An underwater vehicle time-varying parameter identification method, device, equipment and medium

Abstract

The application relates to the technical field of autonomous navigation and motion control of underwater vehicles, and particularly provides a time-varying parameter identification method, device, equipment and medium for an underwater vehicle, which comprises the following steps: S1, acquiring motion state parameters and control input parameters; S2, generating an observation output vector set and a prediction output vector set according to the motion state parameters and the control input parameters; S3, for each degree of freedom, analyzing whether the norm of a regression vector is greater than or equal to a preset threshold value, if yes, executing step S4, and if not, taking the time-varying parameter vector at the last moment as the time-varying parameter vector at the current moment, and generating a covariance matrix based on the observation output vector and the prediction output vector; S4, generating the time-varying parameter vector at the current moment based on the observation output vector and the prediction output vector, the gain matrix at the current moment and the time-varying parameter vector at the last moment; the method can improve the precision and reliability of autonomous navigation and motion control of underwater vehicles.

Description

Technical Field

[0001] This application relates to the field of autonomous navigation and motion control technology for underwater vehicles, and more specifically, to a method, apparatus, equipment, and medium for identifying time-varying parameters of underwater vehicles. Background Technology

[0002] In the field of autonomous navigation and motion control of underwater vehicles, accurate identification of dynamic model parameters is crucial for ensuring system stability and control precision. Existing technologies suffer from the following problems: Traditional methods are mostly based on three-degree-of-freedom models in the horizontal plane, which only consider sway, roll, and pitch motions, while ignoring the coupling effect of roll motion with other degrees of freedom. In reality, when underwater vehicles are disturbed by wind, waves, currents, or when operating their thrusters, they are very prone to rolling motion. Excessive roll angles may cause the vehicle to capsize. Therefore, using only a three-degree-of-freedom model cannot meet the motion prediction requirements in complex and variable environments.

[0003] Existing identification methods typically treat dynamic parameters as fixed values, failing to adequately consider the impact of environmental changes, load adjustments, and attitude changes experienced by underwater vehicles during actual operation. This fixed-parameter model struggles to accurately capture the dynamic characteristics of parameter changes, leading to a continuous accumulation of identification errors and severely reducing the accuracy of predicting vehicle maneuverability.

[0004] There is currently no effective technical solution to the above problems. Summary of the Invention

[0005] The purpose of this application is to provide a method, device, equipment and medium for identifying time-varying parameters of underwater vehicles, which can improve the accuracy and reliability of autonomous navigation and motion control of underwater vehicles.

[0006] In a first aspect, this application provides a method for identifying time-varying parameters of an underwater vehicle, which includes the following steps: S1. Obtain the motion state parameters and control input parameters of the underwater vehicle at the current moment; S2. Generate the observation output vector set and the prediction output vector set at the current moment based on the motion state parameters and control input parameters; the observation output vector set includes the observation output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom, and the prediction output vector set includes the prediction output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom. S3. For each degree of freedom, generate the regression vector of that degree of freedom at the current time based on the motion state parameters and control input parameters. Then analyze whether the norm of the regression vector is greater than or equal to a preset threshold. If yes, proceed to step S4. If no, use the time-varying parameter vector of that degree of freedom at the previous time as the time-varying parameter vector of that degree of freedom at the current time. Generate the covariance matrix of that degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to that degree of freedom, and return to step S1. S4. Based on the observed output vector and predicted output vector corresponding to the degree of freedom, the gain matrix of the degree of freedom at the current time and the time-varying parameter vector of the degree of freedom at the previous time, generate the time-varying parameter vector of the degree of freedom at the current time, and return to step S1; the gain matrix of the degree of freedom at the current time is generated based on the covariance matrix of the degree of freedom at the previous time.

[0007] This application provides a time-varying parameter identification method for underwater vehicles. By introducing a four-degree-of-freedom model and an adaptive parameter update mechanism, it effectively solves the problem that traditional fixed-parameter models cannot accurately identify the dynamic parameters of underwater vehicles in complex and variable environments, thereby improving the accuracy and reliability of autonomous navigation and motion control of underwater vehicles.

[0008] Optionally, step S1 includes: S11. Obtain the motion state parameters and control input parameters of the underwater vehicle at the current moment; S12. Perform outlier removal and linear interpolation replacement on the motion state parameters and control input parameters.

[0009] Optionally, the motion state parameters include the current pitch speed, sway speed, roll angle, roll rate, and yaw rate; the control input parameters include the current propeller speed and thruster angle; and step S2 includes: S21. Calculate the regression vector of the sway degree of freedom at the current moment based on the sway velocity, sway velocity, yaw rate, propeller speed, and thruster angle. Then, calculate the predicted output vector of the sway degree of freedom at the current moment based on the regression vector of the sway degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S22. Calculate the regression vector of the sway degree of freedom at the current moment based on the sway velocity, yaw rate, roll angle, pitch velocity and thruster angle. Then, calculate the predicted output vector of the sway degree of freedom at the current moment based on the regression vector of the sway degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S23. Calculate the regression vector of the roll degree of freedom at the current moment based on the roll angular velocity, roll angle, sway velocity, yaw angular velocity, pitch velocity and thruster angle. Then, calculate the predicted output vector of the roll degree of freedom at the current moment based on the regression vector of the roll degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S24. Calculate the regression vector of the bow degree of freedom at the current moment based on the bow angular velocity, sway velocity, roll angle, pitch velocity and thruster angle. Then, calculate the predicted output vector of the bow degree of freedom at the current moment based on the regression vector of the bow degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S25. Integrate all predicted output vectors into a set of predicted output vectors for the current time step; S26. Calculate the observation output vectors corresponding to the pitch, sway, roll, and yaw degrees of freedom based on the pitch velocity, sway velocity, roll angle, roll angular velocity, yaw angular velocity, propeller speed, and thruster angle, respectively. S27. Integrate all observation output vectors into the observation output vector set at the current time.

[0010] Optionally, the formula for calculating the regression vector of the sway degrees of freedom at the current moment is: ; in, Let u[k] represent the regression vector of the sway degree of freedom at the current moment, v[k] represent the sway velocity at the current moment, r[k] represent the bow roll rate at the current moment, and n[k] represent the propeller rotation speed at the current moment. Indicates the thruster angle at the current moment; The formula for calculating the regression vector of the sway degrees of freedom at the current moment is: ; in, This represents the regression vector of the sway degrees of freedom at the current moment. Indicates the current roll angle; The formula for calculating the regression vector of the roll degree of freedom at the current moment is: ; in, p[k] represents the regression vector of the roll degree of freedom at the current moment, and p[k] represents the roll angular velocity at the current moment; The formula for calculating the regression vector of the bow roll degree of freedom at the current moment is: ; in, This represents the regression vector of the bow roll degree of freedom at the current moment; The formulas for calculating the predicted output vectors of the sway, roll, and pitch degrees of freedom at the current time are the same. The formula for calculating the predicted output vector of the sway degree of freedom at the current time is: ; Among them, y yu [k] represents the predicted output vector of the sway degrees of freedom at the current moment. θ represents the transpose of the regression vector of the sway degrees of freedom at the current moment. yu [k-1] represents the time-varying parameter vector of the sway degrees of freedom at the previous time step.

[0011] Optionally, the formula for calculating the observed output vector of the sway degrees of freedom at the current moment is: ; Among them, y gu [k] represents the observed output vector of the sway degrees of freedom at the current moment, X H This represents the force along the X-axis of the underwater vehicle body. P This represents the force exerted by the propeller along the X-axis, X R This represents the force of the thruster along the X-axis, X uu X represents the dynamic coefficient of the first underwater vehicle. vv X represents the dynamic coefficient of the second underwater vehicle. rr X represents the dynamic coefficient of the third underwater vehicle. vr X represents the dynamic coefficient of the fourth underwater vehicle. n Let represent the propeller correlation coefficient, u[k] represent the sway velocity at the current moment, v[k] represent the yaw velocity at the current moment, r[k] represent the bow roll rate at the current moment, and n[k] represent the propeller rotational speed at the current moment. This indicates the thruster angle at the current moment. Indicates the force coefficient of the first thruster; The formula for calculating the observed output vector of the sway degree of freedom at the current moment is: ; Among them, y gv [k] represents the observed output vector of the sway degrees of freedom at the current moment, Y H This represents the force along the Y-axis of the underwater vehicle body. P This represents the force of the propeller along the Y-axis, Y R This represents the force of the thruster along the Y-axis, Y v Y represents the dynamic coefficient of the fifth underwater vehicle. |v|v Y represents the dynamic coefficient of the sixth underwater vehicle. r|r|This indicates the dynamic coefficient of the seventh underwater vehicle. Y represents the dynamic coefficient of the eighth underwater vehicle. r Y represents the dynamic coefficient of the ninth underwater vehicle. |v|r This indicates the dynamic coefficient of the tenth underwater vehicle. Indicates the current roll angle. Indicates the force coefficient of the second thruster; The formula for calculating the observed output vector of the roll degree of freedom at the current moment is: ; Among them, y gp [k] represents the observed output vector of the roll degree of freedom at the current moment, K H K represents the torque of the underwater vehicle body about the X-axis. P K represents the torque of the propeller about the X-axis. R K represents the torque of the thruster about the X-axis. p This indicates the dynamic coefficient of the eleventh underwater vehicle. K represents the dynamic coefficient of the twelfth underwater vehicle. v K represents the dynamic coefficient of the thirteenth underwater vehicle. r p[k] represents the dynamic coefficient of the fourteenth underwater vehicle, and p[k] represents the roll rate at the current moment. Indicates the torque coefficient of the first thruster; The formula for calculating the observation output vector of the bow degree of freedom at the current moment is: ; Among them, y gr [k] represents the observation output vector of the bow roll degree of freedom at the current moment, N H The torque (N) representing the force on the underwater vehicle body about the Z-axis. P The torque of the propeller about the Z-axis, N R The torque of the thruster about the Z-axis, N r N represents the dynamic coefficient of the fifteenth underwater vehicle. r|r| N represents the dynamic coefficient of the sixteenth underwater vehicle. v N represents the dynamic coefficient of the seventeenth underwater vehicle. vvr N represents the dynamic coefficient of the eighteenth underwater vehicle. vrr This indicates the dynamic coefficient of the nineteenth underwater vehicle. This indicates the dynamic coefficient of the twentieth underwater vehicle. This represents the torque coefficient of the second thruster.

[0012] Optionally, step S3 includes: S31. For each degree of freedom, generate the regression vector of that degree of freedom at the current moment based on the motion state parameters and control input parameters, and then analyze whether the norm of the regression vector is greater than or equal to the preset threshold. If yes, proceed to step S4; otherwise, proceed to step S32. S32. Use the time-varying parameter vector of the degree of freedom at the previous time step as the time-varying parameter vector of the degree of freedom at the current time step, and set the gain matrix of the degree of freedom at the current time step to 0. S33. Calculate the posterior prediction bias at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom, and then calculate the forgetting factor at the current time based on the posterior prediction bias, the preset lower limit of the forgetting factor and the preset sensitivity coefficient. S34. Calculate the covariance matrix at the current time based on the covariance matrix of the degree of freedom at the previous time and its regression vector at the current time, and return to step S1. Step S4 includes: S41. Calculate the posterior prediction bias at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom. S42. Calculate the forgetting factor at the current time based on the posterior prediction bias, the preset lower limit of the forgetting factor, and the preset sensitivity coefficient; S43. Calculate the gain matrix at the current time based on the covariance matrix of the degree of freedom at the previous time and its regression vector at the current time. S44. Generate the time-varying parameter vector of the degree of freedom at the current time based on the posterior prediction bias and the gain matrix of the degree of freedom at the current time and its time-varying parameter vector at the previous time. S45. Generate the covariance matrix of the degree of freedom at the current time based on the forgetting factor, the identity matrix, the regression vector of the degree of freedom at the current time, and the covariance matrix of the degree of freedom at the previous time, and return to step S1; the dimension of the identity matrix is ​​the same as the dimension of the covariance matrix.

[0013] Optionally, the formula for calculating the posterior prediction bias at the current time is: ; Where e[k] represents the posterior prediction bias at the current time, y g [k] represents the observed output vector at the current time corresponding to the degrees of freedom of the regression vector whose norm is greater than or equal to a preset threshold. y [k] represents the predicted output vector at the current time corresponding to the norm of the regression vector that is greater than or equal to the preset threshold; The formula for calculating the forgetting factor at the current moment is: ; Where λ[k] represents the forgetting factor at the current time, λmin represents the preset lower limit of the forgetting factor, and γ represents the preset sensitivity coefficient; The formula for calculating the gain matrix at the current moment is: ; Where G[k] represents the gain matrix at the current time step, This represents the covariance matrix of the degrees of freedom corresponding to the norm of regression vectors that are greater than or equal to a preset threshold, at the previous time step. This represents the regression vector at the current time corresponding to the norm of regression vectors that are greater than or equal to a preset threshold. This represents the transpose of the regression vector at the current time, corresponding to the degrees of freedom of the regression vector whose norm is greater than or equal to a preset threshold. The formula for calculating the time-varying parameter vector at the current moment is: ; Where θ[k] represents the time-varying parameter vector of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the current time, and θ[k-1] represents the time-varying parameter vector of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the previous time. The formula for calculating the covariance matrix at the current time is: ; in, I represents the covariance matrix of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the current time, where I represents the identity matrix.

[0014] Secondly, this application also provides a time-varying parameter identification device for underwater vehicles, comprising: The parameter acquisition module is used to acquire the motion state parameters and control input parameters of the underwater vehicle at the current moment; The vector generation module is used to generate the observation output vector set and the prediction output vector set at the current moment based on the motion state parameters and control input parameters. The observation output vector set includes the observation output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom, and the prediction output vector set includes the prediction output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom. The analysis module is used to generate a regression vector for each degree of freedom at the current time based on the motion state parameters and control input parameters. Then, it analyzes whether the norm of the regression vector is greater than or equal to a preset threshold. If so, it triggers the update module. If not, it uses the time-varying parameter vector of the degree of freedom at the previous time as the time-varying parameter vector of the degree of freedom at the current time. Based on the observed output vector and predicted output vector corresponding to the degree of freedom, it generates the covariance matrix of the degree of freedom at the current time and triggers the parameter acquisition module. The update module is used to generate the time-varying parameter vector of the degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom, the gain matrix of the degree of freedom at the current time and the time-varying parameter vector of the degree of freedom at the previous time, and to trigger the parameter acquisition module; the gain matrix of the degree of freedom at the current time is generated based on the covariance matrix of the degree of freedom at the previous time.

[0015] This application provides a time-varying parameter identification device for underwater vehicles. By introducing a four-degree-of-freedom model and an adaptive parameter update mechanism, it effectively solves the problem that traditional fixed parameter models cannot accurately identify the dynamic parameters of underwater vehicles in complex and variable environments, thereby improving the accuracy and reliability of autonomous navigation and motion control of underwater vehicles.

[0016] Thirdly, this application provides an electronic device including a processor and a memory, the memory storing computer-readable instructions, which, when executed by the processor, perform the steps of the method provided in the first aspect above.

[0017] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the method provided in the first aspect above.

[0018] As can be seen from the above, the underwater vehicle time-varying parameter identification method, device, equipment and medium provided in this application effectively solves the problem that traditional fixed parameter models cannot accurately identify the dynamic parameters of underwater vehicles in complex and variable environments by introducing a four-degree-of-freedom model and an adaptive parameter update mechanism, thereby improving the accuracy and reliability of the autonomous navigation and motion control of underwater vehicles. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a method for identifying time-varying parameters of an underwater vehicle, as provided in an embodiment of this application.

[0020] Figure 2 This is a schematic diagram of the structure of an underwater vehicle time-varying parameter identification device provided in an embodiment of this application.

[0021] Figure 3This is a schematic diagram of an electronic device structure provided in an embodiment of this application.

[0022] Reference numerals in the attached figures: 1. Parameter acquisition module; 2. Vector generation module; 3. Analysis module; 4. Update module; 101. Processor; 102. Memory; 103. Communication bus. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0024] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this application, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0025] Firstly, such as Figure 1 As shown, this application provides a method for identifying time-varying parameters of an underwater vehicle, which includes the following steps: S1. Obtain the motion state parameters and control input parameters of the underwater vehicle at the current moment; S2. Generate the observation output vector set and the prediction output vector set at the current moment based on the motion state parameters and control input parameters; the observation output vector set includes the observation output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom, and the prediction output vector set includes the prediction output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom. S3. For each degree of freedom, generate the regression vector of that degree of freedom at the current time based on the motion state parameters and control input parameters. Then analyze whether the norm of the regression vector is greater than or equal to a preset threshold. If yes, proceed to step S4. If no, use the time-varying parameter vector of that degree of freedom at the previous time as the time-varying parameter vector of that degree of freedom at the current time. Generate the covariance matrix of that degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to that degree of freedom, and return to step S1. S4. Based on the observed output vector and predicted output vector corresponding to the degree of freedom, the gain matrix of the degree of freedom at the current time and the time-varying parameter vector of the degree of freedom at the previous time, generate the time-varying parameter vector of the degree of freedom at the current time, and return to step S1; the gain matrix of the degree of freedom at the current time is generated based on the covariance matrix of the degree of freedom at the previous time.

[0026] For ease of understanding, some key terms in this embodiment are explained below. The underwater vehicle in this embodiment refers to a device capable of autonomous or remotely controlled underwater navigation. Its motion state is influenced by various dynamic parameters, which may change with time, environment, and its own state. The motion state parameters in this embodiment refer to physical quantities describing the motion of the underwater vehicle at a given moment, such as velocity, angular velocity, and attitude angles. These parameters are fundamental data for identifying the dynamic characteristics of the underwater vehicle. The control input parameters in this embodiment refer to external inputs acting on the underwater vehicle to change its motion state, such as propeller speed and thruster rudder angle. These parameters are closely related to the vehicle's dynamic response. The observed output vector set in this embodiment refers to the output obtained by substituting the motion state parameters and control input parameters into a pre-constructed empirical formula. This vector set reflects the actual motion response of the underwater vehicle in different degrees of freedom. The predicted output vector set in this embodiment refers to the vector set of motion responses of the underwater vehicle in different degrees of freedom predicted by the underwater vehicle's dynamic model based on the current motion state parameters and control input parameters. By comparing it with the observed output vector set, the accuracy of the dynamic model parameters can be evaluated. In this embodiment, the regression vector refers to the vector constructed from input and output data to estimate system parameters in system identification. Its norm reflects the information content or excitation level of the data. The time-varying parameter vector of the dynamic model refers to the set of parameters that change over time in the underwater vehicle's dynamic model. This method aims to update these parameters in real time when the norm of the regression vector is greater than or equal to a preset threshold, adapting to changes in the vehicle's operating environment and its own state. In this embodiment, the covariance matrix reflects the prediction uncertainty in time-varying parameter prediction. The updating process of this matrix is ​​a key part of the adaptive identification algorithm, used to adjust the step size and direction of parameter updates. In this embodiment, the gain matrix maps the prediction error to the parameter update amount in the adaptive identification algorithm; this matrix is ​​an important component for achieving effective parameter adjustment.

[0027] This embodiment provides a method for identifying time-varying parameters of underwater vehicles. This method aims to address the problem of dynamic changes in the parameters of underwater vehicle dynamic models under complex and variable environments, particularly by incorporating the roll degree of freedom to capture coupling effects and achieve online identification of time-varying parameters. The method includes the following steps: In step S1, the system acquires the motion state parameters and control input parameters of the underwater vehicle at the current moment. Specifically, during the operation of the underwater vehicle, it is necessary to acquire its motion state parameters and control input parameters in real time. The motion state parameters can be acquired through sensors such as inertial measurement units (IMUs) and Doppler velocimeters (DVLs) installed on the vehicle. For example, the vehicle's pitch speed, sway speed, roll angle, roll rate, and bow rate can be acquired. The control input parameters can be acquired from the vehicle's control system, such as propeller speed and thruster rudder angle. The acquisition of these parameters is the basis for the subsequent identification process. In this embodiment, sensor data and control commands can be directly read through the data acquisition module, or data can be received from the vehicle's control computer through the communication interface.

[0028] In step S2, the system generates the observed output vector set and the predicted output vector set for the current moment based on the motion state parameters and control input parameters. Specifically, after obtaining the motion state parameters and control input parameters, it is necessary to construct the observed output vector set and the predicted output vector set. The observed output vector set is calculated based on actual measurement data and reflects the actual response of the vehicle in each degree of freedom. For example, the observed output vectors corresponding to the pitch, sway, roll, and yaw degrees of freedom can be calculated based on the current pitch velocity, thruster angle, sway velocity, roll angle, propeller speed, and thruster angle, respectively. The predicted output vector set is calculated based on the underwater vehicle's dynamic model and the time-varying parameter vectors identified at the previous moment, combined with the current motion state parameters and control input parameters. For example, the regression vector of the sway degree of freedom at the current moment can be calculated based on the current sway velocity, yaw velocity, yaw rate, propeller speed, and thruster angle. Then, the predicted output vector of the sway degree of freedom at the current moment can be calculated based on the regression vector of the sway degree of freedom at the current moment and its time-varying parameter vector at the previous moment. In this way, a corresponding observed output vector and predicted output vector can be generated for each degree of freedom, and they can be integrated into a corresponding vector set.

[0029] In step S3, for each degree of freedom, the system generates a regression vector for that degree of freedom at the current moment based on the motion state parameters and control input parameters. Then, it analyzes whether the norm of the regression vector is greater than or equal to a preset threshold. If yes, it proceeds to step S4; otherwise, it uses the time-varying parameter vector of that degree of freedom from the previous moment as the time-varying parameter vector for that degree of freedom at the current moment. Based on the observed output vector and predicted output vector corresponding to that degree of freedom, it generates the covariance matrix for that degree of freedom at the current moment and returns to step S1. Specifically, for each degree of freedom, a corresponding regression vector needs to be generated based on the motion state parameters and control input parameters at the current moment. The norm of the regression vector can reflect the information content or excitation level of the data at the current moment. When the norm of the regression vector is less than a preset threshold, it indicates that the current data contributes little to the parameter update or the system is in a steady state. In this case, there is no need to update the time-varying parameter vector. Therefore, the time-varying parameter vector of that degree of freedom at the previous time step can be directly used as the time-varying parameter vector at the current time step. Based on the observed output vector and predicted output vector corresponding to that degree of freedom, the covariance matrix of that degree of freedom at the current time step is generated. Then, the process returns to step S1 to continue the identification at the next time step. This approach avoids introducing noise or unnecessary parameter fluctuations when data information is insufficient, thus improving the stability of the identification.

[0030] In step S4, the system generates the time-varying parameter vector for the degree of freedom at the current moment based on the observed and predicted output vectors, the gain matrix of the degree of freedom at the current moment, and the time-varying parameter vector of the degree of freedom at the previous moment, and returns to step S1. Specifically, when the norm of the regression vector is greater than or equal to a preset threshold, it indicates that the current data contains sufficient information to update the time-varying parameter vector. At this time, based on the observed and predicted output vectors for the degree of freedom, combined with the gain matrix of the degree of freedom at the current moment and the time-varying parameter vector of the degree of freedom at the previous moment, the time-varying parameter vector of the degree of freedom at the current moment is generated using an adaptive algorithm (e.g., recursive least squares). The calculation of the gain matrix typically involves the covariance matrix and the regression vector. After the parameter update is completed, the system returns to step S1 to continue the identification at the next moment. This dynamic update mechanism enables the identification method to track the changes in the dynamic parameters of the underwater vehicle in real time, improving the adaptability and accuracy of the model.

[0031] The following example provides a more detailed explanation of the above technical solution: Suppose an underwater vehicle is performing a cruise mission underwater, and its dynamic parameters are affected by environmental factors such as water flow, temperature, and salinity, as well as changes in its own load. Traditional methods may fail to accurately capture these time-varying characteristics, leading to a decrease in the vehicle's control precision.

[0032] The method of this embodiment first acquires the current motion state parameters, such as pitch speed, sway speed, roll angle, roll rate, and bow rate, in real time through the sensor system onboard the aircraft in step S1. Simultaneously, it acquires control input parameters, such as propeller speed and thruster angle, from the aircraft control system. These data are then sent to the identification module for processing.

[0033] In step S2, the identification module generates observation output vectors and prediction output vectors for the four degrees of freedom (sway, roll, pitch, and yaw) based on the real-time acquired motion state parameters and control input parameters. For example, for the sway degree of freedom, the observation output vector is calculated based on actual measurement data and known force models of the vehicle body, propeller, and thruster, while the prediction output vector is calculated based on the time-varying parameter vector of the sway degree of freedom identified at the previous moment and the regression vector at the current moment. In this way, a vector set reflecting the actual motion and the model-predicted motion can be obtained.

[0034] Next, in step S3, for each degree of freedom, the identification module calculates its regression vector at the current moment and analyzes its norm. For example, if the vehicle is in uniform linear motion at the current moment, with little change in motion, the norm of the regression vector may be less than a preset threshold. In this case, to avoid unnecessary parameter perturbations, the identification module directly uses the time-varying parameter vector of the sway degree of freedom from the previous moment as the time-varying parameter vector of the sway degree of freedom at the current moment, and updates the covariance matrix of the sway degree of freedom at the current moment based on the observed output vector and the predicted output vector at the current moment. Subsequently, the system returns to step S1 to continue acquiring data for the next moment.

[0035] However, if the vehicle performs maneuvers such as turning or depth adjustment, its motion state changes significantly, and the norm of the regression vector may be greater than or equal to a preset threshold. For example, when the norm of the regression vector for the sway degree of freedom meets the condition, the system will proceed to step S4. In step S4, the identification module updates the time-varying parameter vector of the sway degree of freedom at the current moment using a recursive least squares algorithm based on the observed output vector, predicted output vector, gain matrix at the current moment, and time-varying parameter vector from the previous moment. This update process allows the identification parameters to adapt to the dynamic changes of the vehicle during maneuvers in real time. After the update is completed, the system returns to step S1 to perform identification for the next moment.

[0036] As demonstrated by the examples above, this method achieves online and adaptive identification of underwater vehicle dynamic parameters by acquiring data in real time, constructing observation and prediction outputs, and determining whether to update parameters based on the regression vector norm. This mechanism enables the vehicle model to dynamically adjust to adapt to the complex and ever-changing underwater environment and the changes in the vehicle's own state.

[0037] The underwater vehicle time-varying parameter identification method proposed in this embodiment has significant technical contributions compared to traditional methods. Existing traditional identification methods are mostly based on a three-degree-of-freedom model in the horizontal plane, considering only pitch, sway, and roll motions, while neglecting the coupling effect of roll motion with other degrees of freedom. In reality, when underwater vehicles are disturbed by wind, waves, currents, or when operating their thrusters, they are prone to roll motion. Excessive roll angles can lead to capsizing. Therefore, a three-degree-of-freedom model alone cannot meet the motion prediction requirements in complex and variable environments. This method constructs a four-degree-of-freedom model by explicitly incorporating the observation output vector and prediction output vector corresponding to the roll degree of freedom in step S2. This allows for a more comprehensive capture of the underwater vehicle's motion characteristics, especially the coupling effect of roll motion with other degrees of freedom. This results in a more accurate and robust identified dynamic model in complex environments.

[0038] Furthermore, existing identification methods typically treat dynamic parameters as fixed values, failing to fully consider the impact of environmental changes, load adjustments, and attitude changes experienced by underwater vehicles during actual operation. This fixed-parameter model struggles to accurately capture the dynamic characteristics of parameter changes, leading to a continuous accumulation of identification errors and severely reducing the prediction accuracy of vehicle handling performance. This method introduces the concept of time-varying parameter vectors and designs an adaptive update mechanism based on the regression vector norm in steps S3 and S4, achieving online parameter identification and dynamic adjustment. When the regression vector norm is greater than or equal to a preset threshold, the parameters are updated in real time, ensuring the model can track the dynamic changes of the parameters; when the norm is less than the threshold, the parameters remain stable, avoiding unnecessary disturbances. This adaptive mechanism allows the identified parameters to better reflect the true dynamic characteristics of the underwater vehicle under different operating conditions, significantly improving the prediction accuracy of vehicle handling performance and the adaptability of the control system.

[0039] In summary, this method effectively solves the problem that traditional fixed-parameter models cannot accurately identify the dynamic parameters of underwater vehicles in complex and variable environments by introducing a four-degree-of-freedom model and an adaptive parameter update mechanism, thereby improving the accuracy and reliability of autonomous navigation and motion control of underwater vehicles.

[0040] In some preferred embodiments, step S1 includes: S11. Obtain the motion state parameters and control input parameters of the underwater vehicle at the current moment; S12. Perform outlier removal and linear interpolation replacement on the motion state parameters and control input parameters.

[0041] Step S12 aims to perform outlier removal and linear interpolation replacement on the motion state parameters and control input parameters to improve data quality and ensure the accuracy and robustness of the identification algorithm. For outlier removal, statistical methods can be used, such as based on the interquartile range (IQR) or the 3σ criterion, to identify and remove outliers that exceed the normal data distribution range. For example, for a parameter, if its value deviates from the mean by more than three standard deviations, it is marked as an outlier. Furthermore, reasonable upper and lower limits for parameters can be set based on the physical characteristics and kinematic constraints of the underwater vehicle; values ​​exceeding these physical boundaries are considered outliers and removed. For linear interpolation replacement, for missing data points after outlier removal or due to sensor malfunction, linear interpolation can be used. This involves connecting the two nearest valid data points before and after the missing point with a straight line and calculating the value of the missing point on that line to fill the gap.

[0042] This scheme first obtains the raw motion state parameters and control input parameters of the underwater vehicle at the current moment through step S11. Given that this raw data may be affected by sensor noise, environmental interference, or transmission errors, resulting in outliers or missing data, direct use may lead to deviations in subsequent identification results. Therefore, after obtaining the raw data, this scheme introduces step S12 to perform outlier removal and linear interpolation replacement on these parameters. Outlier removal effectively identifies and removes outliers in the data, preventing erroneous data from misleading the identification algorithm. Subsequently, linear interpolation replacement fills in the data gaps caused by outlier removal or sensor failure, ensuring the continuity and integrity of the data sequence. Through this data preprocessing, this scheme provides high-quality, continuous, and reliable input data for subsequent parameter identification. These processed motion state parameters and control input parameters will be used to generate the observation output vector set and prediction output vector set at the current moment, as well as the regression vector for each degree of freedom at the current moment. High-quality input data ensures the accuracy of these vectors, which in turn makes the updating of time-varying parameter vectors in steps S3 and S4 more accurate and stable, thereby improving the robustness and accuracy of the entire underwater vehicle time-varying parameter identification method.

[0043] In some preferred embodiments, the motion state parameters include the current pitch speed, sway speed, roll angle, roll rate, and yaw rate; the control input parameters include the current propeller speed and thruster angle; and step S2 includes: S21. Calculate the regression vector of the sway degree of freedom at the current moment based on the sway velocity, sway velocity, yaw rate, propeller speed, and thruster angle. Then, calculate the predicted output vector of the sway degree of freedom at the current moment based on the regression vector of the sway degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S22. Calculate the regression vector of the sway degree of freedom at the current moment based on the sway velocity, yaw rate, roll angle, pitch velocity and thruster angle. Then, calculate the predicted output vector of the sway degree of freedom at the current moment based on the regression vector of the sway degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S23. Calculate the regression vector of the roll degree of freedom at the current moment based on the roll angular velocity, roll angle, sway velocity, yaw angular velocity, pitch velocity and thruster angle. Then, calculate the predicted output vector of the roll degree of freedom at the current moment based on the regression vector of the roll degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S24. Calculate the regression vector of the bow degree of freedom at the current moment based on the bow angular velocity, sway velocity, roll angle, pitch velocity and thruster angle. Then, calculate the predicted output vector of the bow degree of freedom at the current moment based on the regression vector of the bow degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S25. Integrate all predicted output vectors into a set of predicted output vectors for the current time step; S26. Calculate the observation output vectors corresponding to the pitch, sway, roll, and yaw degrees of freedom based on the pitch velocity, sway velocity, roll angle, roll angular velocity, yaw angular velocity, propeller speed, and thruster angle, respectively. S27. Integrate all observation output vectors into the observation output vector set at the current time.

[0044] This application clarifies the specific composition of the underwater vehicle's motion state parameters and control input parameters, and details the specific calculation process for generating the observation output vector set and prediction output vector set in step S2. This ensures the accuracy of input data identification and the accuracy of model prediction, effectively reducing error accumulation caused by inaccurate models or improper data processing. Specifically, this application first defines the underwater vehicle's motion state parameters at the current moment as pitch velocity, sway velocity, roll angle, roll angular velocity, and yaw angular velocity. Simultaneously, it defines the control input parameters as propeller speed and thruster angle. The precise definition of these parameters lays a solid foundation for subsequent dynamic model construction and parameter identification, ensuring accurate mapping from raw data to model input. Based on this, step S2 generates the observation output vector set and prediction output vector set at the current moment through a series of detailed calculations. First, for the pitch, sway, roll, and yaw degrees of freedom, regression vectors are calculated at the current moment based on the aforementioned defined motion state parameters and control input parameters. These regression vectors are mathematical representations of the influence of various forces or torques on the motion state in the dynamic model, and their accurate construction directly affects the model's ability to describe the physical process. Then, using these regression vectors and the time-varying parameter vectors identified at the previous moment, the predicted output vectors for each degree of freedom at the current moment are calculated. These predicted output vectors represent the model's theoretical prediction of the vehicle's motion, and their accuracy depends on the precision of the regression vectors and the effectiveness of the time-varying parameter vectors. All these predicted output vectors are integrated into a set of predicted output vectors for the current moment. Simultaneously, this application also calculates the observed output vectors corresponding to the pitch, sway, roll, and yaw degrees of freedom based on the same motion state parameters and control input parameters. These observed output vectors reflect the actual motion response of the vehicle at the current moment and serve as the benchmark for comparison with the predicted output vector in the identification algorithm. The accuracy of their calculation directly determines the degree to which the identification algorithm reflects the actual situation. All these observed output vectors are also integrated into the observed output vector set at the current moment. Through the detailed parameter definitions and calculation procedures described above, this application ensures the accuracy of the identification process and the applicability of the model. Precise motion state parameters and control input parameters are used as inputs, making the calculation of regression vectors and observed output vectors closer to the actual physical process. In particular, by incorporating the roll degree of freedom and defining corresponding motion state parameters (roll angle, roll angular velocity) and calculation procedures, the model can capture the coupling effect between roll motion and other degrees of freedom, which is crucial for motion prediction of underwater vehicles in complex and variable environments. The accurate generation of the predicted output vector set and the observed output vector set provides a reliable basis for updating the time-varying parameter vectors in subsequent steps S3 and S4, thereby effectively reducing the accumulation of identification errors and improving the prediction accuracy of the vehicle's maneuverability.

[0045] In some preferred embodiments, the formula for calculating the regression vector of the sway degree of freedom at the current moment is: ; Where represents the regression vector of the sway degree of freedom at the current moment, u[k] represents the sway velocity at the current moment, v[k] represents the sway velocity at the current moment, r[k] represents the yaw rate at the current moment, and n[k] represents the propeller speed at the current moment. Indicates the thruster angle at the current moment; The formula for calculating the regression vector of the sway degrees of freedom at the current moment is: ; in, This represents the regression vector of the sway degrees of freedom at the current moment. Indicates the current roll angle; The formula for calculating the regression vector of the roll degree of freedom at the current moment is: ; in, p[k] represents the regression vector of the roll degree of freedom at the current moment, and p[k] represents the roll angular velocity at the current moment. The formula for calculating the regression vector of the bow roll degree of freedom at the current moment is: ; in, This represents the regression vector of the bow roll degree of freedom at the current moment; The formulas for calculating the predicted output vectors of the sway, roll, and pitch degrees of freedom at the current time are the same. The formula for calculating the predicted output vector of the sway degree of freedom at the current time is: ; Among them, y yu [k] represents the predicted output vector of the sway degrees of freedom at the current moment. θ represents the transpose of the regression vector of the sway degrees of freedom at the current moment. yu [k-1] represents the time-varying parameter vector of the sway degrees of freedom at the previous time step.

[0046] In some preferred embodiments, the formula for calculating the observed output vector of the sway degree of freedom at the current moment is: ; Among them, y gu [k] represents the observed output vector of the sway degrees of freedom at the current moment, X HThis represents the force along the X-axis of the underwater vehicle body. P This represents the force exerted by the propeller along the X-axis, X R This represents the force of the thruster along the X-axis, X uu X represents the dynamic coefficient of the first underwater vehicle. vv X represents the dynamic coefficient of the second underwater vehicle. rr X represents the dynamic coefficient of the third underwater vehicle. vr X represents the dynamic coefficient of the fourth underwater vehicle. n Let represent the propeller correlation coefficient, u[k] represent the sway velocity at the current moment, v[k] represent the yaw velocity at the current moment, r[k] represent the bow roll rate at the current moment, and n[k] represent the propeller rotational speed at the current moment. This indicates the thruster angle at the current moment. Indicates the force coefficient of the first thruster; The formula for calculating the observed output vector of the sway degree of freedom at the current moment is: ; Among them, y gv [k] represents the observed output vector of the sway degrees of freedom at the current moment, Y H This represents the force along the Y-axis of the underwater vehicle body. P This represents the force of the propeller along the Y-axis, Y R This represents the force of the thruster along the Y-axis, Y v Y represents the dynamic coefficient of the fifth underwater vehicle. |v|v Y represents the dynamic coefficient of the sixth underwater vehicle. r|r| This indicates the dynamic coefficient of the seventh underwater vehicle. Y represents the dynamic coefficient of the eighth underwater vehicle. r Y represents the dynamic coefficient of the ninth underwater vehicle. |v|r This indicates the dynamic coefficient of the tenth underwater vehicle. Indicates the current roll angle. Indicates the force coefficient of the second thruster; The formula for calculating the observed output vector of the roll degree of freedom at the current moment is: ; Among them, y gp [k] represents the observed output vector of the roll degree of freedom at the current moment, K H K represents the torque of the underwater vehicle body about the X-axis. P K represents the torque of the propeller about the X-axis. R K represents the torque of the thruster about the X-axis. p This indicates the dynamic coefficient of the eleventh underwater vehicle. K represents the dynamic coefficient of the twelfth underwater vehicle. v K represents the dynamic coefficient of the thirteenth underwater vehicle. r p[k] represents the dynamic coefficient of the fourteenth underwater vehicle, and p[k] represents the roll rate at the current moment. Indicates the torque coefficient of the first thruster; The formula for calculating the observation output vector of the bow degree of freedom at the current moment is: ; Among them, y gr [k] represents the observation output vector of the bow roll degree of freedom at the current moment, N H The torque (N) representing the force on the underwater vehicle body about the Z-axis. P The torque of the propeller about the Z-axis, N R The torque of the thruster about the Z-axis, N r N represents the dynamic coefficient of the fifteenth underwater vehicle. r|r| N represents the dynamic coefficient of the sixteenth underwater vehicle. v N represents the dynamic coefficient of the seventeenth underwater vehicle. vvr N represents the dynamic coefficient of the eighteenth underwater vehicle. vrr This indicates the dynamic coefficient of the nineteenth underwater vehicle. This indicates the dynamic coefficient of the twentieth underwater vehicle. This represents the torque coefficient of the second thruster. It should be understood that the acquisition of all underwater vehicle body dynamic coefficients in this application is prior art. The acquisition of propeller correlation coefficients, first thruster force coefficients, second thruster force coefficients, first thruster torque coefficients, and second thruster torque coefficients is also prior art, and the acquisition process of these coefficients will not be discussed in detail here. In this embodiment, all underwater vehicle body dynamic coefficients represent the viscous drag, wave-making drag, lift, and coupling torque generated when the underwater vehicle body moves relative to the water. In this embodiment, the first thruster force coefficient, second thruster force coefficient, first thruster torque coefficient, and second thruster torque coefficient represent the forces or torques corresponding to the four degrees of freedom: sway, roll, pitch, and bow.

[0047] In some preferred embodiments, step S3 includes: S31. For each degree of freedom, generate the regression vector of that degree of freedom at the current moment based on the motion state parameters and control input parameters, and then analyze whether the norm of the regression vector is greater than or equal to the preset threshold. If yes, proceed to step S4; otherwise, proceed to step S32. S32. Use the time-varying parameter vector of the degree of freedom at the previous time step as the time-varying parameter vector of the degree of freedom at the current time step, and set the gain matrix of the degree of freedom at the current time step to 0. S33. Calculate the posterior prediction bias at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom, and then calculate the forgetting factor at the current time based on the posterior prediction bias, the preset lower limit of the forgetting factor and the preset sensitivity coefficient. S34. Calculate the covariance matrix at the current time based on the covariance matrix of the degree of freedom at the previous time and its regression vector at the current time, and return to step S1. Step S4 includes: S41. Calculate the posterior prediction bias at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom. S42. Calculate the forgetting factor at the current time based on the posterior prediction bias, the preset lower limit of the forgetting factor, and the preset sensitivity coefficient; S43. Calculate the gain matrix at the current time based on the covariance matrix of the degree of freedom at the previous time and its regression vector at the current time. S44. Generate the time-varying parameter vector of the degree of freedom at the current time based on the posterior prediction bias and the gain matrix of the degree of freedom at the current time and its time-varying parameter vector at the previous time. S45. Generate the covariance matrix of the degree of freedom at the current time based on the forgetting factor, the identity matrix, the regression vector of the degree of freedom at the current time, and the covariance matrix of the degree of freedom at the previous time, and return to step S1; the dimension of the identity matrix is ​​the same as the dimension of the covariance matrix.

[0048] Step S31 preferably uses the regression vector calculation formula of the above embodiment to generate the regression vector of the degree of freedom at the current moment based on the motion state parameters and control input parameters. The norm of the regression vector is analyzed to determine whether it is greater than or equal to a preset threshold. This analysis is used to determine whether the input data at the current moment has sufficient information or excitation intensity to reliably update the model parameters. When the norm of the regression vector is small, it indicates that the current system input change is not significant and the data excitation is insufficient. In this case, parameter updates may introduce noise or cause parameter drift. The norm can be calculated using the L2 norm (Euclidean norm), which is the square root of the sum of the squares of the vector elements, or the L1 norm (Manhattan norm), which is the sum of the absolute values ​​of the vector elements. The preset threshold can be set based on experience, system noise level, or through simulation experiments to balance the sensitivity and stability of parameter updates.

[0049] In step S32, when the regression vector norm is less than a preset threshold, this step aims to avoid unnecessary or potentially harmful updates to the time-varying parameter vector under insufficient data stimulation. By directly using the time-varying parameter vector from the previous time step, parameter stability can be maintained, preventing parameter drift caused by noise interference. Simultaneously, setting the gain matrix to 0 means that the current observation data contributes zero to the parameter update, further ensuring the parameters remain frozen in the face of insufficient data and effectively suppressing the accumulation of identification errors.

[0050] In step S33, calculating the posterior prediction bias at the current time step aims to quantify the difference between the model's predicted values ​​and the actual observed values, serving as the basis for parameter updates. The posterior prediction bias can be simply obtained by subtracting the predicted output vector from the observed output vector. This bias reflects the accuracy of the current model's prediction of system behavior, and its magnitude directly affects the magnitude and direction of subsequent parameter adjustments. Dynamically calculating the forgetting factor at the current time step allows the identification algorithm to better adapt to the time-varying characteristics of system parameters. Specifically, a larger posterior prediction bias indicates a significant difference between the model's prediction and the actual observation; in this case, a smaller forgetting factor at the current time step allows for greater weighting of new data, accelerating parameter adjustments to adapt to the new system state. Conversely, when the bias is small, the forgetting factor at the current time step is increased to maintain parameter stability. A preset lower limit for the forgetting factor ensures that it is not too small, avoiding over-reliance on the latest data and the introduction of noise. A preset sensitivity coefficient controls the speed and extent of the forgetting factor's response to changes in prediction bias.

[0051] In step S34, calculating the gain matrix at the current time step plays a crucial role in the recursive least squares algorithm. It determines how the posterior prediction bias is weighted and used to update the time-varying parameter vector. The calculation of the gain matrix depends on the covariance matrix from the previous time step and the regression vector at the current time step. The covariance matrix reflects the uncertainty of the parameter estimation, while the regression vector provides the input information at the current time step. The gain matrix calculated in this way ensures that the direction and magnitude of the parameter update are based on an optimal trade-off between the current data information content and the uncertainty of historical estimates.

[0052] In step S41, the calculation of the posterior prediction bias at the current time has the same purpose as the calculation in step S33, namely, quantifying the difference between the model's predicted value and the actual observed value. When the regression vector norm is greater than or equal to a preset threshold, this bias will be used to drive the actual update of the parameters.

[0053] In step S42, the calculation of the forgetting factor at the current time moment has the same purpose as the calculation in step S33, namely, dynamically adjusting the forgetting factor based on the difference between the model prediction and the actual observation. When the regression vector norm is greater than or equal to a preset threshold, the dynamically adjusted forgetting factor will be used to update the covariance matrix, thereby affecting the weight of the parameter update.

[0054] In step S43, the calculation of the gain matrix at the current time moment serves the same purpose as the calculation in step S34. When the norm of the regression vector is greater than or equal to a preset threshold, the calculated gain matrix will be directly used to update the time-varying parameter vector, ensuring the effectiveness of parameter adjustment.

[0055] In step S44, generating the time-varying parameter vector for that degree of freedom at the current moment is the core of the actual parameter update. It uses the time-varying parameter vector from the previous moment as a basis, combines the posterior prediction bias and gain matrix at the current moment, and calculates the new time-varying parameter vector using a recursive formula. The gain matrix appropriately weights the posterior prediction bias and feeds it back into the parameter vector from the previous moment, thereby correcting the model parameters to make them closer to the true time-varying characteristics of the system.

[0056] In step S45, the covariance matrix of this degree of freedom at the current time step is generated to reflect the change in parameter estimation uncertainty. By introducing a dynamically calculated forgetting factor at the current time step, the memory length of the covariance matrix can be effectively adjusted, enabling it to respond more quickly to changes in system parameters while avoiding over-updating when data stimulation is insufficient. The identity matrix I is used for matrix operations in the covariance matrix update formula, and its dimension is consistent with that of the covariance matrix, ensuring the correctness of matrix operations. This update process allows the covariance matrix to dynamically reflect the confidence level of parameter estimation, providing an accurate basis for subsequent gain matrix calculation.

[0057] The proposed solution for underwater vehicle time-varying parameter identification achieves accurate and robust identification of time-varying parameters by introducing a conditional judgment mechanism based on the regression vector norm and a dynamic forgetting factor adjustment strategy. The method first acquires the motion state parameters and control input parameters of the underwater vehicle at the current moment, and generates an observation output vector set and a prediction output vector set, providing basic data for subsequent parameter identification. In the core step S3, for each degree of freedom, the system generates a regression vector for that degree of freedom at the current moment based on the motion state parameters and control input parameters. Subsequently, by analyzing whether the norm of this regression vector is greater than or equal to a preset threshold, it is determined whether the data excitation at the current moment is sufficient. This judgment mechanism is the key deflection point of the entire scheme. If the norm of the regression vector is less than the preset threshold, it indicates that the current data information is insufficient to reliably update the parameters. At this time, the system executes step S32, directly using the time-varying parameter vector of that degree of freedom at the previous moment as the parameter vector at the current moment, and setting its gain matrix to 0. This processing method effectively avoids invalid or harmful parameter updates in low-excitation or noisy environments, thereby preventing the accumulation of identification errors. Based on this, the system continues to execute steps S33 and S34. In step S33, the posterior prediction bias at the current time is calculated based on the observed output vector and the predicted output vector, and the forgetting factor at the current time is dynamically calculated based on this bias, the preset lower limit of the forgetting factor, and the preset sensitivity coefficient. This dynamic forgetting factor can adaptively adjust the weight of historical data in the covariance matrix update according to the magnitude of the model prediction error, enhancing the algorithm's adaptability to the time-varying characteristics of the system. Subsequently, in step S34, the gain matrix at the current time is calculated based on the covariance matrix of the previous time step and the current regression vector to prepare for subsequent parameter updates, and the system returns to step S1 to proceed to the identification of the next time step.

[0058] If the norm of the regression vector is greater than or equal to a preset threshold, it indicates that the current data stimulus is sufficient, and reliable parameter updates can be performed. At this point, the system executes step S4. In step S4, firstly, in S41 and S42, the posterior prediction bias and dynamic forgetting factor at the current time are calculated to ensure that the basis for parameter updates is up-to-date and adaptively adjusted. Next, in S43, the gain matrix at the current time is calculated based on the covariance matrix of the previous time step and the current regression vector. This gain matrix will be used to guide parameter correction. Subsequently, in S44, based on the posterior prediction bias, the gain matrix, and the time-varying parameter vector of the previous time step, the time-varying parameter vector for that degree of freedom at the current time step is generated, achieving accurate correction of the model parameters. Finally, in S45, based on the dynamic forgetting factor, the identity matrix, the current regression vector, and the covariance matrix of the previous time step, the covariance matrix for that degree of freedom at the current time step is generated. The dynamic update of the covariance matrix, especially with the introduction of the forgetting factor, allows the algorithm to more flexibly track parameter changes, reduce error propagation, and provide a more accurate uncertainty estimate for the next parameter update. After completing step S45, the system returns to step S1 to continue identification at the next time step. Through the refined steps S3 and S4 described above, the scheme of this application introduces intelligent data stimulus judgment and an adaptive parameter update strategy on the basis of the basic underwater vehicle time-varying parameter identification method. This mechanism enables the identification process to flexibly select the parameter update path and intensity according to the data quality and the dynamic changes of the system. When the data stimulus is insufficient, freezing the parameters and setting the gain matrix to zero effectively avoids noise introduction and error accumulation; when the data stimulus is sufficient, dynamically adjusting the forgetting factor and accurately updating the parameters and covariance matrix ensures the accuracy of parameter identification and rapid response to time-varying characteristics.

[0059] In some preferred embodiments, the formula for calculating the posterior prediction bias at the current time is: ; Where e[k] represents the posterior prediction bias at the current time, y g [k] represents the observed output vector at the current time corresponding to the degrees of freedom of the regression vector whose norm is greater than or equal to a preset threshold. y [k] represents the predicted output vector at the current time corresponding to the norm of the regression vector that is greater than or equal to the preset threshold; The formula for calculating the forgetting factor at the current moment is: ; Where λ[k] represents the forgetting factor at the current time, λmin represents the preset lower limit of the forgetting factor, and γ represents the preset sensitivity coefficient; The formula for calculating the gain matrix at the current moment is: ; Where G[k] represents the gain matrix at the current time step, This represents the covariance matrix of the degrees of freedom corresponding to the norm of regression vectors that are greater than or equal to a preset threshold, at the previous time step. This represents the regression vector at the current time corresponding to the norm of regression vectors that are greater than or equal to a preset threshold. This represents the transpose of the regression vector at the current time, corresponding to the degrees of freedom of the regression vector whose norm is greater than or equal to a preset threshold. The formula for calculating the time-varying parameter vector at the current moment is: ; Where θ[k] represents the time-varying parameter vector of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the current time, and θ[k-1] represents the time-varying parameter vector of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the previous time. The formula for calculating the covariance matrix at the current time is: ; in, I represents the covariance matrix of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the current time, where I represents the identity matrix.

[0060] As can be seen from the above, the underwater vehicle time-varying parameter identification method provided in this application effectively solves the problem that traditional fixed parameter models cannot accurately identify the dynamic parameters of underwater vehicles in complex and variable environments by introducing a four-degree-of-freedom model and an adaptive parameter update mechanism, thereby improving the accuracy and reliability of the autonomous navigation and motion control of underwater vehicles.

[0061] Secondly, such as Figure 2 As shown, this application also provides a time-varying parameter identification device for underwater vehicles, which includes: Parameter acquisition module 1 is used to acquire the motion state parameters and control input parameters of the underwater vehicle at the current moment; Vector generation module 2 is used to generate the observation output vector set and the prediction output vector set at the current moment based on the motion state parameters and control input parameters. The observation output vector set includes the observation output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom, and the prediction output vector set includes the prediction output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom. Analysis module 3 is used to generate a regression vector for each degree of freedom at the current time based on the motion state parameters and control input parameters. Then, it analyzes whether the norm of the regression vector is greater than or equal to a preset threshold. If so, it triggers update module 4. If not, it uses the time-varying parameter vector of the degree of freedom at the previous time as the time-varying parameter vector of the degree of freedom at the current time. Based on the observed output vector and predicted output vector corresponding to the degree of freedom, it generates the covariance matrix of the degree of freedom at the current time and triggers parameter acquisition module 1. The update module 4 is used to generate the time-varying parameter vector of the degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom, the gain matrix of the degree of freedom at the current time and the time-varying parameter vector of the degree of freedom at the previous time, and to trigger the parameter acquisition module 1; the gain matrix of the degree of freedom at the current time is generated based on the covariance matrix of the degree of freedom at the previous time.

[0062] The underwater vehicle time-varying parameter identification device provided in this application includes a parameter acquisition module 1, a vector generation module 2, an analysis module 3, and an update module 4. The underwater vehicle time-varying parameter identification device provided in this embodiment is preferably used to perform the steps in the underwater vehicle time-varying parameter identification method provided in the first aspect above. The principle of the underwater vehicle time-varying parameter identification device provided in this embodiment is the same as the principle of the underwater vehicle time-varying parameter identification method provided in the first aspect above, and will not be repeated here.

[0063] Please refer to Figure 3 , Figure 3This application provides a schematic diagram of the structure of an electronic device according to an embodiment of the present application. The electronic device includes a processor 101 and a memory 102. The processor 101 and the memory 102 are interconnected and communicate with each other via a communication bus 103 and / or other forms of connection mechanisms (not shown). The memory 102 stores computer-readable instructions executable by the processor 101. When the electronic device is running, the processor 101 executes the computer-readable instructions to perform the method in any optional implementation of the above embodiments, thereby achieving the following functions: Step S1: Obtain the motion state parameters and control input parameters of the underwater vehicle at the current moment; Step S2: Generate an observation output vector set and a prediction output vector set at the current moment based on the motion state parameters and control input parameters; The observation output vector set includes observation output vectors corresponding to the sway, roll, pitch, and yaw degrees of freedom; The prediction output vector set includes observation output vectors corresponding to the sway, roll, pitch, and yaw degrees of freedom. The predicted output vectors corresponding to the degrees of freedom, sway, roll, and pitch; Step S3: For each degree of freedom, generate the regression vector of that degree of freedom at the current time based on the motion state parameters and control input parameters, and then analyze whether the norm of the regression vector is greater than or equal to a preset threshold. If yes, proceed to step S4; otherwise, use the time-varying parameter vector of that degree of freedom at the previous time as the time-varying parameter vector of that degree of freedom at the current time, generate the covariance matrix of that degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to that degree of freedom, and return to step S1; Step S4: Generate the time-varying parameter vector of that degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to that degree of freedom, the gain matrix of that degree of freedom at the current time, and the time-varying parameter vector of that degree of freedom at the previous time, and return to step S1; The gain matrix of that degree of freedom at the current time is generated based on the covariance matrix of that degree of freedom at the previous time.

[0064] This application embodiment also provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it executes the method in any optional implementation of the above embodiments to achieve the following functions: Step S1: Obtain the motion state parameters and control input parameters of the underwater vehicle at the current moment; Step S2: Generate an observation output vector set and a prediction output vector set at the current moment based on the motion state parameters and control input parameters; The observation output vector set includes observation output vectors corresponding to the pitch, sway, roll, and yaw degrees of freedom, and the prediction output vector set includes prediction output vectors corresponding to the pitch, sway, roll, and yaw degrees of freedom; Step S3: For each degree of freedom, based on the motion state parameters and control input parameters... The parameters generate the regression vector of the degree of freedom at the current time, and then analyze whether the norm of the regression vector is greater than or equal to a preset threshold. If yes, proceed to step S4; otherwise, use the time-varying parameter vector of the degree of freedom at the previous time as the time-varying parameter vector of the degree of freedom at the current time, generate the covariance matrix of the degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom, and return to step S1; Step S4: Generate the time-varying parameter vector of the degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom, the gain matrix of the degree of freedom at the current time, and the time-varying parameter vector of the degree of freedom at the previous time, and return to step S1; The gain matrix of the degree of freedom at the current time is generated based on the covariance matrix of the degree of freedom at the previous time. The computer-readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0065] As can be seen from the above, the underwater vehicle time-varying parameter identification method, device, equipment and medium provided in this application effectively solves the problem that traditional fixed parameter models cannot accurately identify the dynamic parameters of underwater vehicles in complex and variable environments by introducing a four-degree-of-freedom model and an adaptive parameter update mechanism, thereby improving the accuracy and reliability of the autonomous navigation and motion control of underwater vehicles.

[0066] In the embodiments provided in this application, it should be understood that the disclosed apparatus and method can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of the above units is only a logical functional division, and there may be other division methods in actual implementation. Furthermore, multiple units or components may be combined or integrated into another robot, or some features may be ignored or not executed. Additionally, the coupling or direct coupling or communication connection shown or discussed may be through some communication interface; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0067] Furthermore, the units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0068] Furthermore, the functional modules in the various embodiments of this application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0069] In this document, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, without necessarily requiring or implying any such actual relationship or order between these entities or operations.

[0070] The above are merely embodiments of this application and are not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for identifying time-varying parameters of an underwater vehicle, characterized in that, The method for identifying time-varying parameters of underwater vehicles includes the following steps: S1. Obtain the motion state parameters and control input parameters of the underwater vehicle at the current moment; S2. Generate the observation output vector set and the prediction output vector set at the current moment based on the motion state parameters and the control input parameters; the observation output vector set includes the observation output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom, and the prediction output vector set includes the prediction output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom; S3. For each degree of freedom, generate a regression vector for that degree of freedom at the current moment based on the motion state parameters and the control input parameters. Then analyze whether the norm of the regression vector is greater than or equal to a preset threshold. If yes, proceed to step S4. If no, use the time-varying parameter vector of that degree of freedom at the previous moment as the time-varying parameter vector of that degree of freedom at the current moment. Generate the covariance matrix of that degree of freedom at the current moment based on the observed output vector and predicted output vector corresponding to that degree of freedom, and return to step S1. S4. Based on the observed output vector and predicted output vector corresponding to the degree of freedom, the gain matrix of the degree of freedom at the current time and the time-varying parameter vector of the degree of freedom at the previous time, generate the time-varying parameter vector of the degree of freedom at the current time, and return to step S1; the gain matrix of the degree of freedom at the current time is generated based on the covariance matrix of the degree of freedom at the previous time.

2. The method for identifying time-varying parameters of underwater vehicles according to claim 1, characterized in that, Step S1 includes: S11. Obtain the motion state parameters and control input parameters of the underwater vehicle at the current moment; S12. Perform outlier removal and linear interpolation replacement on the motion state parameters and the control input parameters.

3. The method for identifying time-varying parameters of underwater vehicles according to claim 1, characterized in that, The motion state parameters include the current pitch speed, sway speed, roll angle, roll rate, and yaw rate. The control input parameters include the current propeller speed and thruster angle. Step S2 includes: S21. Calculate the regression vector of the sway degree of freedom at the current moment based on the sway velocity, the sway velocity, the yaw rate, the propeller speed, and the thruster angle. Then, calculate the predicted output vector of the sway degree of freedom at the current moment based on the regression vector of the sway degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S22. Calculate the regression vector of the sway degree of freedom at the current moment based on the sway velocity, the yaw rate, the roll angle, the pitch velocity, and the thruster angle. Then, calculate the predicted output vector of the sway degree of freedom at the current moment based on the regression vector of the sway degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S23. Calculate the regression vector of the roll degree of freedom at the current moment based on the roll angular velocity, the roll angle, the sway velocity, the yaw angular velocity, the pitch velocity, and the thruster angle. Then, calculate the predicted output vector of the roll degree of freedom at the current moment based on the regression vector of the roll degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S24. Calculate the regression vector of the bow degree of freedom at the current moment based on the bow angular velocity, the sway velocity, the roll angle, the pitch velocity, and the thruster angle. Then, calculate the predicted output vector of the bow degree of freedom at the current moment based on the regression vector of the bow degree of freedom at the current moment and its time-varying parameter vector at the previous moment. S25. Integrate all the predicted output vectors into a set of predicted output vectors for the current time. S26. Based on the sway velocity, the sway velocity, the roll angle, the roll angular velocity, the yaw angular velocity, the propeller speed, and the thruster angle, calculate the observation output vectors corresponding to the sway degree of freedom, the sway degree of freedom, the roll degree of freedom, and the yaw degree of freedom, respectively. S27. Integrate all the observation output vectors into the observation output vector set at the current time.

4. The method for identifying time-varying parameters of underwater vehicles according to claim 3, characterized in that, The formula for calculating the regression vector of the sway degree of freedom at the current moment is: ； in, Let u[k] represent the regression vector of the sway degree of freedom at the current moment, v[k] represent the sway velocity at the current moment, r[k] represent the bow roll rate at the current moment, and n[k] represent the propeller rotation speed at the current moment. Indicates the thruster angle at the current moment; The formula for calculating the regression vector of the sway degree of freedom at the current moment is: ； in, This represents the regression vector of the sway degrees of freedom at the current moment. Indicates the current roll angle; The formula for calculating the regression vector of the roll degree of freedom at the current moment is: ； in, p[k] represents the regression vector of the roll degree of freedom at the current moment, and p[k] represents the roll angular velocity at the current moment; The formula for calculating the regression vector of the bow roll degree of freedom at the current moment is: ； in, This represents the regression vector of the bow roll degree of freedom at the current moment; The calculation formulas for the predicted output vectors of the sway, roll, pitch, and yaw degrees of freedom at the current moment are the same. The calculation formula for the predicted output vector of the sway degree of freedom at the current moment is as follows: ； Among them, y yu [k] represents the predicted output vector of the sway degrees of freedom at the current moment. θ represents the transpose of the regression vector of the sway degrees of freedom at the current moment. yu [k-1] represents the time-varying parameter vector of the sway degrees of freedom at the previous time step.

5. The method for identifying time-varying parameters of underwater vehicles according to claim 3, characterized in that, The formula for calculating the observed output vector of the sway degree of freedom at the current moment is: ； Among them, y gu [k] represents the observed output vector of the sway degrees of freedom at the current moment, X H This represents the force along the X-axis of the underwater vehicle body. P This represents the force exerted by the propeller along the X-axis, X R This represents the force of the thruster along the X-axis, X uu X represents the dynamic coefficient of the first underwater vehicle. vv X represents the dynamic coefficient of the second underwater vehicle. rr X represents the dynamic coefficient of the third underwater vehicle. vr X represents the dynamic coefficient of the fourth underwater vehicle. n Let represent the propeller correlation coefficient, u[k] represent the sway velocity at the current moment, v[k] represent the yaw velocity at the current moment, r[k] represent the bow roll rate at the current moment, and n[k] represent the propeller rotational speed at the current moment. This indicates the thruster angle at the current moment. Indicates the force coefficient of the first thruster; The formula for calculating the observed output vector of the sway degree of freedom at the current moment is: ； Among them, y gv [k] represents the observed output vector of the sway degrees of freedom at the current moment, Y H This represents the force along the Y-axis of the underwater vehicle body. P This represents the force of the propeller along the Y-axis, Y R This represents the force of the thruster along the Y-axis, Y v Y represents the dynamic coefficient of the fifth underwater vehicle. |v|v Y represents the dynamic coefficient of the sixth underwater vehicle. r|r| This indicates the dynamic coefficient of the seventh underwater vehicle. Y represents the dynamic coefficient of the eighth underwater vehicle. r Y represents the dynamic coefficient of the ninth underwater vehicle. |v|r This indicates the dynamic coefficient of the tenth underwater vehicle. Indicates the current roll angle. Indicates the force coefficient of the second thruster; The formula for calculating the observed output vector of the roll degree of freedom at the current moment is: ； Among them, y gp [k] represents the observed output vector of the roll degree of freedom at the current moment, K H K represents the torque of the underwater vehicle body about the X-axis. P K represents the torque of the propeller about the X-axis. R K represents the torque of the thruster about the X-axis. p This indicates the dynamic coefficient of the eleventh underwater vehicle. K represents the dynamic coefficient of the twelfth underwater vehicle. v K represents the dynamic coefficient of the thirteenth underwater vehicle. r p[k] represents the dynamic coefficient of the fourteenth underwater vehicle, and p[k] represents the roll rate at the current moment. This indicates the torque coefficient of the first thruster; The formula for calculating the observed output vector of the bow roll degree of freedom at the current moment is: ； Among them, y gr [k] represents the observation output vector of the bow roll degree of freedom at the current moment, N H The torque (N) representing the force on the underwater vehicle body about the Z-axis. P The torque of the propeller about the Z-axis, N R The torque of the thruster about the Z-axis, N r N represents the dynamic coefficient of the fifteenth underwater vehicle. r|r| N represents the dynamic coefficient of the sixteenth underwater vehicle. v N represents the dynamic coefficient of the seventeenth underwater vehicle. vvr N represents the dynamic coefficient of the eighteenth underwater vehicle. vrr This indicates the dynamic coefficient of the nineteenth underwater vehicle. This indicates the dynamic coefficient of the twentieth underwater vehicle. This represents the torque coefficient of the second thruster.

6. The method for identifying time-varying parameters of an underwater vehicle according to claim 1, characterized in that, Step S3 includes: S31. For each degree of freedom, generate a regression vector for that degree of freedom at the current moment based on the motion state parameters and the control input parameters. Then analyze whether the norm of the regression vector is greater than or equal to a preset threshold. If yes, proceed to step S4; otherwise, proceed to step S32. S32. Use the time-varying parameter vector of the degree of freedom at the previous time step as the time-varying parameter vector of the degree of freedom at the current time step, and set the gain matrix of the degree of freedom at the current time step to 0. S33. Calculate the posterior prediction bias at the current time based on the observation output vector and prediction output vector corresponding to the degree of freedom, and then calculate the forgetting factor at the current time based on the posterior prediction bias, the preset forgetting factor lower limit and the preset sensitivity coefficient. S34. Calculate the covariance matrix at the current time based on the covariance matrix of the degree of freedom at the previous time and its regression vector at the current time, and return to step S1. Step S4 includes: S41. Calculate the posterior prediction bias at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom. S42. Calculate the forgetting factor at the current time based on the posterior prediction bias, the preset lower limit of the forgetting factor, and the preset sensitivity coefficient; S43. Calculate the gain matrix at the current time based on the covariance matrix of the degree of freedom at the previous time and its regression vector at the current time. S44. Generate the time-varying parameter vector of the degree of freedom at the current time based on the posterior prediction bias and the gain matrix of the degree of freedom at the current time and its time-varying parameter vector at the previous time. S45. Generate the covariance matrix of the degree of freedom at the current time based on the forgetting factor, the identity matrix, the regression vector of the degree of freedom at the current time, and the covariance matrix of the degree of freedom at the previous time, and return to step S1; the dimension of the identity matrix is ​​the same as the dimension of the covariance matrix.

7. The method for identifying time-varying parameters of an underwater vehicle according to claim 1, characterized in that, The formula for calculating the posterior prediction bias at the current moment is: ； Where e[k] represents the posterior prediction bias at the current time, y g [k] represents the observed output vector at the current time corresponding to the degrees of freedom of the regression vector whose norm is greater than or equal to a preset threshold. y [k] represents the predicted output vector at the current time corresponding to the norm of the regression vector that is greater than or equal to the preset threshold; The formula for calculating the forgetting factor at the current moment is: ； Where λ[k] represents the forgetting factor at the current time, λmin represents the preset lower limit of the forgetting factor, and γ represents the preset sensitivity coefficient; The formula for calculating the gain matrix at the current moment is: ； Where G[k] represents the gain matrix at the current time step. This represents the covariance matrix of the degrees of freedom corresponding to the norm of regression vectors that are greater than or equal to a preset threshold, at the previous time step. This represents the regression vector at the current time corresponding to the norm of regression vectors that are greater than or equal to a preset threshold. This represents the transpose of the regression vector at the current time, corresponding to the degrees of freedom of the regression vector whose norm is greater than or equal to a preset threshold. The formula for calculating the time-varying parameter vector at the current moment is: ； Where θ[k] represents the time-varying parameter vector of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the current time, and θ[k-1] represents the time-varying parameter vector of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the previous time. The formula for calculating the covariance matrix at the current moment is: ； in, I represents the covariance matrix of the degrees of freedom corresponding to the norm of the regression vector that is greater than or equal to the preset threshold at the current time, where I represents the identity matrix.

8. A device for identifying time-varying parameters of an underwater vehicle, characterized in that, The underwater vehicle time-varying parameter identification device includes: The parameter acquisition module is used to acquire the motion state parameters and control input parameters of the underwater vehicle at the current moment; The vector generation module is used to generate an observation output vector set and a prediction output vector set at the current moment based on the motion state parameters and the control input parameters; the observation output vector set includes observation output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom, and the prediction output vector set includes prediction output vectors corresponding to the sway, roll, pitch and yaw degrees of freedom; The analysis module is used to generate a regression vector for each degree of freedom at the current time based on the motion state parameters and the control input parameters. Then, it analyzes whether the norm of the regression vector is greater than or equal to a preset threshold. If so, it triggers the update module. If not, it uses the time-varying parameter vector of the degree of freedom at the previous time as the time-varying parameter vector of the degree of freedom at the current time. Based on the observed output vector and predicted output vector corresponding to the degree of freedom, it generates the covariance matrix of the degree of freedom at the current time and triggers the parameter acquisition module. The update module is used to generate the time-varying parameter vector of the degree of freedom at the current time based on the observed output vector and predicted output vector corresponding to the degree of freedom, the gain matrix of the degree of freedom at the current time and the time-varying parameter vector of the degree of freedom at the previous time, and to trigger the parameter acquisition module; the gain matrix of the degree of freedom at the current time is generated based on the covariance matrix of the degree of freedom at the previous time.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing computer-readable instructions that, when executed by the processor, perform the steps of the method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it performs the steps of the method as described in any one of claims 1-7.

Images