A real-time calculation method for the relative motion state of two ships

Abstract

The present application discloses a method for real-time measurement of the relative motion state of two ships. The measurement method comprises the following steps: defining a coordinate system, establishing a ship motion model, fusing and observing the measurement information of the ship motion state based on an extended Kalman filter, calculating the motion state of any structural point on the hull, and correcting the clock and solving the relative motion state of the two ships. This application addresses the needs of motion state monitoring and motion control when two or more ships are working together in a windy and wavey environment. By fusing the hull posture measurement information with the hull six-degree-of-freedom motion state observation algorithm, the influence of the complex nonlinearity of the ship dynamics model is avoided. The measurement noise is filtered out by the extended Kalman filter algorithm, and redundant measurement information is integrated to obtain the optimal estimate of the real-time motion state of the ship. The relative motion state of the two ships in the longitudinal, transverse, heave, bow roll, roll and pitch directions is calculated based on a time-space consistent coordinate system.

Description

Technical Field

[0001] The present application relates to a real-time measurement method for the relative motion state of two ships, which is applicable to the measurement and calculation of state information such as relative position, relative speed and straight-line distance between two points when two or more ships are working together, and belongs to the field of ship and ocean engineering automation control technology. Background Art

[0002] With the in-depth development of digital and intelligent technologies in the field of shipbuilding and marine engineering, the problem of ship motion control when two or more ships are working together in windy and wavey conditions has become a research hotspot in the field of automated control in shipbuilding and marine engineering. Real-time measurement of the relative motion between two ships is key to solving this motion control problem and achieving efficient collaborative operations. In scenarios such as formation sailing, replenishment, and barge unloading, the relative motion between the two ships is not only affected by their maneuvering and sailing conditions, but is also closely related to their instantaneous seakeeping motion.

[0003] Chinese patent CN113485121A (application number CN2021108880673) invented "a distributed multi-ship collaborative dynamic positioning control method". According to the relationship between the multi-ship dynamic positioning sensors and the ship-to-ship communication network, the multi-ship collaborative error vector is calculated based on the collaborative control target state, and distributed control is performed. The influence of actuator failure is taken into account to improve the operating efficiency of multiple dynamic positioning ships in complex engineering scenarios. The collaborative error vector described in the patent refers to the error between the motion state vector of each ship and the collaborative target, not the real-time relative motion between the two ships. Instead, its collaborative target focuses more on the position and speed state of the navigation control process. Chinese patent CN113589271A (application number CN202110768809.9) invented "a measuring device and method for measuring the relative motion of two ships during docking and supply." This invention targets the impact of the relative heaving motion of the two ships on the floating crane operation during docking operations. It integrates measurement information from binocular cameras and radar ranging, laser ranging, ultrasonic ranging and other devices to measure the distance between the hoisted cargo and the hull deck in real time. Based on this, it compensates and controls the floating crane's lifting and lowering process to improve the accuracy and safety of offshore floating crane control. This patent focuses on the relative motion of the two ships in the vertical direction and does not involve the relative motion in the lateral, longitudinal and speed directions. The invention patent "System and methods for determining relative position and relative motion of objects" (U.S. Patent No. US2022 / 0089416A1, Japanese Patent No. JP2021544543) is based on an optical camera to form a time-series image of a preset target, and obtains the relative position and relative motion between objects by solving the time-series image. It serves as the input of control systems such as ship target tracking, helicopter landing, and floating cranes to provide guarantees for operations. It is usually used in operations such as offshore ship target tracking, helicopter landing, and dock cargo lifting. The above-mentioned patented technologies all involve optical image processing technology. The implementation process not only has a limited number of dimensions for measuring the relative motion of the two ships, but also cannot be applied in multi-ship collaborative operation scenarios. This application obtains the six-degree-of-freedom relative motion state information of the two ships in real time through observation processing and data fusion of high-frequency measurement information of the motion state of the two ships, and the optimal measurement of the relative motion state of the two ships. It has important practical significance for the development of monitoring and control technology for collaborative operations of two or more ships. Summary of the Invention

[0004] The purpose of this application is to provide a real-time measurement method for the relative motion state of two ships. Based on the motion state (six-degree-of-freedom posture and speed) of the collaborative operation ships, the relative motion state information between the two ships is obtained, and feedback information for the motion control and monitoring status of the collaborative operation of two or more ships is provided.

[0005] In order to achieve the above-mentioned object, the technical solution of the present application is to provide a method for real-time measurement of the relative motion state of two ships, characterized by comprising the following steps:

[0006] Step 1: Coordinate system definition, establish the global coordinate system, ship coordinate system and hull structure point data model respectively;

[0007] Step 2: Establish a ship motion model based on the ship kinematic equation;

[0008] Step 3: Perform measurement fusion and filter observation processing on the ship's motion state based on the Kalman filter algorithm;

[0009] Step 4: Calculation of the motion state of any structural point on the hull;

[0010] Step 5: Clock correction processing and calculation of the relative motion state of the two ships.

[0011] In the step 1, the global coordinate system and the ship coordinate system are defined according to the right-hand rule, and the north-east-ground coordinate system is used as the global coordinate system, with the X axis pointing to the north, the Y axis pointing to the east, the Z axis perpendicular to the horizontal plane downward, and the coordinate origin O N Located on the horizontal plane; the origin of the ship's coordinate system is O b Located at the intersection of the mid-longitudinal section, mid-transverse section and the waterline at the height of the ship's center of gravity, the x-axis is perpendicular to the mid-transverse section and points to the bow, and the y-axis is perpendicular to the mid-longitudinal section and points to the starboard. The right-hand rule determines the positive direction of the z-axis. The ship-borne coordinate system is fixed to the hull and moves synchronously with the hull's swaying. The northeast coordinate system is denoted as {n}, {b1} and {b2} are the two ship-borne coordinate systems, and the coordinate vectors of the origins of the two coordinate systems in {n} are and A and B are arbitrary structural points on the two hulls, and the corresponding coordinate vectors are and

[0012] In the second step, a motion model is established based on the ship's six-degree-of-freedom kinematic equation:

[0013]

[0014] In the above formula, η = (XYZ φ θ ψ) T is the position and attitude of the ship coordinate system {b} in the local coordinate system {n}, is the Euler angle, Δ t is the time step;

[0015] is the translation speed and rotation speed of the ship in the direction of each coordinate axis of the ship coordinate system, V b|0is the initial velocity, u, v, w represent the translational velocities of the ship in the surge, sway, and heave directions respectively, q, p, r represent the rotational velocities of the ship in the roll, pitch, and yaw directions respectively;

[0016] J(η) is the transformation matrix, which consists of the rotation matrix R and the translation matrix T. It corresponds to the transformation matrix of the linear velocity and angular velocity from {b} to {n}, respectively, and is only related to the Euler angle:

[0017]

[0018] Where c represents the cosine function, s represents the sin function, and t represents the tan function.

[0019] In step 3, a ship motion process model is established based on the ship motion equation, and an extended Kalman filter is used to form a design filter observation algorithm to achieve filtering, fusion and observation estimation of the ship motion state measurement information:

[0020]

[0021] in:

[0022] State vector x = [η; V b ];

[0023] Measurement vector y = (XY φ θ ψ uvwqpr) T ;

[0024] Nonlinear vector field

[0025] H is the measurement matrix, an 11x12 constant matrix;

[0026] ε P is the process noise vector;

[0027] ε M is the measurement noise vector;

[0028] E is the transformation matrix of process noise.

[0029] The forward Euler method is used to discretize the process model of formula (005):

[0030]

[0031] in: Γ k =Δ t ·E;

[0032] Δ t is the time step;

[0033] It is the predicted value at time k+1 based on the state estimation at time k;

[0034] is the estimated value of the state vector after correction at time k;

[0035] is the vector value of the estimated value of the state vector after correction in the nonlinear vector domain;

[0036] The Hessen matrix is obtained by taking the partial derivative of the vector value of the corrected estimate of the state vector in the nonlinear vector domain.

[0037] The steps of the observation method based on the extended Kalman filter are as follows:

[0038]

[0039] Among them, K k is the Kalman gain matrix, is the estimated value of the state vector after correction at time k-1; is the estimated value of the state covariance matrix after correction at time k-1; Φ k-1 is the state transfer matrix at time k-1; is the estimated value of the state vector after correction at time k-1; Q k is the noise matrix of the process at time k; is the predicted value of the state covariance matrix at time k; H k is the measurement matrix at time k; y k is the y-axis coordinate at time k.

[0040] In step 4, the motion state of any structural point of the hull is calculated as:

[0041] The optimal estimated value of the ship's current motion state is obtained through step 3; the motion state of the {b1} coordinate system is recorded as:

[0042]

[0043] is the estimated value of the corrected position and attitude of the ship coordinate system {b} in the local coordinate system {n} at time k;

[0044] is the estimated value of the translational velocity and rotational velocity of the ship in the directions of each coordinate axis of the ship coordinate system at time k after correction.

[0045] For point A in the {b1} coordinate system, its position and linear velocity in the north-east coordinate system {n} are calculated as follows:

[0046]

[0047] In the above formula:

[0048] The coordinate vector of point A in the hull {b1};

[0049] The coordinate vector of the origin of the hull {b1} in {n} at time k; The coordinate vector of point A at time k in {n};

[0050] {b1} Euler angle in {n} at time k;

[0051] The velocity vector of point A in the {n} coordinate system;

[0052] The angular velocity vector of the hull {b1} in the direction of the {n} coordinate axis;

[0053] is the rotation matrix that transforms the linear velocity from {b1} to {n};

[0054] is the translational velocity of the ship in the directions of each coordinate axis of the ship coordinate system.

[0055] is based on the hull Euler angle angular velocity vector The antisymmetric matrix is:

[0056]

[0057] By calculating formula (008), the coordinate vector and linear velocity vector of point A in the {b1} coordinate system and point B in the {b2} coordinate system in the northeast coordinate system {n} are obtained, which are expressed as follows:

[0058] and

[0059] Where k represents the current time step.

[0060] In step 5, the clock synchronization correction processing and relative motion state calculation of the two ships' motion state information are performed:

[0061] (009) is the coordinate vector and linear velocity vector of point A in the {b1} coordinate system and point B in the {b2} coordinate system in the northeast coordinate system {n}. The above state information and timestamp signal t are transmitted via wireless communication. r Send to the target ship; record {b1} ship as the receiver and {b2} ship as the sender; when {b1} ship receives the motion status information of point B of {b2} ship, based on the current clock information t n With the received clock signal tr Correction processing: Assuming that the rate of change of linear velocity and angular velocity is small, the azimuth change caused by time delay can be corrected according to the linear velocity, that is:

[0062]

[0063] in, is the coordinate vector of the north-east coordinate system {n} at the current time step k, is the velocity vector of the north-east coordinate system {n} at the current time step k, t k is the time t at the current time step k.

[0064] Therefore, the relative position and velocity of ship point B {b2} relative to ship point A {b1} are:

[0065]

[0066] in is the coordinate vector of point B in the northeast coordinate system {n} at time t, The coordinate vector of point A in the northeast coordinate system {n} at time t, The velocity vector of point B in the northeast coordinate system {n} at time t, Velocity vector of point A in the northeast coordinate system {n} at time t.

[0067] Formula (011) is obtained based on the six-degree-of-freedom motion model of the hull, and also includes the effects of the hull's translational and rotational motions.

[0068] The present application provides a method for real-time measurement of the relative motion state of two ships. Based on the real-time measurement of state information such as the ship's position, speed, attitude and angular velocity by ship-borne measurement equipment, and based on the six-degree-of-freedom ship motion model, the measurement information is observed and estimated and the ship-to-ship real-time communication is carried out. The method realizes real-time calculation of the relative position, relative speed and straight-line distance between two ships or two hull structure points, and provides accurate state feedback information for collaborative operation status monitoring of two or more ships and ship motion control. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 Define a schematic diagram for the coordinate system;

[0070] Figure 2 This is a schematic diagram of the shipboard data acquisition and communication system;

[0071] Figure 3 The first simulation test result: Schematic diagram of the position vector changes of points AB of the two ships in the {n} coordinate system;

[0072] Figure 4 This is the second simulation test result: a schematic diagram of the change in the straight-line distance between points AB and the change in the linear velocity of point B relative to point A. DETAILED DESCRIPTION

[0073] In order to make the present application more clear and easy to understand, preferred embodiments are described in detail below with reference to the accompanying drawings.

[0074] Example

[0075] This embodiment provides a real-time measurement method for the relative motion state of two ships. The method can obtain the relative motion state information between the two ships based on the motion state (six-degree-of-freedom posture and speed) of the collaborative operation ships, and provide feedback information for the motion control and monitoring state of the collaborative operation of two or more ships.

[0076] The specific steps include:

[0077] Step 1: Coordinate system definition, establish the global coordinate system, ship coordinate system and hull structure point data model respectively;

[0078] Step 2: Establish a ship motion model based on the ship kinematic equation;

[0079] Step 3: Perform measurement fusion and filter observation processing on the ship's motion state based on the EKF algorithm;

[0080] Step 4: Calculation of the motion state of any structural point on the hull;

[0081] Step 5: Clock correction processing and calculation of the relative motion state of the two ships.

[0082] Specifically, step 1, coordinate system definition: define the global coordinate system and the ship coordinate system according to the right-hand rule, and use the north-east-ground coordinate system as the global coordinate system, with the X axis pointing to the north, the Y axis pointing to the east, the Z axis perpendicular to the horizontal plane downward, and the coordinate origin O N Located on the horizontal plane, the specific position can be predetermined according to the characteristics of multi-ship collaborative operation and unified through the ship-to-ship communication system; the origin of the ship coordinate system O b Located at the intersection of the mid-longitudinal section, mid-transverse section and the waterline at the height of the ship's center of gravity, the x-axis is perpendicular to the mid-transverse section and points to the bow, the y-axis is perpendicular to the mid-longitudinal section and points to the starboard side. The right-hand rule determines the positive direction of the z-axis. The ship coordinate system is fixed to the hull and moves synchronously with the hull's swaying. Figure 1 As shown in the figure, {n} is the northeast coordinate system, {b1} and {b2} are the coordinate systems of the two ships, and the coordinate vectors of the origins of the two coordinate systems in {n} are and A and B are arbitrary structural points on the two hulls, and the corresponding coordinate vectors are and

[0083] Step 2: Establish a motion model based on the ship's six-degree-of-freedom kinematic equation:

[0084]

[0085] In the above formula, η = (XYZ φ θ ψ) T is the position and attitude (Euler angle) of the ship coordinate system {b} in the local coordinate system {n} );

[0086] is the translation speed and rotation speed of the ship in the direction of each coordinate axis of the ship coordinate system, V b|0 is the initial velocity;

[0087] J(η) is the transformation matrix, which consists of the rotation matrix R and the translation matrix T. It corresponds to the transformation matrix of the linear velocity and angular velocity from {b} to {n}, respectively, and is only related to the Euler angle:

[0088]

[0089] Where c represents the cosine function, s represents the sin function, and t represents the tan function. The above formula is only applicable to the relative motion measurement of surface ships, and the maximum roll angle does not exceed 45 degrees. In addition, according to the actual application scenario, the R and T matrices can be linearized based on the small angle assumption for the motion dimension of interest to improve the calculation efficiency.

[0090] Step 3: Ship motion observation based on the Extended Kalman Filter (EKF):

[0091] A ship motion process model is established based on the ship motion equation, and a filter observation algorithm is designed using an extended Kalman filter to achieve filtering, fusion, and observation estimation of the ship motion state measurement information:

[0092]

[0093] in:

[0094] State vector x = [η; V b ];

[0095] Measurement vector y = (XY φ θ ψ uvwqpr) T ;

[0096] Nonlinear vector field

[0097] H is the measurement matrix, an 11x12 constant matrix;

[0098] ε P is the process noise vector. The observation model is established based on the exact kinematic equation, which does not include dynamic factors. The process noise is mainly caused by acceleration changes.

[0099] ε M The measurement noise vector includes the measurement noise of GNSS position measuring instruments, 6-DOF gyroscopes, compasses, and other devices.

[0100] The forward Euler method is used to discretize the process model (005):

[0101]

[0102] in: Γ k =Δ t ·E;

[0103] Δ t is the time step;

[0104] It is the predicted value at time k+1 based on the state estimation at time k;

[0105] is the estimated value of the state vector after correction at time k.

[0106] The observation method based on the extended Kalman filter (EKF) is as follows:

[0107] Table 1 Ship posture observation method

[0108]

[0109] Among them, K k is the Kalman gain matrix.

[0110] Step 4: Calculation of the motion state of any structural point on the hull:

[0111] By using the method in step 3, the optimal estimate of the ship's current motion state is obtained. The motion state of the {b1} coordinate system can be written as:

[0112]

[0113] For point A in the {b1} coordinate system, its position and linear velocity in the north-east coordinate system {n} are calculated as follows:

[0114]

[0115] In the above formula:

[0116] The coordinate vector of point A in the hull {b1};

[0117] The coordinate vector of the origin of the hull {b1} in {n} at time k; The coordinate vector of point A at time k in {n};

[0118] {b1} Euler angle in {n} at time k;

[0119] The velocity vector of point A in the {n} coordinate system;

[0120] The angular velocity vector of the hull {b1} in the direction of the {n} coordinate axis;

[0121] is based on the hull Euler angle angular velocity vector The antisymmetric matrix is:

[0122]

[0123] By calculating formula (008), the coordinate vector and linear velocity vector of point A in the {b1} coordinate system and point B in the {b2} coordinate system in the northeast coordinate system {n} are obtained, which are expressed as follows:

[0124] and

[0125] Where k represents the current time step.

[0126] Step 5: Clock synchronization correction processing of the two ships' motion state information and relative motion state calculation:

[0127] Equation (009) is the coordinate vector and linear velocity vector of point A in the {b1} coordinate system and point B in the {b2} coordinate system in the northeast coordinate system {n}, through Figure 2 The ship-to-ship wireless communication system shown in FIG. r To facilitate explanation, assume that {b1} ship is the receiver and {b2} ship is the sender. When {b1} ship receives the motion status information of point B of {b2} ship, based on the current clock information t n With the received clock signal t r Correction processing: Assuming that the rate of change of linear velocity and angular velocity is small, the azimuth change caused by time delay can be corrected according to the linear velocity, that is:

[0128]

[0129] As can be seen from the above formula, the time delay generated by the ship-to-ship communication process has a direct impact on the measurement accuracy of the relative motion state of the two ships, especially the calculation of the linear velocity. Therefore, to ensure the measurement accuracy, ship-to-ship wireless communication equipment with high real-time performance should be used to reduce the time delay generated by the signal sending, transmission, receiving and processing processes.

[0130] Therefore, the relative position and velocity of ship point B {b2} relative to ship point A {b1} are:

[0131]

[0132] Equation (011) is calculated based on the hull's six-degree-of-freedom motion model and includes the effects of the hull's translational and rotational motion. In practical applications, the above method can be simplified according to specific application requirements. For example, in formation sailing, the main focus is on the ship's relative position, heading, and speed in the horizontal plane, and the influence of the rocking motion caused by the wave environment can be ignored. The above method can be correspondingly simplified to a three-degree-of-freedom motion equation in the horizontal plane (X, Y, ψ). For ship lateral supply operations and floating crane transfer operations, the ship's six-degree-of-freedom rocking motion has a significant impact on operational efficiency and process safety.

[0133] The present invention utilizes real-time measurement information from a GNSS measuring instrument (for measuring position, speed, heading, etc.), a compass unit (heading), and a six-degree-of-freedom gyroscope (capable of outputting axial acceleration, linear velocity, and angular velocity). Based on the six-degree-of-freedom motion model of a ship, an extended Kalman filter (EKF) is used to observe and estimate the real-time motion state of the ship. The coordinate position and linear velocity of any structural point of the ship in the northeast coordinate system are obtained according to the principle of rigid body rotation transformation. The real-time relative motion state between any structural points of the two ships is calculated through a wireless communication link between the ships. In practical applications, different types of measurement sensors can be configured in a redundant manner according to specific application scenarios, and the state vector, transfer matrix, and observation matrix in equation (005) and the method can be adjusted to achieve multi-sensor measurement fusion, obtain high-precision state estimation, and improve overall functional reliability. The method is based on the six-degree-of-freedom motion equation of the ship and the principle of rigid body rotation change. It is general and can accurately measure the relative motion between swaying ships, provide real-time state feedback for state monitoring and motion control of the collaborative operation of two ships in a windy and wavey environment, and is of great significance for ensuring the efficiency and safety of collaborative operations.

[0134] The implementation of this method relies on conventional navigation and communication equipment on engineering vessels, making it easy to integrate and apply, such as computer systems, hull position and attitude measurement instruments, and ship-to-ship wireless communication systems. The computer system receives real-time status information such as time, ship position and speed from the ship-borne position and attitude measurement equipment. It uses an extended Kalman filter to observe and estimate the hull motion state. The ship-to-ship wireless communication system enables state information to be shared between two or more ships, and the relative motion state between the two ships is calculated.

[0135] The hull attitude measuring instrument mainly includes GNSS positioning measuring instruments, such as Figure 2 GNSS; six-degree-of-freedom gyroscope (or inertial navigation unit IMU), such as Figure 2 IMU; compass unit, such as Figure 2 Gyro. GNSS measures the ship's position, speed (ground speed), heading and UTC time (millisecond level) in real time. Figure 1 In the coordinate system established in , first determine the coordinate vector of the GNSS antenna in {b} as And according to the GNSS measurement output: the position vector in the {n} coordinate system (GNSS does not output vertical position, assuming ), ground speed U, heading angle χ, and calculate the coordinate vector of the origin of the {b} coordinate system in {n} through the principle of rigid body rotation transformation. And horizontal speed u, v (i.e. longitudinal and transverse speed of the ship):

[0136]

[0137] The six-degree-of-freedom gyroscope (IMU) can measure and output the angular velocity of the hull in real time and the linear acceleration at its installation location and instantaneous linear velocity Or the Euler angle of the hull. Assume that its coordinate vector in {b} is Through transformation processing, the linear acceleration and linear velocity at the origin of the {b} coordinate system can be obtained according to the IMU measurement output:

[0138]

[0139] According to the above formula, the acceleration at the IMU installation point in the {b} coordinate system consists of three parts: the linear acceleration vector of the point in the direction of the {n} coordinate axis, the centrifugal acceleration generated by the rotation of the {b} coordinate system at this point, and the {b} coordinate system rotation acceleration. The resulting tangential acceleration can usually be assumed to be The errors can be processed through observation estimation. Based on the coordinate transformation processing formulas (011)-(013) of the GNSS and IMU measurement information, the measurement matrix H is directly obtained. To avoid the above complex transformation processing, the IMU can be installed at the origin of the {b} coordinate system, or the gyroscope supplier can be contacted and the gyroscope installation position can be determined in advance. The conversion processing is performed within the gyroscope to directly output the linear acceleration and linear velocity of the {b} coordinate system origin. To ensure the measurement accuracy of the gyroscope, GNSS position information is usually connected to achieve accurate correction of the gravity field.

[0140] A ship's heading angle is key information for navigation. While an IMU can output this information, it's typically measured with specialized measurement devices such as a magnetic compass, gyrocompass, or fiber optic compass. Because wind and wave conditions create wave-frequency characteristics in ship motion, and relative motion requires observation and calculation of the ship's wave-frequency motion, the measurement equipment's information acquisition and output frequency should be no less than 10Hz.

[0141] Figure 2 In the equation (1), PAS represents the shipborne attitude monitoring and processing unit, which can be a dedicated attitude monitoring computer or a dynamic positioning control computer with this function integrated. It automatically synchronizes with the UTM time from the global navigation satellite system (GNSS) and receives and processes position measurement information from GNSS, IMU, and GYRO. It estimates the hull motion state through the EKF observation method (Table 1). According to the collaborative operation requirements and the hull structure scale characteristics, it calculates the coordinate vector and linear velocity of the hull structure point in the {n} coordinate system (Equation 009). The state information is packaged and sent to the PAS system of the target ship through the ship-to-ship wireless communication system, or the target ship's motion state information package is received, thereby completing the calculation and processing of the relative motion state of the two ships in the unified time and space coordinate system (Equation 010).

[0142] The real-time measurement method of the relative motion state of two ships provided in this application is mainly applicable to the collaborative operation of two or more ships, including the monitoring of the relative motion state and the control of ship motion in scenarios such as replenishment, barge unloading, formation navigation, and target tracking of two or more ships. The implementation of this measurement method relies on the state information collected by the ship's posture measuring instrument and the posture information calculation and processing unit (PAS), and the transmission of information through the real-time communication system of two or more ships. The real-time communication system adopts a wireless communication link that complies with the 4G standard and has self-organizing network function to meet the communication bandwidth and real-time requirements. It is based on equipment such as the global navigation satellite system (GNSS) position measuring instrument, a six-degree-of-freedom gyroscope (or inertial navigation unit, IMU), and a compass. The GNSS position measuring instrument measures the ship's position and speed, outputting information such as the ship's longitude and latitude position, the ship's speed and heading relative to the ground, and the UTM clock. The IMU measures and outputs the ship's linear acceleration and angular velocity in the longitudinal (Surge), lateral (Sway), and heave (Heave) directions, and calculates and outputs the linear velocity and hull attitude angle. The compass measures the ship's heading angle in real time and can simultaneously output the bow rotation speed. All of the above measurement sensors use an RS422 serial interface, the protocol complies with NMEA0183, and the output frequency is no less than 10Hz. The ship's posture information processing unit has built-in integrated calculation and processing functions for ship posture information, mainly including the establishment of a time-space consistent coordinate system based on real-time ship-to-ship communication, the ship's six-degree-of-freedom motion state observation and estimation based on the EKF, the calculation of the position and linear velocity of ship feature points, and the calculation and processing of the relative position, relative velocity, and straight-line distance between two ships or feature points. The EKF-based ship six-degree-of-freedom state observation and estimation method has a process model as shown in equation (005), a linearization process as shown in equation (006), and specific method steps as described in Table 1. The relative position, relative velocity, and straight-line distance between two ships or feature points are calculated and processed as shown in equations (008) and (011). The method for real-time measurement of the relative motion state of two ships provided by the present invention is universal and can calculate the relative position, relative attitude, and relative linear velocity between two or more ships in real time. It can also calculate the relative state information and straight-line distance between any two points based on the coordinate vectors of the hull structure points.

[0143] The core of this technical solution is multi-sensor fusion processing based on an extended Kalman filter. It uses the six-degree-of-freedom equation of motion to establish a motion observation model, ignoring the influence of ship dynamics. It comprehensively considers the noise characteristics of the measurement equipment to optimally estimate the ship's motion state, and obtains the relative motion state between the two ships through clock synchronization and real-time communication. This method is general and can be adjusted to the specific application requirements of two or more ships' collaborative operations to simplify the processing process. For example, when ships are sailing in formation, only the horizontal position of the ships needs to be considered, and the influence of other states can be ignored. If the collaborative operation involves relative vertical motion between the two ships, the heave position measurement information must be configured during implementation.

Claims

1. A method for real-time measurement of the relative motion state of two ships, characterized in that: The following steps are involved: Step 1: Coordinate system definition, establish the global coordinate system, ship coordinate system and hull structure point data model respectively; Step 2: Establish a ship motion model based on the ship's six-degree-of-freedom kinematic equation; In the above formula, η = (XYZ φ θ ψ) T is the position and attitude of the ship coordinate system {b} in the local coordinate system {n}, is the Euler angle; is the translation speed and rotation speed of the ship in the direction of each coordinate axis of the ship coordinate system, u, v, w represent the translation speed of the ship in the longitudinal, transverse and heaving directions respectively, q, p, r represent the rotation speed of the ship in the rolling, pitching and bowing directions respectively, V b|0 is the initial velocity; Δ t is the time step; J(η) is the transformation matrix, which consists of the rotation matrix R and the translation matrix T. It corresponds to the transformation matrix of the linear velocity and angular velocity from {b} to {n}, respectively, and is only related to the Euler angle: Where c represents the cosine function, s represents the sin function, and t represents the tan function. The above formula is only applicable to the relative motion measurement of surface ships, and the maximum roll angle does not exceed 45 degrees; Step 3: Perform measurement fusion and filter observation processing on the ship's motion state based on the Kalman filter algorithm; in: State vector x = [η; V b ]; Measurement vector y = (XY φ θ ψ uvwqpr) T ; Nonlinear vector field E is the transformation matrix of process noise; H is the measurement matrix; ε P is the process noise vector; ε M The noise vector is the measurement noise, which includes the measurement noise of the GNSS position measuring instrument, the six-degree-of-freedom gyroscope, and the compass equipment. Step 4: Calculation of the motion state of any structural point on the hull; Step 5: Clock correction processing and calculation of the relative motion state of the two ships.

2. The method for real-time calculation of the relative motion state of two ships according to claim 1, characterized in that: In the step 1, the global coordinate system and the ship coordinate system are defined according to the right-hand rule, and the north-east-ground coordinate system is used as the global coordinate system, with the X axis pointing to the north, the Y axis pointing to the east, the Z axis perpendicular to the horizontal plane downward, and the coordinate origin O N Located on the horizontal plane; the origin of the ship's coordinate system is O b Located at the intersection of the mid-longitudinal section, mid-transverse section and the waterline at the height of the ship's center of gravity, the x-axis is perpendicular to the mid-transverse section and points to the bow, and the y-axis is perpendicular to the mid-longitudinal section and points to the starboard. The right-hand rule determines the positive direction of the z-axis. The ship-borne coordinate system is fixed to the hull and moves synchronously with the hull's swaying. The northeast coordinate system is denoted as {n}, {b1} and {b2} are the two ship-borne coordinate systems, and the coordinate vectors of the origins of the two coordinate systems in {n} are and A and B are arbitrary structural points on the two hulls, and the corresponding coordinate vectors are and 3. The method for real-time calculation of the relative motion state of two ships according to claim 2, characterized in that: In step 3, a ship motion process model is established based on the ship motion equation, and an extended Kalman filter is used to form a design filter observation algorithm to achieve filtering, fusion and observation estimation of the ship motion state measurement information: The forward Euler method is used to discretize the process model (005): Among them: C k =D t ·E; Δ t is the time step; It is the predicted value at time k+1 based on the state estimation at time k; is the estimated value of the state vector after correction at time k; is the vector value of the estimated value of the state vector after correction in the nonlinear vector domain, The Hessen matrix is obtained by taking the partial derivative of the vector value of the corrected estimate of the state vector in the nonlinear vector domain; The steps of the observation method based on the extended Kalman filter are as follows: Among them, K k is the Kalman gain matrix, is the estimated value of the state vector after correction at time k-1, is the estimated value of the state covariance matrix after correction at time k-1, Φ k-1 is the state transfer matrix at time k-1, is the estimated value of the state vector after correction at time k-1, Q k is the k-time process noise matrix, is the predicted value of the state covariance matrix at time k, H k is the measurement matrix at time k, y k is the y-axis coordinate at time k.

4. The method for real-time calculation of the relative motion state of two ships according to claim 3, characterized in that: In step 4, the motion state of any structural point on the hull is calculated as follows: the optimal estimated value of the motion state of the ship at the current moment is obtained through step 3; the motion state of the {b1} coordinate system is recorded as: in, is the estimated value of the corrected position and attitude of the ship coordinate system {b} in the local coordinate system {n} at time k, is the estimated value of the translational velocity and rotational velocity of the ship in the directions of the coordinate axes of the ship coordinate system at time k after correction; For point A in the {b1} coordinate system, its position and linear velocity in the north-east coordinate system {n} are calculated as follows: in, is the rotation matrix that transforms the linear velocity from {b1} to {n}, is the translation speed of the ship in the directions of each coordinate axis of the ship coordinate system; In the above formula: The coordinate vector of point A in the hull {b1}; The coordinate vector of the origin of the hull {b1} in {n} at time k; The coordinate vector of point A at time k in {n}; {b1} Euler angle in {n} at time k; The velocity vector of point A in the {n} coordinate system; The angular velocity vector of the hull {b1} in the direction of the {n} coordinate axis; is based on the hull Euler angle angular velocity vector The antisymmetric matrix is: By calculating formula (008), the coordinate vector and linear velocity vector of point A in the {b1} coordinate system and point B in the {b2} coordinate system in the northeast coordinate system {n} are obtained, which are expressed as follows: Where k represents the current time step.

5. The method for real-time measurement of the relative motion state of two ships according to claim 4, characterized in that: In step 5, the clock synchronization correction processing and relative motion state calculation of the two ships' motion state information are performed: (009) is the coordinate vector and linear velocity vector of point A in the {b1} coordinate system and point B in the {b2} coordinate system in the northeast coordinate system {n}. The above state information and timestamp signal t are transmitted via wireless communication. r Send to the target ship; record {b1} ship as the receiver and {b2} ship as the sender; When the {b1} ship receives the motion status information of point B of the {b2} ship, based on the current clock information t n With the received clock signal t r Correction processing: Assuming that the rate of change of linear velocity and angular velocity is small, the azimuth change caused by time delay can be corrected according to the linear velocity, that is: in, is the coordinate vector of the north-east coordinate system {n} at the current time step k, is the velocity vector of the north-east coordinate system {n} at the current time step k, t k is the time t at the current time step k; Therefore, the relative position and velocity of ship point B {b2} relative to ship point A {b1} are: in is the coordinate vector of point B in the northeast coordinate system {n} at time t, The coordinate vector of point A in the northeast coordinate system {n} at time t, The velocity vector of point B in the northeast coordinate system {n} at time t, The velocity vector of point A in the northeast coordinate system {n} at time t; Formula (011) is obtained based on the six-degree-of-freedom motion model of the hull, and also includes the effects of the hull's translational and rotational motions.

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