Low-frequency data ionospheric amplitude flicker monitoring method and device
By combining 1Hz low-frequency GNSS data with MW and GF algorithms, the high cost and low accuracy problems of ionospheric amplitude scintillation monitoring have been solved, realizing low-cost and high-precision ionospheric amplitude scintillation monitoring, reducing hardware costs and improving the accuracy of cycle slip detection.
Patent Information
- Application Number
- CN202610003519.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-05
- Publication Date
- 2026-02-03
AI Technical Summary
In existing technologies, ionospheric amplitude scintillation monitoring suffers from high hardware costs, insufficient cycle slip detection accuracy, and a lack of adaptability in static thresholds, resulting in high monitoring difficulty and low accuracy.
Using 1Hz low-frequency GNSS data, cycle slip detection is performed by combining the MW linear combination method and the GF ionospheric residual method. The scintillation index S4 is calculated by the signal-to-noise ratio-carrier-to-noise ratio conversion model and the sliding window algorithm, thus achieving low-cost and high-precision ionospheric amplitude scintillation monitoring.
It achieves low-cost, low-frequency data ionospheric amplitude scintillation monitoring, reducing hardware costs to 1/10 of traditional solutions, monitoring accuracy comparable to high-frequency data, reducing cycle slip false detection rate to below 5%, and false judgment rate to 40%.
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Figure CN121454557A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of GNSS satellite ionospheric technology, specifically relating to a method and device for monitoring low-frequency data ionospheric amplitude scintillation. Background Technology
[0002] Ionospheric amplitude scintillation index monitoring is a crucial research area in the Global Navigation Satellite System (GNSS) field because ionospheric amplitude scintillation is a phenomenon caused by the uneven density of free electrons in the ionosphere, which can severely impact GNSS performance. Since communication, navigation, positioning, and many other systems rely on GNSS, the monitoring and early warning of ionospheric amplitude scintillation is of paramount importance. The radio wave propagation process required for ionospheric amplitude scintillation monitoring is complex, thus effective and accurate data acquisition and processing always present challenges.
[0003] Typically, a professional receiver with a 50Hz sampling rate is used to acquire the raw intermediate frequency signal. Digital down-conversion is then used to obtain the in-phase component I and the quadrature component Q, and the S4 exponent is calculated using a sliding window variance. While this achieves an S4 exponent resolution on the order of 0.1, it suffers from two major technical bottlenecks: firstly, the receiver hardware cost is high; secondly, real-time processing of high-frequency data is difficult. Furthermore, existing technologies have the following problems:
[0004] 1. Insufficient accuracy in cycle slip detection: Existing cycle slip detection algorithms (such as single MW linear combination or GF ionospheric residual method) have the risk of missing detections. For example, the MW combination is sensitive to small cycle slips but has a high rate of missing detection for large cycle slips, while the GF method is sensitive to large cycle slips but cannot effectively detect small cycle slips.
[0005] 2. Static threshold lacks adaptability: In the existing scintillation threshold determination, a threshold of 0.4 is set to be considered scintillation. However, the intensity of ionospheric scintillation and the background noise level are dynamically affected by geographical location, time (day and night / season) and space weather activities (such as solar flares and geomagnetic storms). Summary of the Invention
[0006] To address the aforementioned technical problems, this invention proposes a method and device for monitoring ionospheric amplitude scintillation using low-frequency data. By leveraging the amplitude fluctuation characteristics implicit in the 1Hz signal-to-noise ratio (SNR) data output from a GNSS board, which possess equivalent information content to high-frequency I / Q data, a signal-to-noise ratio to carrier-to-noise ratio (SNR-CA) conversion model is established. Combined with an improved sliding window standard deviation algorithm, this method achieves, for the first time, accurate calculation of the S4 exponent based on 1Hz low-frequency data. Comparative testing shows that this solution reduces monitoring costs to less than 5% of traditional methods while maintaining comparable monitoring accuracy (error <0.05), thus solving the problem of low-cost, low-frequency ionospheric amplitude scintillation monitoring.
[0007] The specific technical solution is as follows:
[0008] A method for monitoring low-frequency data ionospheric amplitude scintillation includes the following steps:
[0009] Step 1: Collect low-frequency satellite data. By decoding the low-frequency satellite data, obtain satellite observation data and satellite navigation information.
[0010] Step 2: Perform satellite observation data preprocessing. Use a combination algorithm of MW linear combination method and GF ionospheric residual method to detect cycle slips and remove satellite observation data that have cycle slips to obtain processed satellite observation data.
[0011] Step 3: Calculate the satellite orbit based on the satellite navigation information, obtain the satellite time and position, calculate the satellite's elevation angle and azimuth angle, and discard satellite observation data with an elevation angle less than 10°;
[0012] Step 4: Obtain the carrier-to-noise ratio (CNR) from satellite observation data that has no cycle slips and an elevation angle greater than 10° after filtering in Steps 2 and 3. Calculate the CNR based on the CNR and CNR conversion formulas. Then, calculate the scintillation index S4 using a sliding window method and a formula constructed based on the amplitude scintillation index.
[0013] Step 5: Perform binary classification voting decision based on the scintillation index S4. Calculate the scintillation index S4 for each frequency point of each satellite. When the scintillation index S4 exceeds the threshold, mark it as ionospheric scintillation. Then, vote for all satellites and all frequencies. If the percentage exceeds a certain proportion, ionospheric scintillation is detected and an early warning is issued.
[0014] A low-frequency data ionospheric amplitude scintillation monitoring device includes the following modules:
[0015] The satellite observation data and satellite navigation information acquisition module is used to collect low-frequency satellite data and obtain satellite observation data and satellite navigation information by decoding the low-frequency satellite data;
[0016] The satellite observation data processing module performs satellite observation data preprocessing. It uses a combination algorithm of MW linear combination method and GF ionospheric residual method to detect cycle slips and remove satellite observation data that have cycle slips, thus obtaining processed satellite observation data.
[0017] The satellite observation data elimination module calculates the satellite orbit, obtains the satellite time and position based on the satellite navigation information, calculates the satellite's elevation angle and azimuth angle, and eliminates satellite observation data with an elevation angle less than 10°.
[0018] The Scintillation Index S4 calculation module obtains the carrier-to-noise ratio from satellite observation data without cycle slips and with an elevation angle greater than 10°. Based on the carrier-to-noise ratio and signal-to-noise ratio conversion formula, it calculates the signal-to-noise ratio. Then, using a sliding window approach, it constructs a formula based on the amplitude scintillation index to calculate the scintillation index S4.
[0019] The early warning module uses a binary classification voting decision based on the scintillation index S4. It calculates the scintillation index S4 for each frequency point of each satellite. When the scintillation index S4 exceeds the threshold, it marks it as ionospheric scintillation. Then, it votes on all satellites and all frequency points. If the voting exceeds a certain proportion, ionospheric scintillation is detected and an early warning is issued.
[0020] An electronic device includes: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method.
[0021] A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described thereon.
[0022] The present invention has the following beneficial effects:
[0023] Low cost and wide coverage: By using 1Hz low-frequency GNSS data to replace the high-frequency receiver (50Hz), the hardware cost is reduced to 1 / 10 of the traditional solution, enabling large-scale deployment. Through low-frequency carrier-to-noise ratio and signal-to-noise ratio conversion algorithms, the ionospheric characteristics of 1Hz data are fully extracted, and the monitoring accuracy is comparable to that of high-frequency data.
[0024] High-precision cycle slip detection: By integrating the MW linear combination method and the GF ionospheric residual method, the cycle slip false detection rate is reduced from 15% of the traditional single algorithm to below 5%.
[0025] Adaptive decision-making mechanism: Based on the environmental noise baseline, the S4 judgment threshold is adaptively adjusted, reducing the misjudgment rate by 40% compared to the fixed threshold method. Attached Figure Description
[0026] Figure 1 This is a flowchart of the present invention. Detailed Implementation
[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.
[0028] This invention provides a method and device for monitoring low-frequency ionospheric amplitude scintillation. It employs a GNSS antenna to transmit 1Hz raw data, decodes the data using an ionospheric amplitude scintillation index monitoring algorithm to obtain satellite observation and navigation data, preprocesses the data, and uses a combination of the MW linear combination method and the GF ionospheric residual method for cycle slip detection. Then, it calculates the satellite elevation and azimuth angles using station and satellite information. After acquiring the processed data, it calculates the amplitude scintillation index S4 using carrier-to-noise ratio and signal-to-noise ratio conversion formulas in a sliding window format. Finally, it uses a binary classification voting algorithm to classify and vote on the monitoring results to determine whether scintillation has occurred and provides a scintillation warning.
[0029] like Figure 1 As shown, the low-frequency data ionospheric amplitude scintillation monitoring method of the present invention specifically includes the following steps:
[0030] Step 1: Connect the GNSS antenna to the low-frequency data ionospheric amplitude scintillation monitoring terminal to collect 1Hz low-frequency satellite data. By decoding the 1Hz low-frequency satellite data, obtain the satellite observation data and satellite navigation information.
[0031] Step 2: Preprocess the observation data by using a combination algorithm of the MW linear combination method and the GF ionospheric residual method to detect cycle slips and remove satellite data that have cycle slips in that time period, thus obtaining the processed satellite data.
[0032] Step 3: Calculate the satellite orbit based on the satellite navigation information, obtain the satellite time and position, calculate the satellite's elevation angle and azimuth angle, and discard satellite observation data with an elevation angle less than 10°;
[0033] Step 4: Obtain the carrier-to-noise ratio C / N0 from the satellite observation data that has no cycle slip and an elevation angle greater than 10° after filtering in Steps 2 and 3. Calculate the signal-to-noise ratio (SNR) based on the carrier-to-noise ratio and SNR conversion formulas. Then, calculate the scintillation index S4 using a sliding window method and a formula constructed based on the amplitude scintillation index.
[0034] Step 5: Perform a binary classification voting decision based on the scintillation index S4. Calculate the scintillation index S4 for each frequency point of each satellite. When the scintillation index S4 exceeds a threshold (e.g., 0.4), mark it as having ionospheric scintillation. Then, aggregate all satellites and all frequency points for voting. If the threshold is exceeded by a certain percentage (e.g., 50%), ionospheric scintillation is detected, and an early warning is issued.
[0035] The combined algorithm of the MW linear combination method and the GF ionospheric residual method in step 2 includes: In the data preprocessing of ionospheric amplitude scintillation monitoring, the MW linear combination method and the GF ionospheric residual method adopt a complementary fusion strategy to achieve efficient detection and repair of various cycle slips. The specific calculation process is as follows:
[0036] The MW linear combination method utilizes the unambiguous characteristic of code phase measurement to detect significant cycle slips exceeding one cycle. The formula for the MW linear combination method is as follows:
[0037] (1)
[0038] In the above formula, The combined carrier phase values after MW combination. and The phase values at frequencies L1 and L2 are... and For the frequencies of L1 and L2, and The wavelengths of L1 and L2 are... and For pseudorange observations at frequencies L1 and L2.
[0039] The formula for the GF ionospheric residual method is as follows:
[0040] (2)
[0041] The GF ionospheric residual method identifies small cycle slips of less than one cycle through statistical tests.
[0042] Combine the two algorithms using the following steps:
[0043] Coarse processing of MW linear combination (extraction and correction of two-frequency differential cycle slip):
[0044] In the calendar Let the cycle slip increments at frequencies L1 and L2 be denoted as . , (Unit: week, integer). Break it down into:
[0045] , (3)
[0046] These are common cycle slip components, i.e., integer cycle slips (unit: cycle, integer) that occur simultaneously with L1 and L2 and are of the same magnitude. Differential cycle slip component (inter-frequency / wide-lane) reflects the part of the cycle slip that is inconsistent between two frequency points (unit: cycle, integer).
[0047] The cycle slip difference obtained by the MW linear combination method is:
[0048] (4)
[0049] This yields the estimated value of the differential cycle slip. Equalization repair is performed on both frequencies:
[0050] , (5)
[0051] Ideally there is That is, the frequency jump difference between the two frequencies after MW combination approaches zero, and only the common frequency jump component is retained.
[0052] Fine-grained detection using the GF ionospheric residual method (identifying and repairing minute common cycle slips):
[0053] On the MW-equalized data, GF residuals are constructed and statistical tests are performed to identify any potentially residual small common cycle slips. The estimated value of the common cycle slips is denoted as... Then, after repair, the cycle slip at the two frequency points satisfies:
[0054] , (6)
[0055] Equivalently, the original two-frequency cycle jumps can be expressed using the final estimate as:
[0056] , (7)
[0057] in, Estimates from MW portfolio Fine probing of residuals from GF.
[0058] A closed-loop iterative process of "MW equalization - GF fine-tuning - statistical testing" is adopted: the iteration terminates when the test statistic of the GF residual is lower than the preset threshold (chi-square threshold) and is satisfied for several consecutive epochs; the repaired continuous phase observations and cycle slip markers are output. If the test fails, the system is updated. , Then continue iterating until the termination condition is met.
[0059] The calculation method for the flicker index S4 in step 4 includes:
[0060] Carrier-to-noise ratio The signal-to-noise ratio is obtained from low-frequency observation data and calculated using the following formula:
[0061] (8)
[0062] In the above formula For signal-to-noise ratio, This represents the carrier-to-noise ratio.
[0063] Based on the obtained signal-to-noise ratio, the signal strength is... Detrending, sliding calculation of the signal strength after detrending for:
[0064] (9)
[0065] In the above formula, Epoch (time index, 1 second per step at 1 Hz sampling);
[0066] : Sliding window length (used for detrending / mean statistics), unit: epoch (seconds);
[0067] Carrier-to-noise ratio (dB-Hz) is determined by the receiver at epochs. Output;
[0068] Carrier-to-noise ratio The reciprocal of the product is summed over a window from epoch k-1 to kn.
[0069] Based on the signal strength after detrending The scintillation index S4 is calculated according to formula 10:
[0070] (10)
[0071] Step 5, which involves binary classification voting decision based on the flicker index S4 value, includes:
[0072] First, each frequency point can be considered an independent decision-making unit, based on its corresponding flicker index. The index determines whether flickering occurs (i.e., If the value is greater than 0.4, the result is "Yes"; otherwise, it is "No". This provides frequency-level decision data for ionospheric scintillation for each satellite.
[0073] A voting decision is made for each satellite, that is, the proportion of "Yes" in the decision results for all its frequencies is counted. If the proportion of "Yes" exceeds a predetermined threshold (e.g., 50%), the satellite is considered to be in an ionospheric scintillation state;
[0074] Finally, a vote is held among all satellites to determine the proportion of satellites classified as ionospheric scintillation. If the proportion of ionospheric scintillation satellites exceeds a predetermined threshold (e.g., 60%), then the ionosphere is ultimately classified as scintillation.
[0075] In this process, based on voting principles, numerous frequency point decisions are processed at the satellite and system levels to arrive at the final decision. This mechanism is fault-tolerant and robust, thus improving the accuracy and quality of decision-making. It also makes full use of all available decision-making information, avoiding information waste.
[0076] Another aspect of the present invention provides a low-frequency data ionospheric amplitude scintillation monitoring device, comprising the following modules:
[0077] The satellite observation data and satellite navigation information acquisition module is used to collect low-frequency satellite data and obtain satellite observation data and satellite navigation information by decoding the low-frequency satellite data;
[0078] The satellite observation data processing module performs satellite observation data preprocessing. It uses a combination algorithm of MW linear combination method and GF ionospheric residual method to detect cycle slips and remove satellite observation data that have cycle slips, thus obtaining processed satellite observation data.
[0079] The satellite observation data elimination module calculates the satellite orbit, obtains the satellite time and position based on the satellite navigation information, calculates the satellite's elevation angle and azimuth angle, and eliminates satellite observation data with an elevation angle less than 10°.
[0080] The Scintillation Index S4 calculation module obtains the carrier-to-noise ratio from satellite observation data without cycle slips and with an elevation angle greater than 10°. Based on the carrier-to-noise ratio and signal-to-noise ratio conversion formula, it calculates the signal-to-noise ratio. Then, using a sliding window approach, it constructs a formula based on the amplitude scintillation index to calculate the scintillation index S4.
[0081] The early warning module uses a binary classification voting decision based on the scintillation index S4. It calculates the scintillation index S4 for each frequency point of each satellite. When the scintillation index S4 exceeds the threshold, it marks it as ionospheric scintillation. Then, it votes on all satellites and all frequency points. If the voting exceeds a certain proportion, ionospheric scintillation is detected and an early warning is issued.
[0082] Another aspect of the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method.
[0083] Another aspect of the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described thereon.
Claims
1. A method for monitoring low-frequency data ionospheric amplitude scintillation, characterized in that, Includes the following steps: Step 1: Collect low-frequency satellite data. By decoding the low-frequency satellite data, obtain satellite observation data and satellite navigation information. Step 2: Perform satellite observation data preprocessing. Use a combination algorithm of MW linear combination method and GF ionospheric residual method to detect cycle slips and remove satellite observation data that have cycle slips to obtain processed satellite observation data. Step 3: Calculate the satellite orbit based on the satellite navigation information, obtain the satellite time and position, calculate the satellite's elevation angle and azimuth angle, and discard satellite observation data with an elevation angle less than 10°; Step 4: Obtain the carrier-to-noise ratio (CNR) from satellite observation data that has no cycle slips and an elevation angle greater than 10° after filtering in Steps 2 and 3. Calculate the CNR based on the CNR and CNR conversion formulas. Then, calculate the scintillation index S4 using a sliding window method and a formula constructed based on the amplitude scintillation index. Step 5: Perform binary classification voting decision based on the scintillation index S4. Calculate the scintillation index S4 for each frequency point of each satellite. When the scintillation index S4 exceeds the threshold, mark it as ionospheric scintillation. Then, vote for all satellites and all frequencies. If the percentage exceeds a certain proportion, ionospheric scintillation is detected and an early warning is issued.
2. The method for monitoring low-frequency data ionospheric amplitude scintillation according to claim 1, characterized in that, The specific calculation process of the MW linear combination method in step 2 is as follows: The MW linear combination method is used to detect significant cycle slips greater than one cycle. The formula for the MW linear combination method is as follows: (1) In the above formula, The combined carrier phase values after MW combination. and The phase values at frequencies L1 and L2 are... and The frequencies of L1 and L2 are... and The wavelengths of frequencies L1 and L2 are... and For pseudorange observations at frequencies L1 and L2.
3. The method for monitoring low-frequency data ionospheric amplitude scintillation according to claim 2, characterized in that, The formula for the GF ionospheric residual method in step 2 is as follows: (2) In the above formula, The carrier phase combination value after GF combination. and The phase values at frequencies L1 and L2 are... and The wavelengths of L1 and L2 frequencies are used; the GF ionospheric residual method identifies microcycle slips of less than one cycle through statistical tests.
4. The method for monitoring low-frequency data ionospheric amplitude scintillation according to claim 3, characterized in that, The MW linear combination method and the GF ionospheric residual method are combined according to the following steps: The MW linear combination method is used for coarse processing to extract and correct the two-frequency differential cycle slips. In the calendar Let the cycle slip increments at frequencies L1 and L2 be denoted as . , Decompose it into and : , (3) These are common cycle slip components, meaning integer cycle slips that occur simultaneously in L1 and L2 and are of the same magnitude. Differential cycle slip components; The cycle slip difference obtained by the MW linear combination method is: (4) This yields the estimated value of the differential cycle slip. Equalization repair is performed on both frequencies: , (5) Ideally there is That is, the cycle slip difference between the two frequencies after MW combination approaches zero, and only the common cycle slip component is retained; GF ionospheric residual method detection, identification and repair of small common cycle slips: On the data equalized by MW, GF residuals are constructed and statistical tests are performed to identify any small common cycle slips that may remain. The estimated value of the common cycle slips is denoted as... Then, after repair, the cycle slip increments at the two frequency points satisfy: , (6) The original two-frequency cycle slips are expressed using the final estimate as follows: , (7) in, Estimates from MW portfolio Detected by GF ionospheric residual method; The iteration terminates when the test statistic of the GF ionospheric residual method is lower than the preset threshold and is satisfied for several consecutive epochs. Output the repaired continuous phase observations and cycle slip markers. If the check fails, update... , Then continue iterating until the termination condition is met.
5. The method for monitoring low-frequency data ionospheric amplitude scintillation according to claim 1, characterized in that, The calculation method for the flicker index S4 in step 4 includes: Carrier-to-noise ratio The signal-to-noise ratio is obtained from low-frequency observation data and calculated using the following formula: (8) In the above formula For signal-to-noise ratio, Carrier-to-noise ratio; Based on the obtained signal-to-noise ratio, the signal strength is... Detrending, sliding calculation of the signal strength after detrending for: (9) In the above formula Indicates the epoch; The length of the sliding window; The carrier-to-noise ratio is determined by the receiver at the epoch. Output; Carrier-to-noise ratio The reciprocal of the product is summed over a window from epoch k-1 to kn; Based on the signal strength after detrending The scintillation index S4 is calculated according to formula (10): (10)。 6. The method for monitoring low-frequency data ionospheric amplitude scintillation according to claim 5, characterized in that, Step 5, which involves binary classification voting decision based on the flicker index S4 value, includes: First, each frequency point is considered an independent decision-making unit, based on its corresponding flicker index. The index determines whether flickering has occurred. If a predetermined threshold is set, the result is "Yes"; otherwise, it is "No". In this way, frequency-level decision data on ionospheric scintillation for each satellite is obtained. A voting decision is made for each satellite, that is, the proportion of "Yes" in the decision results of all its frequency points is counted. If the proportion of "Yes" exceeds a predetermined threshold, the satellite is considered to be in an ionospheric scintillation state. A voting decision is made among all satellites, and the proportion of satellites judged to be in an ionospheric scintillation state is counted. If the proportion of satellites in an ionospheric scintillation state exceeds a predetermined threshold, then the ionosphere is finally judged to be in a scintillation state.
7. A method for monitoring low-frequency data ionospheric amplitude scintillation according to claim 6, characterized in that, The predetermined threshold is set to 0.
4.
8. A low-frequency data ionospheric amplitude scintillation monitoring device, characterized in that, Includes the following modules: The satellite observation data and satellite navigation information acquisition module is used to collect low-frequency satellite data and obtain satellite observation data and satellite navigation information by decoding the low-frequency satellite data; The satellite observation data processing module performs satellite observation data preprocessing. It uses a combination algorithm of MW linear combination method and GF ionospheric residual method to detect cycle slips and remove satellite observation data that have cycle slips, thus obtaining processed satellite observation data. The satellite observation data elimination module calculates the satellite orbit, obtains the satellite time and position based on the satellite navigation information, calculates the satellite's elevation angle and azimuth angle, and eliminates satellite observation data with an elevation angle less than 10°. The Scintillation Index S4 calculation module obtains the carrier-to-noise ratio from satellite observation data without cycle slips and with an elevation angle greater than 10°. Based on the carrier-to-noise ratio and signal-to-noise ratio conversion formula, it calculates the signal-to-noise ratio. Then, using a sliding window approach, it constructs a formula based on the amplitude scintillation index to calculate the scintillation index S4. The early warning module uses a binary classification voting decision based on the scintillation index S4. It calculates the scintillation index S4 for each frequency point of each satellite. When the scintillation index S4 exceeds the threshold, it marks it as ionospheric scintillation. Then, it votes on all satellites and all frequency points. If the voting exceeds a certain proportion, ionospheric scintillation is detected and an early warning is issued.
9. An electronic device, characterized in that, include: One or more processors; A memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to perform the method described in any one of claims 1 to 7.
Citation Information
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