A method for continuous localization of moving targets by multiple unmanned surface vessels based on orientation information

Abstract

A method for continuous positioning of moving targets by multiple unmanned surface vessels (USVs) based on azimuth information belongs to the field of cooperative control of USVs. To address the shortcomings of existing technologies that rely on GNSS signals and struggle to achieve continuous high-precision positioning of maneuvering targets in complex dynamic environments, this invention provides a technical solution including: obtaining the position, velocity, and heading status information of each USV; acquiring the relative azimuth information of communicable neighboring vessels and the suspected target, and performing coordinate transformation by combining the USVs' own status data; estimating the real-time position vector of the suspected target in the geodetic coordinate system; estimating the velocity vector of the suspected target; constructing an error system and performing stability analysis; and collaboratively fusing the estimation results from each USV. This method is suitable for cooperative multi-USV operations for continuous high-precision positioning and tracking of maneuvering targets at sea in GNSS denial or signal obstruction environments.

Description

Technical Field

[0001] It belongs to the field of unmanned vessel cooperative control, and specifically involves the continuous positioning of moving targets by multiple unmanned vessels based on azimuth information. Background Technology

[0002] Unmanned surface vessel (USV) systems, with their flexibility, maneuverability, and remote control capabilities, have been widely used for the detection and tracking of maritime targets. Continuous, stable, and accurate target positioning is a fundamental prerequisite for effective target management and intelligent collaborative operations. Currently, most USV target positioning methods rely on Global Navigation Satellite System (GNSS) signals, such as using GNSS to obtain the target's or the USV's own position and then using data fusion to track the target. These methods offer high accuracy and reliability in environments with unobstructed GNSS signals.

[0003] However, in practical applications, GNSS signals are highly susceptible to electromagnetic interference, obstruction, or deliberate interference (such as counter-jamming devices and signal spoofing), leading to positioning system failure. Therefore, researchers have begun exploring target localization methods in GNSS-denied environments. For example, some studies have attempted to use visual information, lidar, or inertial navigation systems (INS) as alternatives, but these methods generally face the following limitations: visual methods rely on stable lighting and clear imaging environments, making them difficult to adapt to strong reflections and adverse weather conditions at sea; lidar has limited stability and detection range in sea environments; and INS suffers from severe error accumulation during long-term operation. Furthermore, some studies assume that the target is stationary or moving at a constant velocity in a straight line, an assumption that is not universally applicable in tracking highly maneuverable targets.

[0004] In recent years, some studies have introduced bearing-only observation methods to achieve passive target localization. In these studies, azimuth information is usually obtained by a single unmanned platform and a filter is constructed to estimate the target position. However, due to the lack of multi-source observation and coordination mechanisms, this method is susceptible to factors such as target maneuverability and changes in observation angle, resulting in problems such as large positioning errors and slow convergence speed.

[0005] In summary, existing technologies suffer from drawbacks such as reliance on GNSS signals and difficulty in achieving continuous high-precision positioning of moving targets in complex dynamic environments. Summary of the Invention

[0006] To address the shortcomings of existing technologies that rely on GNSS signals and struggle to achieve continuous, high-precision positioning of moving targets in complex dynamic environments, the present invention provides the following technical solution:

[0007] A method for continuous localization of moving targets by multiple unmanned surface vessels based on orientation information, comprising:

[0008] The steps to construct a kinematic and dynamic mathematical model of multiple unmanned vessels in a two-dimensional plane and obtain the position, velocity and heading state information of each unmanned vessel are to be used as inputs for subsequent observer design.

[0009] The steps involve acquiring the relative bearing information of the communicating neighboring vessel and the suspected target in the coordinate system of each unmanned vessel, and combining it with the unmanned vessel's own state data to complete the coordinate transformation and generate the bearing observation input for target state estimation.

[0010] Based on the aforementioned azimuth observation input and the unmanned vessel's own state data, a nonlinear position observer is constructed to estimate the real-time position vector of the suspected target in the geodetic coordinate system.

[0011] Based on the nonlinear position observer, a velocity observer including an acceleration compensation term is constructed to estimate the velocity vector of the suspected target, thus realizing the step of dynamic continuous estimation;

[0012] The steps involved in constructing an error system and performing stability analysis based on the position and velocity estimation results;

[0013] The steps involve merging the estimation results from various unmanned vessels to achieve continuous localization and tracking of suspicious targets in GNSS-denied environments.

[0014] Furthermore, in a preferred embodiment, the method further includes the step of considering the longitudinal velocity, lateral velocity, and bow roll velocity of the unmanned vessel and their corresponding hydrodynamic disturbance parameters.

[0015] Furthermore, in a preferred embodiment, the coordinate transformation uses a rotation matrix to transform between the geodetic coordinate system and the attached coordinate system, and a dynamic transformation relationship is constructed based on the initial and current heading angles of the unmanned vessel.

[0016] Furthermore, in a preferred embodiment, the relative bearing information is obtained in real time by a camera or other visual sensor, which acquires the relative angle of the target or adjacent vessel in the field of view, and performs bearing estimation in conjunction with the heading information provided by the IMU.

[0017] Furthermore, in a preferred embodiment, the acceleration compensation term introduced in the velocity observer is constructed from the derivative term of the estimated velocity, which is used to improve the system's adaptability to non-uniform targets and the observation accuracy.

[0018] Furthermore, in a preferred embodiment, an error system is constructed and stability analysis is performed by constructing the characteristic equation of the state matrix and determining the sign of its real part.

[0019] A continuous positioning device for moving targets by multiple unmanned surface vessels based on orientation information is also provided, comprising:

[0020] A mathematical model of the kinematics and dynamics of multiple unmanned vessels in a two-dimensional plane is constructed to obtain the position, velocity and heading state information of each unmanned vessel, which serves as the input module for the subsequent design of the observer;

[0021] In the coordinate system of each unmanned vessel, the relative bearing information of the communicable neighboring vessel and the suspected target is obtained, and the coordinate transformation is completed by combining the unmanned vessel's own state data to generate a module for bearing observation input for target state estimation.

[0022] Based on the azimuth observation input and the unmanned vessel's own state data, a nonlinear position observer is constructed to estimate the real-time position vector of the suspected target in the geodetic coordinate system.

[0023] Based on the nonlinear position observer, a velocity observer including an acceleration compensation term is constructed to estimate the velocity vector of the suspected target, thus realizing a module for dynamic continuous estimation.

[0024] A module that constructs an error system and performs stability analysis based on the position and velocity estimation results;

[0025] This module integrates the estimation results from various unmanned vessels to achieve continuous localization and tracking of suspicious targets in GNSS-denied environments.

[0026] A computer storage medium is also provided for storing a computer program, which, when read by the computer, executes the method.

[0027] A computer is also provided, including a processor and a storage medium, wherein the computer executes the method when the processor reads a computer program stored in the storage medium.

[0028] A computer program product is also provided, which, when executed, implements the method described.

[0029] Compared with the prior art, the advantages of the technical solution provided by the present invention are as follows:

[0030] By designing a nonlinear position and velocity observer in the unmanned surface vessel's attached coordinate system, target state estimation relying solely on azimuth information was achieved, overcoming the limitations of traditional GNSS-dependent methods. This approach enables each unmanned surface vessel to independently estimate the target's position and velocity without acquiring the target's absolute position information, effectively enhancing the system's continuous positioning capability in GNSS-denied environments. Compared to positioning methods relying on GNSS or inertial navigation systems, this approach is more robust and practical.

[0031] By constructing a kinematic and dynamic model of the unmanned surface vessel and combining local coordinate transformation relationships with a nonlinear observer structure, the global convergence of target state estimation is ensured. Compared with linear filtering methods such as extended Kalman filtering used in some studies, this scheme can still maintain good stability and response speed when facing highly maneuverable targets, avoiding the problem of positioning error accumulation caused by the failure of the linear assumption of the filter.

[0032] An acceleration compensation term is introduced into the observer structure, enabling the system to adaptively adjust to changes in target velocity, thereby significantly improving the tracking accuracy for high-speed, non-uniformly moving targets. Compared to traditional methods that only observe static azimuth changes, this enhances the system's dynamic adaptability and target recognition capabilities, making it particularly suitable for scenarios where the target's motion state is unpredictable in actual combat or complex environments.

[0033] By employing a multi-unmanned vessel collaborative approach, distributed target state estimation is achieved through sharing the respective azimuth observation information, thereby improving the system's observation coverage and redundancy. Compared to single-platform systems that are susceptible to factors such as obstruction and limited field of view, this invention, under multi-platform collaboration, possesses higher anti-interference capabilities and information fusion capabilities, effectively avoiding problems such as target loss and misjudgment, and improving the overall intelligence level and reliability of the system.

[0034] It is suitable for multi-unmanned vessel collaborative operations to perform continuous high-precision positioning and tracking of mobile targets at sea in GNSS denial or signal obstruction environments. Attached Figure Description

[0035] Figure 1 This is a schematic diagram illustrating the estimation of the target's position in the attached coordinate system.

[0036] Figure 2 This is a flowchart illustrating a method for continuous localization of moving targets by multiple unmanned surface vessels based on orientation information.

[0037] Figure 3 This is a graph showing the change in position error.

[0038] Figure 4 This is a graph showing the change in speed error. Detailed Implementation

[0039] To make the advantages and benefits of the technical solution provided by the present invention clearer, the technical solution provided by the present invention will now be described in further detail with reference to the accompanying drawings, specifically:

[0040] Implementation Method 1: This implementation method provides a continuous positioning method for moving targets by multiple unmanned surface vessels based on azimuth information, including:

[0041] The steps to construct a kinematic and dynamic mathematical model of multiple unmanned vessels in a two-dimensional plane and obtain the position, velocity and heading state information of each unmanned vessel are to be used as inputs for subsequent observer design.

[0042] The steps involve acquiring the relative bearing information of the communicating neighboring vessel and the suspected target in the coordinate system of each unmanned vessel, and combining it with the unmanned vessel's own state data to complete the coordinate transformation and generate the bearing observation input for target state estimation.

[0043] Based on the aforementioned azimuth observation input and the unmanned vessel's own state data, a nonlinear position observer is constructed to estimate the real-time position vector of the suspected target in the geodetic coordinate system.

[0044] Based on the nonlinear position observer, a velocity observer including an acceleration compensation term is constructed to estimate the velocity vector of the suspected target, thus realizing the step of dynamic continuous estimation;

[0045] The steps involved in constructing an error system and performing stability analysis based on the position and velocity estimation results;

[0046] The steps involve merging the estimation results from various unmanned vessels to achieve continuous localization and tracking of suspicious targets in GNSS-denied environments.

[0047] It also includes steps that take into account the longitudinal velocity, lateral velocity, and bow roll velocity of the unmanned vessel and their corresponding hydrodynamic disturbance parameters.

[0048] The coordinate transformation uses a rotation matrix to transform between the geodetic coordinate system and the attached coordinate system, and constructs a dynamic transformation relationship based on the initial and current heading angles of the unmanned vessel.

[0049] The relative bearing information is obtained in real time by a camera or other visual sensor, which acquires the relative angle of the target or adjacent vessel in the field of view, and uses the heading information provided by the IMU to estimate the bearing.

[0050] The acceleration compensation term introduced in the velocity observer is constructed from the derivative term of the estimated velocity and is used to improve the system's adaptability to non-uniform targets and the accuracy of observation.

[0051] An error system is constructed and its stability is analyzed by constructing the characteristic equation of the state matrix and determining the sign of its real part.

[0052] Implementation Method Two: This implementation method is a further detailed description of the technical solution provided in Implementation Method One, specifically:

[0053] A method for continuous positioning of moving targets by multiple unmanned surface vessels (USVs) based on azimuth information is proposed to address the problem of insufficient or complete failure of target positioning accuracy in environments with GNSS denial or signal obstruction, thereby improving the independent perception and continuous tracking capabilities of the USV system.

[0054] like Figure 1 and Figure 2 As shown, it includes the following steps:

[0055] The first step is to construct a kinematic and dynamic model of the unmanned vessel.

[0056] An unmanned surface vessel (USV) swarm system is defined, and a kinematic mathematical model is established for each USV in a two-dimensional plane. This model includes motion state variables such as its position coordinates, heading angle, longitudinal and lateral velocities, and bow roll rate, while considering inertial forces, hydrodynamic disturbances, and control input torques. The parameters introduced into the model can be obtained through tank experiments or empirical formulas. This model provides a complete theoretical foundation for the subsequent construction of observers and records the initial heading angle as the basis for subsequent local coordinate transformations.

[0057] The second step is to obtain azimuth observation information and perform coordinate transformation.

[0058] In each unmanned surface vessel's attached coordinate system, cameras or other visual sensors are used to perform image recognition of visible targets and neighboring vessels, extracting their relative azimuth information. Simultaneously, the current attitude information (such as heading angle, angular velocity, etc.) is acquired through the onboard inertial measurement unit (IMU). Based on the difference between the current heading and the initial heading, a rotation matrix is ​​constructed to realize the transformation of the target's relative azimuth vector from the local coordinate system to the unified geodetic coordinate system, providing a coordinate basis for target state estimation.

[0059] The third step is to construct a target state observer.

[0060] Based on the target's bearing information after coordinate transformation and the ship's own motion state, a nonlinear target position observer is designed to estimate the target's two-dimensional position vector. Considering that the target may be a time-varying velocity target, a velocity estimator is further introduced, incorporating an acceleration compensation term to enhance the system's response to changes in target velocity. This compensation term can be constructed based on current and historical velocity change trends, improving dynamic tracking accuracy. The observer structure satisfies the global stability conditions of a continuous-time system.

[0061] The fourth step is to establish the error system and analyze its convergence.

[0062] The position estimation error and velocity estimation error variables are defined, and the dynamic system of the error is modeled based on the constructed observer structure, deriving its derivative expression. Furthermore, the state matrix of the error system is constructed and its characteristic equation is obtained. By selecting appropriate control gain parameters, the real parts of all eigenvalues ​​are negative, i.e., the system satisfies the Hurwitz condition, ensuring the global asymptotic stability of the error system, meaning that the position and velocity estimation errors tend to zero over time.

[0063] The fifth step is to collaboratively integrate observation information from multiple unmanned surface vessels.

[0064] In a multi-platform collaborative architecture, each unmanned surface vessel (USV) shares its observed target azimuth data or state estimation results via a communication network. This invention employs a distributed weighted average or minimum variance fusion strategy to calculate the global target state estimate at the central node or locally on each vessel. This fusion mechanism not only improves the overall observation coverage of the system but also enhances robustness and anti-interference capabilities, avoiding target loss due to single-vessel malfunctions or limited field of view.

[0065] Step 6: Simulation verification and effect analysis.

[0066] Multiple simulation scenarios of unmanned surface vessels (USVs) tracking moving targets were built using a simulation platform. The targets were set to move along trajectories with varying speeds, and some USVs had their field of vision restricted or communication interrupted. The results show that the method of this invention can still achieve continuous and high-precision estimation of target position and velocity under complete GNSS rejection conditions. Moreover, the error converges quickly and the system is highly stable, verifying the feasibility and practicality of the proposed scheme.

[0067] In summary, by establishing an unmanned vessel dynamics model, designing a nonlinear state observer, constructing an error system, and introducing a collaborative fusion mechanism, the problem of continuous target positioning in environments where GNSS signals are unavailable has been solved, demonstrating good practical value and promising prospects for engineering application.

[0068] Implementation Method 3: Combination Figure 1-4 This embodiment describes the technical solution provided above in further detail through specific examples. Specifically:

[0069] (1) Establish a mathematical model of unmanned vessel motion.

[0070] Define the unmanned surface vessel swarm system as The mathematical model for each unmanned vessel is represented as follows:

[0071]

[0072]

[0073] In the formula, Indicates the coordinates of the unmanned surface vessel's position. Indicates the bow direction of the unmanned vessel. , and These represent the longitudinal velocity, lateral velocity, and bow roll velocity of the unmanned vessel, respectively. , and This represents the inertial force coefficient. and These represent longitudinal thrust and turning moment, respectively. , . .and This represents the hydrodynamic coefficient, which can be approximated through pool tests or relevant empirical formulas. , and It indicates external interference.

[0074] definition Indicates unmanned ship The position vector, Indicates unmanned ship The velocity vector. We can obtain:

[0075]

[0076] In the formula, The rotation matrix is ​​represented in the following form:

[0077]

[0078] Define a set of multi-objective systems as In the geodetic coordinate system In the middle, the first The goal is at any time Location information is represented as Speed ​​information is represented as On unmanned boats attached coordinate system In the middle, unmanned ships Pointing to target The position vector is represented as Unmanned boat Pointing to target The position unit vector is represented as ,Target The speed is expressed as Unmanned boat and target The distance between them is expressed as .

[0079] Assuming unmanned ships Only able to acquire the target Location information, then for unmanned ships Target status information and All of these are unknown quantities.

[0080] Defining unmanned ships Pointing to target The estimated position vector value is Unmanned boat and target The estimated distance between them is Unmanned boat Pointing to target The unit vector of the position estimation error is .

[0081] (2) Design the target position and velocity vector observer

[0082] definition Indicates the unmanned ship at the initial moment. The heading angle, Indicates the current time of the unmanned ship The heading angle. Then, the initial time and the current time... Heading error can be expressed as The rotation matrix at the current moment can be represented as:

[0083]

[0084] The rotation matrix satisfies the following relationship:

[0085]

[0086] The transformation relationship between the geodetic coordinate system and the attached coordinate system is as follows:

[0087]

[0088] Known Differentiating both sides simultaneously, we get:

[0089]

[0090] Therefore, in the attached coordinate system In the middle, unmanned ships Target The position vector observer can be designed as follows:

[0091]

[0092] In order to better capture time-varying velocities For the target system, adding an acceleration term to the target velocity observer can further improve the unmanned surface vessel (USV) performance. For the target The velocity observer is:

[0093]

[0094] In the formula, the acceleration term can be derived from... We obtain, among which Represents any small positive number. Acceleration term. The design is intended to ensure the safety of unmanned ships. For the target Position observation error and velocity observation error Global convergence property.

[0095] (3) Proof of stability

[0096] Defining unmanned ships For the target Position observation error and velocity observation error They are respectively:

[0097]

[0098]

[0099] Differentiating both sides simultaneously, we obtain the following relationship:

[0100]

[0101] achievable The derivative satisfies the following relationship:

[0102]

[0103] Rewritten in a simpler and more compact form, it can be represented as follows:

[0104]

[0105] In the formula,

[0106]

[0107] definition State matrix An eigenvalue. State matrix. The characteristic equation can be expressed as The eigenvalues ​​can be obtained through the characteristic equation. for In the formula, Representation matrix A characteristic value. This is determined by selecting control parameters. and , making The real part of all of them is negative, that is Then the state matrix It is the Herwitz matrix. Given the above reasoning, it can be proven that the unmanned ship... For the target Position observation error and velocity observation error The global asymptotic convergence is to zero.

[0108] The technical effect is as follows:

[0109] (1) A method for locating a moving target that relies solely on azimuth information, which can achieve continuous positioning of the moving target in a GNSS denied environment, and each unmanned vessel can estimate the position and velocity of the target in real time.

[0110] (2) It can realize real-time positioning of moving targets with varying degrees, which improves the ability of target positioning methods in complex task environments and realizes the estimation of target speed through neighbor information and target orientation information.

[0111] (3) The designed nonlinear observer has undergone rigorous theoretical analysis, which ensures that the target position and velocity estimation errors can converge globally to zero, thereby ensuring the high-precision positioning performance of the entire system.

[0112] (4) It provides a high-precision positioning solution that does not rely on GNSS signals, which greatly expands the application capabilities of multi-unmanned vessel systems in complex marine environments (such as nearshore, island and reef areas, and electromagnetic interference areas) or military GNSS denial scenarios for continuous monitoring and target tracking.

[0113] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for continuous localization of moving targets by multiple unmanned surface vessels based on orientation information, characterized in that, include: The steps to construct a kinematic and dynamic mathematical model of multiple unmanned vessels in a two-dimensional plane and obtain the position, velocity and heading state information of each unmanned vessel are to be used as inputs for subsequent observer design. The steps involve acquiring the relative azimuth information of the communicable neighboring vessel and the suspected target in the coordinate system of each unmanned vessel, and combining it with the unmanned vessel's own state data to complete the coordinate transformation and generate the azimuth observation input for target state estimation. Based on the azimuth observation input and the unmanned vessel's own state data, the steps are as follows: to construct a nonlinear position observer and estimate the real-time position vector of the suspicious target in the geodetic coordinate system. Based on the nonlinear position observer, a velocity observer containing an acceleration compensation term is constructed. The acceleration compensation term introduced in the velocity observer is constructed from the derivative term of the estimated velocity to estimate the velocity vector of the suspected target, thus realizing the step of dynamic continuous estimation. Based on the position and velocity estimation results, the steps for constructing an error system and performing stability analysis include: Define the position observation error of unmanned vessel i to target j. and velocity observation error They are respectively: In the attached coordinate system of unmanned vessel i, the position vector of unmanned vessel i pointing towards target j is represented as: The estimated position vector value is The speed at which unmanned vessel i points towards target j is denoted as Speed ​​estimate is Differentiating both sides simultaneously, we obtain the following relationship: have to The derivative satisfies the following relationship: The compact representation is as follows: In the formula, and The control parameters are represented by g; the unit vector representing the position of the unmanned vessel i pointing to the target j is denoted by g. ij ; Indicates the initial heading relative to the current time t (forward direction) The error; r i express Represents the rotation matrix at the current time; Representing the rotation matrix The derivative; Representing the rotation matrix The inverse of; define λ as an eigenvalue of the state matrix Υ1; The estimated distance between unmanned surface vessel i and target j is represented by the value of [missing information]. This represents the estimated position vector of unmanned surface vessel i pointing towards target j; the characteristic equation of the state matrix Y1 is expressed as... The eigenvalue λ can be obtained from the characteristic equation. In the formula, b represents the matrix. A characteristic value; by selecting control parameters and If all real parts of λ are negative, i.e. Re(λ) < 0, then the state matrix Υ1 is a Herwitz matrix; The steps involve merging the estimation results from various unmanned vessels to achieve continuous localization and tracking of suspicious targets in GNSS-denied environments. The collaborative fusion adopts a distributed weighted average or minimum variance fusion strategy to calculate the global estimation result of the target state at the central node or locally on each ship. The coordinate transformation uses a rotation matrix to transform between the geodetic coordinate system and the attached coordinate system, and constructs a dynamic transformation relationship based on the initial and current heading angles of the unmanned vessel.

2. The method for continuous positioning of a moving target by multiple unmanned surface vessels based on azimuth information according to claim 1, characterized in that, It also includes steps that take into account the longitudinal velocity, lateral velocity, and bow roll velocity of the unmanned vessel and their corresponding hydrodynamic disturbance parameters.

3. The method for continuous positioning of a moving target by multiple unmanned surface vessels based on azimuth information according to claim 1, characterized in that, The relative bearing information is obtained in real time by a camera or other visual sensor, which acquires the relative angle of the target or adjacent vessel in the field of view, and uses the heading information provided by the IMU to estimate the bearing.

4. A continuous positioning device for moving targets by multiple unmanned surface vessels based on orientation information, used to implement the continuous positioning method for moving targets by multiple unmanned surface vessels based on orientation information as described in any one of claims 1-3, characterized in that, include: A mathematical model of the kinematics and dynamics of multiple unmanned vessels in a two-dimensional plane is constructed to obtain the position, velocity and heading state information of each unmanned vessel, which serves as the input module for the subsequent design of the observer; In the coordinate system of each unmanned vessel, the relative azimuth information of the communicable neighboring vessel and the suspected target is obtained, and the coordinate transformation is completed by combining the unmanned vessel's own state data to generate a module for azimuth observation input for target state estimation. Based on the azimuth observation input and the unmanned vessel's own state data, a nonlinear position observer is constructed to estimate the real-time position vector of the suspicious target in the geodetic coordinate system. Based on the nonlinear position observer, a velocity observer including an acceleration compensation term is constructed to estimate the velocity vector of the suspected target, thus realizing a module for dynamic continuous estimation; A module that constructs an error system and performs stability analysis based on the position and velocity estimation results; This module integrates the estimation results from various unmanned vessels to achieve continuous localization and tracking of suspicious targets in GNSS-denied environments.

5. A computer storage medium for storing computer programs, characterized in that, When the computer program is read by the computer, the computer executes the method according to any one of claims 1-3.

6. A computer, comprising a processor and a storage medium, characterized in that, When the processor reads the computer program stored in the storage medium, the computer executes the method according to any one of claims 1-3.

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