Ocean engineering structure extended Kalman filter parameter estimation method based on attitude angle virtual observation

Abstract

The invention discloses an ocean engineering structure extended Kalman filter parameter estimation method based on attitude angle virtual observation, and relates to the technical field of ocean engineering, and the method comprises the following steps: S1, initializing a system process noise covariance matrix and an observation noise covariance matrix, and obtaining an extended Kalman filter attitude angle estimation value; s2, establishing a high-precision angular velocity-attitude angle dynamic conversion model, generating attitude angle virtual observed quantity and using the attitude angle virtual observed quantity for online evaluation of a Kalman filtering result; s3, setting a multi-dimensional performance evaluation index system, and quantitatively evaluating the amplitude error and trend stability of the extended Kalman filter estimated attitude angle; s4, adjusting scale factors of a system process noise covariance matrix and an observation noise covariance matrix by using a gradient descent algorithm based on the attitude angle virtual observation quantity and the error measurement of the multi-dimensional performance evaluation index, and carrying out real-time iteration on the scale factors of the system process noise covariance matrix and the observation noise covariance matrix; the problem that attitude parameters cannot be accurately measured and predicted in real time in the prior art is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ocean engineering, and more particularly, it relates to a method for estimating parameters of an extended Kalman filter for an ocean engineering structure based on virtual observation of attitude angles. BACKGROUND

[0002] Ocean engineering structures such as semi-submersible platforms, floating wind turbines, and tension leg platforms are long-term served in the random external load environment of wind, wave, and current coupling. Small changes in the attitude angles (pitch angle, roll angle, and heading angle) of the ocean engineering structures will have a significant impact on deck operation safety, mooring line tension distribution, and structural fatigue life. Therefore, accurate measurement and real-time prediction of these attitude parameters are crucial to ensuring the safe operation of ocean engineering structures.

[0003] To obtain the attitude information of the ocean engineering structure, a lightweight inertial measurement unit (IMU) composed of an accelerometer, a gyroscope, and a magnetometer is usually used, and multi-source sensor data is processed by information fusion. Specifically, under static or low dynamic conditions, the projection of the gravity vector measured by the accelerometer in the carrier coordinate system can be used to solve the pitch angle and roll angle; the geomagnetic field vector measured by the magnetometer and corrected by soft and hard ferromagnetic correction can be used to solve the heading angle; and the instantaneous angular velocity signal output by the gyroscope can be integrated in time to obtain the relative attitude increment.

[0004] However, significant linear acceleration caused by wave excitation, magnetic field distortion caused by complex sea area electromagnetic environment, and inherent zero drift of low-cost gyroscopes all reduce the accuracy of single sensor solution. In engineering practice, Kalman filter and its variant algorithms are widely used to fuse multi-source sensor data by constructing system state equations and observation equations and using a prediction-update mechanism. This method can fully utilize the measurement characteristics of different sensors, effectively suppress measurement noise interference and model error accumulation, and significantly improve the accuracy and accuracy of attitude estimation.

[0005] The Kalman filter can achieve optimal estimation in the sense of minimum mean square error when the noise satisfies the linear Gaussian assumption, and its performance is highly dependent on the accuracy of the noise statistics. Therefore, the reasonable setting of the process noise covariance matrix Q and the observation noise covariance matrix R is the key to ensuring the accuracy of state estimation and the numerical stability of the algorithm.

[0006] In the attitude monitoring scenario of the ocean engineering structure, it is difficult to accurately simulate the time-varying noise characteristics caused by complex factors such as waves and ocean currents in the actual marine environment in the laboratory or simulation environment; in addition, due to the limitations of offshore operation conditions, there is often a lack of high-precision attitude "true value" benchmarks for long-term comparison, making it difficult for the process noise covariance matrix Q and the observation noise covariance matrix R obtained by traditional offline calibration to remain effective for a long time.

[0007] The application of traditional Kalman filter algorithm in the attitude estimation of ocean engineering structures faces three key problems: firstly, the Kalman filter algorithm relies on pre-calibrated fixed noise parameters, which cannot adapt to the complex and changeable noise characteristics in the marine environment, resulting in significant fluctuations in estimation accuracy with environmental changes; secondly, due to the limitations of space and cost in the operating water area, it is difficult to configure a high-precision attitude reference for a long time, so there is a lack of objective and continuous performance evaluation means, and the adjustment of Kalman filter parameters often relies on experience; thirdly, the existing adaptive Kalman filter algorithm often uses a feedback mechanism based on innovation sequence when recursively estimating the process noise covariance matrix Q, when the initial state estimation has a deviation, the deviation will be amplified and continuously accumulated in the subsequent update, resulting in continuous degradation of filter performance over time, and under sudden sea conditions or strong interference conditions, the mechanism is also prone to parameter jump, further deteriorating the attitude estimation result. SUMMARY

[0008] In view of the deficiencies in the prior art, the purpose of the present application is to provide an ocean engineering structure extended Kalman filter parameter estimation method based on attitude angle virtual observation, which has the advantages of accuracy and high precision.

[0009] To achieve the above purpose, the present application provides the following technical scheme: an ocean engineering structure extended Kalman filter parameter estimation method based on attitude angle virtual observation, comprising the following steps:

[0010] S1, initializing the system process noise covariance matrix Q and the observation noise covariance matrix R, and realizing the optimal fusion of accelerometer, gyroscope and magnetometer data based on the extended Kalman filter to obtain the extended Kalman filter attitude angle estimation value;

[0011] S2, establishing a high-precision angular velocity-attitude angle dynamic conversion model based on the structure kinematics model, generating attitude angle virtual observation and using it to evaluate the Kalman filter result online;

[0012] S3, setting up a multi-dimensional performance evaluation index system, and quantitatively evaluating the amplitude error and trend stability of the extended Kalman filter estimated attitude angle;

[0013] S4, based on the attitude angle virtual observation of step S2 and the error measurement of the multi-dimensional performance evaluation index of S3, adjusting the scale factor γ of the system process noise covariance matrix Q and the observation noise covariance matrix R using the gradient descent algorithm in the exponential space, and iterating γ in real time.

[0014] By adopting the technical scheme, the relative attitude angle in a given time interval can be accurately obtained under various complex sea conditions by adopting the angular velocity-attitude angle dynamic conversion model, the cumulative error of the traditional numerical integral method can be effectively avoided, a robust and reliable attitude angle evaluation benchmark is provided for adaptive estimation of process noise and observation noise covariance of the extended Kalman filter, the multi-dimensional performance evaluation index can quantitatively evaluate the amplitude error and trend stability of the estimated attitude angle of the extended Kalman filter, and the estimated attitude angle of the extended Kalman filter is ensured to meet the expected accuracy, and through real-time iterative updating of γ, the change of the statistical characteristics of the sensor noise under complex working conditions can be quickly tracked and compensated, so that the key system parameters of the extended Kalman filter are quickly and stably estimated.

[0015] Further, in step S1, the extended Kalman filter is divided into a prediction stage and an update stage, wherein,

[0016] Prediction stage:

[0017] (1)

[0018] Update stage:

[0019] (2)

[0020] In formula (1), is the prior estimation of the system state at the kth sampling time; is the posterior state estimation at k-1 time; is the control input acting on the system in the interval ; f is a nonlinear dynamic model function of the system; is the prediction mean square error matrix, which recursively depends on the posterior covariance at the previous time and the process noise covariance matrix ; F is the Jacobian matrix of the nonlinear dynamic model function f with respect to the state vector x;

[0021] In formula (2), is the deviation between the actual observation and the model prediction at k time, which is called innovation; is the observation value at k time; h is a nonlinear observation function model, which maps the state space to the measurement space; S k is the innovation covariance matrix at k time; H is the Jacobian matrix of the observation function model h with respect to the state vector x; is the observation noise covariance matrix; is the Kalman gain, used to balance the weight of model prediction and actual observation; is the state estimation mean square error matrix.

[0022] By adopting the technical scheme, the above quantities jointly constitute the whole process of observation update of the extended Kalman filter.

[0023] Further, in step S1, the system process noise covariance matrix Q is:

[0024] (3)

[0025] In the formula, is the system process noise covariance matrix at the kth sampling time; is the isotropic white noise variance of the three-axis gyroscope; W k is the Jacobian matrix of the derivative of the state transition matrix with respect to the angular velocity;

[0026] The observation noise covariance matrix R is:

[0027] (4)

[0028] In the formula, represents the isotropic white noise level of the three axes of the accelerometer; represents the isotropic white noise level of the three axes of the magnetometer; is a 3x3 unit matrix, reflecting that the noise statistical performance of the sensor in three orthogonal directions is the same and complementary.

[0029] By adopting the technical scheme, since the system process noise Q is mainly affected by the noise of the gyroscope in each direction, and the observation noise covariance matrix R mainly reflects the sensor noise characteristics of the accelerometer and the magnetometer; after setting the process noise covariance matrix Q, the observation noise covariance matrix R, and the initial value of the state estimation mean square error matrix P, the iterative calculation formula (1), (2) of the extended Kalman filter is calculated, and the attitude angle estimation can be completed based on the current parameters.

[0030] Further, in step S2, the angular velocity-attitude angle dynamic conversion model is:

[0031] (5)

[0032] In the formula, ;

[0033] In the formula, represents the three-axis angular velocity vector at the kth sampling time, wherein , , respectively correspond to the angular velocity around the x, y, and z axes; represents the attitude angle of the marine engineering structure at the kth sampling time; ​is the order of the angular velocity-pose angle dynamic conversion model; is a complex amplitude coefficient of the component, used to represent the amplitude and phase offset of the component; is a complex eigenvalue of the signal component, used to reflect the oscillation frequency and damping coefficient of the component; and are the amplitude and initial phase of the pth mode, respectively; and are the damping ratio and natural frequency of the pth mode, respectively; is the sampling frequency of the signal; represents taking the real part of a complex number; i represents the imaginary unit.

[0034] By adopting the above technical solutions, the angular velocity-pose angle dynamic conversion can be realized when the marine engineering structure is in small angle motion, and the error accumulation generated by traditional numerical integration can be effectively suppressed.

[0035] Further, in step S3, the multi-dimensional performance evaluation index system includes an amplitude error index and a trend error index, wherein,

[0036] The amplitude error index is:

[0037] (6)

[0038] In the formula, is the pose angle at time k calculated by the extended Kalman filter; is the trend component of the pose angle at time k calculated by the extended Kalman filter; is the virtual observation value of the pose angle at time k obtained by the angular velocity-pose angle dynamic conversion model;

[0039] The trend error index is:

[0040] (7)

[0041] In the formula, is the trend component of the pose angle calculated by the extended Kalman filter; is the trend component of the pose angle at time k obtained by the geometric mapping relationship of the three-axis acceleration; is the trend component of the pose angle virtual observation value at time k obtained by the angular velocity-pose angle dynamic conversion model; N is the sample length; k = 1, …, N.

[0042] By adopting the above technical solutions, the estimation effect of the extended Kalman filter can be quantitatively evaluated from the instantaneous tracking error and the long-term trend error, and the output performance of the extended Kalman filter under the given parameter condition can be more comprehensively evaluated.

[0043] Further, in step S4, the implementation method of the gradient descent algorithm is:

[0044] (8)

[0045] (9)

[0046] wherein, is the objective function of the gradient descent algorithm; is the logarithmic scale variable; is the small perturbation quantity, usually taking ; represents the gradient of the objective function under the current parameters, which is used to guide the parameter update.

[0047] By adopting the above technical solution, the global optimal solution can be efficiently found.

[0048] Further, the gradient descent update rule is:

[0049] (10)

[0050] wherein, η is the learning rate, which controls the step size of each iteration; is the single-step maximum change quantity, usually taking ; is the sign function; is the gradient of the objective function calculated at the kth iteration; is the parameter value at the kth iteration, is the updated parameter; the operator represents taking the smaller one between the learning rate adjustment value and the maximum step constraint.

[0051] By adopting the above technical solution, the stability of the parameter optimization process and the real-time performance of the algorithm can be ensured.

[0052] Further, the iteration process termination condition is set to satisfy any one of the following conditions:

[0053] (11)

[0054] (12)

[0055] (13)

[0056] wherein, formula (11) indicates that the logarithmic parameter change rate is less than the threshold ; formula (12) indicates that the evaluation index change is less than the threshold ; and formula (13) indicates that the iteration number k reaches the maximum value .

[0057] By adopting the technical scheme, different threshold parameters are set, different precision requirements and optimization speeds can be realized.

[0058] In summary, the present application has the following advantages:

[0059] The method of the present application is based on the engineering characteristics of limited rotation amplitude of marine engineering structures, establishes an angular velocity-pose angle dynamic conversion model based on structure kinematics, realizes virtual observation of the pose angle, and provides accurate pose virtual observation for the extended Kalman filter to estimate the pose angle; this innovative method avoids the dependence of traditional methods on expensive external reference equipment such as optical motion capture systems or high-precision IMUs for parameter calibration, and is particularly suitable for application scenarios such as marine engineering structures that lack external reference true values.

[0060] The method of the present application sets up a multi-dimensional evaluation index system, comprehensively considers the amplitude error and drift term changes of the filter output; this index system provides guidance for the optimization of the system parameters of the extended Kalman filter.

[0061] The method of the present application couples the virtual observation error and the evaluation index into gradient information, uses the gradient descent strategy to adjust the process noise and observation noise covariance in real time, realizes the rapid adaptation of the parameters, can effectively cope with the time-varying nature of the sensor noise characteristics under complex working conditions, significantly improves the accuracy and robustness of the attitude estimation algorithm, and provides a new technical approach for attitude perception in complex environments such as marine engineering structures. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 is the distribution curve of the optimization variable X of the method of the present application and the comprehensive evaluation standard J(x);

[0063] Figure 2 is the extended Kalman (EKF) calculation result of the method after determining the parameters and the measurement result of the optical motion capture system (OMCS); wherein (a) is the time course curve of the entire test process, and (b) is the time course curve of the 10th to 30th second. DETAILED DESCRIPTION

[0064] The present application will be further described in detail below in combination with embodiments.

[0065] The method of the present application for estimating the parameters of the extended Kalman filter of marine engineering structures based on virtual observation of the pose angle comprises the following steps:

[0066] S1, initialize the system process noise covariance matrix Q and the observation noise covariance matrix R, and realize optimal fusion of the accelerometer, gyroscope and magnetometer data based on the extended Kalman filter to obtain the extended Kalman filter pose angle estimation value.

[0067] An inertial measurement unit consisting of an accelerometer, a gyroscope and a magnetometer is deployed on the main structure of the offshore structure c where T c is not less than one complete structural vibration period , the angular velocity and the magnetometer data sequence of the acceleration

[0068] According to the typical system noise value marked in the technical manual of each sensor , and Set the initial value of the system process noise covariance matrix Q and the observation noise covariance matrix R in the extended Kalman filter algorithm and .

[0069] Use quaternion q as a system variable, directly use angular velocity observation value as control input, and use acceleration and magnetometer as observation, through the prediction-update iteration process of the extended Kalman filter algorithm, real-time estimate the three-axis spatial attitude angle of the offshore structure .

[0070] Among them, the prediction stage is:

[0071] (1)

[0072] The update stage is:

[0073] (2)

[0074] In formula (1), is the priori estimate of the system state at the k-th sampling time; is the posteriori state estimate at k-1 time; is the control input acting on the system in the interval; f is the nonlinear dynamic model function of the system; is the prediction mean square error matrix, which recursively depends on the posteriori covariance and the process noise covariance matrix at the previous time; F is the Jacobian matrix of the nonlinear dynamic model function f with respect to the state vector x;

[0075] In formula (2), is the deviation between the actual observation and the model prediction at k time, called innovation; is the observation value at k time; h is the nonlinear observation function model, which maps the state space to the measurement space; S k is kThe innovation covariance matrix of the time instant; H is the Jacobian matrix of the observation function model h with respect to the state vector x; is the observation noise covariance matrix; is the Kalman gain, used to balance the weight of model prediction and actual observation; is the state estimation mean square error matrix.

[0076] The system process noise covariance matrix Q is:

[0077] (3)

[0078] In the formula, is the system process noise covariance matrix at the kth sampling instant; is the white noise variance of the three-axis gyroscope in each direction; W k is the Jacobian matrix of the state transition matrix with respect to the angular velocity.

[0079] The observation noise covariance matrix R is:

[0080] (4)

[0081] In the formula, represents the white noise level of the three axes of the accelerometer in each direction; represents the white noise level of the three axes of the magnetometer in each direction; I3 is a 3x3 unit matrix, reflecting that the noise statistical performance of the sensor in three orthogonal directions is the same and complementary.

[0082] S2, a high-precision angular velocity-pose angle dynamic conversion model is established based on the structural kinematic model, and a pose angle virtual observation quantity is generated and used for online evaluation of the Kalman filtering result.

[0083] The angular velocity-pose angle dynamic conversion model is:

[0084] (5)

[0085] wherein, ;

[0086] In the formula, represents the three-axis angular velocity vector at the kth sampling instant, wherein , , correspond to the angular velocity around the x, y, and z axes, respectively; represents the pose angle of the offshore engineering structure at the kth sampling instant; is the order of the angular velocity-pose angle dynamic conversion model; is the complex amplitude coefficient of the component, used to represent the amplitude and phase bias of the component; are the complex eigenvalues of the signal components, which reflect the oscillation frequency and damping coefficient of the components; and are the amplitude and initial phase of the p-th mode, respectively; and are the damping ratio and natural frequency of the p-th mode, respectively; is the sampling frequency of the signal; denotes the operation of taking the real part of a complex number; i denotes the imaginary unit.

[0087] For the main motion direction of the offshore engineering structure, the roll angle of rotation around the X-axis is taken as an example, the roll angle of rotation around the X-axis is decomposed, analyzed and summed according to formula (5) to obtain the relative rotation angle of the structure in time as a virtual observation.

[0088] S3, a multi-dimensional performance evaluation index system is set up, and the amplitude error and trend stability of the estimated attitude angle by the extended Kalman filter are quantitatively evaluated.

[0089] The multi-dimensional performance evaluation index system includes an amplitude error index and a trend error index, wherein,

[0090] The amplitude error index is:

[0091] (6)

[0092] In the formula, is the attitude angle at time k calculated by the extended Kalman filter; is the trend component of the attitude angle at time k calculated by the extended Kalman filter; is the virtual observation value of the attitude angle at time k obtained by the angular velocity-attitude angle dynamic conversion model;

[0093] The trend error index is:

[0094] (7)

[0095] In the formula, is the trend component of the attitude angle calculated by the extended Kalman filter; is the trend component of the attitude angle at time k obtained by the geometric mapping relationship of the three-axis acceleration; is the trend component of the virtual observation value of the attitude angle at time k obtained by the angular velocity-attitude angle dynamic conversion model; N is the sample length; k=1,…,N.

[0096] The amplitude error and trend error indexes under the current parameter configuration are calculated according to formula (6) and (7).

[0097] S4, based on the attitude angle virtual observation of step S2 and the error measurement of the multi-dimension performance evaluation index of S3, using gradient descent algorithm to adjust the scale factor γ of the system process noise covariance matrix Q and the observation noise covariance matrix R in the index space, and iterating γ in real time.

[0098] According to the scale invariance of Kalman filter, the original multi-variable optimization problem is reduced to adjusting the relative weight of the system process noise covariance matrix Q and the observation noise covariance matrix R: let the standard deviation of the gyroscope, accelerometer and magnetometer noise be ; the standard deviation of the gyroscope noise is normalized to a constant 1; then, for the estimation of the pitch and roll angles, the logarithmic scale variable is introduced as the only optimization independent variable; for the heading angle, the same weight adjustment is performed by using ; by searching for the optimal solution in the one-dimensional parameter x space, the optimal trade-off between Q and R can be realized on the premise of ensuring the calculation efficiency, so as to significantly improve the estimation accuracy and robustness of the extended Kalman filter in each attitude channel.

[0099] In order to take into account the contribution of different indexes to the system performance, the following root mean square evaluation index is introduced:

[0100] (8)

[0101] wherein, is the objective function of the gradient descent algorithm, represents the amplitude error index; represents the trend error index;

[0102] The implementation method of the gradient descent algorithm is:

[0103] (9)

[0104] wherein, is the objective function of the gradient descent algorithm; is the logarithmic scale variable; is a small perturbation, usually ; represents the gradient of the objective function under the current parameters, which is used to guide the parameter update. The gradient descent update rule is:

[0105] (10)

[0106] wherein, η is the learning rate, which controls the step size of each iteration; is the maximum change amount of a single step, usually ; is the sign function; is the gradient of the objective function calculated at the kth iteration; is the parameter value at the kth iteration, is the updated parameter; The operator represents taking the smaller one between the learning rate adjustment value and the maximum step constraint.

[0107] The gradient descent iteration is performed according to formulas (8), (9), and (10) until converging to the global optimal parameter configuration , so that the evaluation function J(x) reaches a minimum value.

[0108] The following takes a floating pontoon pool experiment as an example to verify the method of the present application. The experimental device is as follows: an inertial measurement unit (IMU) is fixed near the centroid of the pontoon, and an optical reflective marker is pasted on the IMU shell; at the same time, a high-precision optical motion capture system is arranged around the pool. The two systems synchronously collect the transient attitude information of the pontoon under wave excitation with a unified time base, providing consistent data sources for subsequent algorithm evaluation and comparison.

[0109] The data is processed according to steps S1-S4, the parameter x iteration process is recorded, and the distribution curve of the optimized variable x and the comprehensive evaluation standard J(x) is obtained, as shown in Figure 1 The pitch angle calculated by the extended Kalman filter parameters determined by the method is compared with the measured results of the optical motion capture system, and the results are as shown in Figure 2 , fully proving the accuracy and reliability of the method.

[0110] The specific embodiments are only an explanation of the present application, and are not a limitation of the present application. Those skilled in the art can make modifications to the embodiments without creative contribution after reading the present specification, as long as the modifications are within the scope of the claims of the present application.

Claims

1. A method for estimating the parameters of an extended Kalman filter for marine engineering structures based on virtual attitude angle observation, characterized in that, Includes the following steps: S1. Initialize the system process noise covariance matrix Q and the observation noise covariance matrix R, and achieve optimal fusion of accelerometer, gyroscope and magnetometer data based on the extended Kalman filter to obtain the extended Kalman filter attitude angle estimate. S2. Based on the structural kinematics model, a high-precision dynamic conversion model of angular velocity-attitude angle is established to generate virtual observations of attitude angles and use them to evaluate the Kalman filter results online. S3. Set up a multi-dimensional performance evaluation index system and quantitatively evaluate the magnitude error and trend stability of the attitude angle estimation by the extended Kalman filter. S4. Based on the virtual attitude angle observation in step S2 and the error measurement of the multi-dimensional performance evaluation index in S3, the scaling factor γ of the system process noise covariance matrix Q and the observation noise covariance matrix R is adjusted in the exponential space using the gradient descent algorithm, and γ is iterated in real time.

2. The method according to claim 1, characterized in that, In step S1, the extended Kalman filter is divided into a prediction phase and an update phase. The prediction phase includes: （1）， Update phase: （2）， In equation (1), It is the prior estimate of the system state at the k-th sampling time; It is the posterior state estimate at time k-1; Is The control input acting on the system within the interval; f is the nonlinear dynamic model function of the system; It is the prediction mean squared error matrix, which recursively depends on the posterior covariance of the previous time step. and process noise covariance matrix F is the Jacobian matrix of the nonlinear dynamic model function f with respect to the state vector x; In equation (2), The difference between the actual observation and the model prediction at time k is called the innovation. is the observation value at time k; h is the nonlinear observation function model that maps the state space to the measurement space; S k yes k The information covariance matrix at time t; H is the Jacobian matrix of the observation function model h with respect to the state vector x; It is the observation noise covariance matrix; It is the Kalman gain, used to balance the weights of model predictions and actual observations; It is the mean square error matrix of the state estimation.

3. The method according to claim 1, characterized in that, In step S1, the system process noise covariance matrix Q is: （3）， In the formula, It is the system process noise covariance matrix at the k-th sampling time; The variance of the isotropic white noise of the three-axis gyroscope; W k The Jacobian matrix is ​​the derivative of the state transition matrix with respect to the angular velocity; The observation noise covariance matrix R is: （4）， In the formula, This indicates the level of white noise, which is isotropic across the three axes of the accelerometer. I3 represents the white noise level of the magnetometer, which is isotropic across its three axes; I3 is a 3×3 identity matrix that reflects the same and complementary noise statistical performance of the sensor in the three orthogonal directions.

4. The method according to claim 1, characterized in that, In step S2, the dynamic conversion model of angular velocity-attitude angle is as follows: （5）， in, ; In the formula, Let represent the three-axis angular velocity vector at the k-th sampling time, where , , These correspond to the angular velocities about the x, y, and z axes, respectively. This represents the attitude angle of the marine engineering structure at the k-th sampling time; It is the order of the angular velocity-attitude angle dynamic conversion model; It is the complex amplitude coefficient of the component, used to characterize the amplitude and phase offset of the component; These are the complex characteristic roots of the signal component, used to reflect the oscillation frequency and damping coefficient of that component; and These are the amplitude and initial phase of the p-th mode, respectively; and These are the damping ratio and natural frequency of the p-th mode, respectively; It is the sampling frequency of the signal; This indicates the operation of taking the real part of a complex number; i represents the imaginary unit.

5. The method according to claim 1, characterized in that, In step S3, the multi-dimensional performance evaluation index system includes amplitude error index and trend error index, among which, The amplitude error index is: （6）， In the formula, It is the attitude angle calculated by the extended Kalman filter at the k-th sampling time; It is the time-trend component of the attitude angle calculated by the extended Kalman filter at the k-th sampling time; It is the virtual observation value of the attitude angle at the kth sampling moment obtained from the angular velocity-attitude angle dynamic conversion model; The trend error index is: （7）， In the formula, It is the trend component of the attitude angle calculated by the extended Kalman filter; It is the trend component of the attitude angle at time k, obtained by geometric mapping relationship of the three-axis acceleration; It is the trend component of the virtual attitude angle observation value obtained from the angular velocity-attitude angle dynamic conversion model at time k; N is the sample length; k=1,…,N.

6. The method according to claim 1, characterized in that, In step S4, the gradient descent algorithm is implemented as follows: （8）， （9）， In the formula, Let be the objective function of the gradient descent algorithm; It is a logarithmic scaling variable; For small perturbations, usually take ; This represents the gradient of the objective function under the current parameters, and is used to guide parameter updates.

7. The method according to claim 6, characterized in that, The gradient descent update rule is as follows: （10）， In the formula, η is the learning rate, which controls the step size of each iteration; The maximum change in a single step is usually taken as... ; It is a symbolic function; The gradient of the objective function is calculated at the k-th iteration; The parameter value is for the k-th iteration. The updated parameters; The operator indicates taking the smaller of the learning rate adjustment value and the maximum step size constraint.

8. The method according to claim 1, characterized in that, The termination condition for the iterative process is set to satisfy any of the following conditions: （11）， （12）， （13）， Formula (11) indicates that the rate of change of the logarithmic parameter is less than the threshold. Formula (12) indicates that the change in the evaluation index is less than the threshold. Formula (13) indicates that the number of iterations k reaches its maximum value. .

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