Imaging method and device of vehicle-mounted frequency-modulated continuous wave ice radar and electronic equipment

Abstract

The disclosure provides an imaging method and device of a vehicle-mounted frequency-modulated continuous wave ice radar and electronic equipment, which can be applied to the technical field of ice exploration and the technical field of signal processing. The method comprises the following steps: performing mixing processing on a to-be-extracted beat frequency time sequence signal based on a predetermined delay line corresponding to a predetermined delay time length, so as to extract a nonlinear phase from the to-be-extracted beat frequency time sequence signal; estimating the nonlinear phase to obtain an estimated transmission nonlinear phase; correcting an ice cover shallow layer beat frequency time sequence signal according to the estimated transmission nonlinear phase, so as to obtain a corrected time sequence signal in which the nonlinear phase has been removed; removing a residual phase from the corrected time sequence signal according to a predetermined function, so as to obtain a target time sequence signal; performing motion error compensation on the target time sequence signal according to a motion compensation function, so as to obtain a compensated time sequence signal; and performing Fourier transform processing on the compensated time sequence signal, so as to obtain imaging corresponding to a target object.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of glacier exploration and the technical field of signal processing, and more particularly, to an imaging method and device of a vehicle-mounted frequency-modulated continuous wave ice radar and an electronic device. BACKGROUND

[0002] Compared with a traditional pulse radar, a frequency-modulated continuous wave radar has higher range resolution, stronger penetration ability, and can eliminate the range blind area, and thus, the frequency-modulated continuous wave radar is widely used in the field of high-precision ranging and imaging. The vehicle-mounted frequency-modulated continuous wave ice radar can be used to detect the shallow layer of an ice sheet, and the measured data can be used to calculate the accumulation rate of the ice sheet surface, and the accumulation rate is an important parameter for calculating the mass balance of the ice sheet and ice sheet surface and estimating the rise of sea level.

[0003] In the process of implementing the present disclosure, the inventors have found that at least the following problem exists in the prior art: the detection of the frequency-modulated continuous wave radar is affected by the nonlinear phase, thereby reducing the measurement accuracy and the imaging resolution. SUMMARY

[0004] Therefore, the present disclosure provides an imaging method and device of a vehicle-mounted frequency-modulated continuous wave ice radar and an electronic device.

[0005] One aspect of the present disclosure provides an imaging method of a vehicle-mounted frequency-modulated continuous wave ice radar, comprising:

[0006] mixing the to-be-extracted difference frequency time sequence signal based on a predetermined delay line corresponding to a predetermined delay duration, to extract a nonlinear phase from the to-be-extracted difference frequency time sequence signal, wherein the nonlinear phase is a difference between a transmission nonlinear phase and a reception nonlinear phase after a predetermined delay duration; estimating the nonlinear phase to obtain an estimated transmission nonlinear phase; correcting an ice sheet shallow layer difference frequency time sequence signal according to the estimated transmission nonlinear phase, to obtain a corrected time sequence signal in which the nonlinear phase has been removed; removing a residual phase from the corrected time sequence signal according to a predetermined function, to obtain a target time sequence signal; performing motion error compensation on the target time sequence signal according to a motion compensation function, to obtain a compensated time sequence signal; and performing Fourier transform processing on the compensated time sequence signal, to obtain an image corresponding to a target object.

[0007] According to an embodiment of the present disclosure, the mixing processing is performed on the to-be-extracted beat frequency timing signal based on a predetermined delay line corresponding to a predetermined delay duration to extract a nonlinear signal from the to-be-extracted beat frequency timing signal, including: obtaining the to-be-extracted beat frequency timing signal corresponding to the predetermined delay duration based on the predetermined delay line corresponding to the predetermined delay duration; constructing an ideal beat frequency timing signal according to the to-be-extracted beat frequency timing signal; and performing conjugate multiplication on the to-be-extracted beat frequency timing signal and the ideal beat frequency timing signal to realize mixing of the to-be-extracted beat frequency timing signal and the ideal beat frequency timing signal.

[0008] According to an embodiment of the present disclosure, the ice cover shallow layer beat frequency timing signal is corrected according to the estimated emission nonlinear phase to obtain a corrected timing signal in which the nonlinear phase is removed, including: determining an integral path corresponding to the ice cover shallow layer beat frequency timing signal according to the estimated emission nonlinear phase; and performing matched Fourier transform on the ice cover shallow layer beat frequency timing signal according to the integral path corresponding to the ice cover shallow layer beat frequency timing signal to obtain the corrected timing signal in which the nonlinear phase is removed.

[0009] According to an embodiment of the present disclosure, a residual phase is removed from the corrected timing signal according to a predetermined function to obtain a target timing signal, including: multiplying the predetermined function with the corrected timing signal to remove the residual phase from the corrected timing signal to obtain the target timing signal.

[0010] According to an embodiment of the present disclosure, the target timing signal is subjected to motion error compensation according to a motion compensation function to obtain a compensated timing signal, including: performing inverse fast Fourier transform in a distance direction and fast Fourier transform in an azimuth direction on the target timing signal to obtain a target time domain signal; and multiplying the target time domain signal with the compensation function to obtain the compensated timing signal to compensate the target timing signal for motion error.

[0011] According to an embodiment of the present disclosure, the compensated timing signal is subjected to Fourier transform processing to obtain imaging corresponding to a target object, including: performing compression and interpolation processing on the compensated timing signal to obtain a focused timing signal; and performing inverse fast Fourier transform in a distance direction and fast Fourier transform in an azimuth direction on the focused timing signal to obtain the imaging corresponding to the target object.

[0012] According to an embodiment of the present disclosure, the compensated timing signal is subjected to compression and interpolation processing to obtain a focused timing signal, including: multiplying the compensated timing signal with a filter function to obtain a compressed signal to complete focusing of the target object at a reference distance; and performing interpolation processing on the compressed signal to obtain the focused timing signal to complete focusing of the target object other than at the reference distance.

[0013] According to an embodiment of the present disclosure, the filter function comprises a range-frequency modulation filter function obtained according to a moving speed of the ice radar and a shortest distance from the target object to a moving direction of the ice radar.

[0014] A second aspect of the present disclosure provides an imaging device of a vehicle-mounted frequency-modulated continuous wave ice radar, comprising:

[0015] The mixing module is configured to mix the to-be-extracted beat frequency time series signal based on a predetermined delay line corresponding to a predetermined delay duration, so as to extract a nonlinear phase from the to-be-extracted beat frequency time series signal, wherein the nonlinear phase is a difference between a transmission nonlinear phase and a reception nonlinear phase after the predetermined delay duration.

[0016] The estimation module is configured to estimate the nonlinear phase to obtain an estimated transmission nonlinear phase.

[0017] The correction module is configured to correct the ice cover shallow layer beat frequency time series signal according to the estimated transmission nonlinear phase, so as to obtain a corrected time series signal in which the nonlinear phase is removed.

[0018] The removal module is configured to remove a residual phase from the corrected time series signal according to a predetermined function, so as to obtain a target time series signal.

[0019] The compensation module is configured to perform motion error compensation on the target time series signal according to a motion compensation function, so as to obtain a compensated time series signal.

[0020] The imaging module is configured to perform Fourier transform processing on the compensated time series signal, so as to obtain an image corresponding to the target object.

[0021] Another aspect of the present disclosure provides an electronic device, comprising:

[0022] One or more processors;

[0023] A memory configured to store one or more programs,

[0024] When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described above.

[0025] According to the embodiment of the present disclosure, the nonlinear phase is extracted from the to-be-extracted beat frequency timing signal of the frequency-modulated continuous wave radar through a mixing process, the transmitted nonlinear phase in the nonlinear phase is estimated by using a coherent integration method, the obtained estimated transmitted nonlinear phase is used for correction of the ice cover shallow layer beat frequency timing signal, the target timing signal from which the nonlinear phase is removed is subjected to range migration correction through a compensation function, and imaging corresponding to the target object is obtained. Since the nonlinear phase is corrected, the measurement accuracy of the radar is higher, and even when applied to large-scale measurement at a relatively long distance, a smaller error can still be maintained. In addition, the nonlinear correction and the range migration correction are combined, and high-resolution imaging of the underground target is realized. BRIEF DESCRIPTION OF DRAWINGS

[0026] The above and other objects, features and advantages of the present disclosure will become more apparent from the following description of embodiments of the present disclosure, taken in conjunction with the accompanying drawings, in which:

[0027] Figure 1 A working principle schematic diagram of a vehicle-mounted frequency-modulated continuous wave ice radar according to an embodiment of the present disclosure is schematically shown;

[0028] Figure 2 A flowchart of an imaging method of a vehicle-mounted frequency-modulated continuous wave ice radar according to an embodiment of the present disclosure is schematically shown;

[0029] Figure 3 An initial imaging effect without any correction according to an embodiment of the present disclosure is schematically shown;

[0030] Figure 4 An ideal imaging effect according to an embodiment of the present disclosure is schematically shown;

[0031] Figure 5 An imaging effect without nonlinear phase correction according to an embodiment of the present disclosure is schematically shown;

[0032] Figure 6 An imaging effect of an imaging method of a vehicle-mounted frequency-modulated continuous wave ice radar according to an embodiment of the present disclosure is schematically shown;

[0033] Figure 7 A profile schematic diagram of range direction imaging according to an embodiment of the present disclosure is schematically shown;

[0034] Figure 8 An imaging process schematic diagram of a vehicle-mounted frequency-modulated continuous wave ice radar according to an embodiment of the present disclosure is schematically shown;

[0035] Figure 9 A block diagram of an imaging device of a vehicle-mounted frequency-modulated continuous wave ice radar according to an embodiment of the present disclosure is schematically shown;

[0036] Figure 10A block diagram of an electronic device suitable for implementing an imaging method of a vehicle-mounted frequency-modulated continuous wave ice radar according to an embodiment of the present disclosure is shown schematically. DETAILED DESCRIPTION

[0037] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. It should be understood, however, that the description is merely for illustration, and is not intended to limit the scope of the present disclosure. In the following detailed description of embodiments of the present disclosure, numerous specific details are set forth in order to provide a thorough understanding of the embodiments. However, it would be apparent to those skilled in the art that the embodiments can be practiced without these specific details. In other instances, well-known structures and functions have not been described in detail in order to avoid obscuring the concepts of the present disclosure.

[0038] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure. As used herein, the term "includes" and tautological expressions thereof, such as "including," "includes," "include," "contains," "containing," and so on, mean the presence of stated features, steps, operations, elements, and / or components but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0039] All terms used herein (including technical and scientific terms) have the meanings commonly understood by one of ordinary skill in the art, unless otherwise defined. It should be noted that the terms used herein should be interpreted as having meanings that are consistent with the context of the specification, and should not be interpreted in an idealized or overly formal manner.

[0040] In the case of using expressions similar to "at least one of A, B, and C, etc.", it should generally be interpreted to include any of them alone, any combination of two or more of them, and the like.

[0041] In embodiments of the present disclosure, the collection, updating, analysis, processing, use, transmission, provision, disclosure, storage, etc. of data involved (for example, including but not limited to user personal information) comply with relevant legal regulations, are used for legal purposes, and do not violate public order and good customs. In particular, necessary measures are taken to prevent illegal access to user personal information data, and to maintain user personal information security and network security.

[0042] In embodiments of the present disclosure, the authorization or consent of the user is obtained before the user's personal information is acquired or collected.

[0043] Since the shallow ice radar equipment is mostly of the frequency-modulated continuous wave system, which belongs to an ultra-wideband system, the transmitting signal of the ice radar usually has a nonlinear phase. The nonlinear phase can reduce the measurement accuracy and imaging quality of the radar, especially when a large range is detected at a long distance. Meanwhile, the nonlinear phase can also cause a large sidelobe in imaging, thus leading to unclear division between the ice layers and affecting the calculation of the accumulation rate and the inversion of the related parameters.

[0044] The existing frequency-modulated continuous wave radar imaging technology is mostly used for imaging of ground targets, and there is almost no mature imaging technology for underground targets. Although the related technology performs nonlinear correction, the corrected result is not subjected to motion compensation, which cannot realize focusing of part of the targets and causes the generated image to have low resolution.

[0045] Therefore, the embodiment of the present disclosure provides an imaging method of a vehicle-mounted frequency-modulated continuous wave ice radar, which comprises the following steps:

[0046] Based on a predetermined delay line corresponding to a predetermined delay duration, the nonlinear phase is extracted from the to-be-extracted difference frequency time sequence signal by performing a mixing processing on the to-be-extracted difference frequency time sequence signal, wherein the nonlinear phase is the difference between the transmitting nonlinear phase and the receiving nonlinear phase after the predetermined delay duration; the estimated transmitting nonlinear phase is obtained by estimating the nonlinear phase; the corrected time sequence signal in which the nonlinear phase is removed is obtained by correcting the ice cover shallow layer difference frequency time sequence signal according to the estimated transmitting nonlinear phase; the target time sequence signal is obtained by removing the residual phase from the corrected time sequence signal according to a predetermined function; the compensation time sequence signal is obtained by performing motion error compensation on the target time sequence signal according to a motion compensation function; and the imaging corresponding to the target object is obtained by performing Fourier transform processing on the compensation time sequence signal.

[0047] Figure 1 The working principle of the vehicle-mounted frequency-modulated continuous wave ice radar according to the embodiment of the present disclosure is schematically shown.

[0048] It should be noted that, Figure 1 The shown is only an example of an application scenario to which the embodiment of the present disclosure can be applied, to help those skilled in the art understand the technical content of the present disclosure, but does not mean that the embodiment of the present disclosure cannot be applied to other devices, systems, environments or scenarios.

[0049] As Figure 1 shown, the snow vehicle drags the vehicle-mounted frequency-modulated continuous wave radar equipment to travel at a constant speed V along a direction parallel to the ice surface, wherein the x-axis is the ice surface parallel direction, the y-axis is the ice layer depth direction, O is the origin of the coordinate system, and the beam width of the radar is as shown in the figure.

[0050] According to an embodiment of this disclosure, taking nine radar detection target points as an example, they are (-20, 60), (0, 60), (20, 60), (-20, 80), (0, 80), (20, 80), (-20, 100), (0, 100), (20, 100).

[0051] According to embodiments of this disclosure, when the radar scans the target point Q(x) c y c When the antenna phase center is located at point Q'(x), the antenna phase center is at point Q'(x). n y n According to the imaging geometry, the instantaneous slant range R between the radar antenna phase center and the target point can be obtained by the following formula (1).

[0052] (1)

[0053] in, , t r For distance to fast time, t m For azimuth slow time, R0 is the shortest distance between point Q' and point Q (zero Doppler slant distance). .

[0054] According to embodiments of this disclosure, the above formula (1) is applied at t r First-order Taylor expansion at =0 It can be expressed as formula (2).

[0055] (2)

[0056] in, This refers to the range migration error caused by platform movement during radar frequency modulation.

[0057] According to embodiments of this disclosure, the transmitted signal of the vehicle-mounted frequency-modulated continuous wave radar is a sawtooth-shaped linear frequency-modulated continuous wave signal. It can be expressed as the following formula (3).

[0058] (3)

[0059] Among them, T p For frequency modulation bandwidth, K is the center frequency of the transmitted signal. r For the range-direction frequency modulation, .

[0060] By comparing the above formula (2) with that of traditional synthetic aperture radar, it can be seen that the modulation time of frequency modulated continuous wave signal is relatively long, and it is no longer applicable to the stop-and-go model of traditional synthetic aperture radar.

[0061] Figure 2 A flowchart of an imaging method of a vehicle-mounted frequency-modulated continuous wave ice radar is shown schematically.

[0062] As shown in Figure 2 , the method 200 includes operations S210-S260.

[0063] At operation S210, a mixing processing is performed on a to-be-extracted beat frequency time sequence signal based on a predetermined delay line corresponding to a predetermined delay duration, to extract a nonlinear phase from the to-be-extracted beat frequency time sequence signal.

[0064] At operation S220, the nonlinear phase is estimated to obtain an estimated transmission nonlinear phase.

[0065] At operation S230, an ice cover shallow layer beat frequency time sequence signal is corrected according to the estimated transmission nonlinear phase, to obtain a corrected time sequence signal with the nonlinear phase removed.

[0066] At operation S240, a residual phase is removed from the corrected time sequence signal according to a predetermined function, to obtain a target time sequence signal.

[0067] At operation S250, a motion error compensation is performed on the target time sequence signal according to a motion compensation function, to obtain a compensated time sequence signal.

[0068] At operation S260, a Fourier transform processing is performed on the compensated time sequence signal, to obtain an imaging corresponding to a target object.

[0069] According to an embodiment of the present disclosure, the nonlinear phase is a difference between a transmission nonlinear phase and a reception nonlinear phase after a predetermined delay duration, the transmission nonlinear phase corresponding to a transmission signal, and the reception nonlinear phase corresponding to a reception signal. The nonlinear phase can be expressed as formula (4) as follows.

[0070] (4)

[0071] wherein, is the nonlinear phase in the to-be-extracted beat frequency time sequence signal, τ ref is the predetermined delay duration, is the transmission nonlinear phase, is the reception nonlinear phase.

[0072] According to an embodiment of the present disclosure, a mixer can be used to perform the mixing processing on the to-be-extracted beat frequency time sequence signal, which is an echo signal received by a reception antenna of the radar after the predetermined delay duration. The echo signal may be expressed as formula (5) as follows.

[0073] (5)

[0074] where c is the velocity of electromagnetic wave in ice layer, and c = 0.185 m / ns is commonly used.

[0075] According to the embodiment of the present disclosure, the emitted nonlinear phase can be estimated from the to-be-extracted difference frequency time sequence signal using a coherent integration method.

[0076] According to the embodiment of the present disclosure, the detection distance of the shallow ice radar is short, and only about 100 m in the ice layer can be accurately detected, so the maximum double-path delay duration of the electromagnetic wave in the ice layer is only about 1 us, and therefore when the delay duration is very small, the estimated emitted nonlinear phase can be obtained by the Lagrange mean value theorem. The estimated phase can be expressed as formula (6) as follows.

[0077] (6)

[0078] where C is a constant.

[0079] According to the embodiment of the present disclosure, the ice cover shallow layer difference frequency time sequence signal can be corrected by using a matched Fourier transform to obtain a corrected time sequence signal in which the nonlinear phase has been removed.

[0080] According to the embodiment of the present disclosure, the predetermined function can be expressed as formula (7) as follows.

[0081] (7)

[0082] where, represents the range frequency.

[0083] According to the embodiment of the present disclosure, the residual phase is an additional phase term introduced in the to-be-extracted difference frequency time sequence signal due to the modulation characteristics of the emitted signal and the motion of the radar platform, and the existence of the residual phase will affect the range resolution and imaging quality of the radar signal, and therefore the residual phase is eliminated by the predetermined function.

[0084] According to the embodiment of the present disclosure, the motion error is an error generated in the continuous motion of the vehicle-mounted frequency-modulated continuous wave ice radar platform. The motion compensation function H IPMC can be expressed as formula (8) as follows.

[0085] (8)

[0086] where, is the azimuth frequency, and λ is the wavelength.

[0087] According to embodiments of this disclosure, to better demonstrate the imaging effect of the vehicle-mounted frequency-modulated continuous wave (FMMC) ice radar according to embodiments of this disclosure, the vehicle-mounted FMMC ice radar is simulated according to the simulation parameters shown in Table 1 below, so as to achieve the desired effect. Figures 3-7 The effect of the imaging method of the vehicle-mounted frequency-modulated continuous wave ice radar according to the embodiments of this disclosure is illustrated, with the target object being... Figure 1 Take the nine target points as an example.

[0088] Table 1

[0089]

[0090] Among them, FMCW (Frequency Modulated Continuous Wave) is an abbreviation for frequency modulated continuous wave, RF (Radio Frequency) is an abbreviation for radio frequency, and PRF (pulse repetition frequency) is the pulse repetition frequency.

[0091] Figure 3 The illustration schematically shows the initial imaging effect without any correction according to an embodiment of the present disclosure.

[0092] like Figure 3 As shown, the horizontal axis represents the azimuth migration, and the vertical axis represents the range migration. Due to the influence of the nonlinear phase, the range migration of the nine target points is more significant. The nonlinear phase added in the simulation can be expressed as the following formula (9).

[0093] (9)

[0094] Among them, A sl For the parameters of the first periodic term, here we take... , For the parameters of the second periodic term, take... a1 is the coefficient of the cubic nonlinear term. a2 is the coefficient of the fourth-order nonlinear term. .

[0095] Figure 4 The illustration schematically shows the ideal imaging effect according to an embodiment of the present disclosure.

[0096] like Figure 4 As shown, the images of all nine target points are well focused.

[0097] According to embodiments of this disclosure, the horizontal axis represents azimuth migration and the vertical axis represents distance migration.

[0098] Figure 5 The illustration schematically shows the imaging effect without nonlinear phase correction according to an embodiment of the present disclosure.

[0099] As shown in Figure 5 the abscissa represents the azimuth migration, and the ordinate represents the range migration. Due to the non-linear phase correction, the 9 target points have obvious tailing in the range direction, the imaging cannot be focused, the range information is inaccurate, and the subsequent accumulation rate calculation is affected.

[0100] Figure 6 The imaging effect of the imaging method of the vehicle-mounted frequency-modulated continuous wave ice radar is schematically shown.

[0101] As shown in Figure 6 the abscissa represents the azimuth migration, and the ordinate represents the range migration. Compared with Figure 6 and Figure 5 , it can be clearly seen that the imaging after the non-linear phase correction and the motion error compensation can effectively suppress the tailing in the range direction, and the imaging of the target points is more focused.

[0102] Figure 7 The profile schematic diagram of the range direction imaging is schematically shown.

[0103] As shown in Figure 7 , in the profile diagram at (0, 80), the graph line after the correction by the embodiment 200 is closer to the ideal state.

[0104] According to the embodiment of the present disclosure, the non-linear phase is extracted from the to-be-extracted difference frequency time sequence signal of the frequency-modulated continuous wave radar through the mixing processing, the transmitted non-linear phase in the non-linear phase is estimated by using the coherent integration method, the obtained estimated transmitted non-linear phase is used for correcting the ice cover shallow layer difference frequency time sequence signal, and the target time sequence signal after removing the non-linear phase is corrected by the compensation function to obtain the imaging corresponding to the target object. Since the non-linear phase is corrected, the measurement accuracy of the radar is higher, and even when applied to a large range measurement at a long distance, a small error can still be maintained. In addition, the non-linear correction and the range migration correction are combined to realize the high-resolution imaging of the underground target.

[0105] According to the embodiment of the present disclosure, based on the predetermined delay line corresponding to the predetermined delay time length, the to-be-extracted difference frequency time sequence signal is mixed to extract the non-linear signal from the to-be-extracted difference frequency time sequence signal, which comprises: obtaining the to-be-extracted difference frequency time sequence signal corresponding to the predetermined delay time length based on the predetermined delay line corresponding to the predetermined delay time length; constructing an ideal difference frequency time sequence signal according to the to-be-extracted difference frequency time sequence signal; and performing conjugate multiplication on the to-be-extracted difference frequency time sequence signal and the ideal difference frequency time sequence signal to realize the mixing of the to-be-extracted difference frequency time sequence signal and the ideal difference frequency time sequence signal.

[0106] According to an embodiment of the present disclosure, the difference frequency timing signal to be extracted can be expressed as formula (10) as follows.

[0107] (10)

[0108] According to an embodiment of the present disclosure, the process of constructing the ideal difference frequency timing signal from the difference frequency timing signal to be extracted can be expressed as formula (10) as follows.

[0109] (11)

[0110] According to an embodiment of the present disclosure, the mixing result obtained by conjugate multiplication of the difference frequency timing signal to be extracted and the ideal difference frequency timing signal can be expressed as formula (12) as follows.

[0111] (12)

[0112] wherein the nonlinear phase is expressed as .

[0113] According to an embodiment of the present disclosure, the process of correcting the ice cover shallow layer difference frequency timing signal according to the estimated transmission nonlinear phase to obtain the corrected timing signal removing the nonlinear phase includes: determining an integral path corresponding to the difference frequency timing signal to be extracted according to the target estimated phase; and performing matched Fourier transform on the difference frequency timing signal to be extracted according to the integral path corresponding to the difference frequency timing signal to be extracted, so as to obtain the corrected timing signal removing the nonlinear phase.

[0114] According to an embodiment of the present disclosure, the matched Fourier transform is similar to the traditional Fourier transform form, and only the integral path needs to be changed to convert the difference frequency timing signal to be extracted into a linear expression, so as to remove the nonlinear phase.

[0115] According to an embodiment of the present disclosure, the integral path corresponding to the difference frequency timing signal to be extracted can be expressed as formula (13) as follows.

[0116] (13)

[0117] According to an embodiment of the present disclosure, the process of performing matched Fourier transform on the ice cover shallow layer difference frequency timing signal according to the determined integral path can be expressed as formula (14) as follows.

[0118] (14)

[0119] wherein the corrected timing signal is , the ice cover shallow layer difference frequency timing signal to be corrected is , and the distance direction frequency is​​ The range of values ​​is , This is the sampling frequency of the analog-to-digital converter.

[0120] According to an embodiment of this disclosure, the corrected timing signal after matched Fourier transform can be expressed as the following formula (15).

[0121] (15)

[0122] According to embodiments of this disclosure, after nonlinear phase correction by matched Fourier transform, each target point is focused into a Sink function at the corresponding position, the side lobes of the tail are effectively suppressed, the main peak is clearer, and it is closer to the real physical scene, reducing the distortion caused by nonlinear effects.

[0123] According to an embodiment of the present disclosure, removing residual phase from a corrected timing signal to obtain a target timing signal based on a predetermined function includes: multiplying the predetermined function with the corrected timing signal to remove residual phase from the corrected timing signal to obtain the target timing signal.

[0124] According to embodiments of this disclosure, residual phase removal can be performed in the frequency domain by multiplying the above formula (7) with the above formula (15) to remove residual video phase other than nonlinear phase. The target timing signal has more accurate phase information, which enables the radar detection results to have smaller errors, so as to facilitate subsequent range migration correction and imaging.

[0125] According to embodiments of this disclosure, motion error compensation is performed on the target time-series signal according to the motion compensation function to obtain a compensated time-series signal, including: performing a range-upward inverse fast Fourier transform and an azimuth-upward fast Fourier transform on the target time-series signal to obtain a target time-domain signal; multiplying the target time-domain signal with the compensation function to obtain a compensated time-series signal, so as to perform motion error compensation on the target time-series signal.

[0126] According to embodiments of this disclosure, the target time-domain signal includes range information in the time domain and azimuth information in the frequency domain. The compensation function is typically designed based on the motion model of the radar platform (such as velocity, acceleration, etc.) and the modulation characteristics of the signal.

[0127] According to embodiments of this disclosure, the range of values ​​for the azimuth frequency in formula (8) above can be... PRF stands for Frequency Modulated Pulse Repetition Frequency.

[0128] According to embodiments of this disclosure, after correcting the nonlinear characteristics, motion error compensation can further improve the accuracy of vehicle-mounted frequency-modulated continuous wave ice radar imaging and reduce blurring and distortion caused by platform motion.

[0129] According to embodiments of this disclosure, performing Fourier transform processing on the compensation timing signal to obtain an image corresponding to the target object includes: compressing and interpolating the compensation timing signal to obtain a focusing timing signal; and performing a range-up fast Fourier transform and an azimuth-up inverse fast Fourier transform on the focusing timing signal to obtain an image corresponding to the target object.

[0130] According to embodiments of this disclosure, the compensation timing signal is compressed and interpolated to obtain a focusing timing signal that can achieve focusing not only at the reference distance but also at non-reference distances. However, for partial focusing at non-reference distances, it is necessary to compensate for residual RCMC (Range Cell Migration Correction) and residual SRC (Scene-to-Scene Range Cell Migration), as well as compress residual orientation.

[0131] According to embodiments of this disclosure, performing a range-up Fast Fourier Transform and an azimuth-up Inverse Fast Fourier Transform on the focusing timing signal to obtain an image corresponding to the target object includes: performing a range-up Fast Fourier Transform and an azimuth-up Inverse Fast Fourier Transform on the focusing timing signal, then multiplying by a frequency shift function to achieve a translation of the reference distance, moving the target point to the corresponding position in the scene, and finally performing an azimuth-up Inverse Fast Fourier Transform to complete azimuth compression to obtain the target image.

[0132] According to embodiments of this disclosure, compressing and interpolating the compensation timing signal to obtain a focusing timing signal includes: multiplying the compensation timing signal by a filter function to obtain a compressed signal to achieve focusing of the target object at a reference distance; and interpolating the compressed signal to obtain a focusing timing signal to achieve focusing of the target object at a distance other than the reference distance.

[0133] According to embodiments of this disclosure, consistent compression is achieved by multiplying the compensation timing signal with a filter function, so that the signal of the target object is focused at the reference distance, but only partially focused at non-reference distances. The compressed signal can be expressed as the following formula (16).

[0134] (16)

[0135] in, This is a compressed signal.

[0136] According to embodiments of this disclosure, interpolation can be performed to compensate for residual phase at other locations and to complete residual RCMC, residual SRC, and residual azimuth compression. (Difference variable) The substitution expression is as follows (17).

[0137] (17)

[0138] According to embodiments of this disclosure, for the above formula (17) at t r A first-order Taylor expansion at =0 allows the interpolation variable substitution expression to be rewritten as equation (18).

[0139] (18)

[0140] According to embodiments of this disclosure, the above formula (18) is used to modify t in the above formula (16). r Replacement is performed to achieve interpolation.

[0141] According to embodiments of this disclosure, the signal after nonlinear phase correction and range migration correction is compressed and interpolated, thereby enabling the target object to be focused at both reference and non-reference distances, resulting in more significant imaging details.

[0142] According to embodiments of this disclosure, the filter function includes a range-frequency modulation filter function, which is obtained based on the movement speed of the ice radar and the shortest distance from the target object to the direction of movement of the ice radar.

[0143] According to embodiments of this disclosure, a filter function is constructed to compress the compensation timing signal, thereby achieving focusing of the target object at a reference distance. The filter function can be expressed as the following formula (19).

[0144] (19)

[0145] Among them, R c This represents the shortest distance from the target object to the direction of movement of the ice radar.

[0146] To better understand the overall imaging process of the vehicle-mounted frequency-modulated continuous wave ice radar according to the embodiments of this disclosure, the following will be explained... Figure 8 The entire process will be further explained.

[0147] Figure 8 The illustration shows a schematic diagram of the imaging process of a vehicle-mounted frequency-modulated continuous wave ice radar according to an embodiment of the present disclosure.

[0148] like Figure 8 As shown, this embodiment 800 includes operations S810 to S880.

[0149] When operating the S810, input the difference frequency timing signal to be extracted.

[0150] In operation of S820, the nonlinear phase is estimated.

[0151] When operating the S830, a matched Fourier transform is performed on the differential frequency timing signal of the shallow surface of the ice sheet to remove nonlinear phase.

[0152] In operation S840, residual phase is removed, and inverse fast Fourier transform in the range direction and fast Fourier transform in the azimuth direction are performed. Then, operation S850 is executed.

[0153] Motion error compensation during S850 operation.

[0154] In operation S860, compression and interpolation are performed, and a fast Fourier transform is performed in the distance direction. Then, operation S870 is executed.

[0155] In operation S870, the reference distance is translated and an inverse fast Fourier transform is performed in the azimuth direction, and then operation S880 is executed.

[0156] When operating the S880, an image corresponding to the target object is output.

[0157] Figure 9 A block diagram of a noise reduction apparatus for ice radar-based stratigraphic data according to an embodiment of the present disclosure is shown schematically.

[0158] like Figure 9 As shown, the device 900 includes a mixing module 910, an estimation module 920, a correction module 930, a removal module 940, a compensation module 950, and an imaging module 960.

[0159] The mixing module is used to perform mixing processing on the difference frequency timing signal to be extracted based on a predetermined delay line corresponding to a predetermined delay duration, so as to extract the nonlinear phase from the difference frequency timing signal to be extracted, wherein the nonlinear phase is the difference between the transmitted nonlinear phase and the received nonlinear phase after the predetermined delay duration.

[0160] The estimation module is used to estimate the nonlinear phase and obtain the estimated transmission nonlinear phase.

[0161] The correction module is used to correct the differential frequency timing signal of the shallow surface of the ice sheet based on the estimated nonlinear phase of the transmission, so as to obtain a corrected timing signal with the nonlinear phase removed.

[0162] The removal module is used to remove residual phase from the corrected timing signal according to a predetermined function to obtain the target timing signal.

[0163] The compensation module is used to perform motion error compensation on the target time sequence signal according to the motion compensation function to obtain the compensated time sequence signal.

[0164] The imaging module is used to perform Fourier transform processing on the compensated time-series signal to obtain an image corresponding to the target object.

[0165] According to embodiments of this disclosure, the mixer module 910 includes an obtaining submodule, a constructing submodule, and a conjugate submodule.

[0166] The submodule is used to obtain the difference frequency timing signal to be extracted based on the predetermined delay line corresponding to the predetermined delay duration.

[0167] A submodule is constructed to build an ideal difference frequency timing signal based on the difference frequency timing signal to be extracted.

[0168] The conjugate submodule is used to perform conjugate multiplication of the difference frequency timing signal to be extracted and the ideal difference frequency timing signal to achieve mixing of the difference frequency timing signal to be extracted and the ideal difference frequency timing signal.

[0169] According to embodiments of this disclosure, the correction module 930 includes a determining submodule and a obtaining submodule.

[0170] The determination submodule is used to determine the integration path corresponding to the difference frequency timing signal to be extracted based on the estimated transmit nonlinear phase.

[0171] The resulting submodule is used to perform a matched Fourier transform on the difference frequency time-series signal to be extracted based on the integral path corresponding to the difference frequency time-series signal to be extracted, so as to obtain a corrected time-series signal with nonlinear phase removed.

[0172] According to embodiments of this disclosure, the removal module 940 includes a removal submodule.

[0173] The removal submodule is used to multiply a predetermined function with the correction timing signal to remove residual phase from the correction timing signal and obtain the target timing signal.

[0174] According to embodiments of this disclosure, the compensation module 950 includes a transformation submodule and an acquisition submodule.

[0175] The transform submodule is used to perform range-up inverse fast Fourier transform and azimuth-up fast Fourier transform on the target time-series signal to obtain the target time-domain signal.

[0176] The resulting submodule is used to multiply the target time-domain signal with the compensation function to obtain the compensated time-series signal, which is then used to compensate for motion errors in the target time-series signal.

[0177] According to embodiments of the present disclosure, the imaging module 960 includes a processing submodule and an obtaining submodule.

[0178] The processing submodule is used to compress and interpolate the compensation timing signal to obtain the focused timing signal.

[0179] The resulting submodule is used to perform range-up Fast Fourier Transform and azimuth-up Inverse Fast Fourier Transform on the focusing timing signal to obtain an image corresponding to the target object.

[0180] According to embodiments of this disclosure, the processing submodule includes a first focusing unit and a second focusing unit.

[0181] The first focusing unit is used to multiply the compensation timing signal with the filter function to obtain a compressed signal, so as to complete the focusing of the target object at the reference distance.

[0182] The second focusing unit is used to interpolate the compressed signal to obtain a focusing timing signal, so as to complete the focusing of the target object at a distance other than the reference distance.

[0183] Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure, or at least part of the functions of any one or more of them, can be implemented in one module. Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be implemented by dividing them into multiple modules. Any one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be at least partially implemented as hardware circuitry, such as a Field-Programmable Gate Array (FPGA), a Programmable Logic Array (PLA), a System-on-Chip, a System-on-a-Substrate, a System-on-Package, an Application-Specific Integrated Circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, one or more of the modules, submodules, units, and subunits according to embodiments of the present disclosure can be at least partially implemented as computer program modules, which, when run, can perform corresponding functions.

[0184] For example, any multiple of the mixing module 910, estimation module 920, correction module 930, removal module 940, compensation module 950, and imaging module 960 can be combined into a single module / unit / subunit, or any one of these modules / units / subunits can be split into multiple modules / units / subunits. Alternatively, at least some of the functionality of one or more of these modules / units / subunits can be combined with at least some of the functionality of other modules / units / subunits and implemented in a single module / unit / subunit. According to embodiments of this disclosure, at least one of the mixing module 910, estimation module 920, correction module 930, removal module 940, compensation module 950, and imaging module 960 can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), programmable logic array (PLA), system-on-a-chip, system-on-a-substrate, system-on-package, application-specific integrated circuit (ASIC), or any other reasonable method of integrating or packaging the circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three methods. Alternatively, at least one of the mixing module 910, estimation module 920, correction module 930, removal module 940, compensation module 950, and imaging module 960 can be at least partially implemented as a computer program module, which, when run, can perform corresponding functions.

[0185] Figure 10 A block diagram of an electronic device suitable for implementing the methods described above, according to embodiments of the present disclosure, is illustrated schematically. Figure 10 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0186] like Figure 10 As shown, an electronic device 1000 according to an embodiment of the present disclosure includes a processor 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage portion 1008 into a random access memory (RAM) 1003. The processor 1001 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 1001 may also include onboard memory for caching purposes. The processor 1001 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present disclosure.

[0187] RAM 1003 stores various programs and data required for the operation of electronic device 1000. Processor 1001, ROM 1002, and RAM 1003 are interconnected via bus 1004. Processor 1001 performs various operations of the method flow according to embodiments of the present disclosure by executing programs in ROM 1002 and / or RAM 1003. It should be noted that the programs may also be stored in one or more memories other than ROM 1002 and RAM 1003. Processor 1001 may also perform various operations of the method flow according to embodiments of the present disclosure by executing programs stored in said one or more memories.

[0188] According to embodiments of this disclosure, the electronic device 1000 may further include an input / output (I / O) interface 10010, which is also connected to the bus 1004. The electronic device 1000 may also include one or more of the following components connected to the input / output (I / O) interface 10010: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the input / output (I / O) interface 10010 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 1010 as needed so that computer programs read from it can be installed into the storage section 1008 as needed.

[0189] According to embodiments of this disclosure, the method flow according to embodiments of this disclosure can be implemented as a computer software program. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowchart. In such embodiments, the computer program can be downloaded and installed from a network via communication section 1009, and / or installed from removable medium 1011. When the computer program is executed by processor 1001, it performs the functions defined in the system of embodiments of this disclosure. According to embodiments of this disclosure, the systems, devices, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0190] This disclosure also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs that, when executed, implement the method according to the embodiments of this disclosure.

[0191] According to embodiments of this disclosure, the computer-readable storage medium can be a non-volatile computer-readable storage medium. Examples include, but are not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, the computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0192] For example, according to embodiments of this disclosure, a computer-readable storage medium may include the ROM 1002 and / or RAM 1003 described above and / or one or more memories other than ROM 1002 and RAM 1003.

[0193] Embodiments of this disclosure also include a computer program product comprising a computer program containing program code for performing the methods provided in the embodiments of this disclosure. When the computer program product is run on an electronic device, the program code is used to enable the electronic device to implement the denoising method for ice radar-based stratigraphic data provided in the embodiments of this disclosure.

[0194] When the computer program is executed by the processor 1001, it performs the functions defined in the system / apparatus of this disclosure embodiment. According to embodiments of this disclosure, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0195] In one embodiment, the computer program may rely on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may also be transmitted and distributed in the form of signals over a network medium, and may be downloaded and installed via the communication section 1009, and / or installed from a removable medium 1011. The program code contained in the computer program can be transmitted using any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination thereof.

[0196] According to embodiments of this disclosure, program code for executing the computer programs provided in embodiments of this disclosure can be written in any combination of one or more programming languages. Specifically, these computational programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, languages ​​such as Java, C++, Python, "C", or similar programming languages. The program code can execute entirely on a user's computing device, partially on a user's device, partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0197] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions. Those skilled in the art will understand that the features described in the various embodiments of the present disclosure can be combined and / or combined in various ways, even if such combinations are not explicitly described in the present disclosure. In particular, the features described in the various embodiments of this disclosure may be combined and / or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

[0198] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. An imaging method for a vehicle-mounted frequency-modulated continuous wave ice radar, comprising: Based on a predetermined delay line corresponding to a predetermined delay duration, the difference frequency timing signal to be extracted is mixed to extract a nonlinear phase from the difference frequency timing signal to be extracted, wherein the nonlinear phase is the difference between the transmitted nonlinear phase and the received nonlinear phase after the predetermined delay duration. The nonlinear phase is estimated to obtain the estimated transmission nonlinear phase; Based on the estimated nonlinear phase of the transmission, the difference frequency timing signal of the shallow surface layer of the ice sheet is corrected to obtain a corrected timing signal with the nonlinear phase removed. According to a predetermined function, the residual phase is removed from the corrected timing signal to obtain the target timing signal; According to the motion compensation function, motion error compensation is performed on the target time-series signal to obtain the compensated time-series signal; The compensated timing signal is subjected to Fourier transform processing to obtain an image corresponding to the target object.

2. The method according to claim 1, wherein, The step of performing frequency mixing processing on the difference frequency timing signal to be extracted based on a predetermined delay line corresponding to the predetermined delay duration, in order to extract a nonlinear signal from the difference frequency timing signal to be extracted, includes: Based on the predetermined delay line corresponding to the predetermined delay duration, the difference frequency timing signal to be extracted corresponding to the predetermined delay duration is obtained; Based on the difference frequency timing signal to be extracted, construct an ideal difference frequency timing signal; The differential frequency timing signal to be extracted and the ideal differential frequency timing signal are multiplied by conjugate to achieve mixing of the differential frequency timing signal to be extracted and the ideal differential frequency timing signal.

3. The method according to claim 1, wherein, The step of correcting the differential frequency timing signal of the shallow surface layer of the ice sheet based on the estimated transmission nonlinear phase to obtain a corrected timing signal with the nonlinear phase removed includes: Based on the estimated nonlinear phase of the transmission, an integral path corresponding to the difference frequency timing signal of the shallow surface layer of the ice sheet is determined; Based on the integral path corresponding to the differential frequency time-series signal of the shallow surface of the ice sheet, a matched Fourier transform is performed on the differential frequency time-series signal of the shallow surface of the ice sheet to obtain a corrected time-series signal with the nonlinear phase removed.

4. The method according to claim 1, wherein, The step of removing residual phase from the corrected timing signal according to a predetermined function to obtain the target timing signal includes: The predetermined function is multiplied by the corrected timing signal to remove the residual phase from the corrected timing signal, thereby obtaining the target timing signal.

5. The method according to claim 1, wherein, The step of performing motion error compensation on the target time-series signal according to the motion compensation function to obtain the compensated time-series signal includes: The target time-domain signal is obtained by performing a range-up inverse fast Fourier transform and an azimuth-up fast Fourier transform on the target time-series signal. The target time-domain signal is multiplied by the compensation function to obtain the compensated time-series signal, which is used to compensate for motion errors in the target time-series signal.

6. The method according to claim 1, wherein, The step of performing Fourier transform processing on the compensated time-series signal to obtain an image corresponding to the target object includes: The compensation timing signal is compressed and interpolated to obtain the focusing timing signal; The focusing timing signal is subjected to a range-up Fast Fourier Transform and an azimuth-up Inverse Fast Fourier Transform to obtain an image corresponding to the target object.

7. The method according to claim 6, wherein, The step of compressing and interpolating the compensated timing signal to obtain the focused timing signal includes: The compensation timing signal is multiplied by the filter function to obtain the compressed signal, thereby completing the focusing of the target object at the reference distance; The compressed signal is interpolated to obtain a focusing timing signal, so as to complete the focusing of the target object at a distance other than the reference distance.

8. The method according to claim 7, wherein, The filter function includes a range-frequency modulation filter function, which is obtained based on the movement speed of the ice radar and the shortest distance from the target object to the direction of movement of the ice radar.

9. An imaging device for a vehicle-mounted frequency-modulated continuous wave ice radar, comprising: A mixing module is used to perform mixing processing on the difference frequency timing signal to be extracted based on a predetermined delay line corresponding to a predetermined delay duration, so as to extract a nonlinear phase from the difference frequency timing signal to be extracted, wherein the nonlinear phase is the difference between the transmitted nonlinear phase and the received nonlinear phase after the predetermined delay duration. The estimation module is used to estimate the nonlinear phase to obtain the estimated transmission nonlinear phase; The correction module is used to correct the differential frequency timing signal of the shallow surface layer of the ice sheet according to the estimated nonlinear phase of the transmission, so as to obtain a corrected timing signal with the nonlinear phase removed. The removal module is used to remove residual phase from the corrected timing signal according to a predetermined function to obtain the target timing signal; The compensation module is used to perform motion error compensation on the target time-series signal according to the motion compensation function to obtain the compensated time-series signal; The imaging module is used to perform Fourier transform processing on the compensated timing signal to obtain an image corresponding to the target object.

10. An electronic device, comprising: One or more processors; Memory, used to store one or more programs. Wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the method of any one of claims 1 to 8.

Images