A digital chirp matched filtering FMCW laser radar signal demodulation method

Abstract

A digital chirped matched-filter (FMCW) lidar signal demodulation method relates to the field of absolute distance measurement technology for non-cooperative targets based on frequency-sweeping interferometry. To address the shortcomings of existing technologies, such as limited spectral demodulation accuracy, reliance on coarse measurements, difficulty in correcting nonlinear modulation, and slow processing speed, the present invention provides a solution comprising: acquiring a measurement interferometer signal and an auxiliary interferometer signal; resampling the measurement interferometer signal based on the auxiliary interferometer signal to compensate for nonlinearity; constructing a chirped signal and mixing it with the resampled signal to obtain a signal containing target distance information; and performing matched filtering on the signal containing target distance information and a known reference signal to output the absolute distance information of the target. This method is suitable for high-precision absolute distance measurement and fast real-time demodulation scenarios for non-cooperative targets, such as lidar ranging, 3D imaging, and autonomous driving perception systems.

Description

Technical Field

[0001] This invention relates to the field of absolute distance measurement technology for non-cooperative targets based on frequency sweep interferometry, specifically to a digital chirped matched filter (FMCW) lidar signal demodulation method. Background Technology

[0002] Frequency-sweeping interferometric absolute range measurement technology originated from the traditional microwave radar field. Its basic principle is to linearly or nonlinearly modulate the frequency of the transmitted signal in the time dimension, and then use the beat frequency information between the received target reflected signal and the original transmitted signal for difference frequency processing. By analyzing the frequency components of the beat frequency signal, the absolute range of the target can be deduced. At any given moment, the beat frequency is linearly related to the target distance, thus enabling high-precision range measurement.

[0003] With the development of optoelectronic devices, especially the maturity of highly coherent lasers and stable frequency sweep control technology, lidar systems based on the FMCW (Frequency Modulated Continuous Wave) principle have become a measurement solution with greater advantages in ranging accuracy, spatial resolution, and anti-interference capability than microwave radar. Currently, this technology is widely used in various scenarios, such as laser sensing systems in autonomous driving, 3D imaging radar, industrial-grade precision measurement equipment, robot navigation and obstacle avoidance systems, and elevation modeling and target recognition in aerospace.

[0004] In FMCW lidar systems, a linearly frequency-modulated chirped signal is typically used as the modulation source. After reflection from the target, the transmitted signal interferes with the local light, yielding a beat frequency signal containing target distance information. Subsequently, by performing spectral analysis operations such as Fourier transform on this signal, the distance between the target and the sensor can be obtained from the position of the dominant frequency peak. However, the accuracy of this spectral peak is highly dependent on the spectral resolution, which is limited by the system's sampling rate and signal sampling duration. When multiple targets are close together or the measurement range is far, insufficient spectral resolution can lead to peak aliasing, significantly increasing distance measurement errors and even making it impossible to distinguish between multiple targets.

[0005] To improve spectral resolution, existing technologies often introduce the Chirp Z-Transform (CZT) algorithm to replace the traditional Fast Fourier Transform (FFT). CZT flexibly adjusts the transform path, achieving higher frequency resolution within a specific frequency band, thereby refining distance information between targets. However, the CZT computation process is dependent on the frequency band range, typically requiring the approximate frequency range of the beat frequency signal to be obtained before processing. This forces the system to perform a coarse measurement or estimation of the frequency band range first. This prior step not only increases processing complexity but also introduces real-time issues detrimental to time-sensitive systems.

[0006] Furthermore, the CZT method exhibits significant limitations when dealing with frequency sweep nonlinearity. In practical lasers, frequency drift and nonlinear characteristics often exist during frequency sweeping, directly affecting the spectral structure of the interference signal, making it difficult for the CZT algorithm to extract accurate and effective target information. To achieve nonlinear compensation, additional calibration modules or more complex model fitting algorithms are typically required, further increasing the computational burden and system complexity.

[0007] In contrast, matched filtering, as a classic optimal linear filter, has the advantage of achieving the maximum signal-to-noise ratio output under known signal structure conditions. In the field of traditional radar target detection, matched filtering has been proven to effectively improve the identification capability of weak target signals. However, its direct application to FMCW lidar systems still faces two key challenges: First, the original measurement signal is affected by swept-frequency nonlinear modulation, making it difficult to directly meet the requirements of matched filtering for a standard chirped structure; second, the reference signal required for matched filtering must have modulation characteristics highly similar to the signal to be detected. Therefore, a construction method needs to be designed that can both reflect the known reference distance and structurally satisfy the filtering matching conditions.

[0008] As can be seen from the above issues, current FMCW lidar technology still faces several technical bottlenecks in practical engineering applications, including but not limited to limited spectral demodulation accuracy, heavy reliance on coarse estimation in the algorithm, high sensitivity to the linearity of laser frequency modulation, high system computational burden, and processing speed that cannot meet real-time requirements. Therefore, there is an urgent need to develop a novel signal demodulation scheme that can simplify the computation process, enhance robustness to nonlinear frequency sweeps, and improve overall demodulation speed while maintaining high ranging accuracy, in order to meet the future needs of multi-target measurement in complex environments.

[0009] In summary, existing technologies suffer from limitations in spectral demodulation accuracy, reliance on coarse measurements in algorithms, difficulty in correcting nonlinear modulation, and slow processing speed. Summary of the Invention

[0010] To address the shortcomings of existing technologies, such as limited spectral demodulation accuracy, reliance on coarse measurements, difficulty in correcting nonlinear modulation, and slow processing speed, the technical solution provided by this invention is as follows: A method for demodulating digital chirped matched-filter (FMCW) lidar signals, comprising: The steps for acquiring the measurement interference signal and the auxiliary interference signal; The step of resampling the measured interference signal based on the auxiliary interference signal to compensate for nonlinearity; The steps include constructing a chirped signal and mixing it with a resampled signal to obtain a signal containing target distance information; The steps involve performing matched filtering on a signal containing target distance information and a known reference signal to output the target's absolute distance information.

[0011] Furthermore, a preferred embodiment is provided in which the auxiliary interference signal is used to reflect the nonlinear changes during the laser frequency sweep process and serves as a reference sequence for resampling.

[0012] Furthermore, a preferred embodiment is provided in which the chirped signal is constructed by applying linear frequency modulation to a resampled sequence.

[0013] Furthermore, a preferred embodiment is provided in which the complex form of the resampled signal processed by Hilbert transform is multiplied with the chirped signal to obtain a signal containing target distance information.

[0014] Furthermore, a preferred implementation method is provided, which calculates the absolute distance information of the target based on the time delay difference.

[0015] Based on the same inventive concept, the present invention also provides a digital chirped matched filter (FMCW) lidar signal demodulation device, comprising: A module for acquiring the measurement interference signal and the auxiliary interference signal; A module that resamples the measured interference signal based on the auxiliary interference signal to compensate for nonlinearity; A module that constructs a chirped signal and mixes it with a resampled signal to obtain a signal containing target distance information; This module performs matched filtering on the signal containing target distance information and a known reference signal to output the absolute distance information of the target.

[0016] Based on the same inventive concept, this invention also provides a digital chirped matched filter (FMCW) lidar signal demodulation system for implementing the method, comprising: A laser used to output a swept-frequency laser signal; An isolator, connected to the laser, is used to prevent reflected light from returning to the laser. The first coupler, connected to the isolator, is used to split the laser signal into two paths; The second and fourth couplers form the optical path of the auxiliary interferometer, used to acquire the auxiliary interference signal that reflects the frequency sweep nonlinearity; The third and fifth couplers constitute the optical path of the measurement interferometer, used to acquire measurement interferometric signals containing target distance information; The first balanced detector is connected to the optical path of the auxiliary interferometer and is used to output auxiliary interference signals; The second balanced detector is connected to the optical path of the measurement interferometer and is used to output the measurement interference signal; A circulator, placed in the measurement optical path, is used to transmit laser signals to the target and receive reflected signals; An optical system, connected to a circulator, is used to focus a laser beam onto a target and collect the target's reflected signal.

[0017] Based on the same inventive concept, the present invention also provides a computer storage medium for storing a computer program, wherein when the computer program is read by a computer, the computer executes the method described thereon.

[0018] Based on the same inventive concept, the present invention also provides a computer, including a processor and a storage medium, wherein when the processor reads a computer program stored in the storage medium, the computer executes the method described thereon.

[0019] Based on the same inventive concept, the present invention also provides a computer program product, which, when executed, implements the method described.

[0020] Compared with the prior art, the advantages of the technical solution provided by the present invention are as follows: By employing an auxiliary interferometer to acquire sweep frequency nonlinearity information and resampling the measurement signal, errors caused by laser sweep frequency nonlinearity can be effectively eliminated. Compared to traditional FMCW systems that directly perform spectrum analysis, this method avoids spectral peak drift, improving signal stability and reconstruction accuracy.

[0021] By constructing a chirped signal in complex form from the resampled signal and performing a Hilbert transform, the signal can be better adapted to the subsequent matched filtering process. This approach improves the structural integrity of the signal processing and makes it easier to extract key features containing distance information compared to traditional frequency domain transformation methods, thereby enhancing the overall response sensitivity of the system.

[0022] By introducing a reference chirp signal constructed from a known reference distance and performing matched filtering with the measurement signal, the precise time delay difference between the target and the reference is obtained, effectively avoiding the strong dependence on frequency band range in the traditional CZT algorithm. This method avoids demodulation failure caused by frequency band estimation errors and has stronger anti-interference capabilities.

[0023] The matched filtering process introduces an amplification factor due to resampling, resulting in a final distance resolution that is much smaller than the original time-domain resolution. This overcomes the sampling rate limitation of traditional FFT and CZT methods. This approach achieves high-sensitivity detection of small distance changes without improving the performance of the sampling equipment.

[0024] The overall process eliminates the steps of coarse spectrum measurement and complex rotation factor generation, significantly reducing computational complexity. Compared with traditional CZT-based FMCW demodulation algorithms, this invention achieves faster real-time processing capabilities and is more suitable for rapid scanning and measurement tasks of distant targets.

[0025] Suitable for high-precision absolute distance measurement and fast real-time demodulation scenarios for non-cooperative targets, such as lidar ranging, 3D imaging, and autonomous driving perception systems. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the optical path; Figure 2 The spectrum of the chirped signal; Figure 3 The result of the matched filtering; Figure 4 This is a schematic diagram of the software processing flow.

[0027] In this diagram, 1 represents the laser, 2 represents the polarization maintaining isolator, 3 represents coupler one, 4 represents coupler two, 5 represents coupler three, 6 represents coupler four, 7 represents coupler five, 8 represents balanced detector one, 9 represents balanced detector two, 10 represents the circulator, 11 represents the optical system, and 12 represents the target. Detailed Implementation

[0028] To make the advantages and benefits of the technical solution provided by the present invention clearer, the technical solution provided by the present invention will now be described in further detail with reference to the accompanying drawings, specifically: Implementation Method 1: This implementation method provides a digital chirped matched filter (FMCW) lidar signal demodulation method, including: The steps for acquiring the measurement interference signal and the auxiliary interference signal; The step of resampling the measured interference signal based on the auxiliary interference signal to compensate for nonlinearity; The steps include constructing a chirped signal and mixing it with a resampled signal to obtain a signal containing target distance information; The steps involve performing matched filtering on a signal containing target distance information and a known reference signal to output the target's absolute distance information.

[0029] The auxiliary interference signal is used to reflect the nonlinear changes during the laser frequency sweep process and serves as a reference sequence for resampling.

[0030] The chirped signal is constructed by applying linear frequency modulation to the resampled sequence.

[0031] The complex-form resampled signal processed by Hilbert transform is multiplied by the chirped signal to obtain a signal containing target distance information.

[0032] The absolute distance information of the target is calculated based on the time delay difference.

[0033] A digital chirped matched filter (FMCW) lidar signal demodulation system is also provided for implementing the method, comprising: A laser used to output a swept-frequency laser signal; An isolator, connected to the laser, is used to prevent reflected light from returning to the laser. The first coupler, connected to the isolator, is used to split the laser signal into two paths; The second and fourth couplers form the optical path of the auxiliary interferometer, used to acquire the auxiliary interference signal that reflects the frequency sweep nonlinearity; The third and fifth couplers constitute the optical path of the measurement interferometer, used to acquire measurement interferometric signals containing target distance information; The first balanced detector is connected to the optical path of the auxiliary interferometer and is used to output auxiliary interference signals; The second balanced detector is connected to the optical path of the measurement interferometer and is used to output the measurement interference signal; A circulator, placed in the measurement optical path, is used to transmit laser signals to the target and receive reflected signals; An optical system, connected to a circulator, is used to focus a laser beam onto a target and collect the target's reflected signal.

[0034] Implementation Method Two: This implementation method is a further detailed description of the technical solution provided in Implementation Method One, specifically: A demodulation method for FMCW lidar signals based on digital chirped matched filtering is proposed, suitable for high-precision absolute distance measurement of non-cooperative targets. This method effectively improves ranging accuracy and computational efficiency through steps such as nonlinear compensation, chirped signal construction, frequency mixing, and matched filtering.

[0035] The following is combined with Figure 1 The structure shown is described in detail: Step 1: Light source signal transmission and optical path beam splitting like Figure 1 As shown, laser 1 is used to output a swept-frequency laser signal. The laser signal first passes through polarization-maintaining isolator 2 to ensure unidirectional propagation of the optical path and avoid back reflection interference with the stability of the laser source.

[0036] The output laser signal then enters coupler 3, which distributes the beam power according to a predetermined ratio, guiding it to coupler 4 and coupler 5 respectively, forming two interference optical paths. Coupler 4 forms the auxiliary interferometer optical path for frequency sweep nonlinearity compensation; coupler 5 forms the measurement interferometer optical path for acquiring target distance information.

[0037] Step 2: Construction of the Auxiliary Interferometer and Nonlinear Compensation Coupler 2 (4) feeds the input optical signal proportionally into a section of fiber delay line, forming a closed-loop structure to realize the reference interference path. The optical signals within this path are combined by coupler 4 (6) and then input into the balanced detector 1 (8) to generate an auxiliary interference signal, which is used to reflect the real-time nonlinear characteristics of the laser's frequency sweep.

[0038] The output signal provided by the auxiliary interferometer serves as a reference and will be used to resample and correct the measurement signal, thereby eliminating the distance error caused by nonlinear frequency modulation.

[0039] Step 3: Measurement Interferometer Signal Construction Meanwhile, coupler 3 (5) introduces the optical signal into the path of the measurement interferometer. Coupler 5 (7) combines the two beams on this path and inputs them into the balanced detector 2 (9), outputting a measurement interferometric signal containing target distance information. Due to the nonlinearity of the laser's frequency sweep characteristics, the distance information cannot yet be directly demodulated from this measurement signal.

[0040] Step 4: Resampling and Chirped Signal Construction The measured interference signal from step three is combined with the auxiliary interference signal output from step two and resampled to compensate for the distortion caused by nonlinear frequency modulation, so that the measured signal is restored to an ideal linear frequency modulation structure.

[0041] Subsequently, the resampled measurement signal is converted into a complex form and constructed into a signal form with distinct chirp characteristics to prepare for subsequent mixing and matched filtering.

[0042] Step 5: Acquisition of target echo signal A beam of light in the measurement interference path is led out by circulator 10, focused by optical system 11 and then irradiated onto target 12. The echo signal reflected by the target returns through the same optical system 11, is guided by circulator 10 into the interference path, and interferes with another beam of reference light, thereby generating a modulated signal containing target distance information.

[0043] Step 6: Construct a reference chirped signal and perform mixing. A reference chirped signal with known distance information is constructed, with the same structure and modulation as the measured signal. The resampled measured signal is then mixed with the reference signal to obtain a new signal containing the distance difference information.

[0044] Step 7: Matched Filtering and Distance Recovery The mixed signal is input into a matched filter and subjected to matched filtering with a reference chirped signal to extract the time delay difference between the two. Because matched filtering has high time resolution enhancement capabilities, the final delay difference result, after conversion, can be used to recover the absolute distance of the target.

[0045] This process eliminates the need to generate the rotation factor required for spectral analysis and requires no prior coarse measurement information, significantly simplifying the computational process and improving demodulation efficiency.

[0046] Implementation Method 3: Combination Figure 1-4 This embodiment describes the technical solution provided above in further detail through specific examples. Specifically: A method for demodulating FMCW lidar signals based on matched filtering is presented below. The invention will be briefly described from the perspectives of optical path structure, measurement principle, and processing flow.

[0047] Figure 1 This invention employs an optical path structure in which the optical path of the measuring interferometer is primarily used for calculating the absolute distance to the target, while the optical path of the auxiliary interferometer is used to correct the nonlinearity of the laser's frequency sweep. The time-domain signal output from the above optical path can be divided into: the ranging interferometric signal received by the balanced detector (measuring interferometer). The auxiliary interferometer signal received by the balanced detector 2 (auxiliary interferometer) The mathematical expression for the signal received by the balanced detector is as follows: (1) In the formula, It is the frequency sweep rate (including nonlinearity). It is the time delay for measuring the difference in arm lengths of the interferometer. The initial frequency of the laser contains nonlinearity, so the target distance information cannot be directly obtained through spectrum analysis. Therefore, it is necessary to resample the measurement signal using the signal from an auxiliary interferometer to correct the effects of frequency sweep nonlinearity. The balanced detector two receives the signal from the auxiliary interferometer. (2) In the formula It is the time delay for measuring the difference in arm lengths of the interferometer. Equation (1) is obtained by resampling and correcting the nonlinearity using equation (2). (3) In the formula, k represents the resampling sequence. This indicates that the signal frequency changes with the target distance. In traditional FMCW, the next step is to perform spectral subdivision analysis on the signal represented by equation (3), which requires the CZT algorithm. However, CZT requires prior frequency band information to perform subsequent calculations. Therefore, to reduce the computational load, CZT is not used for spectral subdivision here, but matched filtering is used instead. However, to complete the matched filtering algorithm, the signal needs to be constructed as a chirped state, and Equation (3) needs to be Hilbert transformed and rewritten in complex form. (4) Constructing chirped signals using resampled sequences (5) In the formula The chirp coefficient is represented by equation (4). Mixing equation (4) and equation (5) yields a chirped signal containing target distance information, with the spectrum as shown below. Figure 2 As shown (6) Furthermore, a reference signal with a known arm length difference is constructed using the resampled sequence to complete the matched filtering. Its signal expression is as follows: (7) In the formula, This is the time delay of the reference interferometer arm length difference. At this point, matched filtering can be applied to the signals from equations (6) and (7). (8) The result obtained by matched filtering is as follows Figure 3 As shown, the time delay difference between the measuring interferometer and the reference interferometer is used to recover the actual time delay difference, as shown in the following formula. (9) (10) in the formula It measures the difference in arm lengths of the interferometer. The time delay is the distance difference between the two interferometers. It's the speed of light. Here, N represents the arm length difference of the reference interferometer, and N is the result of matched filtering. The result of matched filtering is amplified due to resampling, therefore the actual time delay obtained by matched filtering will be much smaller than the time domain resolution. This improves the measurement accuracy of matched filtering. The overall signal processing flow is as follows: Figure 4 As shown.

[0048] The advantages of this implementation method are: Building upon traditional FMCW ranging methods, this invention introduces an innovative processing mechanism. It constructs a standard chirped signal with known distance parameters and mixes it with a beat frequency signal extracted from the target echo signal, effectively embedding target information into a regularly structured mixed signal. This mixed signal is then used as input for matched filtering, thereby demodulating the target distance information. Compared to the CZT (Chirp-Z Transform) spectrum subdivision algorithm used in traditional methods, this method significantly simplifies the processing flow. While the CZT algorithm possesses high frequency resolution within a specific frequency band, it requires approximate frequency band information of the beat frequency signal, often necessitating a coarse measurement step. This coarse measurement process not only introduces additional computational overhead but also significantly impacts system efficiency and real-time response capabilities, particularly hindering high-speed dynamic target measurement in complex scenarios.

[0049] This invention replaces CZT with matched filtering, eliminating reliance on spectrum prediction and rotation factor generation processes. This effectively avoids the dependence of traditional methods on high-performance computing resources, significantly reducing the computational complexity and memory usage of the demodulation process. As a result, it provides the measurement system with higher real-time processing capabilities and faster overall computing speed, making it particularly suitable for large-scale, high-frequency measurement applications.

[0050] Furthermore, the matched filtering technique employed in this invention possesses significant structural advantages. During the construction of the chirped signal, the resampling process has already performed nonlinear correction on the original beat frequency signal, resulting in a more ideal structure for the obtained chirped signal, and its frequency variation is no longer directly tied to the target distance. In other words, the constructed chirped signal itself does not carry target distance information but serves as a modulation template for mixing with the target signal. Therefore, the output of the matched filter is not a time delay value directly inferred from the position of the dominant frequency peak in the traditional sense, but rather a time offset containing distance-related information. This offset corresponds to the position where the maximum correlation peak with the reference signal is generated under the matched filtering operation.

[0051] Furthermore, since this time offset is calculated based on nonlinear correction and high-resolution matched filtering, it implicitly contains a time amplification factor introduced by resampling. Using this amplification factor for conversion, previously indistinguishable sub-temporal resolution level time delay differences can be transformed into detectable values, thereby greatly improving the time resolution capability of the demodulation system. This approach breaks through the resolution limits inherent in traditional systems set by sampling frequency and signal duration, resulting in a target distance accuracy far exceeding the theoretical lower limit achievable by the original system's time-domain sampling.

[0052] In summary, by introducing a known reference chirp signal and combining it with matched filtering, this invention not only overcomes the technical bottlenecks of high computational complexity and reliance on coarse measurements in the CZT method, but also significantly improves ranging accuracy while increasing computational speed, providing strong technical support for the application of FMCW lidar systems in high-precision, fast-response scenarios.

[0053] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method of digital chirp matched filter FMCW lidar signal demodulation, characterized in that, include: The steps for acquiring the measurement interference signal and the auxiliary interference signal; The step of resampling the measured interference signal based on the auxiliary interference signal to compensate for nonlinearity; The steps include constructing a chirped signal and mixing it with a resampled signal to obtain a signal containing target distance information; The steps involve performing matched filtering on a signal containing target distance information and a known reference signal to output the target's absolute distance information.

2. The method of claim 1, wherein, The auxiliary interference signal is used to reflect the nonlinear changes during the laser frequency sweep process and serves as a reference sequence for resampling.

3. The method of claim 1, wherein, The chirped signal is constructed by applying linear frequency modulation to the resampled sequence.

4. The digital chirped matched filter (FMCW) lidar signal demodulation method according to claim 1, characterized in that, The complex-form resampled signal processed by Hilbert transform is multiplied by the chirped signal to obtain a signal containing target distance information.

5. The digital chirped matched filter (FMCW) lidar signal demodulation method according to claim 1, characterized in that, The absolute distance information of the target is calculated based on the time delay difference.

6. A digital chirped matched filter (FMCW) lidar signal demodulation device, characterized in that, include: A module for acquiring the measurement interference signal and the auxiliary interference signal; A module that resamples the measured interference signal based on the auxiliary interference signal to compensate for nonlinearity; A module that constructs a chirped signal and mixes it with a resampled signal to obtain a signal containing target distance information; This module performs matched filtering on the signal containing target distance information and a known reference signal to output the absolute distance information of the target.

7. A digital chirped matched filter (FMCW) lidar signal demodulation system, characterized in that, To implement the method of claim 1, the method comprises: A laser used to output a swept-frequency laser signal; An isolator, connected to the laser, is used to prevent reflected light from returning to the laser. The first coupler, connected to the isolator, is used to split the laser signal into two paths; The second and fourth couplers form the optical path of the auxiliary interferometer, used to acquire the auxiliary interference signal that reflects the frequency sweep nonlinearity; The third and fifth couplers constitute the optical path of the measurement interferometer, used to acquire measurement interferometric signals containing target distance information; The first balanced detector is connected to the optical path of the auxiliary interferometer and is used to output auxiliary interference signals; The second balanced detector is connected to the optical path of the measurement interferometer and is used to output the measurement interference signal; A circulator, placed in the measurement optical path, is used to transmit laser signals to the target and receive reflected signals; An optical system, connected to a circulator, is used to focus a laser beam onto a target and collect the target's reflected signal.

8. A computer storage medium for storing computer programs, characterized in that, When the computer program is read by the computer, the computer executes the method of claim 1.

9. A computer, comprising a processor and a storage medium, characterized in that, When the processor reads the computer program stored in the storage medium, the computer executes the method of claim 1.

10. A computer program product, as a computer program, is characterized by: When the computer program is executed, it implements the method of claim 1.

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