Method, device and equipment for realizing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity
Through the dual-frequency interference SAR method, the echo data of the SAR system is decomposed and processed, and the calculation is carried out using the dual-frequency defuzzy principle, which solves the folding fuzzy problem in SAR technology and improves the defuzzy accuracy of the remote sensing ground elevation map.
Patent Information
- Application Number
- CN202210113274.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-01-30
- Publication Date
- 2025-02-11
- Estimated Expiration
- 2042-01-30
AI Technical Summary
When using SAR technology to construct remote sensing ground elevation maps, the prior art faces the problem of folding blur in interference phase difference in signal processing, resulting in low accuracy of defuzzy elevation information.
The dual-frequency interference SAR method is used to obtain the echo data sent by the SAR system, and the main radar data and auxiliary radar data are decomposed, and the defuzzy calculation is performed according to the dual-frequency defuzzing principle to obtain the absolute phase difference fuzzy number.
Effectively improve the accuracy of understanding the fuzzy results, avoid errors caused by split subband method, and ensure the accuracy of the absolute phase difference fuzzy number.
Smart Images

Figure CN114594473B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of remote sensing imaging technology, and in particular to a method, device and equipment for realizing absolute relative ambiguity resolution of dual-frequency interferometric SAR. Background Art
[0002] The interferometric SAR principle establishes a corresponding relationship between the ground elevation and the phase difference between two SAR complex images of the ground, and the ground elevation can be inverted from the interferometric phase difference. At present, interferometric SAR technology or system has become one of the practical means of remote sensing ground elevation maps.
[0003] However, due to the folding ambiguity of the interference phase difference in the signal processing of the interferometric SAR technology or system, it is necessary to handle the folding ambiguity when using SAR technology to construct a remote sensing ground elevation map. In practice, the elevation information to be inverted by remote sensing directly corresponds to the absolute interference phase difference, so when handling the folding ambiguity in SAR technology, it can be done by solving the absolute phase difference based on the principal value phase difference.
[0004] In the related art, the methods for solving the absolute phase difference usually include two types: relying on external sources and not relying on external sources. Among them, the method of solving the absolute phase difference by relying on external sources refers to seeking support outside the interferometric SAR system for remote sensing height measurement, such as: using a laser altimetry (LiDAR) system, using ground measurement (GPS), etc., and obtaining high-precision elevations at some discrete points on the ground by these methods. If a point falls into the remote sensing area of interferometric SAR height measurement, the point is defuzzified according to the interferometric imaging geometry through the elevation of the point, and from this point to the surroundings, the fuzziness of adjacent points is gradually resolved until the interferometric phase difference of the entire image is defuzzified. The method of solving the absolute phase difference without relying on external sources is to implement remote sensing by using two or more signals of different frequencies, and to jointly solve the absolute phase difference by using the original phases of the four SAR complex images obtained by multiple frequencies. Among them, multiple signals of different frequencies are usually implemented by splitting a broadband radar signal into two high and low sub-bands (i.e., the split sub-band method).
[0005] However, in the above-mentioned related technologies, the method of solving the absolute phase difference by external sources requires that there must be external source data, and the sample points in the data must fall in the imaging area of the interferometric SAR. In the method of solving the absolute phase difference without external sources, since the resolution of SAR imaging is determined by the bandwidth of its signal, the larger the bandwidth, the higher the resolution. The two sub-bands are split from the original broadband, and the bandwidth of each sub-band can only be half of the bandwidth of the original signal at most. The normal interferometric SAR imaging that needs to solve the folding blur of 2π integer multiples uses the entire broadband signal, which makes the object to be solved (full bandwidth imaging) and the object in the split sub-band (maximum half bandwidth imaging) use significantly different system parameters such as resolution, channel characteristics and signal-to-noise ratio, thereby introducing new errors and ultimately affecting the accuracy of the results. Summary of the invention
[0006] In view of this, the present application proposes a method for realizing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity, which can effectively improve the accuracy of the deambiguation number result.
[0007] According to one aspect of the present application, a method for implementing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity is provided, comprising:
[0008] Acquire echo data sent by the SAR system; wherein the echo data is generated by transmitting a main frequency signal and an auxiliary frequency signal by a radar in the SAR system;
[0009] Preprocessing the echo data, and decomposing the primary radar data and the auxiliary radar data in the SAR system from the echo data;
[0010] According to the primary radar data and the secondary radar data, deambiguation calculation is performed according to the dual-frequency deambiguation principle to obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system.
[0011] In a possible implementation, the radar transmission main frequency signal and the auxiliary frequency signal in the SAR system are generated by mixing at the original imaging frequency.
[0012] In a possible implementation manner, when decomposing the primary radar data and the auxiliary radar data in the SAR system from the echo data, the decomposition is performed according to a preset rule.
[0013] In a possible implementation, the main radar data includes a main radar, a main frequency signal of the main radar, an auxiliary frequency signal of the main radar, and an interferometric height measurement signal of the main radar;
[0014] The auxiliary radar data includes an auxiliary radar, a primary frequency signal of the auxiliary radar, an auxiliary frequency signal of the auxiliary radar, and an interference height measurement signal of the auxiliary radar.
[0015] In a possible implementation, deambiguation calculation is performed according to the dual-frequency deambiguation principle based on the primary radar data and the auxiliary radar data to obtain an absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system, including:
[0016] According to the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, the main frequency signal of the auxiliary radar and the auxiliary frequency signal of the auxiliary radar, the main and auxiliary frequencies of the dual-frequency area in the current imaging area of the SAR system are interfered respectively according to the dual-frequency deambiguation principle to solve the dual-frequency area folding ambiguity number;
[0017] According to the continuity of the absolute phase difference, the main frequency fuzzy number of the dual-frequency zone is calculated based on the obtained dual-frequency zone folding fuzzy number, and then deduced from the dual-frequency zone to the interferometric height measurement area to obtain the folding fuzzy number of the interferometric height measurement area.
[0018] In a possible implementation, after obtaining the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system, the method further includes:
[0019] Based on the obtained absolute phase difference fuzzy number and in combination with the principal value phase difference, an elevation map of the current remote sensing imaging of the SAR system is obtained.
[0020] According to another aspect of the present application, there is also provided a device for realizing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity, comprising a data acquisition module, a data processing module and a data calculation module;
[0021] The data acquisition module is configured to acquire echo data sent by the SAR system; wherein the echo data is generated when the radar in the SAR system transmits a main frequency signal and an auxiliary frequency signal;
[0022] The data processing module is configured to pre-process the echo data and decompose the primary radar data and the auxiliary radar data in the SAR system from the echo data;
[0023] The data calculation module is configured to perform deambiguation calculation according to the main radar data and the auxiliary radar data in accordance with the dual-frequency deambiguation principle to obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system.
[0024] In a possible implementation, the main radar data includes a main radar, a main frequency signal of the main radar, an auxiliary frequency signal of the main radar, and an interferometric height measurement signal of the main radar;
[0025] The auxiliary radar data includes the auxiliary radar, the main frequency signal of the auxiliary radar, the auxiliary frequency signal of the auxiliary radar, and the interference height measurement signal of the auxiliary radar;
[0026] The data calculation module includes a first calculation module and a second calculation module;
[0027] The first calculation module is configured to interfere with the main and auxiliary frequencies of the dual-frequency area in the current imaging area of the SAR system according to the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, the main frequency signal of the auxiliary radar and the auxiliary frequency signal of the auxiliary radar, and solve the dual-frequency area folding ambiguity number according to the dual-frequency deambiguation principle;
[0028] The second calculation module is configured to calculate the main frequency fuzzy number of the dual-frequency zone based on the obtained dual-frequency zone folding fuzzy number according to the continuity of the absolute phase difference, and deduce from the dual-frequency zone to the interference height measurement area to obtain the folding fuzzy number of the interference height measurement area.
[0029] According to another aspect of the present application, a device for implementing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity is also provided, comprising:
[0030] processor;
[0031] a memory for storing processor-executable instructions;
[0032] Wherein, the processor is configured to implement any of the above-mentioned methods when executing the executable instructions.
[0033] According to another aspect of the present application, a non-volatile computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, any of the above-mentioned methods is implemented.
[0034] The radars of the SAR system can all transmit the main frequency signal and the auxiliary frequency signal, so that when the radars in the SAR system transmit the main frequency signal and the auxiliary frequency signal, the corresponding echo data is generated, and the generated echo data is processed, and the main radar data and the auxiliary radar data in the SAR system are decomposed from the echo data, and then the defuzzification calculation is performed according to the dual-frequency defuzzification principle, so as to obtain the absolute phase difference fuzzy number of the current remote sensing imaging of the SAR system. It achieves the purpose of defuzzification calculation without relying on external sources. At the same time, under the premise of not relying on external sources, it does not need to split the full bandwidth signal, and is directly realized by each radar of the SAR system transmitting the main frequency signal and the auxiliary frequency signal, which effectively avoids the error caused by the split subband method in the related technology, thereby ensuring the accuracy of the absolute phase difference fuzzy number finally solved.
[0035] Other features and aspects of the present application will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate exemplary embodiments, features, and aspects of the present application and, together with the description, serve to explain the principles of the present application.
[0037] Figure 1 A schematic diagram showing a method of using a split sub-band method to implement multiple signals of different frequencies in the related art;
[0038] Figure 2 A schematic diagram showing two different frequency signals, namely, a main frequency signal and an auxiliary frequency signal, generated in a method for realizing a dual-frequency interferometric SAR to resolve absolute phase difference ambiguity according to an embodiment of the present application;
[0039] Figure 3 A flow chart showing a method for implementing a dual-frequency interferometric SAR to resolve absolute phase difference ambiguity according to an embodiment of the present application;
[0040] Figure 4 A schematic diagram of SAR imaging geometry and transceiver timing in a method for implementing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity in an embodiment of the present application is shown;
[0041] Figure 5 The sampling t on Schematic diagram of the imaging position at the same time;
[0042] Figure 6 Shown using t off Schematic diagram of the imaging position at the same time;
[0043] Figure 7 A schematic diagram showing close-range dual-frequency timing and imaging area;
[0044] Figure 8 A schematic diagram showing the long-range dual-frequency timing and imaging area;
[0045] Figure 9a The timing diagram of transmitting and receiving the short-range main radar and auxiliary radar designed in the method for realizing the dual-frequency interferometric SAR to resolve the absolute phase difference ambiguity in the embodiment of the present application is shown;
[0046] Figure 9b Shown with Figure 9a Corresponding imaging area result map;
[0047] Fig.10a The timing diagram of transmitting and receiving the long-range main radar and auxiliary radar designed in the method for realizing the dual-frequency interferometric SAR to resolve the absolute phase difference ambiguity in the embodiment of the present application is shown;
[0048] Fig.10b Shown with Fig.10a The corresponding imaging geometry result diagram;
[0049] Fig.11A flow chart showing a method for solving absolute phase difference ambiguity in dual-frequency interferometry SAR according to an embodiment of the present application, in which the absolute ambiguity number of the main frequency of the dual-frequency zone is calculated based on the folded ambiguity number of the dual-frequency zone according to the continuity of the absolute phase difference;
[0050] Fig.12 Another flow chart showing a method for implementing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity according to an embodiment of the present application;
[0051] Fig.13a The main frequency SAR image collected by the SAR system in a specific embodiment is shown;
[0052] Fig.13b The auxiliary frequency SAR image collected by the SAR system in a specific embodiment is shown;
[0053] Fig.14a Shown with Fig.13a The main frequency interferometric phase corresponding to the main frequency SAR image shown;
[0054] Fig.14b Shown with Fig.13b The auxiliary frequency interferometric phase corresponding to the auxiliary frequency SAR image shown.
[0055] Fig.15 Show Fig.13a and Fig.13b The imaging area diagram corresponding to the main frequency SAR image and the auxiliary frequency SAR image when solving the absolute phase difference ambiguity number is shown;
[0056] Fig.16 A schematic diagram showing the process of superimposing a corresponding digital surface model generated by the fuzzy numbers obtained in FIG. 14 onto a Tandem product;
[0057] Fig.17 A structural block diagram showing an apparatus for implementing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity according to an embodiment of the present application is shown;
[0058] Fig.18 A structural block diagram of a device for implementing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity according to an embodiment of the present application is shown. DETAILED DESCRIPTION
[0059] Various exemplary embodiments, features and aspects of the present application will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.
[0060] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.
[0061] In addition, in order to better illustrate the present application, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present application can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the subject matter of the present application.
[0062] In order to more clearly understand the technical solution of the method for resolving absolute phase difference ambiguity in dual-frequency interferometric SAR according to the embodiment of the present application, the relevant terms in the embodiment of the present application are first explained accordingly.
[0063] First, it should be noted that in the method of the embodiment of the present application, the main frequency signal and the auxiliary frequency signal refer to signals of different frequencies emitted by each radar in the SAR system. Among them, in a possible implementation, the signal of the original frequency of the radar can be used as the main frequency signal, and the signal of another frequency can be used as the auxiliary frequency signal. At the same time, the frequency of the main frequency signal is higher than the frequency of the auxiliary frequency signal. That is, the main frequency signal is a high-frequency signal, and the auxiliary frequency signal is a low-frequency signal.
[0064] In conventional techniques, in the method of solving the absolute phase difference without relying on external sources, multiple signals of different frequencies are usually obtained by splitting a broadband radar signal (full bandwidth signal) into two sub-bands (i.e., upper sub-band signal and lower sub-band signal) (e.g., Figure 1 Then, the two sub-bands and the two radars are combined to form the SAR imaging of the four sub-bands required in the dual-frequency deambiguation principle.
[0065] In the method for implementing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity in the embodiment of the present application, different from the above-mentioned split sub-band method, the main frequency signal and auxiliary frequency signal emitted by the radar in the SAR system in the embodiment of the present application are generated in the following manner.
[0066] See also Figure 2 , which shows the principle of generating and receiving the radar auxiliary frequency signal in the method of the embodiment of the present application. Among them, the broadband radio frequency f emitted by the radar S Signal, generally adopt the broadband intermediate frequency f I With point frequency f LO The mixing result can be two kinds, namely, the up-mixing f S =f LO +f I and down-mixing f S =f LO -f I Before the received echo enters the receiver's intermediate frequency amplification, it will use the same frequency as the point frequency f.LO Down-conversion of the local oscillator phase mixing converts the echo signal back to the intermediate frequency (f I =|f S -f LO |) to be enlarged.
[0067] In the method of the embodiment of the present application, the generation of the auxiliary frequency signal utilizes the above-mentioned characteristics of the radar system, and the main frequency signal and the auxiliary frequency signal are two results of mixing. LO +f I As the original imaging signal (i.e., the main frequency signal), the auxiliary frequency signal is down-mixed with f LO -f I On the contrary, if the radar uses the down-mixing f LO -f I As the original imaging signal (i.e., the main frequency signal), the auxiliary frequency signal is mixed up with f LO +f I .
[0068] That is to say, in the method of implementing the embodiment of the present application, it is necessary to set the above-mentioned operating parameters for the radar in the SAR system, so that each radar in the SAR system can transmit and receive the main frequency signal and the auxiliary frequency signal.
[0069] Furthermore, it is necessary to explain that the method of the embodiment of the present application is designed and developed based on the technical background of the folding blur phenomenon existing in the interference phase difference in the signal processing of the interferometric SAR technology or system.
[0070] Among them, the folding blur of the interference phase difference specifically refers to: due to the periodic characteristics of the complex phase, the difference between the two original phases obtained by interference processing can only be the main value remaining within [0, 2π) after the absolute difference between the two original phase values is folded off an integer multiple of the 2π (or 360°) period.
[0071] Right now,
[0072] In the above formula, θ is the original phase before interference, is the difference phase obtained after interference (interference phase difference), N is the multiple value of the folded integer period (relative to the absolute phase difference ), main value Also called relative phase difference.
[0073] Among them, the interference can only directly obtain the main value Its absolute phase difference There is a phase difference of 2π integer multiples, which means that the phase result of interference has a folding blur of 2π integer multiples.
[0074] At the same time, those skilled in the art can also understand that in practice, the elevation information of the remote sensing image inverted by remote sensing mapping through the SAR system directly corresponds to the absolute interference phase difference. Therefore, when the elevation information of the remote sensing image of the SAR system is obtained, the absolute phase difference of the remote sensing imaging needs to be solved. According to the formula shown above, when solving the absolute phase difference, it can be solved according to the main value phase difference and the N value. Among them, the main value phase difference can be directly obtained through interference. The solution of the N value is the method for resolving the absolute phase difference ambiguity in the embodiment of the present application. That is to say, in the method for realizing the dual-frequency interference SAR to resolve the absolute phase difference ambiguity in the embodiment of the present application, the absolute phase difference ambiguity number finally obtained refers to the N value mentioned above.
[0075] Therefore, see Figure 3 , Figure 3 The flowchart of the method for implementing the dual-frequency interferometric SAR to resolve the absolute phase difference ambiguity in the embodiment of the present application is shown. Figure 3 As shown, the method of the embodiment of the present application includes: Step S100, acquiring echo data sent by the SAR system. Those skilled in the art can understand that the echo data is generated by transmitting a main frequency signal and an auxiliary frequency signal by a radar in the SAR system.
[0076] After the echo data is acquired, step S200 can be executed to pre-process the echo data, and decompose the main radar data and auxiliary radar data in the SAR system from the echo data. Here, it should be noted that in the method of the embodiment of the present application, the SAR system includes two radars, one of which is used as the main radar and the other is used as the auxiliary radar. Correspondingly, the main radar data includes the main frequency signal and the auxiliary frequency signal emitted by the main radar, and the auxiliary radar data includes the main frequency signal and the auxiliary frequency signal emitted by the auxiliary radar.
[0077] After the main radar data and the auxiliary radar data in the SAR system are decomposed, step S300 can be executed to perform deambiguation calculation according to the main radar data and the auxiliary radar data according to the dual-frequency deambiguation principle to obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system.
[0078] Therefore, the method for realizing dual-frequency interferometric SAR absolute phase difference ambiguity resolution in the embodiment of the present application is that the radars of the SAR system can all transmit the main frequency signal and the auxiliary frequency signal, so that when the radars in the SAR system transmit the main frequency signal and the auxiliary frequency signal, the corresponding echo data is generated, and the generated echo data is processed, and the main radar data and the auxiliary radar data in the SAR system are decomposed from the echo data, and then the ambiguity resolution calculation is performed according to the dual-frequency ambiguity resolution principle, so as to obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system. It realizes the purpose of realizing the ambiguity resolution calculation without relying on external sources, and at the same time, under the premise of not relying on external sources, it does not need to split the full bandwidth signal, and is directly realized by each radar of the SAR system transmitting the main frequency signal and the auxiliary frequency signal, which effectively avoids the error caused by the split subband method in the related art, thereby ensuring the accuracy of the absolute phase difference ambiguity number finally resolved.
[0079] It should be noted that, in the method of the embodiment of the present application, the echo data is preprocessed, and the primary radar data and the auxiliary radar data can be decomposed according to the preset rules. It should be noted that the preset rules refer to the rules for data encapsulation when the radar in the SAR system is controlled to run. The specific formulation of the preset rules can be flexibly set according to the actual situation, and is not specifically limited here.
[0080] Further, in the method of the embodiment of the present application, after the main radar data and the auxiliary radar data in the SAR system are decomposed from the echo data, the absolute phase difference ambiguity number can be solved based on the decomposed main radar data and the auxiliary radar data. According to the above, in the embodiment of the present application, the absolute phase difference ambiguity number is mainly solved based on the dual-frequency deambiguation principle.
[0081] In order to more clearly illustrate the technical solution of using the dual-frequency deambiguation principle to solve the absolute phase difference ambiguity number in the embodiment of the present application, the dual-frequency deambiguation principle is first described accordingly below.
[0082] It is understood by those skilled in the art that the radar transmission and reception timing corresponds to the imaging geometry. Figure 4 , Figure 4 The relationship between the traditional SAR strip imaging transceiver timing and imaging geometry is shown. After the pulse repetition frequency (PRT) and the transmit pulse width are determined, the radar transceiver timing and the range parameters of SAR imaging include the near-range edge, far-range edge and range width.
[0083] The positions of the near-range edge and the far-range edge are determined relative to the transmission time. Specifically, the near-range edge position corresponds to the start time of the received sampling (t on), the end time of the sampling of the distant edge domain (t off ), the range width and the length of time for receiving samples (i.e., the sampling window t off -t on ) corresponding to.
[0084] Therefore, according to the corresponding relationship between the above-mentioned range parameters and the signal sampling time, if they have the same receiving sampling start time, they have the same SAR imaging near-range edge position (such as Figure 5 If they have the same receiving sampling end time, they have the same SAR imaging far-range edge position (such as Figure 6 shown).
[0085] More specifically, Figure 5 As shown, Figure 5 It is divided into two parts, the upper part is the transmission and reception timing, and the lower part is the imaging area corresponding to the transmission and reception timing. In the transmission and reception timing, the left half is different from the right half. The left half is the same as the front Figure 4 The timing corresponding to the original SAR imaging is shown in FIG. 1 , and the timing on the right is used to illustrate that if the sampling start time is the same, the close-range edge of the imaging is the same.
[0086] Each PRT on the left side has the same t on ,t off With t off -t on , their images have the same near side, far side and image width. The right half itself is the same. But the left and right halves are separated by t on In addition, t off With t off -t on The width of the receiving sampling window on the left (t off -t on ) is larger than the right side, so the width of the left side is larger than the right side after imaging. In addition, the two halves have the same PRT and are closely connected in time, so their imaging is also connected in azimuth.
[0087] Figure 6 The schematic diagram shows that if the sampling end time in the time sequence is the same, the imaging distance edge is the same. Figure 5 The principles shown are the same or similar and will not be described again here.
[0088] Based on the previous Figure 5 and Figure 6 The corresponding relationship shown in FIG. 1 can be used to design a dual-frequency timing sequence that has the same PRT and transmit pulse width as the original SAR imaging and has a common imaging area on the ground (such as Figure 7That is, in the method of the embodiment of the present application, the timing of the main frequency signal and the auxiliary frequency signal transmitted by the radar in the SAR system can be adopted Figure 7 The dual frequency timing is shown.
[0089] Among them, Figure 7 The upper left figure shown is the transmission and reception timing of high (main) frequency imaging, as described above (see Figure 4 ) Its imaging area is the solid line frame in the lower right figure; the lower left figure is the low (auxiliary) frequency imaging sequence, which has the same PRT and t as the upper figure. on With t off , so its imaging area should be the same as the upper left one, which is also the solid line frame in the imaging area of the lower right picture. Because the high and low transmission and reception timings do not conflict in time (there is no common transmission and reception working time), the two timings can be combined into one by time division multiplexing. For a schematic diagram, see Figure 7 Therefore, under the timing of the upper right figure, the received echoes of the high frequency signal (ie, the main frequency signal) and the low frequency signal (ie, the auxiliary frequency signal) are imaged separately, and the two imaged areas are overlapped.
[0090] In the above description of the dual-frequency imaging principle, compared with the original SAR imaging, if the dual-frequency and the original SAR system are set with the same sampling start time t on , then they have the same near edge. Similarly, if the same sampling end time t is set off , we can obtain dual-frequency time series and imaging with the same long-range edge (see Figure 8 , the principle will not be repeated).
[0091] It can be seen that the premise for realizing dual-frequency imaging is that the timing of the two signal frequencies can be time-division multiplexed. That is, the timing of the main frequency signal and the auxiliary frequency signal emitted by each radar in the SAR system can be time-division multiplexed.
[0092] Among them, the SAR range imaging is obtained by echo sampling and pulse compression, and the imaging width corresponds to the sampling time length (sampling window) minus one pulse width (pulse compression will reduce one pulse width). Therefore, the original SAR timing sequence needs to subtract two pulse widths (one for transmission and one for pulse compression) in the PRT, and the remaining time can be used to support the imaging width. In the dual-frequency timing sequence, two frequency signals need to be transmitted and received within the PRT time of the original SAR, so four pulse widths need to be subtracted (two for high frequency and two for low frequency), and the remaining time can be used to support the imaging width (two for high frequency and low frequency).
[0093] According to system requirements, the duty cycle of SAR transceiver timing is high or low, most of which are around 17%, and it has not yet reached 20%. Assuming that the duty cycle is as high as 20%, the four times pulse width will account for 80% of the PRT. Even if half of the remaining 20% is reserved for state switching, there is still 10% of PRT time available to support the realization of dual-frequency imaging width (5% for high and low frequencies respectively). Therefore: as long as the duty cycle of the original SAR is not greater than 20%, dual-frequency time division multiplexing can be achieved.
[0094] Therefore, based on the relationship between the dual-frequency transceiver timing and imaging described above, in the method of the embodiment of the present application, the transceiver timing of the main radar and the auxiliary radar in the SAR system and the corresponding imaging results can be seen in Figures 9a to 10b shown.
[0095] See also Figure 9a , Figure 9b , Fig.10a and Fig.10b , which is also determined by the transmit and receive timing (such as Figure 9a and Fig.10a ) and the imaging area (as shown Figure 9b and Fig.10b The time sequence includes two radars, the main and auxiliary, which are connected in time by the three stages of the first dual-frequency, (main frequency) interferometric height measurement and the last dual-frequency (due to the long time sequence, Figure 9a is divided into two rows in the schematic shown).
[0096] The PRT and transmission signal pulse widths of the three stages are the same and closely connected in time, ensuring that the two-frequency imaging is connected in azimuth, consistent in the near-range edge position, and overlapped in the first and last dual-frequency areas. There are two timing sequences in the three stages. The first dual-frequency and the last dual-frequency are the same timing sequence, and the main frequency interferometric height measurement in the middle is another timing sequence. In the illustration of the imaging area, the final result area is also decomposed into the two frequency regions.
[0097] Among them, for the entire area of interferometric height measurement, the principle process of removing the folding ambiguity problem of 2π integer multiples of the main frequency interference phase difference of height measurement is as follows: the main frequency part completes the imaging of its own area (including single frequency and two dual-frequency areas connected to the single frequency); the first and last auxiliary frequency parts complete their own imaging, and use the dual-frequency method together with the main frequency here to solve the main frequency ambiguity numbers of the two dual-frequency areas; from the first dual frequency upward (or the last dual frequency downward), the connection between the dual frequency and the main frequency in the area is used to solve the ambiguity number to the entire main frequency height measurement area according to the adjacent continuity of the interference phase (the same principle as external source deambiguation).
[0098] Here, it is also necessary to explain that the timing of the main frequency interferometric altimetry between the above three connected stages refers to the working timing of a general interferometric altimetry SAR, that is, the working timing of an interferometric altimetry SAR without the deambiguation capability.
[0099] At the same time, in the explanation of the dual-frequency deblurring principle, as long as the blur of one point in the entire area is resolved, the blur of the entire area can be resolved. That is to say, when the first (or last) dual frequency is used to start deblurring the interference imaging area, the last (or first) dual frequency can be abandoned and can also be used to verify the correctness of the deblurring process.
[0100] In addition, those skilled in the art can understand that in the above description of the dual-frequency deambiguation principle, the dual-frequency is described in the case of the close-range edge, and it can also be described in the case of the long-range edge (such as Fig.10a and Fig.10b The difference is only in the timing, which is mainly in the switching time between the main frequency signal and the auxiliary frequency signal.
[0101] Specifically, the short-range dual-frequency transmits first and then receives on one frequency, and switches to another frequency state after receiving is completed, and then transmits and receives. The long-range dual-frequency receives first and then transmits on one frequency, and switches to another frequency state after transmitting is completed, and then receives and transmits.
[0102] Therefore, when the dual-frequency deambiguation principle is used to solve the absolute phase difference ambiguity number, the setting of the radar receiving and transmitting timing in the SAR system can be set to a close-range dual-frequency mode or a long-range dual-frequency mode. That is, when each radar in the SAR system transmits a signal, the main frequency signal and the auxiliary frequency signal can adopt a close-range dual-frequency mode or a long-range dual-frequency mode, which is not specifically limited here. At the same time, the selection of these two modes can be selected through instructions.
[0103] Furthermore, it should be pointed out that the size requirement of the dual-frequency imaging area can be just one point (correspondingly, only one more pulse needs to be sent and received in the azimuth direction, and only one pulse width needs to be sampled in the range direction), or there can be multiple points. Preferably, the dual-frequency imaging area includes multiple points, so that all points in the dual-frequency imaging area can be statistically processed, which can suppress the influence of some errors and ultimately improve the accuracy of deambiguation more effectively. At the same time, there are some differences in the technical status of the radar working at a single point and multiple points, and the multi-point state is closer to the state of interferometric height measurement.
[0104] It should also be noted that in the method of the embodiment of the present application, the primary radar data includes the primary radar in the SAR system, the primary frequency signal and the secondary frequency signal transmitted by the primary radar, and the interference height measurement signal in the primary frequency signal and the secondary frequency signal. The secondary radar data includes the secondary radar in the SAR system, the primary frequency signal and the secondary frequency signal transmitted by the secondary radar, and the interference height measurement signal in the primary frequency signal and the secondary frequency signal.
[0105] Therefore, based on the principle description of the correspondence between the above-mentioned radar receiving and transmitting timing and the imaging geometry, in the method of the embodiment of the present application, step S300, according to the main radar data and the auxiliary radar data, performs deambiguation calculation according to the dual-frequency deambiguation principle to obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system, which can be achieved in the following way.
[0106] That is, firstly, according to the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, the main frequency signal of the auxiliary radar and the auxiliary frequency signal of the auxiliary radar, the main and auxiliary frequencies of the dual-frequency area in the current imaging area of the SAR system are interfered respectively according to the dual-frequency deambiguation principle to solve the dual-frequency area folding ambiguity number. Then, according to the continuity of the absolute phase difference, the main frequency ambiguity number of the dual-frequency area is deduced based on the obtained dual-frequency area folding ambiguity number, and it is deduced from the dual-frequency area to the interferometric height measurement area to obtain the folding ambiguity number of the interferometric height measurement area.
[0107] Among them, when solving the dual-frequency zone folding fuzzy number, according to the dual-frequency defuzzification principle described above, first, according to the corresponding relationship between the radar transmission and reception timing and the imaging geometry, the corresponding dual-frequency zone imaging area map is obtained from the timing of the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, the main frequency signal of the auxiliary radar, and the auxiliary frequency signal of the auxiliary radar, and then the corresponding folding fuzzy number is obtained based on the obtained dual-frequency zone imaging area map. Here, those skilled in the art can understand that the method of unfolding the fuzzy number (or absolute fuzzy number) based on the obtained dual-frequency zone imaging area map can be implemented by conventional technical means in the field, which will not be repeated here.
[0108] For further information, see Fig.11 As shown in the figure, according to the continuity of the absolute phase difference, the absolute fuzzy number of the main frequency in the dual-frequency zone is calculated based on the folded fuzzy number of the dual-frequency zone, which can be directly calculated according to Fig.11 The method shown is implemented, and no further description is given here. Where: m 主频绝对模糊数 , m 辅频绝对模糊数 They are the absolute fuzzy numbers of the main frequency and auxiliary frequency in the dual-frequency imaging area respectively.
[0109] The unwrapped phase of the main frequency and auxiliary frequency in the dual-frequency area is expressed as follows.
[0110]
[0111]
[0112] Thus, the absolute fuzzy number of the main frequency of the dual-frequency zone based on the folded fuzzy number of the dual-frequency zone is obtained, which is m 主频绝对模糊数 , no further processing is required.
[0113] According to the phase continuity of the absolute phase of the main frequency interference in the dual-frequency zone and the absolute phase of the interference in the imaging zone in the connection area, the folding fuzzy number of the interference height measurement area is obtained by deducing from the dual-frequency zone to the interference height measurement area, which can be specifically achieved in the following way.
[0114] The absolute value of the interference phase of the dual-frequency zone main frequency in the connection area is:
[0115]
[0116] The absolute value of the interference phase of the main frequency of the imaging area in the connection area is:
[0117]
[0118] According to the continuity of the interference phase, the absolute value of the interference phase of the main frequency of the dual-frequency zone in the connection area should be equal to the absolute value of the interference phase of the main frequency of the imaging zone in the connection area, so:
[0119]
[0120] So: N = k 主频模糊数 +m 主频绝对模糊数 , which is the absolute phase difference ambiguity number of the main frequency in the imaging area.
[0121] For further information, see Fig.12 After obtaining the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system in the above manner, the method further includes: obtaining an elevation map of the current remote sensing imaging of the SAR system based on the obtained absolute phase difference ambiguity number and in combination with the principal value phase difference.
[0122] Among them, the main value phase difference can be obtained by interferometric imaging and phase unwrapping. Based on the obtained absolute phase difference fuzzy number, combined with the obtained main value phase difference, the elevation map of the current remote sensing imaging of the SAR system is obtained, which can be obtained by the conversion method of interferometric phase to slant range elevation, specifically, the absolute value of the interferometric phase is divided by 2π and then multiplied by the local fuzzy height. These are all general processing methods in this field and will not be repeated here.
[0123] In addition, according to the foregoing, in the method of executing the embodiment of the present application, it is necessary to first configure the working parameters, operating mode, etc. of each radar in the SAR system accordingly, so that each radar can transmit a main frequency signal and an auxiliary frequency signal, and it can also ensure that the timing of the main frequency signal and the auxiliary frequency signal transmitted by each radar can meet the timing requirements in the above-mentioned dual-frequency deambiguation principle.
[0124] Therefore, see Fig.12 In the method of the embodiment of the present application, firstly, step S001 is required to configure the working mode and operating parameters of the radar in the SAR system accordingly by using the instruction injection method. That is, when the SAR system is specified to work in the deambiguation altimetry mode, on the basis of the radar working parameters of the altimetry imaging, the close-range dual-frequency or long-range dual-frequency is selected, and the radar working parameters (area size, etc.) of the front and rear dual-frequency are generated, and the selected radar working parameters and the altimetry imaging working parameters are injected into the SAR system along with the instruction.
[0125] Then, through step S110, the SAR system is turned on at the time required by the instruction, and each radar runs according to the timing in the above instruction, completes the three-stage transmission of the radio frequency signal and the echo recording, and sends the received echo data to the data transmission module. The data transmission module then transmits the echo data to the ground through the downlink link. Here, it can be understood by those skilled in the art that the data transmission module can use a timed transmission method or a real-time transmission method when transmitting the echo data, which is not specifically limited here. After the echo data is transmitted to the ground through the above steps, the echo data can be received and stored to obtain the echo data.
[0126] Then, through step S200, the ground processor obtains the echo data, pre-processes the echo data, and decomposes the main radar and auxiliary radar in the SAR system, the main frequency signal and auxiliary frequency signal emitted by the main radar, the main frequency signal and auxiliary frequency signal emitted by the auxiliary radar, and the interference height measurement data of each main frequency signal and auxiliary frequency signal from the echo data.
[0127] Next, through step S310, the dual-frequency area is folded and fuzzy solved according to the decomposed main frequency signal and auxiliary frequency signal of the main radar, and the main frequency signal and auxiliary frequency signal of the auxiliary radar, to obtain the absolute phase difference fuzzy number of the dual-frequency area. Then, through step S320, according to the absolute phase difference fuzzy number of the dual-frequency area obtained by the previous solution, according to the continuity of the absolute phase difference, and in combination with the main frequency signal of the main radar and the main frequency signal of the auxiliary radar obtained by the decomposition, the folded fuzzy is solved for the interferometric height measurement area to obtain the absolute phase difference fuzzy number (i.e., folded fuzzy number) of the interferometric height measurement area.
[0128] The folding ambiguity number of the dual-frequency zone obtained in this way plus the folding ambiguity number of the interferometric height measurement zone is the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system. After the folding ambiguity number of the dual-frequency zone and the folding ambiguity number of the interferometric height measurement zone are recorded as the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system through step S330, the deambiguation process is completed.
[0129] After obtaining the absolute phase difference fuzzy number of the current remote sensing imaging of the SAR system through the above steps, step S410 is also included to generate a corresponding elevation map based on the obtained absolute phase difference fuzzy number. Then, map surveying and mapping of the monitoring area are performed based on the generated elevation map. Here, those skilled in the art can understand that the generation of the corresponding elevation map based on the obtained absolute phase difference fuzzy number can be achieved by conventional technical means in the field, which will not be repeated here. When the fuzzy number obtained by the embodiment of the present application is used to generate an elevation map, the obtained elevation map can more accurately reflect the terrain in the surveying area, thereby providing more accurate data for subsequent surveying and mapping.
[0130] At the same time, it should be noted that, see Fig.12 In the method of the embodiment of the present application, after obtaining the elevation map in step S410, the obtained elevation map can also be processed accordingly, such as correction, alignment and splicing, and then the final elevation map is output through step S420.
[0131] Among them, see Fig.13a and Fig.13b , respectively, are the primary-frequency SAR image and the auxiliary-frequency SAR image collected by the SAR system when using the method of the embodiment of the present application. Fig.14a and Fig.14b are the main frequency interference phase and auxiliary frequency interference phase corresponding to each image respectively.
[0132] By using the method of the embodiment of the present application, the corresponding imaging geometry when the absolute phase difference ambiguity number is solved for the above-mentioned main frequency SAR image and auxiliary frequency SAR image is as follows: Fig.15 As shown in the figure, the fuzzy number statistics finally solved is 2. Then, according to the obtained fuzzy number, the corresponding digital surface model (Digital Surface Model, referred to as DSM) is generated. The generated digital surface model is superimposed on the Tandem product (such as Fig.16 As shown), the elevation values are basically consistent, which proves the accuracy of the fuzzy number obtained in the method of the embodiment of the present application.
[0133] Correspondingly, based on any of the above-mentioned methods for implementing dual-frequency interferometry SAR to resolve absolute phase difference ambiguity, the present application also provides a device for implementing dual-frequency interferometry SAR to resolve absolute phase difference ambiguity. Since the working principle of the device for implementing dual-frequency interferometry SAR to resolve absolute phase difference ambiguity provided in the present application is the same or similar to the principle of the method for implementing dual-frequency interferometry SAR to resolve absolute phase difference ambiguity in the present application, the repeated parts will not be repeated.
[0134] See also Fig.17 The device 100 for realizing dual-frequency interferometric SAR absolute phase difference ambiguity resolution provided in the present application includes a data acquisition module 110, a data processing module 120 and a data calculation module 130. The data acquisition module 110 is configured to acquire echo data sent by the SAR system; wherein the echo data is generated when the radar in the SAR system transmits a main frequency signal and an auxiliary frequency signal. The data processing module 120 is configured to pre-process the echo data, and decompose the main radar data and the auxiliary radar data in the SAR system from the echo data. The data calculation module 130 is configured to perform deambiguation calculation according to the dual-frequency deambiguation principle based on the main radar data and the auxiliary radar data, and obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system.
[0135] In a possible implementation, the primary radar data includes the primary radar, the primary frequency signal of the primary radar, the secondary frequency signal of the primary radar, and the interference height measurement signal of the primary radar. The secondary radar data includes the secondary radar, the primary frequency signal of the secondary radar, the secondary frequency signal of the secondary radar, and the interference height measurement signal of the secondary radar.
[0136] Correspondingly, the data calculation module 130 includes a first calculation module and a second calculation module (not shown in the figure). The first calculation module is configured to interfere with the main and auxiliary frequencies of the dual-frequency area in the current imaging area of the SAR system according to the dual-frequency deambiguation principle according to the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, the main frequency signal of the auxiliary radar and the auxiliary frequency signal of the auxiliary radar, and solve the dual-frequency area folding fuzzy number; The second calculation module is configured to deduce the main frequency fuzzy number of the dual-frequency area based on the obtained dual-frequency area folding fuzzy number according to the continuity of the absolute phase difference, and deduce from the dual-frequency area to the interferometric height measurement area to obtain the folding fuzzy number of the interferometric height measurement area.
[0137] Furthermore, according to another aspect of the present application, a device 200 for resolving absolute phase difference ambiguity using dual-frequency interferometric SAR is provided. Fig.18 The device 200 for implementing dual-frequency interferometry SAR to resolve absolute phase difference ambiguity in the embodiment of the present application includes a processor 210 and a memory 220 for storing executable instructions of the processor 210. The processor 210 is configured to implement any of the above-mentioned methods for implementing dual-frequency interferometry SAR to resolve absolute phase difference ambiguity when executing the executable instructions.
[0138] Here, it should be noted that the number of processors 210 may be one or more. Meanwhile, in the device 200 for implementing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity in the embodiment of the present application, an input device 230 and an output device 240 may also be included. Among them, the processor 210, the memory 220, the input device 230 and the output device 240 may be connected via a bus or in other ways, which are not specifically limited here.
[0139] The memory 220, as a computer-readable storage medium, can be used to store software programs, computer executable programs, and various modules, such as: programs or modules corresponding to the method for implementing the dual-frequency interferometric SAR absolute phase difference ambiguity resolution in the embodiment of the present application. The processor 210 executes various functional applications and data processing of the device 200 for implementing the dual-frequency interferometric SAR absolute phase difference ambiguity resolution by running the software programs or modules stored in the memory 220.
[0140] The input device 230 may be used to receive input numbers or signals. The signals may be key signals related to user settings and function control of the device / terminal / server. The output device 240 may include display devices such as display screens.
[0141] According to another aspect of the present application, a non-volatile computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by the processor 210, any of the above-mentioned methods for realizing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity is implemented.
[0142] The embodiments of the present application have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or improvements to the technology in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.
Claims
1. A method for resolving absolute phase difference ambiguity in dual-frequency interferometric SAR, characterized in that: include: Acquire echo data sent by the SAR system; wherein the echo data is generated by transmitting a main frequency signal and an auxiliary frequency signal by a radar in the SAR system; Preprocessing the echo data, and decomposing the primary radar data and the auxiliary radar data in the SAR system from the echo data; According to the primary radar data and the secondary radar data, deambiguation calculation is performed according to the dual-frequency deambiguation principle to obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system; Among them, according to the main radar data and the auxiliary radar data, deambiguation calculation is performed according to the dual-frequency deambiguation principle to obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system, including: According to the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, the main frequency signal of the auxiliary radar and the auxiliary frequency signal of the auxiliary radar, the main and auxiliary frequencies of the dual-frequency area in the current imaging area of the SAR system are interfered respectively according to the dual-frequency deambiguation principle to solve the dual-frequency area folding ambiguity number; According to the continuity of the absolute phase difference, the main frequency fuzzy number of the dual-frequency zone is deduced based on the obtained dual-frequency zone folding fuzzy number, and the folding fuzzy number of the dual-frequency zone is deduced from the dual-frequency zone to the interferometric height measurement area to obtain the folding fuzzy number of the interferometric height measurement area; After obtaining the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system, the method further includes: Based on the obtained absolute phase difference fuzzy number and in combination with the principal value phase difference, an elevation map of the current remote sensing imaging of the SAR system is obtained.
2. The method according to claim 1, characterized in that The radar transmitting main frequency signal and auxiliary frequency signal in the SAR system are generated by mixing the original imaging frequency.
3. The method according to claim 1, characterized in that When decomposing the primary radar data and the auxiliary radar data in the SAR system from the echo data, the decomposition is performed according to a preset rule.
4. The method according to any one of claims 1 to 3, characterized in that: The main radar data includes the main radar, the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, and the interference height measurement signal of the main radar; The auxiliary radar data includes an auxiliary radar, a primary frequency signal of the auxiliary radar, an auxiliary frequency signal of the auxiliary radar, and an interference height measurement signal of the auxiliary radar.
5. A device for realizing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity, characterized in that: It includes a data acquisition module, a data processing module and a data calculation module; The data acquisition module is configured to acquire echo data sent by the SAR system; wherein the echo data is generated when the radar in the SAR system transmits a main frequency signal and an auxiliary frequency signal; The data processing module is configured to pre-process the echo data and decompose the primary radar data and the auxiliary radar data in the SAR system from the echo data; The data calculation module is configured to perform deambiguation calculation according to the main radar data and the auxiliary radar data according to the dual-frequency deambiguation principle to obtain the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system; The main radar data includes the main radar, the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, and the interference height measurement signal of the main radar; The auxiliary radar data includes the auxiliary radar, the main frequency signal of the auxiliary radar, the auxiliary frequency signal of the auxiliary radar, and the interference height measurement signal of the auxiliary radar; The data calculation module includes a first calculation module and a second calculation module; The first calculation module is configured to interfere with the main and auxiliary frequencies of the dual-frequency area in the current imaging area of the SAR system according to the main frequency signal of the main radar, the auxiliary frequency signal of the main radar, the main frequency signal of the auxiliary radar and the auxiliary frequency signal of the auxiliary radar, and solve the dual-frequency area folding ambiguity number according to the dual-frequency deambiguation principle; The second calculation module is configured to calculate the main frequency fuzzy number of the dual-frequency zone based on the obtained dual-frequency zone folding fuzzy number according to the continuity of the absolute phase difference, and deduce from the dual-frequency zone to the interferometric height measurement area to obtain the folding fuzzy number of the interferometric height measurement area; After obtaining the absolute phase difference ambiguity number of the current remote sensing imaging of the SAR system, the method further includes: Based on the obtained absolute phase difference fuzzy number and in combination with the principal value phase difference, an elevation map of the current remote sensing imaging of the SAR system is obtained.
6. A device for realizing dual-frequency interferometric SAR to resolve absolute phase difference ambiguity, characterized in that: include: processor; a memory for storing processor-executable instructions; Wherein, the processor is configured to implement the method described in any one of claims 1 to 4 when executing the executable instructions.
7. A non-volatile computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 4 is implemented.
Citation Information
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