth angle θ3. The azimuth angles θ1, θ2, and θ3 are predetermined.

[0045] According to some aspects, each azimuth angle θ1 , θ2 , θ3 is determined relative to a reference line 141 and a corresponding azimuth bearing 141 , 142 , 143 , where a first azimuth bearing 141 extending toward the first object 150 corresponds to the reference line 141 .

[0046] The transceiver 110 has a relative motion with respect to the objects 150, 160, 170. The radar signals 115, 116, 117 are mixed with the transmit signal to obtain a difference signal constituting an IF (Intermediate Frequency) signal, which is filtered for each radar signal 115, 116, 117.

[0047] By means of, for example, a first FFT (Fast Fourier Transform), the IF signal is converted into a processed signal, such as Figure 2 As shown, the processed signal includes frames 200, where each frame 200 corresponds to a respective time slot dt and, according to some aspects, is comprised of an FFT vector. Each frame 200 includes bins 210 configured according to a range resolution dr of the processed signal, where the range resolution dr is proportional to the corresponding frequency span df of each bin in a known manner. In each bin 210, there is a signal detection 220 having a complex value (i.e., amplitude and phase angle).

[0048] refer to Figure 3Control unit 120 is adapted to determine a range-Doppler representation 300 of the radar signals by processing the acquired radar signals 115, 116, 117, for example, by means of a second FFT, such that received radar signal energy 311 is represented as a function of range d0-d13 and relative velocity v0-v7. According to some aspects, the range-Doppler representation is a matrix comprising matrix indices 310, where each matrix index corresponds to a range d0-d13 and a relative velocity v0-v7.

[0049] The control unit 120 is adapted to detect a blockage of the radar sensor 105 by processing radar signals 115 , 116 , 117 received by the radar sensor 105 , wherein the control unit 120 is adapted to determine the relative speed v0 , v3 , v5 for each predetermined azimuth angle θ1 , θ2 , θ3 .

[0050] According to the present disclosure, the control unit 120 is suitable for obtaining a first distribution 301 of the received energy 311 relative to the distance in the range-Doppler representation 300 of a first azimuth angle θ1, a second distribution 302 of the received energy 311 relative to the distance in the range-Doppler representation 300 of a second azimuth angle θ2, and a third distribution 303 of the received energy 311 relative to the distance in the range-Doppler representation 300 of a third azimuth angle θ3.

[0051] The distributions 301 , 302 , 303 depend, for example, on the radar antenna gain pattern, the vehicle bumper configuration, and the reflectivity of the ground surface.

[0052] According to some aspects, the distributions 301 , 302 , 303 are extracted from the range-Doppler-map representation 300 using interpolation using the relative velocities v0 , v3 , v5 that have been determined at the corresponding angles θ1 , θ2 , θ3 .

[0053] According to some aspects, for a mobile radar sensor, the relative velocity v at an angle θ can be determined according to the following formula: relative :

[0054]

[0055] in

[0056] dx is the x-coordinate of the radar sensor relative to the center of the vehicle's rear axle, in meters;

[0057] dy is the y-coordinate of the radar sensor relative to the center of the vehicle's rear axle, in meters;

[0058] ψ is the vehicle's waw rate in radians per second;

[0059] v host is the vehicle's speed in the x-direction, in meters per second;

[0060] θ is the measured azimuth of the radar detection, in radians; and

[0061] v relative is the expected relative velocity detected by the radar in meters per second.

[0062] According to some aspects, to compensate for sources of error such as background noise, each distribution 301 , 302 , 303 of detected energy versus range is obtained by integrating at least a portion of the range-Doppler representation over time or over multiple radar sensor scans.

[0063] The control unit 120 is further adapted to generate a similarity measure by comparing the first distribution 301 of detected energy versus distance with the other distributions 302 , 303 of detected energy versus distance and detecting a blockage of the radar sensor 105 if the similarity measure meets a similarity criterion.

[0064] According to some aspects, the similarity measure includes any of the following:

[0065] - Difference between means

[0066] - Difference between variances

[0067] -Bhattacharyya distance

[0068] -Kullback-Leibler divergence or

[0069] -Mahalanobis vector distance.

[0070] According to some aspects, the similarity criterion comprises a predetermined threshold.

[0071] In more detail, if the distributions 301, 302, 303 differ from each other to a certain extent, the ground and / or other obstacles are visible to the radar sensor 105. Figure 4 , where the distributions 301 , 302 , 303 corresponding to curve 1 , curve 3 and curve 3 are shown as the relationship between the average signal amplitude and the distance interval after 10 seconds of integration.

[0072] If the radar sensor is blocked, the radar sensor 105 cannot see anything, so the distributions 301, 302, 303 correspond to the thermal noise floor which is the frequency response of the radar system 140 in each direction. In this case, the distributions 301, 302, 303 are similar to each other. Figure 5 , where distributions 301 , 302 , and 303 correspond to curves 1 , 3 and 3 , which are shown as the relationship between the average signal amplitude and the distance interval after 10 seconds of integration.

[0073] In theory, if sensor 105 is obstructed, radar sensor 105 cannot see anything, and distributions 301, 302, and 303 should be identical, showing only the noise floor. However, in practice, they differ slightly. According to some aspects, if larger differences are expected in some ranges than in others, using the Mahalanobi distance vector can account for these differences.

[0074] The spread between the curves after a specific integration is calculated as the difference between the maximum and minimum values ​​of distributions 301, 302, and 303 for each range bin. These values ​​are smoothed and used as the sigma of the Mahalanobis distance. If distributions 301, 302, and 303 consist of n range bins, the pure Mahalanobis distance for an obstructed radar sensor is approximately √n. To make the distance metric independent of the length of the distribution, it should be divided by √n.

[0075] This distance is calculated pairwise between all distributions, and for m distributions, m*(m-1) / 2 distances D(i,j) are obtained; for example, for three distributions, it results in three distances, and the maximum value D among all distances is taken. max to classify.

[0076] An obstructed radar sensor will have D max ≈1.

[0077] An unobstructed radar sensor will have D max >>1.

[0078] For the case where the radar sensor is not moving, everything in the stationary environment is collected in Doppler bin 0, and only thermal noise is visible in other Doppler bins. This means that it is sufficient to compare the distribution at bin 0 with the distribution at any other bin. This can be applied to the first azimuth angle θ1 described above, which corresponds to the first velocity v0, which is zero relative velocity.

[0079] According to some aspects, a sorting filter along the Doppler direction can be applied to suppress the energy of moving targets. If the distributions are similar, then the environment is not visible, and therefore the sensor is blocked. If they are different, then the sensor is not blocked.

[0080] refer to Figure 6The present disclosure relates to a method for detecting obstruction of a radar sensor 105 by processing radar signals 115, 116, 117 received by the radar sensor 105. The method includes obtaining S1 the radar signals 115, 116, 117 and determining a range-Doppler representation 300 of the radar signals by processing the obtained radar signals 115, 116, 117 such that received radar signal energy 311 is represented as a function of ranges d0-d13 and relative velocities v0-v7. The method also includes determining S4 predetermined azimuth angles θ1, θ2, θ3 for the radar sensor 105, wherein each predetermined azimuth angle θ1, θ2, θ3 corresponds to a respective relative velocity v0, v3, v5, and calculating S31 the relative velocity v0, v3, v5 for each predetermined azimuth angle θ1, θ2, θ3. Furthermore, the method includes obtaining S5 a first distribution 301 of received energy 311 versus distance in the range-Doppler representation 300 for a first azimuth angle θ1, and obtaining S6 at least one other distribution 302, 303 of received energy 311 versus distance in the range-Doppler representation 300 for at least one other azimuth angle θ2, θ3 different from the first azimuth angle θ1. The method also includes generating S7 a similarity measure by comparing the first distribution 301 of detected energy versus distance to the at least one other distribution 302, 303 of detected energy versus distance; and detecting S8 an obstruction of the radar sensor 105 if the similarity measure satisfies the similarity criterion.

[0081] According to some aspects, the range-Doppler representation is a matrix comprising matrix indices 310 , where each matrix index corresponds to a range d0 - d13 and a relative velocity v0 - v7 .

[0082] According to some aspects, the first azimuth angle θ1 corresponds to a first velocity v0 , which is a zero relative velocity.

[0083] According to some aspects, each such azimuth angle θ1 , θ2 , θ3 is determined relative to a reference line 141 and an azimuth bearing 141 , 142 , 143 .

[0084] According to some aspects, each distribution 301 , 302 , 303 of detected energy versus range is obtained by integrating at least a portion of the S9 range-Doppler representation over time or over multiple radar sensor scans.

[0085] According to some aspects, the first speed v0 and / or at least one other speed v3, v5 are adjusted based on the yaw rate and / or the vehicle speed as it changes over time or between radar sensor scans.

[0086] According to some aspects, each velocity v0 , v3 , v5 relates to a relative motion of the radar sensor with respect to an object 150 , 160 , 170 in the field of view of radar sensor 105 .

[0087] According to some aspects, the similarity measure includes any of the following:

[0088] - Difference between mean values

[0089] - Difference between variances

[0090] -Bhattacharyya distance

[0091] -Kullback-Leibler divergence.

[0092] According to some aspects, the similarity metric is the Mahalanobis vector distance.

[0093] According to some aspects, the similarity criterion comprises a predetermined threshold.

[0094] The methods and techniques discussed above may be implemented in various forms of hardware. Figure 7 The components of the control unit 120 according to the embodiments discussed above are schematically shown according to a number of functional units. The processing circuit 710 is provided using any combination of one or more of a suitable central processing unit (CPU), a multiprocessor, a microcontroller, a digital signal processor (DSP), etc., capable of executing software instructions stored in a computer program product (e.g., in the form of a storage medium 730). The processing circuit 710 may also be provided as at least one application-specific integrated circuit (ASIC) or a field-programmable gate array (FPGA).

[0095] Specifically, the processing circuit 710 is configured to cause the control unit 120 to perform a set of operations or steps. For example, the storage medium 730 may store the set of operations, and the processing circuit 710 may be configured to retrieve the set of operations from the storage medium 730 to cause the control unit 120 to perform the set of operations. The set of operations may be provided as a set of executable instructions. Thus, the processing circuit 710 is thereby arranged to perform the method as disclosed herein.

[0096] The storage medium 730 may also include persistent storage, which may be, for example, any one or combination of magnetic memory, optical memory, solid-state memory, or even remotely mounted memory.

[0097] The control unit 120 may also include a communication interface 720 for communicating with at least one external device, such as the radar sensor 105. Thus, the communication interface 720 may include one or more transmitters and receivers including analog and digital components and a suitable number of ports for wired or wireless communication. The processing circuit 710 controls the general operation of the control unit 120, for example, by sending data and control signals to the communication interface 720 and the storage medium 730, by receiving data and reports from the communication interface 720, and by retrieving data and instructions from the storage medium 730. Other components of the control unit 120 and related functionality are omitted to avoid obscuring the concepts presented herein.

[0098] Figure 8 A computer program product 800 is shown comprising computer executable instructions 810. The computer executable instructions may be executed, for example, by a control unit 120 as described above to perform the methods disclosed herein.

[0099] Generally, the present disclosure also relates to a radar system 140 comprising a control unit 120, a radar transceiver unit 110 and a radar sensor 105, wherein the control unit 120 is adapted to detect an obstruction of the radar sensor 105 by processing radar signals 115, 116, 117 received by the radar sensor 105, wherein the control unit 120 is adapted to obtain the radar signals 115, 116, 117 and to determine a range-Doppler representation 300 of the radar signals by processing the obtained radar signals 115, 116, 117 such that a received radar signal energy 311 is represented as a function of the range d0-d13 and the relative velocity v0-v7.

[0100] Control unit 120 is further adapted to determine predetermined azimuth angles θ1, θ2, θ3 of radar sensor 105, wherein each predetermined azimuth angle θ1, θ2, θ3 corresponds to a respective relative velocity v0, v3, v5, and to calculate the relative velocity v0, v3, v5 for each predetermined azimuth angle θ1, θ2, θ3. Furthermore, control unit 120 is further adapted to obtain a first distribution 301 of received energy 311 versus distance in a range-Doppler representation 300 for a first azimuth angle θ1, and to obtain at least one other distribution 302, 303 of received energy 311 versus distance in a range-Doppler representation 300 for at least one other azimuth angle θ2, θ3 different from first azimuth angle θ1. Control unit 120 is further adapted to generate a similarity measure by comparing first distribution 301 of detected energy versus distance with at least one other distribution 302, 303 of detected energy versus distance, and to detect an obstruction of radar sensor 105 if the similarity measure satisfies a similarity criterion.

[0101] According to some aspects, the control unit 120 is adapted to integrate at least a portion of the range-Doppler representation over time or over a plurality of radar sensor scans to obtain each distribution 301 , 302 , 303 of detected energy versus range.

[0102] The present disclosure is not limited to the above, but may also vary within the scope of the appended claims.For example, the present disclosure is applicable to all types of radar sensors.

Claims

1. A method for detecting obstruction of a radar sensor (105) by processing radar signals (115, 116, 117) received by the radar sensor (105), wherein the method comprises: Obtaining the radar signal (115, 116, 117); determining a range-Doppler representation (300) of the radar signal by processing the acquired radar signal (115, 116, 117) such that received radar signal energy (311) is represented as a function of range (d0-d13) and relative velocity (v0-v7); determining predetermined azimuth angles (θ1, θ2, θ3) of the radar sensor (105), wherein each predetermined azimuth angle (θ1, θ2, θ3) corresponds to a respective relative velocity (v0, v3, v5); and Calculate the relative velocity (v0, v3, v5) for each predetermined azimuth angle (θ1, θ2, θ3); It is characterized in that the method further comprises: Obtaining a first distribution (301) of received energy (311) versus range in the range-Doppler representation (300) for a first azimuth angle (θ1); obtaining at least one other distribution (302, 303) of received energy (311) versus range in the range-Doppler representation (300) for at least one other azimuth angle (θ2, θ3) different from the first azimuth angle (θ1); generating a similarity measure by comparing the first distribution (301) of detected energy versus distance to the at least one other distribution (302, 303) of detected energy versus distance; and If the similarity measure satisfies a similarity criterion, then an obstruction of the radar sensor (105) is detected.

2. The method of claim 1, wherein the range-Doppler representation is a matrix comprising matrix indices (310), wherein each matrix index corresponds to a range (d0-d13) and a relative velocity (v0-v7).

3. The method according to any one of claims 1 or 2, wherein the first azimuth angle (θ1) corresponds to a first velocity (v0), the first velocity (v0) being a zero relative velocity.

4. A method according to any one of the preceding claims, wherein each azimuth angle (θ1, θ2, θ3) is determined relative to a reference line (141) and an azimuth bearing (141, 142, 143).

5. The method of any of the preceding claims, wherein each distribution (301, 302, 303) of detected energy versus range is obtained by integrating at least a portion of the range-Doppler representation over time or over a plurality of radar sensor scans.

6. The method according to claim 3, wherein the first speed (v0) and / or at least one other speed (v3, v5) are adjusted based on a yaw rate and / or a vehicle speed that varies over time or between radar sensor scans.

7. The method according to any of the preceding claims, wherein each velocity (v0, v3, v5) is related to a relative motion of the radar sensor with respect to an object (150, 160, 170) in the field of view of the radar sensor (105).

8. The method according to any one of the preceding claims, wherein the similarity measure comprises any one of the following: - Difference between means - Difference between variances -Bhattacharyya distance -Kullback-Leibler Divergence -Mahalanobis vector distance.

9. A method according to any one of the preceding claims, wherein the similarity criterion comprises a predetermined threshold value.

10. A radar system (140), comprising a control unit (120), a radar transceiver unit (110), and a radar sensor (105), wherein the control unit (120) is adapted to detect a blockage of the radar sensor (105) by processing radar signals (115, 116, 117) received by the radar sensor (105), wherein the control unit is adapted to: Obtaining the radar signal (115, 116, 117); determining a range-Doppler representation (300) of the radar signal by processing the acquired radar signal (115, 116, 117) such that received radar signal energy (311) is represented as a function of range (d0-d13) and relative velocity (v0-v7); determining predetermined azimuth angles (θ1, θ2, θ3) of the radar sensor (105), wherein each predetermined azimuth angle (θ1, θ2, θ3) corresponds to a respective relative velocity (v0, v3, v5); and Calculate the relative velocity (v0, v3, v5) for each predetermined azimuth angle (θ1, θ2, θ3); It is characterized by The control unit is further adapted to: Obtaining a first distribution (301) of received energy (311) versus range in the range-Doppler representation (300) for a first azimuth angle (θ1); obtaining at least one other distribution (302, 303) of received energy (311) versus range in the range-Doppler representation (300) for at least one other azimuth angle (θ2, θ3) different from the first azimuth angle (θ1); generating a similarity measure by comparing the first distribution (301) of detected energy versus distance to the at least one other distribution (302, 303) of detected energy versus distance; and If the similarity measure satisfies a similarity criterion, then an obstruction of the radar sensor (105) is detected.

11. The radar system (140) of claim 10, wherein the range-Doppler representation is a matrix comprising matrix indices (310), wherein each matrix index corresponds to a range (d0-d13) and a relative velocity (v0-v7).

12. The radar system (140) according to any one of claims 10 or 11, wherein the first azimuth angle (θ1) corresponds to a first velocity (v0), the first velocity (v0) being a zero relative velocity.

13. The radar system (140) according to any one of claims 10 to 12, wherein the control unit (120) is adapted to integrate at least a portion of the range-Doppler representation in time or over a plurality of radar sensor scans to obtain each distribution (301, 302, 303) of detected energy versus range.

14. The radar system (140) of any one of claims 10 to 13, wherein the similarity metric comprises any one of the following: - Difference between mean values - Difference between variances -Bhattacharyya distance -Kullback-Leibler Divergence -Mahalanobis vector distance.

15. The radar system (140) of any one of claims 10 to 14, wherein the similarity criterion comprises a predetermined threshold.

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