Gnss anti-spoofing positioning method and device, computer device and storage medium

Abstract

This application relates to a GNSS anti-spoofing positioning method, apparatus, computer equipment, and storage medium. The method includes: acquiring signals from multiple visible satellites, extracting pseudorange observations, and constructing a set of visible satellites; randomly selecting four satellites from the visible satellite set to form an initial set and performing positioning calculations to obtain preliminary positions and clock errors; calculating the pseudorange residuals of the remaining satellites, comparing them with a preset threshold, and statistically analyzing the number of qualified satellites; repeating the iteration multiple times, selecting the set with the largest number of satellites as the reliable satellite set; and recalculating using the reliable satellite set to obtain a reliable positioning result after eliminating spoofing interference. This method can accurately identify real signals when multiple satellites are simultaneously subjected to spoofing interference, suppress the impact of spoofing interference, and improve the positioning reliability and security of GNSS navigation terminals in complex spoofing scenarios.

Description

Technical Field

[0001] This application relates to the field of satellite navigation anti-interference technology, and in particular to a GNSS anti-spoofing positioning method, device, computer equipment and storage medium. Background Technology

[0002] As a crucial national spatiotemporal infrastructure, satellite navigation systems (GNSS) are widely used in surveying, transportation, aviation, communications, and consumer electronics. However, due to the open nature of civilian GNSS signals and their relatively low power, they are highly susceptible to malicious forgery, forwarding, and tampering, leading to deceptive interference and causing navigation terminals to output incorrect positioning and timing results, seriously threatening the system's operational security.

[0003] Currently, most methods for suppressing GNSS spoofing interference are based on Receiver Autonomous Integrity Monitoring (RAIM), whose core idea is to use pseudorange residuals after positioning calculations to identify abnormal observations. However, traditional RAIM algorithms are only suitable for scenarios where a small number of satellites are subject to spoofing interference. When the spoofing interference source simultaneously broadcasts signals from multiple fake satellites, a large number of observations are synchronously contaminated, the statistical properties of the residuals fail, and the RAIM algorithm cannot effectively detect and eliminate spoofing signals, directly causing the positioning results to deviate completely from the true position.

[0004] Random Sampling Consensus (RANSAC) algorithm, due to its robust estimation properties, is often used to handle observation models with multiple outliers, eliminating abnormal observations through random sampling and consistency checks. However, the conventional RANSAC algorithm uses the minimum residual as the criterion for determining the optimal model. GNSS spoofing signals are characterized by systematicity, consistency, and clustering, and their pseudorange residuals are often smaller. If the traditional RANSAC logic is used directly, spoofing signals are easily identified as valid interior points, ultimately outputting false positioning results, which cannot meet the reliable positioning requirements in complex spoofing environments.

[0005] Therefore, in complex scenarios where multiple satellites are simultaneously subjected to deception interference, how to overcome the limitations of traditional RAIM and conventional RANSAC algorithms, achieve effective identification and reliable elimination of deception signals, and ensure that navigation terminals can still output reliable positioning results in malicious deception environments has become a key technical problem that urgently needs to be solved in the field of GNSS anti-deception. Summary of the Invention

[0006] Therefore, it is necessary to provide a GNSS anti-spoofing positioning method, device, computer equipment, and storage medium that can effectively identify and eliminate spoofed observations when multiple satellites are simultaneously subjected to spoofing interference, and avoid being mistakenly judged as a reliable signal due to the smaller residual of the spoofed signal.

[0007] A GNSS anti-spoofing positioning method, the method comprising: Acquire signals from multiple visible satellites, extract pseudorange observations from each visible satellite signal, and construct a set of visible satellites; Four satellites are randomly selected from the visible satellite set to form an initial satellite set. The pseudorange observations of the initial satellite set are used to perform positioning calculations to obtain the preliminary position and clock error of the navigation terminal. Based on the initial position and clock error, calculate the pseudorange residuals of the remaining satellites in the initial satellite set that have not been extracted, compare the pseudorange residuals with a preset threshold, and filter out satellites with residuals less than the threshold and count their number. The process of random satellite selection, positioning calculation, residual calculation and screening statistics is repeated multiple times to obtain multiple sets of qualified satellites with residuals and their corresponding quantities. The set of qualified satellites with the largest number of satellites is selected as the set of reliable satellites. The positioning solution is then performed again using pseudorange observations from the trusted satellite set to obtain a trusted positioning result after eliminating deception interference.

[0008] In one embodiment, the positioning solution is implemented using Newton's iteration method.

[0009] In one embodiment, the process of randomly selecting four satellites from the set of visible satellites each time is an independent random sampling, which does not depend on the previous sampling result.

[0010] In one embodiment, the process of repeatedly performing random star selection, location calculation, residual calculation and screening statistics is an iterative process with a preset number of iterations.

[0011] This application also proposes a GNSS anti-spoofing positioning device, the device comprising: The satellite observation and acquisition module is used to acquire signals from multiple visible satellites, extract pseudorange observations from each visible satellite signal, and construct a set of visible satellites. The initial satellite selection module is used to randomly select four satellites from the visible satellite set to form an initial satellite set, and use the pseudorange observations of the initial satellite set to perform positioning calculations to obtain the preliminary position and clock error of the navigation terminal. The residual calculation and filtering module is used to calculate the pseudorange residuals of the remaining satellites that were not extracted in the initial satellite set based on the initial position and clock error, compare the pseudorange residuals with a preset threshold, filter out satellites with residuals less than the threshold, and count the number of satellites. The iterative optimization set module is used to repeatedly execute the process of random satellite selection, positioning calculation, residual calculation and screening statistics multiple times to obtain multiple sets of qualified satellites with residuals and their corresponding quantities. The set of qualified satellites with the largest number of satellites is selected as the reliable satellite set. The trusted positioning solution module is used to perform positioning solution again using pseudorange observations from the trusted satellite set to obtain a trusted positioning result after eliminating deception interference.

[0012] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps in the above-described GNSS anti-spoofing positioning method.

[0013] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above-described GNSS anti-spoofing positioning method.

[0014] The aforementioned GNSS anti-spoofing positioning method, device, computer equipment, and storage medium extract pseudorange observations from multiple visible satellite signals and construct a visible satellite set. Four satellites are randomly selected from this set to form an initial satellite set. Positioning calculations are performed using the pseudorange observations from this initial satellite set to obtain the navigation terminal's preliminary position and clock error. Based on the preliminary position and clock error, the pseudorange residuals of the remaining satellites not selected from the initial satellite set are calculated. These residuals are compared with a preset threshold, and satellites with residuals less than the threshold are selected and their numbers are counted. This process of random satellite selection, positioning calculation, residual calculation, and selection is repeated multiple times to obtain multiple sets of qualified residual satellites and their corresponding numbers. The set with the largest number of qualified residuals is selected as the reliable satellite set. Positioning calculations are then performed again using the pseudorange observations from the reliable satellite set to obtain a reliable positioning result after eliminating spoofing interference.

[0015] Beneficial effects: This method effectively identifies and eliminates maliciously forged spoofed signal observations in complex scenarios where multiple satellites are simultaneously subjected to spoofing interference. It solves the technical problems of traditional RAIM algorithms failing to handle multiple spoofing signals and conventional RANSAC algorithms easily misclassifying spoofing signals with smaller residuals as valid signals. This method randomly selects four satellites for positioning calculations and uses the selection criterion of having the largest number of satellites with valid residuals as the basis for choosing the reliable set, rather than the traditional minimum residual criterion. This accurately distinguishes between the set of real satellites and the set of spoofing satellites, avoiding misleading positioning results due to strong consistency and small residuals in spoofing signals.

[0016] Meanwhile, this method requires no additional hardware support and can suppress deception interference simply by using pseudorange observations and iterative filtering. It has low computational cost, strong real-time performance, and high compatibility, and can significantly improve the positioning reliability and security of GNSS navigation terminals in malicious deception environments. It is applicable to various types of civilian GNSS navigation terminals. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a GNSS anti-spoofing positioning method in one embodiment; Figure 2 This is a schematic diagram of the specific process of the method in one embodiment; Figure 3 This is a structural block diagram of a GNSS anti-spoofing positioning device in one embodiment; Figure 4 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0019] To address the problems in existing technologies, such as the inability of traditional RAIM algorithms to handle multi-satellite synchronization spoofing interference and the tendency of conventional RANSAC algorithms to misclassify spoofing signals with smaller residuals as valid signals, leading to insufficient positioning reliability of navigation terminals in complex spoofing scenarios, this application addresses these issues. Figure 1 As shown, a GNSS anti-spoofing positioning method is provided, which specifically includes the following steps: Step S100: Acquire signals from multiple visible satellites, extract pseudorange observations from each visible satellite signal, and construct a set of visible satellites.

[0020] Step S110: Randomly select four satellites from the visible satellite set to form an initial satellite set, and use the pseudorange observations of the initial satellite set to perform positioning calculations to obtain the preliminary position and clock error of the navigation terminal.

[0021] Step S120: Based on the initial position and clock error, calculate the pseudorange residuals of the remaining satellites that were not extracted in the initial satellite set, compare the pseudorange residuals with a preset threshold, and select satellites whose residuals are less than the threshold and count their number.

[0022] Step S130: Repeat the process of random satellite selection, positioning calculation, residual calculation and screening statistics multiple times to obtain multiple sets of qualified residual satellites and their corresponding quantities. Select the set of qualified residual satellites with the largest number of satellites as the reliable satellite set.

[0023] Step S140: Use pseudorange observations from a set of trusted satellites to perform the positioning calculation again, and obtain a trusted positioning result after eliminating deception interference.

[0024] In step S100, the satellite navigation terminal tracks and receives all visible GNSS satellite signals in the current space, acquires pseudorange observations corresponding to all visible satellites, and summarizes the numbers of all visible satellites to construct a visible satellite set. This set includes observations corresponding to real satellites, as well as observations corresponding to possible spoofing interference signals, and the real satellite observations and spoofing signal observations correspond to two sets of positioning results with significantly different spatial positions.

[0025] Specifically, the satellite navigation terminal tracks all visible satellite signals to obtain... pseudorange observations of satellites .

[0026] In step S110, four satellites are randomly selected from the visible satellite set to form an initial satellite set. Based on the pseudorange observations of these four satellites, the Newton-Raphson iteration method is used to perform positioning calculations, solving a set of positioning equations that include the three-dimensional position coordinates and clock bias of the navigation terminal, to obtain the preliminary position coordinates and clock bias parameters of the navigation terminal corresponding to the current sampling combination. Here, four satellites represent the minimum number of satellites required for GNSS positioning calculations.

[0027] Specifically, from the set of visible satellites Four numbers are randomly selected to form a new set, i.e., the initial satellite set. Next, the initial satellite set was used. Corresponding pseudorange To locate the solution, we need to solve the following system of equations using Newton's iterative method: (1) In formula (1), This indicates the location coordinates of the navigation terminal. Indicates the first pseudorange of GNSS satellites Indicates the first The coordinates of a GNSS satellite can be obtained from the broadcast ephemeris. Indicates the clock bias of the navigation terminal. It represents the speed of light.

[0028] In step S120, based on the preliminary position and clock error obtained in step S110, the pseudorange residuals of the remaining satellites in the visible satellite set that have not been sampled are calculated. Then, the pseudorange residuals of each remaining satellite are compared with a pre-set residual threshold. Satellites with pseudorange residuals less than the threshold are selected to form a subset of qualified satellites corresponding to the current sampling, and the number of satellites in the subset is counted.

[0029] Specifically, the preliminary position and clock difference obtained from the solution are denoted as... The remaining satellites are calculated according to formula (2). pseudo-range residual Formula (2) is expressed as: (2) In formula (2), The elements of the set.

[0030] Furthermore, the pseudorange residuals of each satellite With the pre-set threshold For comparison, let's assume the set of satellites smaller than the threshold is... The corresponding number of satellites is Preferred threshold It can be set to 30m.

[0031] In step S130, the process of randomly selecting four satellites, calculating the positioning, calculating the pseudorange residual, and screening the threshold is repeated according to the preset number of iterations to obtain multiple sets of qualified satellites with residuals and their corresponding number of satellites.

[0032] Since real satellite observations constitute a numerical majority in the overall observations, the set with the most qualified satellites can be selected, which is the reliable set containing the most real satellites. In this method, the selection criterion is not based on the smallest residual, but rather on the largest number of qualified satellites, to avoid misclassifying deceptive signal sets with smaller residuals as real sets. Ultimately, the set with the largest number of qualified satellites is selected as the reliable satellite set. Specifically, repeat steps S110 to S120, iteratively performing random star sampling, location calculation, residual calculation, and screening statistics. This yields the satellite set corresponding to each execution. and number of satellites ,in, This is the preset number of times. It is important to note that the process of randomly selecting four satellites from the visible satellite set each time is an independent random sampling, which does not depend on the results of the previous sampling.

[0033] In step S140, all pseudorange observations from the credible satellite set obtained above are used to solve the positioning equations again and perform the final positioning solution using the Newton-Raphson iteration method. This eliminates the influence of all deceptive interference observations and obtains a credible positioning result that is not affected by deceptive signals, thereby improving the positioning reliability of the navigation terminal in scenarios with multiple deceptive signals.

[0034] Specifically, the number of satellites The maximum value and its corresponding set of satellites, assuming the set of satellites is... The number of satellites in the set is The corresponding satellite number is Using a trusted satellite ensemble The pseudorange observations are combined with the equations shown in formula (3), and the Newton-Raphson iteration method is used to solve the positioning problem, so as to obtain a reliable positioning result that is not affected by deception interference:

[0035] like Figure 2 The diagram shown is a schematic representation of the entire method.

[0036] The aforementioned GNSS anti-spoofing positioning method features a simple and intuitive overall implementation process with clear steps. Spoofing interference suppression can be achieved solely through random sampling, pseudorange residual screening, and ensemble optimization, requiring no complex calculations or additional hardware support. This results in low engineering implementation costs and strong versatility. Although the method is relatively simple in form, its core concept breaks through the conventional thinking of existing technologies. It abandons the inherent pattern of using the minimum residual as the selection criterion in traditional RAIM and conventional RANSAC algorithms, innovatively using the largest number of qualified satellites as the selection criterion for the credible satellite set. This fundamentally solves the industry problem of spoofing signals being easily misjudged as valid signals when multiple spoofing signals coexist. Therefore, although the method is simple to implement, it possesses outstanding creativity and significant technical advantages, effectively improving the positioning reliability and security of navigation terminals in complex and malicious spoofing environments, demonstrating significant practical value.

[0037] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0038] In one embodiment, such as Figure 3 As shown, a GNSS anti-spoofing positioning device is provided, comprising: a satellite observation and acquisition module 200, an initial satellite extraction and solution module 210, a residual calculation and screening module 220, an iterative optimization set module 230, and a reliable positioning solution module 240, wherein: The satellite observation and acquisition module 200 is used to acquire signals from multiple visible satellites, extract pseudorange observations from each visible satellite signal, and construct a set of visible satellites. The initial satellite selection and calculation module 210 is used to randomly select four satellites from the visible satellite set to form an initial satellite set, and use the pseudorange observations of the initial satellite set to perform positioning calculations to obtain the preliminary position and clock error of the navigation terminal. The residual calculation and filtering module 220 is used to calculate the pseudorange residuals of the remaining satellites that have not been extracted in the initial satellite set based on the initial position and clock error, compare the pseudorange residuals with a preset threshold, filter out satellites with residuals less than the threshold and count their number. The iterative optimization set module 230 is used to repeatedly execute the process of random satellite selection, positioning calculation, residual calculation and screening statistics multiple times to obtain multiple sets of qualified residual satellites and their corresponding quantities. The set of qualified residuals with the largest number of satellites is selected as the reliable satellite set. The trusted positioning solution module 240 is used to perform positioning solution again using the pseudorange observations of the trusted satellite set to obtain a trusted positioning result after eliminating deception interference.

[0039] Specific limitations regarding GNSS anti-spoofing positioning devices can be found in the limitations of GNSS anti-spoofing positioning methods described above, and will not be repeated here. Each module in the aforementioned GNSS anti-spoofing positioning device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0040] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 4 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a GNSS anti-spoofing positioning method. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0041] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0042] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps: Acquire signals from multiple visible satellites, extract pseudorange observations from each visible satellite signal, and construct a set of visible satellites; Four satellites are randomly selected from the visible satellite set to form an initial satellite set. The pseudorange observations of the initial satellite set are used to perform positioning calculations to obtain the preliminary position and clock error of the navigation terminal. Based on the initial position and clock error, calculate the pseudorange residuals of the remaining satellites in the initial satellite set that have not been extracted, compare the pseudorange residuals with a preset threshold, and filter out satellites with residuals less than the threshold and count their number. The process of random satellite selection, positioning calculation, residual calculation and screening statistics is repeated multiple times to obtain multiple sets of qualified satellites with residuals and their corresponding quantities. The set of qualified satellites with the largest number of satellites is selected as the set of reliable satellites. The positioning solution is then performed again using pseudorange observations from the trusted satellite set to obtain a trusted positioning result after eliminating deception interference.

[0043] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor: Acquire signals from multiple visible satellites, extract pseudorange observations from each visible satellite signal, and construct a set of visible satellites; Four satellites are randomly selected from the visible satellite set to form an initial satellite set. The pseudorange observations of the initial satellite set are used to perform positioning calculations to obtain the preliminary position and clock error of the navigation terminal. Based on the initial position and clock error, calculate the pseudorange residuals of the remaining satellites in the initial satellite set that have not been extracted, compare the pseudorange residuals with a preset threshold, and filter out satellites with residuals less than the threshold and count their number. The process of random satellite selection, positioning calculation, residual calculation and screening statistics is repeated multiple times to obtain multiple sets of qualified satellites with residuals and their corresponding quantities. The set of qualified satellites with the largest number of satellites is selected as the set of reliable satellites. The positioning solution is then performed again using pseudorange observations from the trusted satellite set to obtain a trusted positioning result after eliminating deception interference.

[0044] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0045] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0046] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A GNSS anti-spoofing positioning method, characterized in that, The method includes: Acquire signals from multiple visible satellites, extract pseudorange observations from each visible satellite signal, and construct a set of visible satellites; Four satellites are randomly selected from the visible satellite set to form an initial satellite set. The pseudorange observations of the initial satellite set are used to perform positioning calculations to obtain the preliminary position and clock error of the navigation terminal. Based on the initial position and clock error, calculate the pseudorange residuals of the remaining satellites in the initial satellite set that have not been extracted, compare the pseudorange residuals with a preset threshold, and filter out satellites with residuals less than the threshold and count their number. The process of random satellite selection, positioning calculation, residual calculation and screening statistics is repeated multiple times to obtain multiple sets of qualified satellites with residuals and their corresponding quantities. The set of qualified satellites with the largest number of satellites is selected as the set of reliable satellites. The positioning solution is then performed again using pseudorange observations from the trusted satellite set to obtain a trusted positioning result after eliminating deception interference.

2. The GNSS anti-spoofing positioning method according to claim 1, characterized in that, The positioning solution is implemented using Newton's iterative method.

3. The GNSS anti-spoofing positioning method according to claim 1, characterized in that, Each time four satellites are randomly selected from the set of visible satellites, it is an independent random sampling process that does not depend on the results of the previous sampling.

4. The GNSS anti-spoofing positioning method according to claim 1, characterized in that, The process of repeatedly performing random star selection, location calculation, residual calculation, and screening statistics is an iterative process with a preset number of iterations.

5. A GNSS anti-spoofing positioning device, characterized in that, The device includes: The satellite observation and acquisition module is used to acquire signals from multiple visible satellites, extract pseudorange observations from each visible satellite signal, and construct a set of visible satellites. The initial satellite selection module is used to randomly select four satellites from the visible satellite set to form an initial satellite set, and use the pseudorange observations of the initial satellite set to perform positioning calculations to obtain the preliminary position and clock error of the navigation terminal. The residual calculation and filtering module is used to calculate the pseudorange residuals of the remaining satellites that were not extracted in the initial satellite set based on the initial position and clock error, compare the pseudorange residuals with a preset threshold, filter out satellites with residuals less than the threshold, and count the number of satellites. The iterative optimization set module is used to repeatedly execute the process of random satellite selection, positioning calculation, residual calculation and screening statistics multiple times to obtain multiple sets of qualified satellites with residuals and their corresponding quantities. The set of qualified satellites with the largest number of satellites is selected as the reliable satellite set. The trusted positioning solution module is used to perform positioning solution again using pseudorange observations from the trusted satellite set to obtain a trusted positioning result after eliminating deception interference.

6. A computer 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 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 4.

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