A data-driven based boom error compensation method

Abstract

The application provides a data-driven lever arm error compensation method, and belongs to the technical field of inertial navigation. The application is used for solving the problem that the time-varying equivalent lever arm cannot be directly measured in the inertial navigation of a submerged vehicle, and it is also difficult to accurately separate the lever arm induced error from other sensor errors. The application comprises the following steps: S1, analyzing and modeling the errors affecting transfer alignment; S2, establishing a lever arm error equation and a data-driven compensation model; and S3, velocity error prediction and compensation.

Description

Technical Field

[0001] This invention relates to a data-driven lever error compensation method, belonging to the field of inertial navigation technology. Background Technology

[0002] The sub-inertial navigation system (INS) and the primary INS used for navigation in a submersible are usually not located in the same position; that is, there is a certain distance between the primary and sub-INS, known as the lever arm distance. When the submersible is in motion, the lever arm effect causes the primary and sub-INS to output different specific forces. The difference in specific forces is called the lever arm acceleration, and similarly, the difference in velocity between the primary and sub-INS caused by the lever arm effect is called the lever arm velocity. This error between the primary and sub-INS caused by the lever arm is called the lever arm effect error. For ships, the hull itself is relatively long, and the corresponding lever arm length is also longer than that of aircraft, automobiles, and other carriers, so it is necessary to model and analyze the lever arm effect error.

[0003] However, in practical engineering, the master / sub-inertial navigation lever effect often manifests as complex dynamic characteristics such as "unknown initial value / segmental constant value / abrupt jump / superimposed slow drift". These characteristics may be caused by factors such as assembly tolerance, platform reconstruction, flexible deformation, and temperature load changes. Traditional analytical or state extension methods are difficult to quickly capture such features, especially in the early stages of insufficient maneuver excitation or lever abrupt changes, where compensation performance often lags significantly. Furthermore, due to the combined effect of static bias and flexible deformation between the master and sub-inertial navigation systems, a deterministic but difficult-to-explicitly model systematic error is introduced into the navigation system velocity. In engineering, it is impossible to directly measure the time-varying equivalent lever itself, and it is also difficult to accurately separate the "lever-induced error" from other sensor errors online. Summary of the Invention

[0004] To address the challenges of directly measuring the time-varying equivalent lever arm itself in the inertial navigation of underwater vehicles, and the difficulty in accurately separating lever arm-induced errors from other sensor errors online, this invention proposes a data-driven lever arm error compensation method.

[0005] The technical solution adopted by the present invention to solve the above problems is as follows: The present invention includes the following steps:

[0006] Step 1: Acquire short-time sequence data of the inertial measurement unit of the sub-inertial navigation system; Step 2: Input the short time series data into the Attention-LSTM model with an attention mechanism to obtain the predicted lever speed error; Step 3: Based on the lever arm speed error, compensate for the speed and observation between the main inertial navigation system and the sub-inertial navigation system.

[0007] Furthermore, the short-time series data in step 1 includes: triaxial angular velocity data, angular acceleration data, and triaxial specific force data; The three-axis angular velocity data is obtained by measuring the sub-inertial navigation system of the submersible; based on the three-axis angular velocity data measured at adjacent time points, differential approximation is performed to obtain angular acceleration data; and the three-axis specific force data is collected by the accelerometer in the sub-inertial navigation system.

[0008] Furthermore, in step 2, the Attention-LSTM model includes an input layer, an LSTM layer, a self-attention layer, and a fully connected output layer; The input layer is used to receive short-time series data; LSTM layers are used to extract the original temporal features of short-time series data to obtain the hidden state sequence; The self-attention layer is used to assign corresponding attention weights to each temporal feature in the hidden state sequence, and generate the final context features based on the attention weights; The fully connected layer is used to map the context features to obtain the predicted value of the lever arm speed error.

[0009] Furthermore, the Attention-LSTM model is trained offline, and the offline training steps include: A coupled simulation environment is established, and the relative installation relationship between the main inertial navigation system (INS) and the sub-INS, as well as the parameters of the equivalent lever model, are defined within this environment. Short-time sequence data of the sub-INS system are collected and used as the raw measurement sequence. The sliding window length is set to... L The original measurement sequence is input into the established coupled simulation environment. Combining the relative installation relationship between the main inertial navigation system (INS) and the sub-INS, and the parameters of the equivalent lever arm model, the velocities of the main INS and the sub-INS, including the equivalent lever arm, and the ideal velocity of the sub-INS virtually translated to the position of the main INS are calculated respectively. Based on the difference between the velocities of the main INS and the sub-INS, including the equivalent lever arm, and the ideal velocity, the velocity error caused by the equivalent lever arm effect is determined, and the velocity error is used as a supervision label. The original measurement sequences and supervision labels are standardized by Z-score in one dimension to form a training sample set. The Attention-LSTM model is trained using the training sample set, and the training parameters of the LSTM layer are set. The nonlinear mapping relationship from short time series data to lever speed error is learned by minimizing the mean square error loss function until the Attention-LSTM model converges.

[0010] Furthermore, the steps for obtaining the predicted lever speed error in step 2 include: Set the sliding window length to L The acquired short-time series data is input into the trained Attention-LSTM model. The short-time series data is transmitted from the input layer to the LSTM layer. The LSTM layer extracts the original temporal features of the short-time series data to obtain the hidden state sequence. H , ,in, Let be the hidden state vector at the corresponding time step. The length of the sliding window; The self-attention layer uses a self-attention mechanism to establish a weight matrix. Calculate the hidden state sequence H Scoring of each feature and based on the weight matrix Assign corresponding attention weights, and generate contextual feature representations based on these attention weights. c ; Contextual features of the output are represented by a fully connected layer. c By performing mapping, a normalized estimate of the lever arm speed error is obtained. The velocity error estimate is obtained by inverse normalization using training set statistics. ; estimate the speed error As a feedforward compensation, the difference in lever arm speed after compensation is calculated. ; the speed difference of the lever arm The master / sub-inertial navigation attitude difference is used as the input factor for the joint observation vector. The expression for the self-attention mechanism is: (1); In formula (1), This is the weight matrix of the attention layer; It is the bias vector; This is the attention score vector; For the first t Attention energy level at any given moment; For the first j Attention energy level at any given moment; For the first t Attention weights corresponding to each moment; Contextual feature representation c The expression is: (2); Lever error prediction value The calculation formula is: (3); In formula (3), This is the output layer weight matrix; This is the output layer bias.

[0011] Furthermore, step 3 specifically includes: An 18-dimensional error state vector is used, combined with the lever arm velocity difference to describe the dynamic model of the error state of the sub-inertial navigation system relative to the main inertial navigation system; Discretize the dynamic model to obtain the state equation of the sub-inertial navigation system, and obtain the observation noise based on the state equation; The observation equations of the sub-inertial navigation system are established using a state-driven full-drive modeling strategy, and the observation noise covariance is calculated based on the joint observation vector. The adaptive adjustment is based on the adjusted observation noise covariance. The basic filtering recursion is performed, and after prediction and updating, the compensated velocity and observation compensation results of the sub-inertial navigation system are output. The dynamic model is as follows: (4); In formula (4), For small attitude error, For navigation system speed and position errors, To achieve zero bias for the gyroscope and accelerometer, This refers to the installation error angle; The state equation of the sub-inertial navigation system is: (5); In formula (5), The process noise matrix is... Here is the state transition matrix. This is the process noise vector; The expressions for prediction and update in the basic filter recursion are as follows: (6); (7); In formulas (6) and (7), These are the predicted values ​​of the velocity and observations of the current sub-inertial navigation system. This is the state transition matrix from the previous time step. These are the predicted values ​​of the velocity and observations of the sub-inertial navigation system at the previous moment. Let be the prior error covariance matrix. Let be the prior error covariance matrix of the previous time step. For process noise covariance, T For transpose, For the observation matrix, For the observation vector, It is the identity matrix. For Kalman gain, The compensated velocity and observation results of the sub-inertial navigation system are as follows. This is the updated error covariance; Observation noise covariance The expression for adaptive adjustment is: (8); In formula (8), It is the first The observation residuals of the step; It is the residual fusion coefficient, used to control the weight of the impact of the new residual on the estimation; This is the estimated current observation noise covariance matrix, where, The diagonal elements are limited to and Between, that is: (9); In formula (9), This means taking the diagonal elements to form a vector. This indicates that elements should be truncated to a given range. To minimize the observed noise, This represents the maximum value of the observed noise.

[0012] The beneficial effects of this invention are: This invention transforms the systematic error between the master and sub-inertial navigation systems (INS) caused by the combined effects of static bias and flexible deformation into a purely data-driven time-series mapping. During the training phase, the IMU measurement sequence of the sub-INS within a short time window is used as input, and the component of the velocity difference between the master and sub-INS caused by the lever arm effect is used as the supervision label to learn the nonlinear mapping from short-time IMU segments to lever arm-induced velocity errors. In the online application phase, only the short-time IMU sequence of the sub-INS needs to be input to predict and feedforward compensate the corresponding velocity error, without relying on explicit observation of time-varying lever arm parameters. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating a data-driven lever error compensation method. Figure 2 A schematic diagram for transmitting the misalignment angle. Detailed Implementation

[0014] When the main inertial navigation system (INS) transmits navigation information to the sub-INS, lever arm errors, installation angle errors, and deflection angle errors will inevitably affect the accuracy of the transmission alignment. Therefore, it is necessary to first analyze and model the errors affecting the transmission alignment. For example... Figure 1 As shown, the steps of the data-driven lever error compensation method described in this embodiment include: S1: Analyze and model the errors that affect the transfer alignment; S101: Modeling of flexural deformation angle error; The flexural deformation of a ship can generally be considered as a second-order Markov process, with the flexural deformation along each of the three axes assumed to be independent. Generally defined... It is the triaxial flexural deformation angle. For the angular velocity of flexural deformation, the relevant relationship is: (1); In formula (1), It is a constant value; It is white noise, which satisfies ,in Its noise intensity. The mean square error is the angle of the deflection. The relationship between them is Stochastic process time and The relationship is .

[0015] S102: Attitude error equation; Tie, Tie, Tie, The relationship between departments, such as Figure 2 As shown, in this embodiment, the definition is... The calculated misalignment angle between the master and sub-inertial navigation systems. This refers to the actual installation error angle between the master and slave inertial navigation systems.

[0016] In a grid-based inertial navigation system, the attitude differential equation of the master inertial navigator is: (2); In formula (2), This is the transformation matrix from the sub-inertial navigation system of the underwater vehicle to the grid system; The rotational angular velocities of the master and sub-inertial navigation systems relative to the lattice system are respectively in... Tie, The projection under the system.

[0017] In practical applications, since the accuracy of the main inertial navigation system (INS) is much higher than that of the sub-INS, and the transfer alignment process is relatively short, the error of the main INS is generally not considered when studying transfer alignment. However, the sub-INS does have errors, so the actual attitude differential equation of the sub-INS is: (3); In formula (3), The attitude matrix of the sub-inertial navigation system is calculated. The actual angular velocity measurement of the sub-inertial navigation system relative to the lattice system can be expressed as: (4); In formula (4), The measured angular velocity of the grid frame relative to the inertial frame in the sub-inertial navigation frame; Let be the transformation matrix from the lattice frame to the sub-inertial navigation frame; The measured angular velocity of the grid frame relative to the inertial frame on the grid frame; The actual output angular velocity of the sub-inertial navigation system can be expressed as: (5); In formula (5), For the flexural variable angular velocity; for System relative to The angular velocity of the system is Projection under the system; for System relative to The angular velocity of the system is Projection under the system; Gyroscope drift due to inertial navigation.

[0018] Substituting formula (5) into formula (4), we get: (6); In formula (6), For flexural variable angular velocity; To account for measurement error, it can be used Represented as: (7); In formula (7), This represents the error in the projected angular velocity of the Earth system relative to the inertial frame in the grid system. The error is the angular velocity of the projection of the grid system onto the grid system relative to the Earth system.

[0019] From the above content, it can be seen that and The size is mainly affected by positional error. During the alignment process, because the time is short, the effect of positional error is very slow and can be ignored. and It can be ignored, therefore it can be represented as: (8); At the initial moment of alignment, the attitude of the sub-inertial navigation system is directly transferred from the main inertial navigation system, then: (9); In formula (9), The transformation matrix from the master inertial navigation system to the computational sub-inertial navigation system; Calculate the transpose of the attitude matrix for the sub-inertial navigation system; The attitude matrix is ​​the main inertial navigation system.

[0020] When the misalignment angle is small, measure the misalignment angle during the alignment process. It can be represented as: (10); Differentiating both sides of equation (10) and substituting them into equation (9), we get: (11); Will And by substituting formula (10) into formula (11), we can obtain: (12); Rearranging formula (12) and ignoring second-order minor quantities, we can obtain: (13); In summary, the above analysis results, namely formula (13), are the equation for calculating the misalignment angle error of the polar region rapid transfer alignment.

[0021] S103: Velocity error equation; Similar to the derivation of the misalignment angle equation in S102, the differential equations of the principal and sub-inertial guides in the lattice system can be obtained: (14); (15); In formulas (14) and (15), The lattice system velocities are those of the main and sub-inertial navigation systems, respectively. These are the specific forces output by the main and sub-inertial accelerometers, respectively. These are the projections of the gravitational accelerations experienced by the master and sub-inertial navigation systems in the grid system, respectively.

[0022] Similarly, in the derivation of the velocity error equation, the error of the main inertial navigation system is ignored, but the sub-inertial navigation system has errors in its solution. Therefore, the actual velocity differential equation of the sub-inertial navigation system is: (16); In formula (16), The velocity of the grid system is calculated for the sub-inertial navigation system; The specific force is the actual output of the sub-inertial navigation system; The projection of the actual gravitational acceleration experienced by the inertial navigation system onto the grid system.

[0023] The above content mentions that when deriving the equation for the misalignment angle... and It can be ignored, therefore . It can be represented as: (17); In formula (17), The actual transformation matrix from the main inertial navigation system to the sub-inertial navigation system; The projection of the ratio output of the main inertial navigation system onto the main inertial navigation system; The projection of the lever arm acceleration onto the main inertial navigation system; Zero bias for the sub-inertial accelerometer; The projection of the main inertial navigation output onto the sub-inertial navigation system; This is the projection of the lever arm acceleration onto the sub-inertial navigation system.

[0024] Known Substituting this into formula (16) yields: (18); (19); Subtracting formulas (18) and (19) yields: (20); Because the gravitational components experienced by the master and slave inertial navigation systems are nearly identical over a short period of time, that is... Substituting into formula (20) and simplifying, we get: (twenty one); In formula (21), (twenty two); in, To calculate the transformation matrix from the sub-inertial navigation frame to the main inertial navigation frame.

[0025] Substituting formula (22) into formula (20), we get: (twenty three); Ignoring sub-inertial navigation system drift The higher-order small quantity formed by the product of the small misalignment angle Substituting the values, we get: (twenty four); Differentiating formula (24) yields: (25); In formula (25), Let be the transformation matrix from the inertial frame to the lattice frame; Let be the projected angular velocity of the inertial frame relative to the lattice frame in the inertial frame; This is the projection of the lever arm velocity onto the inertial frame; The angular velocity output by the main inertial navigation system.

[0026] Given the acceleration of the lever arm: (26); Substituting formula (26) into formula (25) yields the following result: (27); among which, This is the differential form of the arm velocity in the grid system.

[0027] In summary, the differential form of the velocity error after lever arm error compensation is defined as follows: (28); Substituting formula (27) into formula (28), we get: (29); Formula (29) is the improved speed error equation that can be applied to transmission alignment.

[0028] S2: Establish the lever arm error equation and data-driven compensation model; Define the lever arm speed as ,in For the actual grid system speed of the sub-inertial navigation, The velocity of the grid system calculated by the main inertial navigation system can be obtained as follows: (30); In formula (30), The transformation matrix from the main inertial navigation system to the lattice system of the underwater vehicle; This represents the angular velocity calculated by the main inertial navigation system of the submersible relative to the inertial frame. The length of the lever arm between the master and sub-inertial navigation systems; It is the differential form of the lever arm length.

[0029] Define the lever arm acceleration as We can obtain: (31); Since the lever arm distance between the main and sub-inertial navigation systems inside the submarine is generally measured before the transfer alignment, and assuming that the lever arm effect and flexural deformation are independent, the lever arm distance is generally considered a constant value. At this moment, the velocity and acceleration of the lever arm are: (32); However, in practical engineering, the master / sub-inertial navigation link effect often manifests as complex dynamic characteristics such as "unknown initial value / segment constant value / abrupt jump / superimposed slow drift". These characteristics may be caused by factors such as assembly tolerance, platform reconstruction, flexible deformation, and temperature load changes. Traditional analytical or state extension methods are difficult to quickly capture such features, especially in the early stages of insufficient maneuver excitation or link abrupt changes, where compensation performance often lags significantly. To address this, this project proposes a feedforward compensation strategy based on attention-enhanced LSTM (Attention-LSTM), which uses only the short-time IMU data sequence of the sub-inertial navigation system to implicitly identify the link dynamic characteristics in real time and output linear velocity error compensation values. Subsequently, the compensated velocity and attitude difference are jointly used to form the observation input to the factor map, achieving an overall improvement in alignment performance.

[0030] The lever error equation described in S1 indicates that due to the combined effects of static bias and flexible deformation, a deterministic but difficult-to-model systematic error is introduced into the navigation system velocity between the master and sub-inertial navigation systems. In engineering, it is impossible to directly measure the time-varying equivalent lever arm itself, and it is also difficult to accurately separate the "lever-induced error" from other sensor errors online. Based on this practical constraint, this project transforms the problem into a purely data-driven time-series mapping: during the training phase, the IMU measurement sequence of the sub-inertial navigation system within a short time window is used as input, and the component of the master / sub-inertial navigation system velocity difference caused by the lever effect is used as the supervision label to learn the nonlinear mapping from short-time IMU segments to the lever-induced velocity error; during the online application phase, only the short-time IMU sequence of the sub-inertial navigation system needs to be input to predict and feedforward compensate the corresponding velocity error, no longer relying on explicit observations of the time-varying lever arm parameters.

[0031] First, the network input uses only short-time IMU sequences from the sub-inertial navigation system, and the discrete-time single-step 9-dimensional observations are as follows: (33); In formula (33), The three-axis angular velocities measured by the sub-inertial navigation system. The angular acceleration is approximated by the difference in angular velocity between adjacent moments. Let the force be a triaxial force. Assume the sliding window length is... Then at time The input tensor is defined as: (34); Corresponding label vector This represents the systematic contribution of the equivalent lever arm in the navigation coordinate system to the difference in velocity between the master and sub-inertial navigation systems, i.e., "the true value of the velocity error that needs to be compensated by the feedforward module." The labels during the training phase are not directly measured, but are constructed offline through a hardware-in-the-loop simulation joint annotation method: First, the original measurement sequence of the sub-inertial navigation IMU is acquired on the turntable platform, and the angular motion commands synchronized with it are recorded; then, the same set of angular motion commands is input into the PSINS coupled simulation environment established above. Under the premise of knowing the relative installation relationship between the master and sub-inertial navigation systems and the parameters of the equivalent lever arm model, the velocities of the master / sub-navigation system "including the equivalent lever arm" and the ideal velocity "virtually translating the sub-inertial navigation system to the master inertial navigation system" are calculated respectively; the stable deterministic component in the difference between the two is regarded as the velocity error caused by the equivalent lever arm and its flexible perturbation, and it is aligned with the measured IMU sequence by timestamp as a supervision label.

[0032] It is important to emphasize that the above annotation is completed entirely offline, relying on prior modeling of the geometric parameters and flexible behavior of representative platforms. Once the network training is complete, the online inference phase only requires inputting the short-time IMU sequence of the sub-inertial navigation system to output the corresponding lever-induced velocity error estimate, no longer relying on explicit measurement or online identification of the equivalent lever in the current task.

[0033] To improve training stability and eliminate the influence of dimensions, dimension-wise Z-score normalization is performed on the input and labels: (35); The sample set is obtained after standardization: .

[0034] And by minimizing the mean squared error loss function: This involves learning the nonlinear mapping from short-time IMU sequences to velocity system errors. This represents the square of the Euclidean norm.

[0035] The compensation model established in this embodiment consists of an LSTM layer, a self-attention layer, and a fully connected output layer. The input layer includes sub-inertial angular velocity... angular acceleration and comparison A total of 9 input dimensions are provided, with the corresponding labels being the predicted values ​​of the 3D lever arm speed error. .

[0036] First, the LSTM layer extracts the original temporal features to obtain the hidden state sequence: (36); In formula (36), Let be the hidden state vector at the corresponding time step. This represents the length of the sliding window.

[0037] To adaptively emphasize key dynamic segments under non-stationary perturbations, a self-attention mechanism is introduced: (37); In formula (37), This is the weight matrix of the attention layer; It is the bias vector; This is the attention score vector; Let be the attention energy value at time t; Let be the attention weight at time t.

[0038] Then, the final contextual feature representation is generated based on the attention weights: (38); Finally, the context features are processed through a fully connected layer. Mapped to the predicted value of lever arm speed error: (39); In formula (39), This is the output layer weight matrix; This is the output layer bias.

[0039] After offline training, the Attention-LSTM model receives short-time IMU sequence sliding windows from the sub-inertial navigation system online. Normalized estimate of the speed difference of the output navigation system Using training set statistics Inverse normalization yields: (40); In formula (40), This represents the Hadamard product. By treating this prediction as a "velocity error introduced by the lever arm equivalence effect" and compensating for it via feedforward, we obtain the online velocity observation term: (41); The specific parameter settings during training are as follows: Table 1

[0040] To align with the compensation parameters, this invention employs a classic 18-dimensional error state vector to describe the error state of the sub-inertial navigation system relative to the main inertial navigation system: (42); In formula (42), For small attitude error, For navigation system speed and position errors, To achieve zero bias for the gyroscope and accelerometer, This is the installation error angle.

[0041] The system state equation is obtained by discretizing the dynamic model of the error state described above, and can be expressed in linear form: (43); In formula (43), The process noise matrix can be specifically represented as: (44); In formula (44), Here is the state transition matrix. Let be the process noise vector, representing the uncertainty introduced by external disturbances or modeling errors during each state propagation step of the system. It is often assumed to be white noise with zero mean and a Gaussian distribution. ,in, Let be the process noise covariance matrix.

[0042] This invention employs a state-driven modeling strategy, and the overall process noise vector is defined as follows: (45); The observation equations consist of two parts: velocity matching and attitude matching. The velocity observations are taken from the compensated main inertial navigation velocity. With sub-inertial navigation velocity Differences: (46); Attitude observations are taken from the antisymmetric portion of the difference between the principal and sub-inertial navigation attitude direction cosine matrices as the observation vector: (47); In formula (47), The symbol represents the inverse mapping, and the joint observation vector is: (48); The basic filtering recursion in Kalman filtering is then performed, including the prediction and update stages, as shown below: Prediction phase: (49); Update phase: (50); In formulas (49) and (50), These are the predicted values ​​of the velocity and observations of the current sub-inertial navigation system. This is the state transition matrix from the previous time step. These are the predicted values ​​of the velocity and observations of the sub-inertial navigation system at the previous moment. Let be the prior error covariance matrix. Let be the prior error covariance matrix of the previous time step. For process noise covariance, T For transpose, For the observation matrix, For the observation vector, It is the identity matrix. For Kalman gain, The compensated velocity and observation results of the sub-inertial navigation system are as follows. This is the updated error covariance.

[0043] Traditional Kalman filtering assumes that the statistical characteristics of process noise and observation noise are known and fixed. However, in actual transport alignment processes, carrier maneuvers and environmental changes often lead to dynamic changes in the statistical characteristics of noise. To improve the accuracy and robustness of the filter estimation, this invention introduces an adaptive adjustment mechanism based on innovation sequences into the filtering framework. The factor graph uses a method based on residual innovation sequences to correct the observation noise covariance in real time: by setting a minimum value for the observation noise... and maximum value The threshold is dynamically adjusted based on the current observation residuals to control the observation noise covariance. This reduces attitude estimation error. During filter updates, as the observation residual increases, the estimated observation noise covariance... Approaching the preset upper bound This reduces the impact of current observations on state updates; conversely, when the observation residuals decrease, Approaching This enhances confidence in current observations. The adaptive adjustment formula for the observation noise covariance is: (51); In formula (51), It is the first The observation residuals of the step, It is the residual fusion coefficient, taken as... This is used to control the weight of the impact of the new residual on the estimation. This is the estimated current observation noise covariance matrix. To avoid the estimated value being too large or too small, The diagonal elements are limited to and Between, that is: (52); In formula (52), This means taking the diagonal elements to form a vector. This indicates truncating to a given interval by element. Finally, use... Replace the observation noise covariance to complete the AKF update.

[0044] In summary, the speed error correction and adaptive filtering strategy based on Attention-LSTM compensation has been successfully developed.

[0045] S3: Speed ​​error prediction and compensation; In the online application phase, the sub-inertial navigation short-time IMU sequence only needs to be input into the trained Attention-LSTM compensation model to predict and feedforward compensate the corresponding velocity error, without relying on the explicit observation of time-varying lever parameters.

[0046] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A data-driven lever arm error compensation method, characterized in that, include: Step 1: Acquire short-time sequence data of the inertial measurement unit of the sub-inertial navigation system; Step 2: Input the short time series data into the Attention-LSTM model with an attention mechanism to obtain the predicted lever speed error; Step 3: Based on the lever speed error, compensate for the speed difference between the main inertial navigation system and the sub-inertial navigation system.

2. The data-driven lever error compensation method according to claim 1, characterized in that, The short-time series data in step 1 includes: triaxial angular velocity data, angular acceleration data, and triaxial specific force data; The triaxial angular velocity data is obtained by measuring the sub-inertial navigation system of the submersible; based on the triaxial angular velocity data measured at adjacent time points, differential approximation is performed to obtain angular acceleration data; triaxial specific force data is collected by the accelerometer in the sub-inertial navigation system.

3. The data-driven lever error compensation method according to claim 1, characterized in that, In step 2, the Attention-LSTM model includes an input layer, an LSTM layer, a self-attention layer, and a fully connected output layer; The input layer is used to receive short-time series data; The LSTM layer is used to extract the original temporal features of short-time sequence data to obtain the hidden state sequence. The self-attention layer is used to assign corresponding attention weights to each temporal feature in the hidden state sequence, and generate the final context features based on the attention weights; The fully connected layer is used to map the context features to obtain the predicted value of the lever arm speed error.

4. The data-driven lever error compensation method according to claim 3, characterized in that, The Attention-LSTM model is trained offline, and the offline training steps include: A coupled simulation environment is established, and the relative installation relationship between the main inertial navigation system (INS) and the sub-INS, as well as the parameters of the equivalent lever model, are defined within this environment. Short-time sequence data of the sub-INS system are collected and used as the raw measurement sequence. The sliding window length is set to... L The original measurement sequence is input into the established coupled simulation environment. Combining the relative installation relationship between the main inertial navigation system (INS) and the sub-INS, and the parameters of the equivalent lever arm model, the velocities of the main INS and the sub-INS, including the equivalent lever arm, and the ideal velocity of the sub-INS virtually translated to the position of the main INS are calculated respectively. Based on the difference between the velocities of the main INS and the sub-INS, including the equivalent lever arm, and the ideal velocity, the velocity error caused by the equivalent lever arm effect is determined, and the velocity error is used as a supervision label. The original measurement sequences and supervision labels are standardized by Z-score in one dimension to form a training sample set. The Attention-LSTM model is trained using the training sample set, and the training parameters of the LSTM layer are set. The nonlinear mapping relationship from short time series data to lever speed error is learned by minimizing the mean square error loss function until the Attention-LSTM model converges.

5. The data-driven lever error compensation method according to claim 1, characterized in that, The steps for obtaining the predicted lever speed error in step 2 include: Set the sliding window length to L The acquired short-time series data is input into the trained Attention-LSTM model. The short-time series data is transmitted from the input layer to the LSTM layer. The LSTM layer extracts the original temporal features of the short-time series data to obtain the hidden state sequence. H , ,in, Let be the hidden state vector at the corresponding time step. The length of the sliding window; The self-attention layer uses a self-attention mechanism to establish a weight matrix. Calculate the hidden state sequence H Scoring of each feature and based on the weight matrix Assign corresponding attention weights, and generate contextual feature representations based on these attention weights. c ; Contextual features of the output are represented by a fully connected layer. c By performing mapping, a normalized estimate of the lever arm speed error is obtained. The velocity error estimate is obtained by inverse normalization using training set statistics. ; estimate the speed error As a feedforward compensation, the difference in lever arm speed after compensation is calculated. ; the speed difference of the lever arm The master / sub-inertial navigation attitude difference is used as the input factor for the joint observation vector. The expression for the self-attention mechanism is: （1）； In formula (1), This is the weight matrix of the attention layer; It is the bias vector; This is the attention score vector; For the first t Attention energy level at any given moment; For the first j Attention energy level at any given moment; For the first t Attention weights corresponding to each moment; Contextual feature representation c The expression is: （2）； Lever error prediction value The calculation formula is: （3）； In formula (3), This is the output layer weight matrix; This is the output layer bias.

6. The data-driven lever error compensation method according to claim 1, characterized in that, Step 3 specifically includes: An 18-dimensional error state vector is used, combined with the lever arm velocity difference to describe the dynamic model of the error state of the sub-inertial navigation system relative to the main inertial navigation system; Discretize the dynamic model to obtain the state equation of the sub-inertial navigation system, and obtain the observation noise based on the state equation; The observation equations of the sub-inertial navigation system are established using a state-driven full-drive modeling strategy, and the observation noise covariance is calculated based on the joint observation vector. The adaptive adjustment is based on the adjusted observation noise covariance. The basic filtering recursion is performed, and after prediction and updating, the compensated velocity and observation compensation results of the sub-inertial navigation system are output. The dynamic model is as follows: （4）； In formula (4), For small attitude error, For navigation system speed and position errors, To achieve zero bias for the gyroscope and accelerometer, This refers to the installation error angle; The state equation of the sub-inertial navigation system is: （5）； In formula (5), The process noise matrix is... Here is the state transition matrix. This is the process noise vector; The expressions for prediction and update in the basic filter recursion are as follows: （6）； （7）； In formulas (6) and (7), These are the predicted values ​​of the velocity and observations of the current sub-inertial navigation system. This is the state transition matrix from the previous time step. These are the predicted values ​​of the velocity and observations of the sub-inertial navigation system at the previous moment. Let be the prior error covariance matrix. Let be the prior error covariance matrix of the previous time step. For process noise covariance, T For transpose, For the observation matrix, For the observation vector, It is the identity matrix. For Kalman gain, The compensated velocity and observation results of the sub-inertial navigation system are as follows. This is the updated error covariance; Observation noise covariance The expression for adaptive adjustment is: （8）； In formula (8), It is the first The observation residuals of the step; It is the residual fusion coefficient, used to control the weight of the impact of the new residual on the estimation; This is the estimated current observation noise covariance matrix, where, The diagonal elements are limited to and Between, that is: （9）； In formula (9), This means taking the diagonal elements to form a vector. This indicates that elements should be truncated to a given range. To minimize the observed noise, This represents the maximum value of the observed noise.

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