An underwater direction-finding system and method based on ultra-short baseline underwater acoustic positioning double beacons

Abstract

The application provides an underwater direction finding system and method based on an ultra-short baseline underwater acoustic positioning double-beacon, and belongs to the technical field of underwater navigation. The system takes the double-antenna direction finding in the satellite navigation technical field as a principle, deploys double-beacons on an underwater navigation carrier, and uses the double-beacons of the USBL system to work cooperatively. The USBL array is used as a coordinate origin, two groups of slant range values and phase differences and time delay differences of signals arriving at each element of the array are measured, the relative position between the array and the target can be calculated through the phase differences of each element, the specific position of the double-beacons relative to the array can be calculated by combining the slant range, the baseline vector between the double-beacons can be obtained, and the direction angle of the underwater navigation carrier in the navigation coordinate system with the north as a reference can be obtained, so that the heading information of the underwater carrier can be measured.

Description

Technical Field

[0001] This invention belongs to the field of underwater navigation technology, specifically, it relates to an underwater direction finding system and method based on ultra-short baseline underwater acoustic positioning dual beacons. Background Technology

[0002] All kinds of maritime activities and underwater military operations rely on underwater vehicles capable of operating stably in the ocean. In the ever-changing marine environment, accurate heading information is a prerequisite for the successful completion of tasks performed by underwater vehicles.

[0003] There are many traditional methods for underwater orientation finding, such as using a strapdown inertial navigation system (SINS) to calculate the vehicle's heading information in real time. However, the most obvious drawback of inertial navigation systems is that navigation errors accumulate over time, making it impossible to provide accurate heading information over a long period of time. It needs to be combined with other navigation systems, which increases the cost of orientation finding and is not economical. Since the Earth's magnetic field is ubiquitous, underwater direction finding can also be performed using a magnetic compass. This method is independent of terrain and can be used in turbid waters or areas with complex underwater topography. However, it is susceptible to the instability of the Earth's magnetic field and interference from external magnetic fields, requiring magnetic field calibration. Moreover, in high-latitude regions, the magnetic field direction changes significantly, causing a decrease in the accuracy of heading measurements. RTK (Real-Time Kinematic) GNSS dual-antenna direction finding has very high accuracy; currently, the common dual-antenna measurement error is approximately 0.2° / m, where L is the baseline length. Its direction finding principle is as follows: two antennas are installed on the mobile device requiring RTK direction finding, and one antenna is used as the reference. Each antenna needs to be pre-calibrated to ensure its baseline is fixed and parallel to the carrier. Real-time dynamic differential positioning technology is used to obtain centimeter-level relative positioning results. Finally, through geometric projection, the precise heading information of the moving carrier is obtained, completing the direction finding. However, the radio signals used in this method attenuate rapidly in water, making it unsuitable for underwater positioning and direction finding. Summary of the Invention

[0004] To address the aforementioned issues, and based on the dual-antenna direction finding principle of surface satellite navigation RTK, this invention proposes an underwater direction finding system and method based on ultra-short baseline underwater acoustic positioning (USBL) dual beacons, which can provide high-precision heading information for underwater vehicles.

[0005] This invention is achieved through the following technical solution:

[0006] An underwater direction finding system based on dual beacons for ultra-short baseline underwater acoustic positioning:

[0007] The direction finding system includes a USBL array, dual beacons deployed on an underwater vehicle, and a direction finding calculation module.

[0008] The direction finding calculation module deploys two beacons on the underwater vehicle, using the USBL array as the origin of the coordinate system. It measures two sets of slant range values ​​and the phase difference and time delay difference of the signals arriving at each element of the array. Then, the relative azimuth between the array and the target can be calculated using the phase difference of each element. Combined with the slant range, the specific position of the two beacons relative to the array can be calculated, thereby obtaining the baseline vector between the two beacons. Furthermore, the heading angle of the underwater vehicle with true north as the reference in the navigation coordinate system can be obtained, thus measuring the heading information of the underwater vehicle.

[0009] An underwater direction finding method based on dual beacons for ultra-short baseline underwater acoustic positioning:

[0010] The method specifically includes the following steps:

[0011] S1: Before using the USBL device, calibrate its installation error to improve positioning accuracy, thereby improving its direction finding accuracy; at the same time, perform coordinate system transformation, converting the geodetic coordinate system to the northeast-sky coordinate system;

[0012] S2: Calculate the slant range based on the round-trip time of the sound wave between the array and the beacon, and perform sound speed correction;

[0013] S3: Calculate the position of the underwater vehicle relative to the array;

[0014] S4: Calculate the phase difference of the received signal between each element of the array in S3 using the adaptive notch filter method;

[0015] S5: Find the coordinate position of the beacon relative to the matrix, and then find the absolute position of the two beacons based on the absolute position of the matrix provided by S1, and then obtain the baseline vector between the two beacons.

[0016] S6: Use the tangent and antitangent formulas to obtain the heading angle, and then obtain the heading of the underwater vehicle.

[0017] Furthermore, in S1, the USBL array is used in conjunction with the RTK antenna during positioning. The RTK antenna provides the absolute position to the array, and the absolute position of the beacon can be determined through the array's calculations. The coordinate system transformation method is as follows: first, the geodetic coordinate system (BLH) is transformed to the geocentric Earth-Fixed Coordinate System (ECEF), and then the geocentric Earth-Fixed Coordinate System (ECEF) is transformed to the North-South Celestial Coordinate System (ENU).

[0018] Establish a coordinate system OXYZ. Assume that the four elements of the array lie on two mutually perpendicular lines, namely the X-axis and the Y-axis, with their centers at the origin. Assume the spacing between the array elements is d, and the beacon position is (x...). ay a , z a The subsequent formulas are all solved in the Northeast-Eastern Sky coordinate system, with the matrix as the origin of the Northeast-Eastern Sky coordinate system.

[0019] Furthermore, in S2, the array transmits an acoustic positioning signal to the underwater target. Upon receiving the signal, the underwater target's beacon transmits an echo pulse back to the array. The slant distance between the beacon and the array center can then be calculated. Where C is the speed of sound on the seabed, and T is the time it takes for the positioning signal to travel from transmission to return;

[0020] The speed of sound, C, on the seabed is affected by depth, salinity, and temperature. It is not constant in water and changes continuously along the vertical direction. Therefore, a sound speed correction algorithm is used to correct it to reduce the impact of sound speed error on direction finding accuracy.

[0021] Furthermore, in S3, the position of the target relative to the acoustic array is determined using trigonometric relationships, i.e.

[0022]

[0023] In the formula, R represents the slant distance from the center of the array to the beacon; θ x θ represents the angle between the position vector from the center of the array to the beacon and the X-axis. y This represents the angle between the position vector from the center of the array to the beacon and the Y-axis;

[0024] θ x and θ y It is not known; it needs to be determined based on the phase difference between the primitives.

[0025] Furthermore, in S4, the phase difference of the received signals between the primitives is related to θ. x and θ y The following relationship exists:

[0026]

[0027] In the formula, This represents the phase difference between the signals received by the two primitives on the X-axis; d represents the phase difference of the signals received by the two primitives on the Y-axis; d represents the distance between the two primitives on the X-axis and Y-axis; λ represents the wavelength of the sound wave.

[0028] Therefore, we can conclude that:

[0029]

[0030] An adaptive notch filter can measure the phase value of a signal under test by using two orthogonal weight coefficients. Using a pair of such filters, the phase difference between two signals under test can be measured.

[0031] Furthermore, in S5, assuming the acoustic array can simultaneously perform positioning calculations for both beacons, and there is no polling mechanism, the array is taken as the origin of the northeast-northeast coordinate system. According to formula (3), the coordinate positions of the two beacons can be obtained as (x a1 ,y a1 ,z a1 ) and (x a2 ,y a2 ,z a2 The baseline vector between the two beacons can be obtained from the baseline vector from the origin to the two beacons.

[0032] Furthermore, in S6,

[0033] In the northeast-northeast coordinate system, its heading angle can be obtained by the following formula:

[0034]

[0035] In the formula, θ is the heading angle. By obtaining the heading angle, the heading information of the underwater vehicle can be determined.

[0036] An electronic device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the above method.

[0037] A computer-readable storage medium for storing computer instructions that, when executed by a processor, implement the steps of the above-described method.

[0038] Beneficial effects of the invention

[0039] This invention utilizes a USBL dual-beacon underwater acoustic positioning device for direction finding, providing high-precision, long-endurance heading information for underwater vehicles. The base station is installed at the bottom of the survey vessel, and the dual beacons are deployed on the underwater hull, consistent with the dual antennas. Their positions need to be pre-calibrated to ensure parallelism with the underwater hull. The base station continuously emits acoustic signals. Upon receiving these signals, the beacons on the underwater vehicle emit an echo pulse. Sensors in the base station's receiving array use the time difference of the received acoustic signals, combined with the speed of sound in water, to calculate the slant range between the beacons on the underwater vehicle and the base station on the ship's bottom. The phase difference of the measured signals reaching each base station array element is used to calculate the azimuth angle of the array relative to the target. With the slant range and azimuth angle, trigonometric relationships can be used to calculate the X, Y, and Z positions of the beacons relative to the base station in the array coordinate system.

[0040] Traditional underwater orientation finding methods, such as inertial navigation orientation finding, suffer from error accumulation response and are difficult to apply to long-term orientation finding operations. However, the novel method for measuring the heading of underwater vehicles provided by this invention can provide high-precision, long-endurance heading information for underwater vehicles. It is applicable to underwater engineering operations, marine scientific research, and underwater robotics, and provides a reliable solution to the long-endurance orientation finding problem of underwater vehicles. It has significant development potential in marine applications that require high-precision, long-endurance orientation finding. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] An underwater direction finding system based on dual beacons for ultra-short baseline underwater acoustic positioning:

[0044] The direction finding system includes a USBL acoustic array, dual beacons deployed on an underwater vehicle, and a direction finding calculation module; by combining the dual beacons and the USBL acoustic array, higher positioning accuracy can be achieved.

[0045] The direction finding calculation module deploys two beacons on the underwater vehicle. The dual-beacon system provides richer information than a single beacon, helping to more accurately determine the direction and position of the target. Using the USBL array as the origin of the coordinate system, two sets of slant range values ​​and the phase difference and time delay difference of the signals arriving at each element of the array are measured. Then, the relative azimuth between the array and the target can be calculated through the phase difference of each element. Combined with the slant range, the specific position of the two beacons relative to the array can be calculated, thereby obtaining the baseline vector between the two beacons. Furthermore, the heading angle of the underwater vehicle with true north as the reference in the navigation coordinate system can be obtained, thus measuring the heading information of the underwater vehicle.

[0046] An underwater direction finding method based on dual beacons for ultra-short baseline underwater acoustic positioning:

[0047] like Figure 1 The method specifically includes the following steps:

[0048] S1: Before using the USBL device, calibrate its installation error to improve positioning accuracy, thereby improving its direction finding accuracy; at the same time, perform coordinate system transformation, converting the geodetic coordinate system to the northeast-sky coordinate system;

[0049] The Northeast-Upper Altitude (ENU) coordinate system is selected as the navigation coordinate system. Since the USBL array is used in conjunction with the RTK antenna during positioning, the RTK antenna provides the absolute position to the array. After the array is calculated, the absolute position of the beacon can be determined. The coordinate system transformation method is as follows: first, the geodetic coordinate system (BLH) is transformed to the Earth-Centered Earth-Fixed (ECEF) coordinate system, and then the Earth-Centered Earth-Fixed (ECEF) coordinate system is transformed to the Northeast-Upper Altitude (ENU) coordinate system.

[0050] Since the coordinates calculated by the array are in the geodetic coordinate system, the Northeast-East-South coordinate system is chosen as the navigation coordinate system. If heading information is required, a coordinate transformation is needed to obtain the heading information in the Northeast-East-South coordinate system. An array coordinate system OXYZ is established, assuming that the four elements in the array are located on two mutually perpendicular straight lines, i.e., the X-axis and Y-axis, with their centers located at the origin. The spacing between the array elements is assumed to be d, and the beacon position is (x...). a y a , z a The subsequent formulas are all solved in the Northeast-Eastern Sky coordinate system, with the matrix as the origin of the Northeast-Eastern Sky coordinate system.

[0051] S2: The slant range is calculated based on the round-trip time of the sound wave between the array and the beacon, and the sound velocity is corrected. The sound velocity correction allows the system to maintain high accuracy under different water temperatures, salinities and depths, enhancing its applicability in variable marine environments.

[0052] An array transmits an acoustic positioning signal to an underwater target. Upon receiving the signal, the target's beacon transmits an echo pulse back to the array. The slant distance between the beacon and the array center can then be calculated. Where C is the speed of sound on the seabed, and T is the time it takes for the positioning signal to travel from transmission to return;

[0053] The speed of sound, C, on the seabed is affected by depth, salinity, and temperature. It is not constant in water and changes continuously along the vertical direction. Therefore, a sound speed correction algorithm is used to correct it to reduce the impact of sound speed error on direction finding accuracy.

[0054] S3: Calculate the position of the underwater vehicle relative to the array;

[0055] Using triangulation, the position of the target relative to the acoustic array can be determined, i.e.

[0056]

[0057] In the formula, R represents the slant distance from the center of the array to the beacon; θ x θ represents the angle between the position vector from the center of the array to the beacon and the X-axis. y This represents the angle between the position vector from the center of the array to the beacon and the Y-axis;

[0058] θ x and θ y It is not known; it needs to be determined based on the phase difference between the primitives.

[0059] S4: The phase difference between the received signals of each element of the array in S3 is calculated by the adaptive notch filter method; the adaptive notch filter can adapt to various noise conditions and improve the signal detection and processing capabilities.

[0060] The phase difference of the received signal between the primitives and θ x and θ y The following relationship exists:

[0061]

[0062] In the formula, This represents the phase difference between the signals received by the two primitives on the X-axis; d represents the phase difference of the signals received by the two primitives on the Y-axis; d represents the distance between the two primitives on the X-axis and Y-axis; λ represents the wavelength of the sound wave.

[0063] Therefore, we can conclude that:

[0064]

[0065] This invention considers that the acoustic waves incident on each element in the array are parallel. The phase difference measurement method is the adaptive notch filter method. The adaptive notch filter can measure the phase value of the signal under test by using two orthogonal weight coefficients. Using a pair of such filters, the phase difference between two signals under test can be measured.

[0066] S5: Find the coordinate position of the beacon relative to the matrix, and then find the absolute position of the two beacons based on the absolute position of the matrix provided by S1, and then obtain the baseline vector between the two beacons.

[0067] Assuming the acoustic array can simultaneously perform positioning calculations for both beacons, and there is no polling mechanism, taking the array as the origin of the northeast-northeast coordinate system, the coordinate positions of the two beacons can be obtained according to formula (3) as (x a1 ,y a1 ,z a1 ) and (x a2 ,y a2 ,z a2 The baseline vector between the two beacons can be obtained from the baseline vector from the origin to the two beacons.

[0068] S6: Use the tangent and antitangent formulas to obtain the heading angle, and then obtain the heading of the underwater vehicle.

[0069] In the northeast-northeast coordinate system, its heading angle can be obtained by the following formula:

[0070]

[0071] In the formula, θ is the heading angle. By obtaining the heading angle, the heading information of the underwater vehicle can be determined.

[0072] The range of θ should be 0-360°. The θ obtained by formula (4) is between -90° and 90°. When solving, attention should be paid to the angle corresponding to the coordinate quadrant.

[0073] An electronic device includes a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the above method.

[0074] A computer-readable storage medium for storing computer instructions that, when executed by a processor, implement the steps of the above-described method.

[0075] The memory in the embodiments of this application can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory of the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0076] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired means such as coaxial cable, optical fiber, digital subscriber line, DSL, or wireless means such as infrared, wireless, microwave, etc. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium such as a floppy disk, hard disk, magnetic tape; an optical medium such as a high-density digital video disc, DVD; or a semiconductor medium such as a solid-state disk, SSD, etc.

[0077] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0078] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as execution by a hardware decoding processor, or as execution by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0079] The above provides a detailed description of the underwater direction finding system and method based on ultra-short baseline underwater acoustic positioning (USBL) dual beacons proposed in this invention. The principles and implementation methods of this invention have been explained. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. An underwater direction finding system based on dual beacons for ultra-short baseline underwater acoustic positioning, characterized in that: The direction finding system includes a USBL array, dual beacons deployed on an underwater vehicle, and a direction finding calculation module. The direction finding calculation module deploys two beacons on the underwater vehicle, using the USBL array as the origin of the coordinate system. It measures two sets of slant range values ​​and the phase difference and time delay difference of the signals arriving at each element of the array. Then, the relative azimuth between the array and the target can be calculated using the phase difference of each element. Combined with the slant range, the specific position of the two beacons relative to the array can be calculated, thereby obtaining the baseline vector between the two beacons. Furthermore, the heading angle of the underwater vehicle with true north as the reference in the navigation coordinate system can be obtained, thus measuring the heading information of the underwater vehicle.

2. An underwater direction finding method based on dual beacons for ultra-short baseline underwater acoustic positioning, characterized in that: The method specifically includes the following steps: S1: Before using the USBL device, calibrate its installation error to improve positioning accuracy, thereby improving its direction finding accuracy; at the same time, perform coordinate system transformation, converting the geodetic coordinate system to the northeast-sky coordinate system; S2: Calculate the slant range based on the round-trip time of the sound wave between the array and the beacon, and perform sound speed correction; S3: Calculate the position of the underwater vehicle relative to the array; S4: Calculate the phase difference of the received signal between each element of the array in S3 using the adaptive notch filter method; S5: Find the coordinate position of the beacon relative to the matrix, and then find the absolute position of the two beacons based on the absolute position of the matrix provided by S1, and then obtain the baseline vector between the two beacons. S6: Use the tangent and antitangent formulas to obtain the heading angle, and then obtain the heading of the underwater vehicle.

3. The direction finding method according to claim 2, characterized in that: In S1, The USBL array is used in conjunction with an RTK antenna for positioning. The RTK antenna provides the absolute position to the array, and the absolute position of the beacon can be determined through the array's calculations. The coordinate system transformation method is as follows: first, the geodetic coordinate system (BLH) is transformed to the geocentric Earth-Fixed Coordinate System (ECEF), and then the geocentric Earth-Fixed Coordinate System (ECEF) is transformed to the North-South Celestial Coordinate System (ENU). Establish a coordinate system OXYZ. Assume the four primitives in the matrix lie on two mutually perpendicular lines, namely the X-axis and Y-axis, with their centers at the origin. Assume the spacing between the primitives is... The beacon location is All subsequent formulas are solved in the Northeast-Eastern Sky coordinate system, with the matrix as the origin of the Northeast-Eastern Sky coordinate system.

4. The direction finding method according to claim 3, characterized in that: In S2, An array transmits an acoustic positioning signal to an underwater target. Upon receiving the signal, the target's beacon transmits an echo pulse back to the array. The slant distance between the beacon and the array center can then be calculated. ,in Let T be the speed of sound propagation on the seabed, and T be the time it takes for the positioning signal to travel from transmission to return. The speed of sound, C, on the seabed is affected by depth, salinity, and temperature. It is not constant in water and changes continuously along the vertical direction. Therefore, a sound speed correction algorithm is used to correct it to reduce the impact of sound speed error on direction finding accuracy.

5. The direction finding method according to claim 4, characterized in that: In S3, Using triangulation, the position of the target relative to the acoustic array can be determined, i.e. (1) In the formula, R represents the slant distance from the center of the array to the beacon; This represents the angle between the position vector from the center of the array to the beacon and the X-axis; This represents the angle between the position vector from the center of the array to the beacon and the Y-axis; It is not known; it needs to be determined based on the phase difference between the primitives.

6. The direction finding method according to claim 5, characterized in that: In S4, The phase difference of the received signal between the primitives and and The following relationship exists: (2) In the formula, This represents the phase difference between the signals received by the two primitives on the X-axis; This represents the phase difference between the signals received by the two primitives on the Y-axis; This represents the distance between two primitives on the X and Y axes; Indicates the wavelength of a sound wave; Therefore, we can conclude that: (3) An adaptive notch filter can measure the phase value of a signal under test by using two orthogonal weight coefficients. Using a pair of such filters, the phase difference between two signals under test can be measured.

7. The direction finding method according to claim 6, characterized in that: In S5, Assuming the acoustic array can simultaneously perform positioning calculations for both beacons, and there is no polling mechanism, taking the array as the origin of the northeast-northeast coordinate system, the coordinate positions of the two beacons can be obtained according to formula (3). and The baseline vector between the two beacons can be obtained from the baseline vector from the origin to the two beacons.

8. The direction finding method according to claim 7, characterized in that: In S6, In the northeast-northeast coordinate system, its heading angle can be obtained by the following formula: (4) In the formula, Given the heading angle, by finding the heading angle, we can know the heading information of the water body.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 2 to 8.

10. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 2 to 8.

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