AUV (Autonomous Underwater Vehicle) adaptive navigation method based on combination of deep learning and physical model

Abstract

The invention relates to the technical field of navigation, in particular to an AUV (Autonomous Underwater Vehicle) adaptive navigation method based on combination of deep learning and a physical model. Comprising the following steps that in the process of modeling an AUV motion system, a weighted gain deviation estimation EKF algorithm is provided, DVL speed bias serves as a state quantity to conduct online estimation and compensation on sensor system errors, and a Kalman gain updating strategy weighted according to state confidence is introduced; constructing a deep learning network for adaptively measuring noise, and dynamically predicting an x-direction time-varying noise standard deviation and a y-direction time-varying noise standard deviation of a DVL speed quantity by using the network; and writing the time-varying noise standard deviation obtained in the above step into a measurement noise covariance matrix at the moment, and calculating the obtained AUV position trajectory. And the navigation adaptability and the navigation precision of the AUV can be obviously improved.

Description

Technical Field

[0001] This invention relates to the field of navigation technology, and in particular to an AUV adaptive navigation method based on a combination of deep learning and physical models. Background Technology

[0002] Although the traditional Extended Kalman Filter (EKF) has been successfully applied in AUV navigation, its performance is heavily dependent on the accuracy of the system model and measurement model, as well as their matching degree with the noise covariance matrix (Q, R).

[0003] In AUV navigation missions, the process noise covariance Q and measurement noise covariance R are typically assumed to be constants, set by prior calibration or experience. However, in actual operation, environmental and sensor characteristics can change. For example, the Doppler Velocity Log (DVL) instrument on the AUV is affected by the diverse marine life and uneven underwater reflections during observation, causing its measurement noise to vary with the environment. This results in a mismatch between the fixed covariance and the true statistics, thus compromising the optimality of the filtered estimation.

[0004] Furthermore, when sensors exhibit unmodeled system biases or environmental interference, traditional EKF modeling fails to account for error bias, leading to easy accumulation and even divergence of filter errors. DVL zero-drift bias is a prominent issue: in long-endurance applications, the forward and lateral velocities measured by DVL may contain small, constant errors, similar to sensor zero-point drift or calibration deviation. This error integrates into a significant position offset during inertial calculations. Uncorrected DVL velocity deviation is equivalent to encountering an unknown, constant ocean current during AUV navigation, causing a continuous deviation between the estimated and actual trajectories. Summary of the Invention

[0005] The purpose of this invention is to overcome the above-mentioned defects in the existing technology and to propose an AUV adaptive navigation method based on the combination of deep learning and physical models, which can significantly improve navigation adaptability and navigation accuracy.

[0006] The technical solution of this invention is: an AUV adaptive navigation method based on a combination of deep learning and physical models, comprising the following steps: S1. In the process of modeling the motion system of AUV, the weighted gain deviation estimation EKF algorithm is proposed, which uses the DVL velocity bias as the state variable for online estimation, to compensate for the sensor system error, and introduces a Kalman gain update strategy weighted by state confidence. S2. Construct a deep learning network that adapts to measurement noise, and use the network to dynamically predict the x-axis time-varying noise standard deviation of the DVL velocity. and the standard deviation of time-varying noise in the y-direction. ; S3. Write the time-varying noise standard deviation obtained in step S2 into the time interval. Measurement noise covariance matrix And calculate the AUV position trajectory .

[0007] In this invention, step S1 includes the following steps: S1.1 Constructing an AUV augmented navigation evolution model; S1.2, Construct an AUV navigation observation model; S1.3, State confidence weighted Kalman gain.

[0008] The specific implementation process of step S1.1 is as follows: S1.1.1. Augment the EKF state vector. The augmented EKF state vector is shown below: , in, , AUV time exist x Xianghe y Planar coordinate position; For a moment The heading angle; , These represent the times in the AUV carrier coordinate system at time [time]. of x Xianghe y The speed of movement in the direction; , These represent the times in the AUV carrier coordinate system at time [time]. of x Xianghe y acceleration in the direction of motion; Indicates the AUV at time z-axis angular velocity; For a moment DVL x Bias towards velocity measurement; For a moment DVL y Bias towards velocity measurement; S1.1.2 Construct a one-step evolution model of the augmented AUV navigation system; Constructing the augmented AUV navigation system From moment to moment A one-step state evolution model. Among them, For time step: , , , , , , , , , , in, , AUV time Planar coordinate positions in the x and y directions; For a moment The heading angle; , These represent the times in the AUV carrier coordinate system at time [time]. The speed of motion in the x and y directions; , These represent the times in the AUV carrier coordinate system at time [time]. The accelerations in the x and y directions; Indicates the AUV at time z-axis angular velocity; For a moment The bias of the x-axis velocity measurement in DVL; For a moment The bias of the y-axis velocity measurement in DVL.

[0009] The specific implementation process of step S1.2 is as follows: S1.2.1 Constructing the augmented AUV navigation system observation vector ; , in, The heading angle of the AUV obtained from INS observations; and These are the x- and y-direction velocities obtained from DVL observations, respectively. and These are the x- and y-axis accelerations obtained from the INS, respectively. The z-axis angular velocity is measured by INS; S1.2.2, Based on the AUV navigation system observation vector obtained in step S1.2.1 An AUV navigation observation model is constructed, and the corresponding observation model is shown below: , , , , , , in, To observe the heading angle of the model; For the x-axis velocity of the observation model; To observe the y-axis velocity of the model; The x-axis acceleration of the observation model; For the y-axis acceleration of the observation model; To measure the angular velocity of the model's heading angle; The measurement noise is for the heading angle; The measurement noise is for the velocity in the x-direction. The noise in the measurement of the y-axis velocity; The measurement noise for the x-axis acceleration; The measurement noise for the y-axis acceleration; The measurement noise for the z-axis angular velocity; The observation matrix corresponding to the measurement equation A 6×10 matrix: , Observation noise covariance matrix for: , in, The standard deviation of the heading angle of the INS is measured; The standard deviation of the speed measurement in DVL; This represents the standard deviation of the INS acceleration measurement noise. This represents the standard deviation of the INS heading angular velocity measurement.

[0010] The specific implementation process of step S1.3 is as follows: During the filtering update phase, the Kalman gain is weighted by a state-specific confidence weight matrix W. As shown in the following formula, where n is the state dimension, , Each diagonal element This represents the confidence coefficient for the corresponding state; during filter updates, the standard Kalman gain K is weighted and multiplied by W to obtain the new Kalman gain. Used to perform subsequent state updates: .

[0011] Step S2 includes the following steps: S2.1, Time Update; The state estimate from the previous time step is used to predict the state at the current time step: , in, The predicted prior system state; Covariance of the prediction state estimation error: , in, To predict covariance; This is the state transition matrix; For a moment The process noise covariance matrix; State transition matrix for: ; S2.2 Construct a deep learning network model for adaptive measurement noise, and use this model to output the time-varying noise standard deviation of the DVL velocity quantity.

[0012] The specific implementation process of step S2.2 is as follows: S2.2.1 Offline training dataset collection; S2.2.2, Feature construction and standardization based on noise causes; The feature values ​​of the training set are globally standardized before being used as input to train the model. The standardization formula is as follows: , in, For multi-source sensor features, the multi-source sensor features input to the model include: constant terms, x-axis velocity, y-axis velocity, z-axis velocity, ground clearance, ground clearance, pitch angle, roll angle detected by DVL, and x-axis acceleration, y-axis acceleration, z-axis acceleration, and z-axis angular velocity detected by IMU; for The mean; S2.2.3, The standardized feature vector obtained in step S2.2.2. Input a deep learning network model that adapts to measurement noise, and dynamically predict the time-varying noise standard deviation of DVL velocity quantities. , ; The deep learning network model for adaptive measurement noise includes a channel interaction branch and a local temporal branch arranged in parallel. The standardized feature vectors are input into the channel interaction branch and the local temporal branch, respectively. The output of the channel interaction branch is connected to the squeezing-excitation attention module, and the output of the local temporal branch is connected to the normalization and regularization module; The outputs of the squeeze-excitement attention module and the normalization and regularization modules are connected to the feature fusion module, respectively. The feature fusion module, gating network, expert network, weighted output module, and positive value constraint module are connected in series.

[0013] The data processing procedure for the deep learning network model that adapts to measurement noise is as follows: In the channel interaction branch, input First, it undergoes linear dimensionality increase to K dimensions, where The standardized feature vector represents the hidden layer dimension. First, a fully connected layer is used to map to a high-dimensional space: , in, This is the output vector of the first hidden layer of the deep learning network; This is the weight matrix corresponding to the fully connected layer. , Represents the set of real numbers; This is the bias vector corresponding to the fully connected layer. ; The GELU activation function provides a smooth nonlinear transformation, and its expression is: , in, The cumulative distribution function of the standard normal distribution; Subsequently, B residual MLP blocks are stacked. Each residual MLP block contains a LayerNorm layer, a first Dense layer, a GELU layer, a Dropout layer, a second Dense layer, and a residual layer connected in sequence. The data processing procedure for each residual MLP block is as follows: , in, For the first The result of the input features in each residual block after layer normalization; For input to the first The original feature data in each residual block; , in, This is the output of the first Dense layer; , in, This is the output vector of the Dropout layer; , in, This is the linear output of the second Dense layer; , in, For the first A new feature representation with residual information is obtained by summing the residuals and activating the GELU of each residual block; Following the residual MLP block, an SE attention mechanism is introduced. The SE attention mechanism consists of two fully connected layers, and its data processing procedure is as follows: , in, It is a D-dimensional vector, which is a representation of the feature map. The channel-level global descriptor obtained after the compression operation. ; It is the original feature map input to the SE attention module, which comes from the output of the residual MLP block; , in, To output the weight vector; For the weights of the second fully connected layer, ; For the weights of the second fully connected layer, ; The bias for the first fully connected layer; For the bias of the second fully connected layer; For the Sigmoid function; , in, For the output weight vector The output feature map after recalibration; This represents channel-by-channel multiplication; The local temporal branch consists of two cascaded causal convolutional layers that convert the standardized feature vectors into a single pass. The input consists of two stacked one-dimensional convolutional layers, each with causal padding: , For length of For sequences, causal padding will pad the beginning of the sequence. The number of output channels for both the first and second convolutional layers is zero. Each convolutional layer is followed by the GELU activation function: , in, This is the deep feature representation after processing with two layers of one-dimensional convolution Conv1D and GELU activation function; The normalization and regularization module includes LayerNorm and Dropout layers. , in, for Output features after normalization and Dropout regularization; The feature fusion module integrates information from the channel interaction branch and the local timing branch, and converts the output of the channel interaction branch into a single data structure. and the output of local timing branches The data is concatenated along the feature dimension and then fused using a fusion layer. , in, The fused feature vector; This is the weight matrix of the fusion layer. ; The bias matrix of the fusion layer. ; Features after fusion Input a two-layer gating network and generate Weights of each expert network: , in, This is the output of the hidden layer of the gated network; This is the weight matrix of the first-layer gated network. ; This is the bias matrix of the first-layer gated network; , in, This is the weight matrix of the second-layer gated network. ; This is the bias matrix for the second-layer gated network; The expert weight vector has dimensions of . , ; The network model consists of E parallel-connected lightweight expert networks, each of which is a two-layer MLP. Each expert network independently learns a mapping from fused features to the noise standard deviation. , in, For the first Hidden layer output of an expert network; For the first The weight matrix of the first layer MLP of an expert network; For the first The bias matrix of the first layer MLP of an expert network; , in, For the first The output of an expert network, ; For the first The bias matrix of a second-layer MLP in an expert network; Final noise standard deviation raw output It is a weighted sum of the outputs from each expert network: , To ensure that the output noise standard deviation is non-negative, the Softplus function is used for transformation: , in, The final time-varying noise standard deviation predicted by a deep learning network model that adaptively measures noise has two dimensions, including ; For the final Apply hard constraints: , in, This is the minimum threshold value; the standard deviation of the predicted time-varying noise must not be lower than this value. This is the maximum threshold value; the predicted time-varying noise standard deviation is not allowed to exceed this value.

[0014] Write the time-varying noise standard deviation obtained in step S2 into the time. Measurement noise covariance matrix : , in, The measurement noise is for the heading angle; The measurement noise for acceleration in the x-axis; The measurement noise is for the y-axis acceleration. The measurement noise for the z-axis angular velocity; Measurement update calculations are performed using sensor data and measurement noise output from a deep learning network model that adapts to measurement noise: This calculates the information between the predicted and actual observations. , in, For the innovation vector, For the observed predicted value, For a moment AUV navigation system observation vector; Calculate the covariance of the innovation vector : , in, Indicates time The observation matrix; For a moment The transpose of the observation matrix.

[0015] Determine the Kalman gain based on the value of the innovation vector covariance. : , Using confidence weights The weighted Kalman gain is obtained by performing a weighted calculation. ; Final moments Navigation system state estimate for: .

[0016] Final moments System state covariance estimate for: , in, It is a unit diagonal matrix; The AUV position trajectory is obtained through iterative calculation at each time step. .

[0017] The beneficial effects of this invention are: (1) This application proposes a weighted gain bias estimation EKF algorithm, which uses the DVL velocity bias as the state variable for online estimation to compensate for sensor system errors, and introduces a Kalman gain update strategy weighted by state confidence to avoid overcorrection of the modeling bias. (2) A convolutional-hybrid expert network is proposed, which uses a deep learning network to regress the noise standard deviation in real time and writes it into the measurement covariance R. This enables channel-level adaptation based on time and working conditions and is combined with positive robust update of Total Variation. It is then used in the state estimation process of the WB-EKF algorithm, thereby significantly improving navigation adaptability and navigation accuracy. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method described in this application; Figure 2This is a structural diagram of a deep learning network model for adaptive measurement noise; Figure 3 This is a comparison diagram of the AUV motion trajectory predicted by the method described in this application and the AUV motion trajectory predicted by the existing EKF method. Detailed Implementation

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0020] Specific details are set forth in the following description to provide a full understanding of the invention. However, the invention can be practiced in many ways other than those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0021] The flowchart of the AUV adaptive navigation method based on a combination of deep learning and physical models described in this application is as follows: Figure 1 As shown, the process of this method is as follows.

[0022] The first step, in the modeling of the AUV motion system, proposes a weighted Kalman-Gain Bias-Estimating EKF (WB-EKF) algorithm. This algorithm uses the DVL velocity bias as an online state variable to compensate for sensor system errors and introduces a Kalman gain update strategy weighted by state confidence to avoid overcorrection of the modeling bias. The specific implementation process is described below.

[0023] First, construct the AUV augmented navigation evolution model, the specific implementation process of which is as follows.

[0024] (a) Augmenting the state vector of EKF.

[0025] The AUV is equipped with an Inertial Navigation System (INS) to acquire its azimuth, angular velocity, and acceleration, while its velocity is obtained through Dynamic Volume Lig (DVL). The navigation system's state vector encompasses the AUV's core navigation physical quantities, including position, velocity, heading, acceleration, and angular velocity. This provides complete state-dimensional support for subsequent motion prediction, ensuring that the model accurately maps the AUV's underwater motion patterns and avoiding prediction errors caused by missing state data. This is a fundamental prerequisite for achieving accurate navigation.

[0026] time The navigation system state vector is .in, and Indicates the AUV at time Location status information, and Indicates the AUV at time Speed ​​status information, Indicates the AUV at time The heading status information, and Indicates the AUV at time acceleration state information, Is it AUV at any time? The heading angular velocity status information.

[0027] For time The navigation system state vector is augmented, and the augmented EKF state vector is shown below: , in, , AUV time exist x Xianghe y Planar coordinate position; For a moment The heading angle; , These represent the times in the AUV carrier coordinate system at time [time]. of x Xianghe y The speed of movement in the direction; , These represent the times in the AUV carrier coordinate system at time [time]. of x Xianghe y acceleration in the direction of motion; Indicates the AUV at time z-axis angular velocity; For a moment DVL x Bias towards velocity measurement; For a moment DVL y Bias towards velocity measurement. , Associating state information with the AUV state vector enables the filtering algorithm to learn and compensate for DVL zero drift bias or scale error during execution, thereby improving the estimation performance of the filtering algorithm.

[0028] To address the systematic deviations such as zero drift and scale errors that easily occur during long-term underwater operation of DVL, online estimation and compensation of deviations are achieved through state augmentation, eliminating the need for additional sensor calibration operations, reducing engineering maintenance costs, and avoiding navigation accuracy degradation caused by deviation accumulation, thus significantly improving the reliability of long-range AUV navigation.

[0029] (ii) Construct a one-step evolution model of the augmented AUV navigation system.

[0030] Based on the kinematic equations, construct the augmented AUV navigation system time. From moment to moment A one-step state evolution model. Among them, For time step: , , , , , , , , , , in, , AUV time Planar coordinate positions in the x and y directions; For a moment The heading angle; , These represent the times in the AUV carrier coordinate system at time [time]. The speed of motion in the x and y directions; , These represent the times in the AUV carrier coordinate system at time [time]. The accelerations in the x and y directions; Indicates the AUV at time z-axis angular velocity; For a moment The bias of the x-axis velocity measurement in DVL; For a moment The bias of the y-axis velocity measurement in DVL.

[0031] In the above model, position , The heading is obtained by integrating the AUV's own velocity after rotating it around the heading; Obtained by integrating angular velocity; velocity , It is obtained by integrating its own acceleration; and acceleration , angular velocity and DVL bias , Modeled as a first-order Gaussian-Markov process, it is treated as constant on short time scales and allows random walks on long time scales. This design reflects our assumption that the acceleration and yaw rate of the AUV are approximately constant over small time steps, but will drift slowly over longer periods; similarly, the DVL bias is treated as a constant deviation but allows for small random variations to simulate the slow change of sensor zero drift over time.

[0032] By combining the actual motion characteristics of AUVs, such as short-term acceleration / angular velocity being approximately constant and long-term slow drift, and sensor bias characteristics such as DVL zero drift and slow variation, the augmented navigation evolution model is optimized to make the model more consistent with the actual engineering scenario, avoid prediction errors caused by the deviation between the ideal model and actual motion, and improve the accuracy of state prediction.

[0033] Second, construct an AUV navigation observation model. The specific implementation process includes the following steps.

[0034] (a) Constructing the augmented AUV navigation system observation vector .

[0035] , in, The heading angle of the AUV obtained from INS observations; and These are the x- and y-direction velocities obtained from DVL observations, respectively. and These are the x- and y-axis accelerations obtained from the INS, respectively. The z-axis angular velocity is measured by INS.

[0036] The augmented AUV observation vector is consistent with the unaugmented vector. The main sensors involved in AUV navigation include the heading angle provided by the INS. Measurements include acceleration, angular velocity, and velocity measurements provided by DVL.

[0037] Maintaining consistency between the observation vector and the original sensor output requires no modification to the sensor hardware or data acquisition process, reducing the engineering deployment difficulty of the algorithm. At the same time, it ensures that the observation data can directly match the augmented state model, avoiding additional errors introduced by data conversion.

[0038] (ii) Observation vectors of the AUV navigation system obtained in step S1.2.1 , and construct an observation model for the AUV navigation system.

[0039] The corresponding observation model can be expressed as follows: , , , , , , in, To observe the heading angle of the model; For the x-axis velocity of the observation model; To observe the y-axis velocity of the model; The x-axis acceleration of the observation model; For the y-axis acceleration of the observation model; To measure the angular velocity of the model's heading angle; The measurement noise is for the heading angle; The measurement noise is for the velocity in the x-direction. The noise in the measurement of the y-axis velocity; The noise is for measuring forward acceleration; The noise in the measurement of lateral motion acceleration; The measurement noise is for the z-axis angular velocity. The corresponding observation matrix is ​​derived from the measurement equation. It is a 6×10 matrix.

[0040] , In the observation matrix, each row corresponds to the linear relationship between the state and the observation in one of the observation equations mentioned above. For example, the second row represents the forward DVL readings. Equal to state and The sum. Therefore, it can be seen that by adding to the state vector... and The observation model can characterize the systematic difference between the measurement and the true state when DVL has zero bias, enabling the filter to estimate and compensate for the bias online, thereby achieving explicit modeling of DVL zero drift error.

[0041] It is important to note that this model does not perform separate dimension-extended modeling of the constant drift of the accelerometer and gyroscope; rather, it is implicitly included in... , , In the stochastic constant model; however, the same idea can be extended to estimate the gyroscope bias and accelerometer bias of INS. In practical engineering, different state extension schemes can be selected as needed.

[0042] Observation noise covariance matrix As shown below, this is a diagonal matrix, where each element represents the variance of the measurement noise for each sensor.

[0043] , in, The standard deviation of the heading angle of the INS is measured; The standard deviation of the speed measurement in DVL; This represents the standard deviation of the INS acceleration measurement noise. This represents the standard deviation of the INS heading angular velocity measurement.

[0044] By explicitly linking DVL measurements, actual velocity, and bias through the observation matrix, the problem of observation-state mismatch caused by neglecting bias in traditional models is solved, enabling filtering to simultaneously estimate state variables and bias variables. The diagonalized noise covariance matrix conforms to the independent characteristics of sensor noise in engineering, simplifying calculations while ensuring the rationality of noise modeling, and providing reliable noise statistics for filter updates.

[0045] Third, state confidence-weighted Kalman gain.

[0046] During the filtering update phase, the Kalman gain is weighted by a state-based confidence weight matrix W to improve filtering performance.

[0047] State confidence weighted matrix As shown in the following formula, where n is the state dimension, , The state dimension of the model constructed in this application is 10, and each diagonal element This represents the confidence coefficient for the corresponding state. During filter updates, the new Kalman gain is obtained by weighted multiplication of the standard Kalman gain K with W. This is used to perform subsequent state updates.

[0048] .

[0049] for The state, the first The row Kalman gain will be reduced, which is equivalent to reducing the amount of information that the state obtains from the current observation, thus making it more reliant on model prediction; and The smaller the value, the more "sluggish" the response to the observed residuals. In particular, if a certain state... This indicates that the observations are completely distrusted in correcting the state; in this case, the filter will not update the state but will only propagate according to the model prediction. By appropriately selecting the states... The value of can, to some extent, suppress estimation divergence caused by observation errors in low-confidence states. It is important to note that the matrix... The settings should be balanced by combining specific applications and parameter tuning experience: Too small a value may slow down the filtering convergence or cause the accumulation of bias, while too large a value will not have the effect of suppression.

[0050] To address scenarios where the reliability of some sensor observations decreases in complex underwater environments, such as DVL lockout or INS interference from turbulence, the algorithm flexibly adjusts the observation confidence of each state through a weight matrix. This avoids low-confidence observations contaminating state estimation and prevents filter divergence. At the same time, it retains the correction effect of high-confidence observations, maximizing the use of effective observation information while ensuring navigation stability, thereby improving the robustness of the algorithm in complex marine environments.

[0051] The second step is to construct a deep learning network that adapts to measurement noise, and then use this deep learning network to regress the measurement noise covariance matrix in real time. The parameter values ​​are used to achieve channel-level adaptive operation based on time and operating conditions, and are updated robustly in conjunction with TotalVariation (TV). This is then used in the WB-EKF algorithm state estimation process, thereby significantly improving AUV navigation accuracy.

[0052] Using the WB-EKF proposed in the first step as the main navigation architecture, WB-EKF consists of two main parts: a time update process and a measurement update process. The specific implementation process of this step is described below.

[0053] First, time updates.

[0054] During the time update process, based on the AUV augmented navigation evolution model constructed in the first step, WB-EKF uses the state estimate from the previous time step to predict the state at the current time step:

[0055] , in, This represents the predicted prior system state.

[0056] Meanwhile, EKF predicts the covariance of the state estimation error based on the system noise model: , in, To predict covariance; This is the state transition matrix; For a moment The process noise covariance matrix is ​​used to quantify the uncertainty of the system model itself.

[0057] The EKF system noise model mainly consists of two parts: process noise and observation noise. Process noise is used to describe the uncertainty of the system model, while observation noise is used to describe the uncertainty of sensor measurements.

[0058] State transition matrix for: , By quantifying the dynamic correlation between states through the state transition matrix, the current state can be predicted based on historical states, thus solving the navigation continuity problem when underwater sensor data transmission is delayed or temporarily interrupted. At the same time, the state error covariance is predicted, providing a basis for the calculation of Kalman gain in subsequent measurement updates, ensuring the scientific nature of the filtering update and avoiding blind fusion of observation data.

[0059] Second, a deep learning network model for adaptive measurement noise is constructed, and this model is used to output the time-varying noise standard deviation of the DVL velocity quantity.

[0060] (a) Offline training dataset collection.

[0061] To train the adaptive noise estimation model, an AUV navigation dataset covering multiple scenarios needs to be constructed. The specific data collection process involves the AUV performing various pre-set trajectory tasks in the marine environment, simultaneously collecting the following data through an integrated sensor system: 1. Attitude information: The pitch angle, roll angle, and yaw angle of the AUV are obtained through the inertial measurement unit (IMU); 2. Motion Information: The Doppler velocity meter (DVL) provides three-axis velocity and bottom height data in the AUV carrier coordinate system; 3. Dynamic information: Triaxial linear acceleration measured by IMU, in m / s²; z-axis angular velocity, in rad / s; 4. Positioning reference: The GPS receiver provides two-dimensional positions in the east and north directions in the UTM coordinate system as the true value of the trajectory.

[0062] The collected data underwent preprocessing. To ensure time alignment, all sensor data were interpolated and synchronized based on the IMU timestamp to guarantee temporal consistency. To avoid the impact of invalid values ​​on model training, missing or abnormal data, such as DVL lockouts or GPS signal interruptions, were filled using linear interpolation, and a valid bitmask was added to the data. The dataset was divided into training, validation, and test sets in a 7:2:1 ratio to ensure distribution diversity.

[0063] The multi-scenario dataset covers different marine environments such as calm waters, turbulent areas, complex terrain, and motion trajectories, ensuring the model's generalization ability. Time synchronization solves the problem of temporal misalignment caused by differences in sampling rates of multiple sensors, and abnormal data processing avoids invalid information interfering with model training. The 7:2:1 partitioning conforms to machine learning engineering practices, ensuring that the model is fully trained and can be effectively validated, providing high-quality model support for online adaptive noise estimation.

[0064] (ii) Problem modeling and objective function.

[0065] We aim to learn a time-varying standard deviation vector of measurement noise that depends only on past and current information, and to write it into time intervals. Measurement noise covariance matrix : , , in, The standard deviation of the time-varying noise in the x-axis velocity is used to describe the accuracy of the x-axis velocity measured by DVL. A noise standard deviation is calculated for the y-axis velocity, which is used to describe the accuracy of the y-axis velocity measured by DVL. For multi-source sensor features, the multi-source sensor features input to the model include: constant term, x-axis velocity detected by DVL, y-axis velocity detected by DVL, z-axis velocity detected by DVL, bottom height detected by DVL, bottom state detected by DVL, pitch angle, roll angle, x-axis acceleration detected by IMU, y-axis acceleration detected by IMU, z-axis acceleration detected by IMU, and z-axis angular velocity; These are learnable parameters; A deep learning network model representing adaptive measurement noise; The measurement noise is for the heading angle; The measurement noise for acceleration in the x-axis; The measurement noise is for the y-axis acceleration. This refers to the measurement noise of the z-axis angular velocity, which is also the measurement noise of the heading angle angular velocity.

[0066] Network output uses activation function To ensure a positive standard deviation, the EKF forward pass uses the Cholesky solution and Joseph form to guarantee numerical robustness. , The AUV position trajectory calculated by WB-EKF is denoted as... The objective function is shown in the following equation: , Where M is the effective quantity of GPS information; the TV item is... Weighting can prevent over-smoothing; These are the time smoothing regularization coefficients. The parameter is the regularization coefficient.

[0067] The objective function described above primarily aims to optimize the RMSE between the WB-EKF predicted trajectory and the GPS 2D trajectory, incorporating time smoothing regularization (TV regularization) and parametric regularization (L2 regularization). The time smoothing regularization term penalizes abrupt changes in noise estimates, calculated according to the time step. Weighting is used to avoid over-smoothing. In this embodiment, Pick The parameter regularization term controls model overfitting. In this embodiment, Pick .

[0068] The primary objective, RMSE, is directly linked to the core navigation performance metric, positional accuracy, ensuring that the model's learning direction aligns with engineering requirements. TV regularization prevents filter oscillations caused by abrupt changes in noise estimation, aligning with the slowly varying noise characteristics of the marine environment. L2 regularization prevents overfitting, ensuring stable operation even in unfamiliar scenarios. Softplus activation and Cholesky solutions ensure numerical stability, preventing algorithm crashes due to numerical anomalies during deployment.

[0069] (III) Characterization and standardization based on the causes of noise.

[0070] The feature values ​​of the training set are globally standardized before being used as input to train the model. The standardization formula is as follows: , in, for The mean.

[0071] Standardized statistics are saved along with the model and strictly reused during inference to avoid training and testing distribution drift.

[0072] The feature vectors comprehensively cover key influencing factors of DVL noise, such as the bottom state reflecting echo quality and attitude angle reflecting geometric relationships, enabling the model to actively predict noise changes rather than passively responding to residuals. Global standardization eliminates differences in feature dimensions, such as velocity (m / s) and angle (rad), avoiding convergence difficulties caused by feature scale imbalance during model training. Reusing standardized statistics prevents distribution drift, ensuring consistency between online inference and offline training, and improving model prediction accuracy.

[0073] (iv) Input the standardized feature vector obtained in the above steps into the deep learning network model for adaptive measurement noise to dynamically predict the x-axis time-varying noise standard deviation of the DVL velocity. and the standard deviation of time-varying noise in the y-direction. .

[0074] The deep learning network model for adaptive measurement noise adopts a dual-branch hybrid expert architecture, which aims to simultaneously capture the cross-channel nonlinear interaction and local time-dependent patterns of sensor features. The overall design strictly follows the principle of causality to ensure that online deployment relies only on historical and current information.

[0075] Adaptive measurement noise deep learning network model, such as Figure 2 As shown. Its specific construction process is described below. This network model includes parallel channel interaction branches and local temporal branches, and the standardized feature vectors... The inputs are channel interaction branches and local temporal branches, respectively. The output of the channel interaction branch is connected to the squeeze-excitation attention module, and the output of the local temporal branch is connected to the normalization and regularization module. The outputs of the squeeze-excitation attention module and the normalization and regularization module are respectively connected to the feature fusion module. The feature fusion module, gating network, expert network, weighted output module, and positive value constraint module are connected in series.

[0076] 1. Channel interaction branch.

[0077] The core objective of the channel interaction branch is to learn the complex nonlinear combination relationships between different sensor features, such as the synergistic effect of DVL velocity and IMU attitude angle on noise.

[0078] In the channel interaction branch, input First, it undergoes linear dimensionality increase to K dimensions, where For the hidden layer dimension.

[0079] Standardized feature vectors First, a fully connected layer is used to map the model to a high-dimensional space to enhance its expressive power. , in, This is the output vector of the first hidden layer of the deep learning network; This is the weight matrix corresponding to the fully connected layer. , Represents the set of real numbers; is the bias vector corresponding to the fully connected layer. .

[0080] The GELU activation function provides a smooth nonlinear transformation, and its expression is: , in, This is the cumulative distribution function of the standard normal distribution.

[0081] Subsequently, B residual MLP blocks are stacked. Each residual MLP block contains a LayerNorm layer, a first Dense layer, a GELU layer, a Dropout layer, a second Dense layer, and a residual layer connected in sequence to learn nonlinear combinations across channels. In this embodiment, B=3, and the features... pass The same residual MLP block.

[0082] The data processing procedure for each residual MLP block is as follows: , in, For the first The result of the input features in each residual block after layer normalization; For input to the first The original feature data in each residual block.

[0083] , in, This is the output of the first Dense layer.

[0084] , in, This is the output vector of the Dropout layer.

[0085] , in, This is the linear output of the second Dense layer.

[0086] , in, For the first A new feature representation with residual information is obtained by summing the residuals and activating the GELU with each residual block.

[0087] Residual MLP blocks can effectively alleviate the gradient vanishing problem in deep networks; at the same time, residual connections allow gradients to propagate directly backward, ensuring effective training of deep networks.

[0088] The output of the channel interaction branch is connected to the squeeze-excitation attention module. After the residual MLP block, an SE attention mechanism is introduced, mimicking the channel attention mechanism, allowing the network to automatically learn the importance weights of each feature channel. The SE attention mechanism consists of two fully connected layers. Its data processing procedure is described below.

[0089] , in, It is a D-dimensional vector, which is a representation of the feature map. The channel-level global descriptor obtained after the compression operation. ; It is the original feature map input to the SE attention module, which comes from the output of the residual MLP block.

[0090] , in, To output the weight vector; For the weights of the second fully connected layer, ; For the weights of the second fully connected layer, ; The bias for the first fully connected layer; For the bias of the second fully connected layer; This is the Sigmoid function.

[0091] , in, For the output weight vector The output feature map after recalibration; This indicates channel-by-channel multiplication.

[0092] The squeeze-excited attention module can effectively enhance the contribution of noise-sensitive feature channels and suppress unimportant channels.

[0093] The residual MLP block addresses the vanishing gradient problem in deep networks, ensuring the model can learn complex nonlinear feature relationships, such as the synergistic effect between DVL speed and IMU pose. The SE attention mechanism automatically focuses on noise-sensitive key feature channels, suppressing redundant information and improving model feature extraction efficiency. The GELU activation function provides smooth nonlinear transformations, enhancing the model's expressive power. The overall design ensures the model can accurately capture complex relationships between multi-sensor features, providing high-quality feature support for noise prediction.

[0094] 2. Local time-series branches.

[0095] The local temporal branch aims to capture short-term degradation patterns in DVL signals, such as momentary beam lock-off, which have local temporal correlations. This branch consists of two cascaded causal convolutional layers.

[0096] The standardized feature vector The input consists of two stacked one-dimensional convolutional layers. To ensure causality—that is, the current output depends only on the current and past inputs—each convolutional layer uses causal padding. , For length of For sequences, causal padding will pad the beginning of the sequence. The first convolutional layer has zeros, ensuring that the output sequence has the same length as the input sequence and that the computation at each time point does not depend on future information. The first convolutional layer has the following output channels: The number of output channels in the second convolutional layer is also [number missing]. Each convolutional layer is followed by the GELU activation function: , in, This is the deep feature representation after processing with two layers of one-dimensional convolution Conv1D and GELU activation function.

[0097] Causal convolution ensures that online deployment does not rely on future data, meeting the real-time requirements of navigation systems. A 5th-order kernel size effectively captures local temporal patterns of short-term DVL signal degradation, such as instantaneous beam lock-out, and solves the prediction lag problem caused by sudden noise changes.

[0098] 3. Normalization and Regularization Module.

[0099] The normalization and regularization module includes LayerNorm and Dropout layers to stabilize training and prevent overfitting.

[0100] , in, for Output features after normalization and Dropout regularization.

[0101] LayerNorm and Dropout layers can improve the training stability and generalization ability of the model, avoid short-term noise prediction failure caused by overfitting, and ensure that the model can respond to instantaneous changes in sensor signals in a timely manner.

[0102] 4. Feature fusion module.

[0103] This module enables information fusion between channel interaction branches and local timing branches.

[0104] This module outputs the channel interaction branch. and the output of local timing branches The data is concatenated along the feature dimension and then fused using a fusion layer. , in, The fused feature vector; This is the weight matrix of the fusion layer. ; The bias matrix of the fusion layer. .

[0105] 5. Gating network.

[0106] Features after fusion Input a two-layer gating network and generate Weights of each expert network: , in, This is the output of the hidden layer of the gated network; This is the weight matrix of the first-layer gated network. ; This is the bias matrix of the first-layer gated network.

[0107] , in, This is the weight matrix of the second-layer gated network. ; This is the bias matrix for the second-layer gated network; The expert weight vector has dimensions of . , .

[0108] Gated networks learn how to dynamically combine the opinions of different experts based on the current input.

[0109] 6. Expert network.

[0110] The network model comprises E parallel-connected lightweight expert networks, each of which is a two-layer MLP. Each expert network independently learns a mapping from fused features to the noise standard deviation. In this embodiment, In other words, the network system contains three lightweight expert networks.

[0111] , in, For the first Hidden layer output of an expert network; For the first The weight matrix of the first layer MLP of an expert network; For the first The bias matrix of the first layer MLP of an expert network.

[0112] , in, For the first The output of an expert network, ; For the first The bias matrix of the second layer MLP of an expert network.

[0113] 7. Weighted output module.

[0114] Final noise standard deviation raw output It is a weighted sum of the outputs from each expert network: , The adaptive measurement noise deep learning network model proposed in this application allows the network to learn more complex functions, and different expert networks can focus on different regions of the input space.

[0115] Dual-branch feature fusion integrates cross-channel nonlinear correlations and local temporal patterns, providing comprehensive feature support for noise prediction; the gated MoE architecture allows different experts to focus on different scenarios such as calm waters, turbulent areas, and DVL lockout recovery periods, with dynamic weighting to achieve scenario adaptation and improve the model's generalization ability in complex and variable marine environments; the lightweight expert network can balance model performance and computational load, ensuring that the real-time requirements of AUV navigation systems can be met when deployed online.

[0116] 8. Positive value constraint module.

[0117] network raw output It can be any real number. To ensure that the noise standard deviation of the output is non-negative, the Softplus function is used for transformation: , in, The final time-varying noise standard deviation predicted by the deep learning network model with adaptive measurement noise has two dimensions, namely: This replaces the fixed measurement noise in the existing EFK.

[0118] The Softplus function is a smoothed version of ReLU, guaranteeing that the output is always positive. This is to prevent numerical underflow and ensure stability.

[0119] In engineering implementation, to prevent extreme values, such as excessively large or small values, from contaminating the WB-EKF measurement noise covariance matrix... For the final Apply hard constraints: , in, This is the minimum threshold value; the predicted noise standard deviation must not be lower than this value. This is the maximum threshold value; the predicted noise standard deviation is not allowed to exceed this value.

[0120] The processing steps implemented by this module are key measures to ensure the numerical robustness of the filter.

[0121] The activation function ensures that the noise standard deviation is positive, which is consistent with the physical meaning and avoids the failure of the filtering model due to negative noise values; the offset prevents numerical underflow and ensures computational stability; the numerical guardrail limits extreme values ​​and avoids excessively large / small noise estimates from polluting the covariance matrix, preventing filter divergence or accuracy decay. It is a key guarantee for the engineering implementation of the algorithm and ensures the long-term stable operation of the navigation system.

[0122] (v) Online testing.

[0123] AUVs perform missions at sea, collecting navigation data in real time from attitude sensors, GPS, and DVL (Driving Vehicle Level) sensors. An offline-trained deep learning network model with adaptive measurement noise is loaded. The collected AUV attitude, acceleration, and DVL state data per unit time are input into this network model to calculate the measurement noise values ​​for the predicted x- and y-axis velocities of the DVL at each time step. The corresponding measurement noise values ​​output by this network model are then written into the measurement noise covariance matrix. This is used in the subsequent filtering update process.

[0124] It enables online adaptive estimation of measurement noise without manual intervention to adjust noise parameters, adapting to dynamic changes in the marine environment, such as transitioning from calm waters to turbulent areas or changes in DVL bottom state; it updates the covariance matrix in real time, enabling the filtering algorithm to dynamically match the current sensor noise characteristics, avoiding the decrease in navigation accuracy caused by fixed noise parameters, and significantly improving the navigation adaptability and reliability of AUVs in complex and variable marine environments.

[0125] Third, measurement updates.

[0126] After predicting the velocity measurement noise in DVL (Device Variation in Velocity), WB-EKF uses sensor data and the measurement noise output from a deep learning network model that adapts to the measurement noise to perform measurement update calculations. This calculates the information between the predicted and actual observations. , in, For the innovation vector, For the observed predicted value, For a moment The observation vector of the AUV navigation system.

[0127] Simultaneously, calculate the covariance of the innovation vector. : , in, Indicates time The observation matrix; For a moment The transpose of the observation matrix.

[0128] The Kalman gain can be determined based on the value of the covariance of the innovation vector. : , Using confidence weights The weighted Kalman gain is obtained by performing a weighted calculation. .

[0129] Final moments Navigation system state estimate for: .

[0130] Final moments System state covariance estimate for: , in, It is a unit diagonal matrix.

[0131] Subsequently, through iterative calculations at each time step, this invention enables precise and adaptive AUV navigation.

[0132] By combining the noise covariance of adaptive prediction with the state confidence weighted gain, the optimal fusion of observed data and predicted state is achieved, and the state estimation error is dynamically corrected. Each iteration forms a closed-loop optimization to ensure that navigation errors do not accumulate, meeting the engineering requirements of long-range, high-precision navigation for AUVs, such as the position accuracy requirements of underwater exploration, target tracking, and pipeline inspection. The weighted gain further improves the estimation robustness, avoids navigation fluctuations caused by abnormal observations, and ensures the stability of the navigation system.

[0133] like Figure 3 As shown, by comparing the AUV trajectory predicted by the WB-EKF method proposed in this application with the AUV trajectory predicted by the existing EKF method, it can be clearly seen that the AUV trajectory predicted by this application is closer to the actual AUV trajectory observed by GPS.

[0134] The AUV adaptive navigation method based on a combination of deep learning and physical models provided by this invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from the principles of this invention, and these improvements and modifications also fall within the protection scope of the claims of this invention. The above description of the disclosed embodiments enables those skilled in the art to implement or use this invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of this invention. Therefore, this invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An AUV adaptive navigation method based on a combination of deep learning and physical models, characterized in that, Includes the following steps: S1. In the process of modeling the motion system of AUV, the weighted gain deviation estimation EKF algorithm is proposed, which uses the DVL velocity bias as the state variable for online estimation, to compensate for the sensor system error, and introduces a Kalman gain update strategy weighted by state confidence. S2. Construct a deep learning network that adapts to measurement noise, and use the network to dynamically predict the x-axis time-varying noise standard deviation of the DVL velocity. and the standard deviation of time-varying noise in the y-direction. ; S3. Write the time-varying noise standard deviation obtained in step S2 into the time interval. Measurement noise covariance matrix And calculate the AUV position trajectory .

2. The AUV adaptive navigation method based on a combination of deep learning and physical models according to claim 1, characterized in that, Step S1 includes the following steps: S1.1 Constructing an AUV augmented navigation evolution model; S1.2, Construct an AUV navigation observation model; S1.3, State confidence weighted Kalman gain.

3. The AUV adaptive navigation method based on a combination of deep learning and physical models according to claim 2, characterized in that, The specific implementation process of step S1.1 is as follows: S1.1.

1. Augment the EKF state vector. The augmented EKF state vector is shown below: ， in, , AUV time exist x Xianghe y Planar coordinate position; For a moment The heading angle; , These represent the times in the AUV carrier coordinate system at time [time]. of x Xianghe y The speed of movement in the direction; , These represent the times in the AUV carrier coordinate system at time [time]. of x Xianghe y acceleration in the direction of motion; Indicates the AUV at time z-axis angular velocity; For a moment DVL x Bias towards velocity measurement; For a moment DVL y Bias towards velocity measurement; S1.1.2 Construct a one-step evolution model of the augmented AUV navigation system; Constructing the augmented AUV navigation system From moment to moment A one-step state evolution model; where, For time step: ， ， ， ， ， ， ， ， ， ， in, , AUV time Planar coordinate positions in the x and y directions; For a moment The heading angle; , These represent the times in the AUV carrier coordinate system at time [time]. The speed of motion in the x and y directions; , These represent the times in the AUV carrier coordinate system at time [time]. The accelerations in the x and y directions; Indicates the AUV at time z-axis angular velocity; For a moment The bias of the x-axis velocity measurement in DVL; For a moment The bias of the y-axis velocity measurement in DVL.

4. The AUV adaptive navigation method based on a combination of deep learning and physical models according to claim 2, characterized in that, The specific implementation process of step S1.2 is as follows: S1.2.1 Constructing the augmented AUV navigation system observation vector ; ， in, The heading angle of the AUV obtained from INS observations; and These are the x- and y-direction velocities obtained from DVL observations, respectively. and These are the x- and y-axis accelerations obtained from the INS, respectively. The z-axis angular velocity is measured by INS; S1.2.2, Based on the AUV navigation system observation vector obtained in step S1.2.1 An AUV navigation observation model is constructed, and the corresponding observation model is shown below: ， ， ， ， ， ， in, To observe the heading angle of the model; For the x-axis velocity of the observation model; To observe the y-axis velocity of the model; The x-axis acceleration of the observation model; For the y-axis acceleration of the observation model; To measure the angular velocity of the model's heading angle; The measurement noise is for the heading angle; The measurement noise is for the velocity in the x-direction. The noise in the measurement of the y-axis velocity; The measurement noise for the x-axis acceleration; The measurement noise for the y-axis acceleration; The measurement noise for the z-axis angular velocity; The observation matrix corresponding to the measurement equation A 6×10 matrix: ， Observation noise covariance matrix for: ， in, The standard deviation of the heading angle of the INS is measured; The standard deviation of the speed measurement in DVL; This represents the standard deviation of the INS acceleration measurement noise. This represents the standard deviation of the INS heading angular velocity measurement.

5. The AUV adaptive navigation method based on a combination of deep learning and physical models according to claim 2, characterized in that, The specific implementation process of step S1.3 is as follows: During the filtering update phase, the Kalman gain is weighted by a state-specific confidence weight matrix W. As shown in the following formula, where n is the state dimension, ， Each diagonal element This represents the confidence coefficient for the corresponding state; during filter updates, the standard Kalman gain K is weighted and multiplied by W to obtain the new Kalman gain. Used to perform subsequent state updates: 。 6. The AUV adaptive navigation method based on a combination of deep learning and physical models according to claim 1, characterized in that, The specific implementation process of step S2 is as follows: S2.1, Time Update; The state estimate from the previous time step is used to predict the state at the current time step: ， in, The predicted prior system state; Covariance of the prediction state estimation error: ， in, To predict covariance; This is the state transition matrix; For a moment The process noise covariance matrix; State transition matrix for: ； S2.2 Construct a deep learning network model for adaptive measurement noise, and use this model to output the time-varying noise standard deviation of the DVL velocity quantity.

7. The AUV adaptive navigation method based on a combination of deep learning and physical models according to claim 6, characterized in that, The specific implementation process of step S2.2 is as follows: S2.2.1 Offline training dataset collection; S2.2.2, Feature construction and standardization based on noise causes; The feature values ​​of the training set are globally standardized before being used as input to train the model. The standardization formula is as follows: ， in, For multi-source sensor features, the multi-source sensor features input to the model include: constant terms, x-axis velocity, y-axis velocity, z-axis velocity, ground clearance, ground clearance, pitch angle, roll angle detected by DVL, and x-axis acceleration, y-axis acceleration, z-axis acceleration, and z-axis angular velocity detected by IMU; for The mean; S2.2.3, The standardized feature vector obtained in step S2.2.

2. Input a deep learning network model that adapts to measurement noise, and dynamically predict the time-varying noise standard deviation of DVL velocity quantities. , ; The deep learning network model for adaptive measurement noise includes a channel interaction branch and a local temporal branch arranged in parallel. The standardized feature vectors are input into the channel interaction branch and the local temporal branch, respectively. The output of the channel interaction branch is connected to the squeezing-excitation attention module, and the output of the local temporal branch is connected to the normalization and regularization module; The outputs of the squeeze-excitement attention module and the normalization and regularization modules are connected to the feature fusion module, respectively. The feature fusion module, gating network, expert network, weighted output module, and positive value constraint module are connected in series.

8. The AUV adaptive navigation method based on a combination of deep learning and physical models according to claim 7, characterized in that, The data processing procedure for the deep learning network model that adapts to measurement noise is as follows: In the channel interaction branch, input First, it undergoes linear dimensionality increase to K dimensions, where The standardized feature vector represents the hidden layer dimension. First, a fully connected layer is used to map to a high-dimensional space: ， in, This is the output vector of the first hidden layer of the deep learning network; This is the weight matrix corresponding to the fully connected layer. , Represents the set of real numbers; This is the bias vector corresponding to the fully connected layer. ; The GELU activation function provides a smooth nonlinear transformation, and its expression is: ， in, The cumulative distribution function of the standard normal distribution; Subsequently, B residual MLP blocks are stacked. Each residual MLP block contains a LayerNorm layer, a first Dense layer, a GELU layer, a Dropout layer, a second Dense layer, and a residual layer connected in sequence. The data processing procedure for each residual MLP block is as follows: ， in, For the first The result of the input features in each residual block after layer normalization; For input to the first The original feature data in each residual block; ， in, This is the output of the first Dense layer; ， in, This is the output vector of the Dropout layer; ， in, This is the linear output of the second Dense layer; ， in, For the first A new feature representation with residual information is obtained by summing the residuals and activating the GELU of each residual block; Following the residual MLP block, an SE attention mechanism is introduced. The SE attention mechanism consists of two fully connected layers, and its data processing procedure is as follows: ， in, It is a D-dimensional vector, which is a representation of the feature map. The channel-level global descriptor obtained after the compression operation. ; It is the original feature map input to the SE attention module, which comes from the output of the residual MLP block; ， in, To output the weight vector; The weights of the second fully connected layer, ; For the weights of the second fully connected layer, ; The bias for the first fully connected layer; For the bias of the second fully connected layer; For the Sigmoid function; ， in, For the output weight vector The output feature map after recalibration; This represents channel-by-channel multiplication; The local temporal branch consists of two cascaded causal convolutional layers that convert the standardized feature vectors into a single pass. The input consists of two stacked one-dimensional convolutional layers, each with causal padding: , For length of For sequences, causal padding will pad the beginning of the sequence. The number of output channels for both the first and second convolutional layers is zero. Each convolutional layer is followed by the GELU activation function: ， in, This is the deep feature representation after processing with two layers of one-dimensional convolution Conv1D and GELU activation function; The normalization and regularization module includes LayerNorm and Dropout layers. ， in, for Output features after normalization and Dropout regularization; The feature fusion module integrates information from the channel interaction branch and the local timing branch, and converts the output of the channel interaction branch into a single data structure. and the output of local timing branches The data is concatenated along the feature dimension and then fused using a fusion layer. ， in, The fused feature vector; This is the weight matrix of the fusion layer. ; The bias matrix of the fusion layer. ; Features after fusion Input a two-layer gating network and generate Weights of each expert network: ， in, This is the output of the hidden layer of the gated network; This is the weight matrix of the first-layer gated network. ; This is the bias matrix of the first-layer gated network; ， in, This is the weight matrix of the second-layer gated network. ; This is the bias matrix for the second-layer gated network; The expert weight vector has dimensions of . , ; The network model consists of E parallel-connected lightweight expert networks, each of which is a two-layer MLP. Each expert network independently learns a mapping from fused features to the noise standard deviation. ， in, For the first Hidden layer output of an expert network; For the first The weight matrix of the first layer MLP of an expert network; For the first The bias matrix of the first layer MLP of an expert network; ， in, For the first The output of an expert network, ; For the first The bias matrix of a second-layer MLP in an expert network; Final noise standard deviation raw output It is a weighted sum of the outputs from each expert network: ， To ensure that the output noise standard deviation is non-negative, the Softplus function is used for transformation: ， in, The final time-varying noise standard deviation predicted by a deep learning network model that adaptively measures noise has two dimensions, including ; For the final Apply hard constraints: ， in, This is the minimum threshold value; the standard deviation of the predicted time-varying noise must not be lower than this value. This is the maximum threshold value; the predicted time-varying noise standard deviation is not allowed to exceed this value.

9. The AUV adaptive navigation method based on a combination of deep learning and physical models according to claim 1, characterized in that, Write the time-varying noise standard deviation obtained in step S2 into the time. Measurement noise covariance matrix : ， in, The measurement noise is for the heading angle; The measurement noise for acceleration in the x-axis; The measurement noise is for the y-axis acceleration. The measurement noise for the z-axis angular velocity; Measurement update calculations are performed using sensor data and measurement noise output from a deep learning network model that adapts to measurement noise: This calculates the information between the predicted and actual observations. , in, For the innovation vector, For the observed predicted value, For a moment AUV navigation system observation vector; Calculate the covariance of the innovation vector : ， in, Indicates time The observation matrix; For a moment The transpose of the observation matrix; Determine the Kalman gain based on the value of the innovation vector covariance. : ， Using confidence weights The weighted Kalman gain is obtained by performing a weighted calculation. ; Final moments Navigation system state estimate for: ； Final moments System state covariance estimate for: , in, It is a unit diagonal matrix; The AUV position trajectory is obtained through iterative calculation at each time step. .

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