Deep-sea flexible buoy in-situ calibration method and system based on augmented state filter

Abstract

The present application relates to the technical field of deep-sea flexible buoy in-situ calibration, and provides a deep-sea flexible buoy in-situ calibration method and system based on augmented state filtering to solve the problem that the current calibration method cannot meet the in-situ, rapid and high-precision calibration requirements of the acoustic node of the buoy. The deep-sea flexible buoy in-situ calibration method based on augmented state filtering comprises the following steps: controlling the calibration trajectory of an autonomous underwater vehicle to maneuver; synchronously acquiring the relevant information of the autonomous underwater vehicle and the buoy during the execution of the maneuver; constructing a physical model of the deformation of the buoy, and incorporating the deformation angle parameters to be estimated into the state vector of the Kalman filter; linearizing the measurement residual by using the Jacobian matrix containing the deformation angle parameters, and performing secondary joint estimation of the driving deformation angle parameters by updating the Kalman filter through iteration; and combining the physical model of the deformation of the buoy to calculate the final horizontal coordinates of the sound emission point of the buoy. The method can be independently completed in a deep-sea in-situ environment, and the position calibration of the acoustic node of the buoy is independent of the mother ship on the sea surface.

Description

Technical Field

[0001] This invention relates to the field of in-situ calibration technology for deep-sea flexible moorings, and in particular to a method and system for in-situ calibration of deep-sea flexible moorings based on augmented state filtering. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In scenarios such as underwater target detection and acoustic-assisted navigation, acoustic positioning networks directly impact the navigation accuracy and mission completion quality of vehicles such as autonomous underwater vehicles (AUVs). Traditional acoustic positioning nodes are mostly rigidly fixed on the seabed, only suitable for positioning needs in localized, fixed areas. In large-scale operational scenarios, acoustic emitting nodes need to be deployed in the middle layer of seawater using underwater buoys to expand acoustic coverage, optimize communication conditions, and provide more flexible and reliable acoustic navigation support for underwater platforms.

[0004] Deep-sea moorings are anchored to the seabed by a bottom anchoring system and equipped with a GNSS (Global Navigation Satellite System) positioning module on top, serving as the acoustic positioning reference for underwater platforms. However, due to the dragging effect of ocean currents, the moorings experience overall swaying and structural deformation, leading to a significant discrepancy between the position measured by the top GNSS and the actual position of the mid-level acoustic emanating point. Directly using the position of the top GNSS to replace the actual coordinates of the mooring's acoustic emanating point introduces systematic geometric errors, severely reducing the positioning accuracy and navigation stability of AUVs. Current underwater acoustic node calibration methods largely rely on surface mother ships equipped with Ultra-Short Baseline (USBL) systems, combined with underway surveys and specific survey lines to calculate the position. These methods are highly dependent on surface platforms, with complex and costly deployment and calibration processes, and are easily affected by sea conditions, mother ship attitude, and changes in sound speed. For underwater acoustic nodes that dynamically shift with ocean currents, traditional methods require repeated measurements and calculations, making it difficult to balance efficiency and accuracy. In deep-sea array scenarios, the process is cumbersome, time-consuming, and costly, completely failing to meet the requirements for in-situ, rapid, and high-precision calibration of underwater acoustic nodes. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method and system for in-situ calibration of deep-sea flexible moorings based on augmented state filtering. This method can be independently completed in a deep-sea in-situ environment and can eliminate the reliance on surface mother ships for mooring acoustic node position calibration. This allows for efficient and accurate acquisition of the dynamic offset angle and position information of the moorings caused by ocean currents through AUV navigation, thereby effectively eliminating acoustic reference errors and ensuring the realization of long-duration, high-precision navigation.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: The first aspect of the present invention provides an in-situ calibration method for deep-sea flexible moorings based on augmented state filtering.

[0007] In one or more embodiments, a method for in-situ calibration of deep-sea flexible moorings based on augmented state filtering is provided, comprising: The autonomous underwater vehicle is controlled to navigate to the preset mooring position and dive to the preset depth. Then, it is controlled to perform preset calibration trajectory maneuvers. During the maneuver, relevant information about the autonomous underwater vehicle and the mooring is acquired simultaneously. A physical model of underwater mooring deformation is constructed, and the spatial offset of the mooring point relative to the GNSS positioning point at the top of the mooring point is equivalently represented as the deflection tilt angle and the deflection azimuth angle, and these are incorporated into the Kalman filter state vector as deformation angle parameters to be estimated. Based on the synchronously acquired information about the autonomous underwater vehicle and the mooring, the prior horizontal position of the autonomous underwater vehicle at the current moment is calculated using inertial navigation, and the time update of the Kalman filter state vector and covariance matrix is ​​completed. Based on the mooring deformation physical model, the predicted horizontal coordinates of the mooring sound point are obtained. Based on the prior horizontal position and the predicted horizontal coordinates of the mooring point, the distance measurement residual between the autonomous underwater vehicle and the mooring point is constructed. The distance measurement residual is linearized using a Jacobian matrix that includes the partial derivative of the deformation angle parameter. The navigation error and deformation angle parameter of the autonomous underwater vehicle are jointly estimated for the first time through Kalman filtering measurement updates. Based on the deformation angle parameters and their covariance obtained from the initial estimation, the initial conditions of the Kalman filter are reset, and the Kalman filter is performed again to obtain the secondary optimized estimation results of the deformation angle parameters. Based on the physical model of the moored glide deformation and the deformation angle parameters estimated by the second optimization, the final horizontal coordinates of the moored glide's sound-emitting point are reconstructed, and the in-situ calibration of the moored glide is completed.

[0008] As one implementation method, the process of constructing the Jacobian matrix containing the partial derivative terms of the deformation angle parameter is as follows: Based on the synchronous acquisition of information related to autonomous underwater vehicles and moorings, the observation distance of the mooring's sound-emitting point is calculated. Based on the prior horizontal position of the autonomous underwater vehicle at the current moment, the GNSS reference coordinates of the top of the mooring, the vertical distance of the mooring's sound source, and the deformation angle parameter, a theoretical distance function between the autonomous underwater vehicle and the mooring's sound source is constructed. The partial derivatives of the theoretical distance function with respect to the horizontal position error and deformation angle parameter in the Kalman filter state vector are calculated to construct a Jacobian matrix containing the partial derivative term of the deformation angle parameter.

[0009] As one implementation method, the process of linearizing the distance measurement residual using the Jacobian matrix containing the partial derivative terms of the deformation angle parameter is as follows: Based on the state transition equation of the Kalman filter state vector, and combined with the relevant information of the autonomous underwater vehicle and the mooring, the prior covariance matrix and the measurement noise covariance matrix are obtained. The Jacobian matrix containing the deformation angle parameter is used as the observation matrix, and then the Kalman gain is calculated by combining the prior covariance matrix and the measurement noise covariance matrix. Multiplying the Kalman gain by the measurement residual yields a correction value for the Kalman filter state vector, which is then used to correct the Kalman filter state vector.

[0010] As one implementation method, in the process of constructing the physical model of the mooring deformation, the mooring cable is regarded as a flexible slender body that is deflected as a whole under the drag of the ocean current, and the GNSS positioning point at the top of the mooring is used as the geometric reference benchmark, and the sound-emitting point of the mooring is used as the actual acoustic reference point after deformation.

[0011] As one implementation, the parameters in the Kalman filter state vector include deformation angle parameters and navigation error-related parameters of the autonomous underwater vehicle.

[0012] As one implementation method, the process of constructing the distance measurement residual between the autonomous underwater vehicle and the buoy's sound emission point is as follows: Based on the predicted horizontal coordinates of the mooring point and the prior horizontal position of the autonomous underwater vehicle at the current moment, the coordinate error of the mooring point is calculated, and then the theoretical horizontal distance is obtained. Subtracting the measured horizontal distance from the theoretical horizontal distance yields the measurement residual of the buoy's sound-emitting point.

[0013] As one implementation method, the information related to the autonomous underwater vehicle and the mooring includes the autonomous underwater vehicle's own status data, the underwater acoustic propagation time and depth parameters between the autonomous underwater vehicle and the mooring's sound emission point.

[0014] A second aspect of the present invention provides an in-situ calibration system for deep-sea flexible moorings based on augmented state filtering.

[0015] In one or more embodiments, a deep-sea flexible mooring in-situ calibration system based on augmented state filtering includes: The calibration trajectory maneuver module is used to control the autonomous underwater vehicle to navigate to the preset mooring position and dive to the preset depth, and then control it to execute the preset calibration trajectory maneuver. During the execution of the maneuver, it simultaneously acquires relevant information about the autonomous underwater vehicle and the mooring. The deformation physical model construction module is used to construct the deformation physical model of the mooring. It represents the spatial offset of the mooring sound point relative to the GNSS positioning point at the top of the mooring as the deflection tilt angle and deflection azimuth angle, and incorporates them as deformation angle parameters to be estimated into the state vector of the Kalman filter. The prior and predicted horizontal calculation module is used to calculate the prior horizontal position of the autonomous underwater vehicle at the current moment based on synchronously acquired information related to the autonomous underwater vehicle and the mooring, and to complete the time update of the Kalman filter state vector and covariance matrix. Based on the mooring deformation physical model, the predicted horizontal coordinates of the mooring sound point are obtained. The joint initial estimation module is used to construct the distance measurement residual between the autonomous underwater vehicle and the mooring point based on the prior horizontal position and the predicted horizontal coordinates of the mooring point, and to linearize the distance measurement residual using a Jacobian matrix containing the partial derivative of the deformation angle parameter. The module then performs a joint initial estimation of the autonomous underwater vehicle's navigation error and deformation angle parameter through Kalman filtering measurement updates. The secondary optimization estimation module is used to reset the initial conditions of the Kalman filter based on the deformation angle parameter and its covariance obtained from the initial estimation, and then perform Kalman filtering again to obtain the secondary optimization estimation result of the deformation angle parameter. The horizontal coordinate reconstruction module is used to reconstruct the final horizontal coordinates of the mooring point based on the physical model of mooring deformation and the deformation angle parameters estimated by secondary optimization, thus completing the in-situ calibration of the mooring.

[0016] A third aspect of the present invention provides a computer-readable storage medium.

[0017] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described above.

[0018] A fourth aspect of the present invention provides an electronic device.

[0019] An electronic device includes a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps in the in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described above.

[0020] Compared with the prior art, the beneficial effects of the present invention are: This invention controls an autonomous underwater vehicle (AUV) to perform pre-set calibration trajectory maneuvers, simultaneously acquiring information related to the AUV and the moored buoy. A physical model of the moored buoy's deformation is constructed, and the spatial offset of the moored buoy's sound point relative to the GNSS positioning point at the top of the moored buoy is equivalently represented as deflection tilt angle and deflection azimuth angle. These are incorporated into the Kalman filter state vector as deformation angle parameters to be estimated. The measurement residuals are linearized using a Jacobian matrix containing the deformation angle parameters, and the deformation angle parameters are updated through iterative Kalman filtering to perform a second joint estimation. Finally, the final horizontal coordinates of the moored buoy's sound point are reconstructed, completing the in-situ calibration of the moored buoy. This achieves independent in-situ calibration in the deep sea environment, eliminating reliance on surface mother ships for moored buoy acoustic node position calibration. This allows for efficient and accurate acquisition of the dynamic offset angle and position information of the moored buoy caused by ocean currents during AUV navigation, effectively eliminating acoustic reference errors and ensuring long-endurance and high-precision navigation. Attached Figure Description

[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0022] Figure 1 This is a flowchart of the in-situ calibration method for deep-sea flexible mooring based on augmented state filtering according to an embodiment of the present invention; Figure 2 This is a schematic diagram of deformation angle modeling according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the deployment of the underwater buoy array and the two-stage flight path of the AUV according to an embodiment of the present invention; Figure 4 This invention relates to the first joint estimation error and coordinate compensation effect under three different maneuver trajectories in this embodiment. Figure 5 This is a comparison of the average level position error and improvement rate before and after the second iteration of the present invention. Figure 6 This is a comparison curve of radial positioning error during the cruise phase in an embodiment of the present invention. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0025] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0026] Figure 1 A schematic diagram of the in-situ calibration method for deep-sea flexible moorings based on augmented state filtering, according to an embodiment of the present invention, is provided. Figure 1 The in-situ calibration method for deep-sea flexible mooring based on augmented state filtering in this embodiment may include the following steps S101 to S106.

[0027] The specific implementation process of steps S101 to S106 is as follows: Step S101: Control the autonomous underwater vehicle to navigate to the preset mooring position and dive to the preset depth, then control it to perform a preset calibration trajectory maneuver, and simultaneously acquire relevant information about the autonomous underwater vehicle and the mooring during the maneuver.

[0028] The target mooring node is preset to the location of the mooring, and it communicates with the underwater acoustic communication device on the autonomous underwater vehicle at a period of 20 seconds to achieve the location calibration of the mooring.

[0029] Specifically, AUVs execute highly observable geometric closed-loop trajectories, such as square or circular trajectories, at or near the center of the moor array to enhance the ability to observe the spatial location of the moor.

[0030] During the maneuver, the information acquired simultaneously about the autonomous underwater vehicle and the mooring includes the autonomous underwater vehicle's own status data, the underwater acoustic propagation time and depth parameters between the autonomous underwater vehicle and the mooring's sound emission point.

[0031] The data acquisition module synchronously acquires information related to the autonomous underwater vehicle and its mooring. The data acquisition module includes an inertial measurement unit (IMU), an underwater acoustic communication device, and a depth gauge.

[0032] Among them, the IMU is used to output the three-axis specific force, angular velocity and attitude change information of the AUV in real time, providing input for motion state propagation and attitude calculation; The underwater acoustic communication device is used to establish two-way communication with the underwater buoy nodes and to measure the propagation time of underwater acoustic signals, providing observations for estimating the horizontal distance between the buoy and the AUV; for example, it can simultaneously acquire the acoustic propagation time between the AUV and three buoy sound emission points. And convert it into horizontal projection distance. ; Depth gauges are used to acquire real-time depth information of an AUV to constrain its vertical position and improve spatial positioning accuracy. For example, depth gauges can be used to obtain depth parameters of both the AUV and the buoy. and .

[0033] During the AUV's maneuver, its own state data, such as inertia and depth, as well as the underwater acoustic propagation time with the mooring buoy, are collected in real time to calculate the ranging information and provide observational input for subsequent parameter estimation.

[0034] Step S102: Construct a physical model of the mooring glide deformation, and represent the spatial offset of the mooring glide's sound source relative to the GNSS positioning point at the top of the mooring glide as an equivalent deflection angle. and deflection azimuth angle And incorporate it as the deformation angle parameter to be estimated into the Kalman filter state vector, such as Figure 2 As shown. This avoids directly describing complex three-dimensional continuous deformations using high-dimensional parameterization.

[0035] In constructing the physical model of the mooring deformation, the mooring cable is regarded as a flexible slender body that deflects as a whole under the drag of the ocean current. The GNSS positioning point at the top of the mooring is used as the geometric reference, and the sound-emitting point of the mooring is used as the actual acoustic reference point after deformation.

[0036] Let the first The nominal GNSS coordinates of the surface of the underwater buoy for: ; in, and They represent the first The nominal coordinates of a GNSS point on the surface of a submersible mooring point in the north and east directions; the superscript T denotes the transpose of the matrix. Let the depth of the mooring point be... The mooring line deflects as a whole due to the dragging effect of the ocean current, and its deflection angle is... The horizontal deflection azimuth angle is Under the assumption of angled equivalent modeling, the first... The horizontal offsets of the buoy's sound source relative to the surface GNSS point in the north and east directions are respectively set as follows: and The corresponding expression is: ; ; Therefore, the physical model of sprue deformation, i.e., the first The actual projected coordinates of the sound-emitting point of each underwater mooring point on the horizontal plane ( , ) is represented as: ; ; The physical meaning of the underwater glider deformation physical model is: deflection angle. The horizontal distance between the buoy's sound source and the GNSS point on the water surface is determined by the azimuth angle. Determine the direction of this horizontal offset within the northeast plane.

[0037] yaw angle Used to characterize the degree of inclination of the cable relative to the vertical direction, reflecting the overall displacement caused by ocean current drag; azimuth angle of deflection. This is used to characterize the direction of the offset in the horizontal plane, reflecting the spatial orientation of the buoy's sound emission point offset.

[0038] For a mooring array with a baseline length of 20 km, considering that when the mooring point is located at a depth of approximately 1000 m, the surrounding ocean current field exhibits strong spatial correlation and gradually varying characteristics within the array scale. It is assumed that the dominant current field direction and velocity experienced by each mooring within the array are approximately the same, meaning that each mooring shares a uniform cable deflection angle. and deflection azimuth angle This assumption is equivalent to believing that the deformation state of each mooring in the array is mainly determined by the same ocean current environment within the same time period. This transforms the originally dispersed local deformation problem into a unified global parameter estimation problem. Through this assumption, model complexity can be significantly reduced, the state dimension decreased, and the stability and solvability of subsequent filtering estimation and mooring point coordinate reconstruction can be improved.

[0039] The parameters in the state vector of the Kalman filter include deformation angle parameters and navigation error-related parameters of the autonomous underwater vehicle.

[0040] Initialize a 10-state extended Kalman filter. Define an augmented state vector. That is, as the state vector of the Kalman filter: ; Among them, the first 8 dimensions ( The AUV navigation errors are: north / east position error, north / east velocity error, heading misalignment angle, zero bias of the two-axis horizontal accelerometer, and zero bias of the azimuth gyroscope; the latter two dimensions ( ) represents the deformation angle of the buoy flow field to be calibrated. The system state transition model for the deformation angle is set as a random constant ( ).

[0041] Step S103: Based on the synchronously acquired information about the autonomous underwater vehicle and the mooring, the prior horizontal position of the autonomous underwater vehicle at the current moment is calculated using inertial navigation, and the time update of the Kalman filter state vector and covariance matrix is ​​completed. Based on the mooring deformation physical model, the predicted horizontal coordinates of the mooring sound point are obtained.

[0042] For the first 8 dimensions of AUV navigation error state, time updates are performed based on the inertial navigation error propagation model; for the last 2 dimensions of deformation angle parameters, since they can be approximated as slowly varying or constant parameters during a short-time calibration process, a stochastic constant model can be used. ; ; Where k represents the current discrete filtering time, and k-1 represents the previous discrete filtering time; and Let represent the prior estimates of the mooring tilt angle and the azimuth angle at time k, respectively; and These represent the posterior estimates of the tilt and azimuth angles after the measurement update at time k-1, respectively. (Superscript "...") The superscript "" indicates the prior estimate before the measurement update, and the superscript "+" indicates the posterior estimate after the measurement update. The corresponding state transition can be written as: ; ; in, This is the 10-dimensional posterior state vector after the measurement update is completed at time k-1. Here is the state transition matrix. The prior state vector at time k is obtained by propagating the state from the previous time step. The prior covariance matrix, Let be the posterior state error covariance matrix at time k-1. Let be the system process noise covariance matrix. For Two angle states can be set to minimize process noise, thus characterizing the uncertainty of the slow change in the deformation angle of the buoy over a short period of time.

[0043] Within each filtering cycle, the specific force and angular velocity output by the IMU are first used to perform inertial navigation mechanical arrangement to obtain the AUV's prior horizontal position at the current moment. : ; in, The coordinates of the matrix at the current time are the prior coordinates in the north and east directions; the superscript T indicates the transpose of the matrix.

[0044] Simultaneously, based on the system error propagation model, the state vector and covariance matrix are updated over time to obtain the prior state estimate. and prior covariance matrix .

[0045] Based on the current prior state and Calculate the first Predicted horizontal coordinates of each underwater buoy's sound source ( , ): ; .

[0046] Step S104: Based on the prior horizontal position and the predicted horizontal coordinates of the mooring point, construct the distance measurement residual between the autonomous underwater vehicle and the mooring point, and linearize the distance measurement residual using a Jacobian matrix containing the partial derivative of the deformation angle parameter. Perform a joint initial estimate of the autonomous underwater vehicle navigation error and deformation angle parameter through Kalman filter measurement update.

[0047] In one or more embodiments, the process of constructing the distance measurement residual between the autonomous underwater vehicle and the buoy's acoustic point is as follows: Based on the predicted horizontal coordinates of the mooring point and the prior horizontal position of the autonomous underwater vehicle at the current moment, the coordinate error of the mooring point is calculated, and then the theoretical horizontal distance is obtained. Subtracting the measured horizontal distance from the theoretical horizontal distance yields the measurement residual of the buoy's sound-emitting point.

[0048] AUV and the The north and east coordinate differences between the sounding points of the underwater moorings are: ; ; Therefore, the theoretical horizontal distance predicted based on the current state is: ; The measured horizontal distance Distance from theoretical level Subtracting, we get the first Measurement residuals corresponding to each buoy : ; When ranging information from three underwater buoys is received simultaneously, the three measurement residuals are stacked into a residual vector. : ; This residual vector reflects the deviation between the "measured horizontal distance" and the "predicted horizontal distance in the current state," and serves as the input for EKF measurement updates. Its physical function is to drive the filter to correct AUV navigation errors and deformation angle parameters.

[0049] In one or more embodiments, the process of constructing the Jacobian matrix, which includes the partial derivative terms of the deformation angle parameter, is as follows: Based on the synchronous acquisition of information related to autonomous underwater vehicles and moorings, the observation distance of the mooring's sound-emitting point is calculated. Based on the prior horizontal position of the autonomous underwater vehicle at the current moment, the GNSS reference coordinates of the top of the mooring, the vertical distance of the mooring's sound source, and the deformation angle parameter, a theoretical distance function between the autonomous underwater vehicle and the mooring's sound source is constructed. The partial derivatives of the theoretical distance function with respect to the horizontal position error and deformation angle parameter in the Kalman filter state vector are calculated to construct a Jacobian matrix containing the partial derivative term of the deformation angle parameter.

[0050] The process of linearizing the distance measurement residual using the Jacobian matrix, which includes the partial derivative terms of the deformation angle parameter, is as follows: Based on the state transition equation of the Kalman filter state vector, and combined with the relevant information of the autonomous underwater vehicle and the mooring, the prior covariance matrix and the measurement noise covariance matrix are obtained. The Jacobian matrix containing the deformation angle parameter is used as the observation matrix, and then the Kalman gain is calculated by combining the prior covariance matrix and the measurement noise covariance matrix. Multiplying the Kalman gain by the measurement residual yields a correction value for the Kalman filter state vector, which is then used to correct the Kalman filter state vector.

[0051] The horizontal ranging equation is actually about the AUV's position error and the mooring deflection angle. and deflection azimuth angle The nonlinear function. Taking a first-order Taylor expansion of it at the current estimated state, we get: ; in, For 10-dimensional error states, For the observation matrix, For measuring noise.

[0052] For the The first buoy, the first observation matrix Behavior: ; Since horizontal ranging only directly constrains the horizontal position of the AUV and the deformation angle of the mooring, the direct partial derivatives with respect to velocity error, heading error, and IMU zero bias are 0; these states are mainly indirectly coupled with position error through the system propagation matrix.

[0053] The partial derivative of the position error term is the conventional spatial geometric projection, which is the direction cosine in the ranging direction: , ; The following derivation and The analytical partial derivative. By the chain rule, we have: ; because: , ; and: , ; so: ; Similarly, for Find the partial derivative: ; therefore: ; Finally, the first The observation matrix rows corresponding to each buoy can be written as: ; in, It is a secant function; It is a sine function; It is a cosine function; It is the tangent function.

[0054] If distance measurements are received from three buoys at the same time, then the distances corresponding to the three buoys will be recorded. Vertical stacking yields the complete result. Observation matrix: ; The function of this matrix is ​​to store the measurement residuals. This is related to the 10-dimensional error state: ; The Kalman gain is then calculated in the EKF: ; in, This is the Kalman filter gain matrix. Let covariance matrix be the variance matrix. For the observation matrix, For measuring the noise matrix, the superscript " "" indicates the prior estimate before the measurement update.

[0055] And use measurement residuals to correct the state: ; Among them, the corrections in the 9th and 10th dimensions correspond to the mooring deflection angle error and azimuth angle error, respectively: ; ; Therefore, the derived analytical partial derivatives are not used alone, but rather as part of the observation matrix. Columns 9 and 10 are entered into the EKF update process to convert the ranging residuals into a logarithmic value. and The correction amount ultimately achieves the estimation of deformation angle parameters and the reconstruction of the coordinates of the underwater glider's sound source.

[0056] Specifically, based on the prior covariance matrix Observation matrix Measurement noise covariance matrix Calculate the residual covariance matrix : ; Then calculate the Kalman gain. : ; Kalman gain This is used to determine the correction weights of the residuals from this underwater acoustic ranging measurement for each state quantity. If the prior covariance... A large measurement residual indicates that the system lacks confidence in its current predicted state, thus increasing the impact of the measurement residual on state updates; if the measurement noise covariance is large... A larger value indicates greater uncertainty in underwater acoustic ranging, which reduces the filter's confidence in the measurement.

[0057] Calculate the state correction using measurement residuals: ; And update the state vector: ; The state correction can be written as: ; Corresponding to the deformation angle parameter, the update format is as follows: ; ; At the same time, update the covariance matrix: ; Alternatively, the Joseph form, which offers better numerical stability, can be used: ; Through the above steps, the underwater acoustic ranging residual is transformed into a joint correction of AUV navigation error, inertial device error, and deformation angle parameter, thereby realizing online estimation of deformation angle parameter.

[0058] Step S105: Based on the deformation angle parameters and their covariance obtained from the initial estimation, reset the initial conditions of the Kalman filter and perform the Kalman filter process again to obtain the secondary optimized estimation result of the deformation angle parameters.

[0059] During the process of performing secondary convergence by updating the driving deformation angle parameter through iterative Kalman filtering, the initial value of the deformation angle parameter and its covariance matrix in the second Kalman filter are reset based on the deformation angle parameter estimation result and corresponding uncertainty obtained from the first Kalman filter, so that the second Kalman filter continues to converge under the initial conditions that are closer to the actual deformation state.

[0060] After the first EKF filtering, the preliminary converged estimates of the mooring tilt angle and azimuth angle are extracted from the state vector: , Simultaneously, extract the covariance submatrices from the covariance matrix at the end of the first filtering step, corresponding to the 9th and 10th dimension angular states: .

[0061] The second iteration does not modify the original underwater acoustic distance data. Instead, it uses the deformation angle estimation result and corresponding uncertainty obtained from the first Kalman filter to reset the initial value of the angle state and its covariance matrix in the second Kalman filter, so that the second Kalman filter continues to converge under initial conditions that are closer to the actual deformation state.

[0062] Specifically, the initial values ​​for the two angle states in the second Kalman filter are set as follows: ; ; The initial covariance corresponding to the angle state in the second Kalman filter is set as follows: In practical engineering applications, to avoid the second Kalman filter being overly confident in the first estimation result, the initial covariance can be adjusted appropriately. Therefore, the initial state of the second Kalman filter can be written as: ; in, This indicates the initial state of AUV navigation error and inertial device error in the second Kalman filter, which can be set based on the results of the first Kalman filter or the engineering initialization strategy.

[0063] The initial covariance matrix of the second Kalman filter can be expressed as: ; in, The result is updated from the first Kalman filter. If the navigation error state is reinitialized by the second Kalman filter, the cross-covariance term... and It can be set to zero as needed for the project; if the state correlation of the first Kalman filter is to be maintained, the cross covariance term corresponding to the end of the first Kalman filter can be inherited.

[0064] Subsequently, based on the new initial angle values ​​and covariance matrix, using the same set of AUV maneuvering ranging data, state propagation, theoretical distance calculation, measurement residual construction, observation matrix calculation, Kalman gain calculation, state update, and covariance update are performed again. The second filtering does not involve re-estimation from zero. and Instead, it continues to absorb the remaining ranging residuals near the first filtering result, making the deformation angle estimation more stable.

[0065] After two iterations, the final converged estimate of the mooring deformation angle is: , .

[0066] Step S106: Based on the physical model of the moored buoy deformation and the deformation angle parameters estimated by the second optimization, reconstruct the final horizontal coordinates of the moored buoy's sound-emitting point to complete the in-situ calibration of the moored buoy.

[0067] The mooring deflection angle after secondary optimization estimation and deflection azimuth angle Substituting into the physical model of underwater glider deformation, calculate the first... The final horizontal coordinates of the sound source of each underwater buoy.

[0068] Let the first The nominal GNSS coordinates of the submersible surface are: in, and The first The nominal coordinates of a GNSS point on the surface of a submersible in the north and east directions. Let the first... The depth of the buoy's sounding point is... Based on the deformation angle parameters after secondary convergence, the final horizontal offset of the mooring point relative to the GNSS point on the water surface is calculated: ; ; in, This represents the northward compensation amount of the underwater buoy's sound source relative to the nominal GNSS point on the water surface. This represents the eastward compensation amount of the underwater buoy's sound source relative to the nominal GNSS point on the water surface.

[0069] Furthermore, the first The final horizontal coordinates of the buoy's sound source points are reconstructed as follows: and : ; ; If three-dimensional physical coordinates are required, the depth of the buoy's sound source should also be included to obtain the third... The final three-dimensional coordinates of the buoy's sound source: ; in, For the first The depth coordinates of each mooring point. If the system uses a "downward is positive" depth coordinate convention, then the third dimension is directly taken as... If the system adopts a coordinate system where "height is positive upwards", then the third dimension can be written as: .

[0070] If it is necessary to further convert the northeast metric coordinates to latitude and longitude coordinates, calculate the latitude compensation based on the local geographic coordinate transformation relationship. and longitude compensation : ; ; in, Let be the radius of curvature of the meridian. Let be the radius of curvature of the circle. For reference height, For the first The nominal latitude of the buoy's surface GNSS. Therefore, the first... The final latitude and longitude coordinates of the sounding point of each underwater mooring ( , )for: ; ; in, For the first The nominal GNSS longitude of the moored surface is determined. Finally, the reconstructed true coordinates of the moored buoy's sound source are used as the reference node coordinates in acoustic-assisted navigation, replacing the previously directly used nominal GNSS coordinates. This process compensates for the dynamic offset of the moored buoy's sound source caused by ocean current drag, reduces systematic positioning errors caused by acoustic reference position errors, and thus completes the in-situ high-precision calibration of the deep-sea flexible moored buoy.

[0071] The following section provides a detailed explanation of the specific execution process and technical effects of the in-situ calibration of a deep-sea flexible mooring based on augmented state filtering, based on simulation test data.

[0072] In this embodiment, the mooring buoy is anchored at a depth of approximately 6000 m on the seabed, with the operating depth of the buoy's sound-emitting point at approximately 1000 m. The GNSS reference point is located at the surface. The depths of the three buoy sound-emitting points are 1000 m, 1015 m, and 985 m, respectively. The true value of the actual cable sag angle of the buoy's sound-emitting point caused by ocean currents is set to 20°, and the true value of the deflection azimuth angle is set to 45°. The positional offset parameters of the three buoys are shown in Table 1.

[0073] Table 1. Depth and horizontal offset parameters of the underwater mooring sound source;

[0074] The experimental setup used 100 Hz IMU data, and injected a zero bias of 0.003° / h into the gyroscope and 10 μg into the accelerometer. Simultaneously, the system was configured with low-frequency underwater acoustic distance measurement data with 10 m observation noise and a ranging period of 20 s.

[0075] Under the above experimental conditions, the system controlled the AUV to strictly follow the preset procedure to perform the in-situ calibration task of the mooring buoy, and cross-validated the results under three maneuvering modes: a closed square trajectory, a closed circular trajectory, and a reciprocating straight trajectory. The closed square trajectory had a side length of 500m, the closed circular trajectory had a radius of 400m, and the reciprocating straight trajectory had a one-way length of 1200m. The global and local magnification effects of the square trajectory are shown below. Figure 3 As shown in (a) and (b) in the figure. Subsequently, the calibration results obtained by the present invention are compared with the calibration results of typical short baseline moorings, and then introduced into the subsequent cruise phase to further verify the improvement effect of the present invention.

[0076] The AUV descended to a depth of approximately 1000m near Mooring 1, operating at a speed of about 1.5m / s, equivalent to approximately 3 knots, and executed closed square routes, closed circular routes, and reciprocating straight routes. Each operation lasted no more than 30 minutes.

[0077] During navigation, the system simultaneously collects IMU data, depth gauge data, and acoustic propagation delay data, providing an observational basis for subsequent state estimation, position compensation, and mooring coordinate reconstruction.

[0078] The built-in 10-state augmented extended Kalman filter is invoked to adjust the mooring tilt angle. Deflection azimuth angle The system performs joint calculations with AUV navigation errors. Through this joint estimation process, the system can simultaneously estimate angle parameters during AUV maneuvering observations and perform initial coordinate compensation for the mooring position accordingly.

[0079] The initial estimation results for the three maneuver trajectories are shown in Table 2 and Figure 4 As shown in (a) and (b) of the figure, the results show that all three maneuvering trajectories can effectively estimate the mooring sag parameters. Among them, the reciprocating straight trajectory has a relatively small estimation error of the sag angle and the lowest estimation error of the average horizontal position deviation after the first position compensation; the closed square trajectory has the highest estimation accuracy of the horizontal sag azimuth angle, with an error of only 0.062°; the closed circular trajectory shows a relatively large estimation error of the first horizontal position deviation in this set of experiments. Overall, the joint state estimation method can effectively reduce the mooring position deviation caused by cable sag and provide a good initial benchmark for subsequent secondary parameter iteration and final coordinate reconstruction.

[0080] Table 2. Initial joint estimation and coordinate compensation results for three maneuver trajectories (real) =20°, =45°);

[0081] To further reduce the estimation error, the position of the mooring after one compensation is used as the new position reference, and the deflection tilt angle and deflection azimuth angle obtained in the first round of estimation are used as the initial inputs and then input into the filter for a second iteration optimization.

[0082] After two iterations, the average position error under all three trajectories was further compressed, such as Figure 5 As shown in (a) and (b) in the figure, the average position error under the closed circular trajectory decreased from 47.563m in the first round to 19.104m, with an error improvement rate of 59.83%; the average position error under the reciprocating straight trajectory decreased from 25.884m to 5.211m, with an error improvement rate of 79.87%; and the average position error under the closed square trajectory decreased from 42.873m to 17.838m, with an error improvement rate of 58.39%.

[0083] The results show that the second-order parameter iteration can further correct residual errors based on the initial coordinate compensation, significantly improving the reconstruction accuracy of the moored glide vehicle's absolute physical coordinates. The improvement effect is most pronounced for the reciprocating straight trajectory, where the average position error is reduced to 5.211m after the second iteration, representing an improvement rate of 79.87%. Finally, the system replaces the initial nominal coordinates with the absolute physical coordinates reconstructed through the second iteration, completing the in-situ calibration of the moored glide vehicle.

[0084] To verify the effectiveness of the calibration results in subsequent navigation tasks, different mooring positions were input into the distance-assisted integrated navigation process during the subsequent cruise phase, and the radial positioning errors were compared and analyzed. The comparison methods included: the uncompensated initial nominal mooring position (Origin), the true mooring position (True), the ultra-short baseline determined mooring position (USBL), and the mooring position after the second calibration (Calib-twice) of this invention.

[0085] The ultra-short baseline method for determining the location of underwater moorings is achieved by adding a fixed horizontal error to the actual mooring sound point location. The horizontal error amplitude for all three moorings is set to 5m, specifically: Mooring 1 is offset 3m eastward and 4m northward; Mooring 2 is offset -4m eastward and 3m northward; Mooring 3 is offset 4m eastward and -3m northward. This setting simulates the fixed positional error present when using an ultra-short baseline system to determine the mooring sound point in engineering applications.

[0086] Taking a circular calibration trajectory as an example, the radial error during the cruise phase is compared to... Figure 6 As shown in Table 3, the error statistics are as follows. The results indicate that the positioning error is largest corresponding to the uncompensated initial nominal moor position, suggesting that mooring deviations caused by ocean currents significantly affect the accuracy of distance-aided navigation. While the actual moor position and the ultra-short baseline determination position can significantly reduce the positioning error, they still rely on additional measurement conditions. In contrast, the method of this embodiment does not require prior acquisition of the actual moor position; it relies solely on AUV maneuvering observations and underwater acoustic distance information to obtain calibration results close to the actual moor coordinates, achieving better combined navigation accuracy during the cruise phase.

[0087] Table 3. Statistical results of radial positioning error during the cruise phase;

[0088] The experimental results from the three trajectory configurations demonstrate that this invention can achieve stable estimation and effective compensation for the dynamic displacement of moorings in complex deep-sea environments, exhibiting strong environmental adaptability and engineering application value. Based on the technical solution of "angle displacement assumption—10-dimensional state augmented filtering—secondary parameter iteration," this invention, even with 10m underwater acoustic ranging noise, can invert and correct the nearly 400m-level mooring position displacement caused by ocean currents through only a single 30-minute spatial maneuver by an AUV. After secondary parameter iteration, all three trajectory configurations can stably control the horizontal reconstruction error of the mooring's absolute coordinates within the range of approximately 5-20m, with an overall error reduction rate approaching or reaching 95%, thereby achieving in-situ high-precision removal of acoustic network reference errors. These results indicate that this invention can complete high-precision in-situ calibration of deep-sea mooring arrays without relying on additional long-term external calibration methods, possessing good practicality and promotional value.

[0089] In one or more embodiments, a deep-sea flexible mooring in-situ calibration system based on augmented state filtering is provided, which can be implemented in software. The deep-sea flexible mooring in-situ calibration system based on augmented state filtering includes the following software modules: The calibration trajectory maneuver module is used to control the autonomous underwater vehicle to navigate to the preset mooring position and dive to the preset depth, and then control it to execute the preset calibration trajectory maneuver. During the execution of the maneuver, it simultaneously acquires relevant information about the autonomous underwater vehicle and the mooring. The deformation physical model construction module is used to construct the deformation physical model of the mooring. It represents the spatial offset of the mooring sound point relative to the GNSS positioning point at the top of the mooring as the deflection tilt angle and deflection azimuth angle, and incorporates them as deformation angle parameters to be estimated into the state vector of the Kalman filter. The prior and predicted horizontal calculation module is used to calculate the prior horizontal position of the autonomous underwater vehicle at the current moment based on synchronously acquired information related to the autonomous underwater vehicle and the mooring, and to complete the time update of the Kalman filter state vector and covariance matrix. Based on the mooring deformation physical model, the predicted horizontal coordinates of the mooring sound point are obtained. The joint initial estimation module is used to construct the distance measurement residual between the autonomous underwater vehicle and the mooring point based on the prior horizontal position and the predicted horizontal coordinates of the mooring point, and to linearize the distance measurement residual using a Jacobian matrix containing the partial derivative of the deformation angle parameter. The module then performs a joint initial estimation of the autonomous underwater vehicle's navigation error and deformation angle parameter through Kalman filtering measurement updates. The secondary optimization estimation module is used to reset the initial conditions of the Kalman filter based on the deformation angle parameter and its covariance obtained from the initial estimation, and then perform Kalman filtering again to obtain the secondary optimization estimation result of the deformation angle parameter. The horizontal coordinate reconstruction module is used to reconstruct the final horizontal coordinates of the mooring point based on the physical model of mooring deformation and the deformation angle parameters estimated by secondary optimization, thus completing the in-situ calibration of the mooring.

[0090] It should be noted that each module in the deep-sea flexible mooring in-situ calibration system based on augmented state filtering in this embodiment of the invention corresponds one-to-one with each step in the deep-sea flexible mooring in-situ calibration method based on augmented state filtering in the above embodiment, and their specific implementation processes are the same, so they will not be repeated here.

[0091] In one or more embodiments, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements as follows: Figure 1 The steps in the in-situ calibration method for deep-sea flexible moorings based on augmented state filtering are shown.

[0092] In one or more embodiments, an electronic device is provided, including a memory, a processor, and a computer program stored on the memory and running on the processor, wherein the processor, when executing the program, implements as follows: Figure 1 The steps in the in-situ calibration method for deep-sea flexible moorings based on augmented state filtering are shown.

[0093] Specifically, according to embodiments of this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program including functions for executing... Figure 1 The program code for the method shown. In such an embodiment, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by the central processing unit, it performs the various functions defined in the apparatus of this application.

[0094] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0095] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for in-situ calibration of deep-sea flexible moorings based on augmented state filtering, characterized in that, include: The autonomous underwater vehicle is controlled to navigate to the preset mooring position and dive to the preset depth. Then, it is controlled to perform preset calibration trajectory maneuvers. During the maneuver, relevant information about the autonomous underwater vehicle and the mooring is acquired simultaneously. A physical model of underwater mooring deformation is constructed, and the spatial offset of the mooring point relative to the GNSS positioning point at the top of the mooring point is equivalently represented as the deflection tilt angle and the deflection azimuth angle, and these are incorporated into the Kalman filter state vector as deformation angle parameters to be estimated. Based on the synchronously acquired information about the autonomous underwater vehicle and the mooring, the prior horizontal position of the autonomous underwater vehicle at the current moment is calculated using inertial navigation, and the time update of the Kalman filter state vector and covariance matrix is ​​completed. Based on the mooring deformation physical model, the predicted horizontal coordinates of the mooring sound point are obtained. Based on the prior horizontal position and the predicted horizontal coordinates of the mooring point, the distance measurement residual between the autonomous underwater vehicle and the mooring point is constructed. The distance measurement residual is linearized using a Jacobian matrix that includes the partial derivative of the deformation angle parameter. The navigation error and deformation angle parameter of the autonomous underwater vehicle are jointly estimated for the first time through Kalman filtering measurement updates. Based on the deformation angle parameters and their covariance obtained from the initial estimation, the initial conditions of the Kalman filter are reset, and the Kalman filter is performed again to obtain the secondary optimized estimation results of the deformation angle parameters. Based on the physical model of the mooring deformation and the deformation angle parameters estimated by the second optimization, the final horizontal coordinates of the mooring sound point are reconstructed, and the in-situ calibration of the mooring is completed. The process of constructing the Jacobian matrix including the partial derivative terms of the deformation angle parameter is as follows: Based on the synchronous acquisition of information related to autonomous underwater vehicles and moorings, the observation distance of the mooring's sound-emitting point is calculated. Based on the prior horizontal position of the autonomous underwater vehicle at the current moment, the GNSS reference coordinates of the top of the mooring, the vertical distance of the mooring's sound source, and the deformation angle parameter, a theoretical distance function between the autonomous underwater vehicle and the mooring's sound source is constructed; the partial derivatives of the theoretical distance function with respect to the horizontal position error and deformation angle parameter in the Kalman filter state vector are calculated, and a Jacobian matrix containing the partial derivative term of the deformation angle parameter is constructed. The process of constructing the distance measurement residual between the autonomous underwater vehicle and the buoy's sound emission point is as follows: Based on the predicted horizontal coordinates of the mooring point and the prior horizontal position of the autonomous underwater vehicle at the current moment, the coordinate error of the mooring point is calculated, and then the theoretical horizontal distance is obtained. Subtracting the measured horizontal distance from the theoretical horizontal distance yields the measurement residual of the buoy's sound-emitting point.

2. The in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described in claim 1, characterized in that, The process of linearizing the distance measurement residuals using the Jacobian matrix containing the partial derivatives of the deformation angle parameter is as follows: Based on the state transition equation of the Kalman filter state vector, and combined with the relevant information of the autonomous underwater vehicle and the mooring, the prior covariance matrix and the measurement noise covariance matrix are obtained. The Jacobian matrix containing the deformation angle parameter is used as the observation matrix, and then the Kalman gain is calculated by combining the prior covariance matrix and the measurement noise covariance matrix. Multiplying the Kalman gain by the measurement residual yields a correction value for the Kalman filter state vector, which is then used to correct the Kalman filter state vector.

3. The in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described in claim 1, characterized in that, In constructing the physical model of the mooring deformation, the mooring cable is regarded as a flexible slender body that deflects as a whole under the drag of the ocean current. The GNSS positioning point at the top of the mooring is used as the geometric reference, and the sound-emitting point of the mooring is used as the actual acoustic reference point after deformation.

4. The in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described in claim 1, characterized in that, The parameters in the state vector of the Kalman filter include deformation angle parameters and navigation error-related parameters of the autonomous underwater vehicle.

5. The in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described in claim 1, characterized in that, The information related to the autonomous underwater vehicle and the mooring includes the autonomous underwater vehicle's own status data, the underwater acoustic propagation time and depth parameters between the autonomous underwater vehicle and the mooring's sound emission point.

6. A deep-sea flexible mooring in-situ calibration system based on augmented state filtering, characterized in that, The in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described in any one of claims 1-5 includes: The calibration trajectory maneuver module is used to control the autonomous underwater vehicle to navigate to the preset mooring position and dive to the preset depth, and then control it to execute the preset calibration trajectory maneuver. During the execution of the maneuver, it simultaneously acquires relevant information about the autonomous underwater vehicle and the mooring. The deformation physical model construction module is used to construct the deformation physical model of the mooring. It represents the spatial offset of the mooring sound point relative to the GNSS positioning point at the top of the mooring as the deflection tilt angle and deflection azimuth angle, and incorporates them as deformation angle parameters to be estimated into the state vector of the Kalman filter. The prior and predicted horizontal calculation module is used to calculate the prior horizontal position of the autonomous underwater vehicle at the current moment based on synchronously acquired information related to the autonomous underwater vehicle and the mooring, and to complete the time update of the Kalman filter state vector and covariance matrix. Based on the mooring deformation physical model, the predicted horizontal coordinates of the mooring sound point are obtained. The joint initial estimation module is used to construct the distance measurement residual between the autonomous underwater vehicle and the mooring point based on the prior horizontal position and the predicted horizontal coordinates of the mooring point, and to linearize the distance measurement residual using a Jacobian matrix containing the partial derivative of the deformation angle parameter. The module then performs a joint initial estimation of the autonomous underwater vehicle's navigation error and deformation angle parameter through Kalman filtering measurement updates. The secondary optimization estimation module is used to reset the initial conditions of the Kalman filter based on the deformation angle parameter and its covariance obtained from the initial estimation, and then perform Kalman filtering again to obtain the secondary optimization estimation result of the deformation angle parameter. The horizontal coordinate reconstruction module is used to reconstruct the final horizontal coordinates of the mooring point based on the physical model of mooring deformation and the deformation angle parameters estimated by secondary optimization, thus completing the in-situ calibration of the mooring.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described in any one of claims 1-5.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the program, it implements the steps in the in-situ calibration method for deep-sea flexible moorings based on augmented state filtering as described in any one of claims 1-5.

Images