Deep learning aided variational bayesian lie group filtering self-alignment method for low-precision SINS

Abstract

The application discloses a deep learning aided variational Bayesian Lie group filtering self-alignment method for low-precision SINS. Firstly, the gyro data obtained by the low-precision SINS is regarded as a time series by using the principle and characteristics of sensor measurement. A neural network model adopting a gated recurrent unit (GRU) is designed to calibrate and compensate the measurement error of the low-precision SINS. Secondly, a novel variational Bayesian Lie group filtering method is developed to process various errors in the Lie group alignment model, especially the state-dependent noise. The variational Bayesian method is extended to the Lie group space to estimate the measurement noise covariance matrix in real time and adaptively. Finally, experiments are carried out on a turntable device to verify and test the performance and advantages of the proposed method. The experimental results show that the proposed initial self-alignment method is significantly superior to existing methods in terms of alignment accuracy and time. The method fully meets the real-time requirements in actual applications without additional equipment and cost.

Description

TECHNICAL FIELD

[0001] The application discloses a deep learning assisted variational Bayesian Lie group filtering self-alignment method for low-precision SINS, and belongs to the technical field of navigation methods and applications. BACKGROUND

[0002] With the rapid development of microelectronics technology, computer technology and sensor technology, low-precision strapdown inertial navigation systems (SINS), especially inertial measurement units based on micro-electromechanical systems (MEMS), have been widely used in navigation positioning, robot control and other fields due to their small size and low cost. As the core component of providing navigation information, its importance is self-evident. Among them, the initial alignment link is particularly critical, aiming to determine the transformation relationship between the navigation coordinate system and the carrier coordinate system at the initial time, and its accuracy and efficiency directly affect the accuracy and real-time performance of subsequent navigation calculation.

[0003] However, due to the problems of large measurement noise and significant drift of MEMS IMU, it faces many challenges in practical application. In the initial alignment link, it is difficult to accurately extract the earth rotation angular velocity information, which increases the difficulty of realizing self-alignment. Traditional self-alignment methods mostly rely on external information or high-precision devices, but in some environments, such as areas with dense shelters or environments with strong magnetic interference, the application of these methods will be limited. In order to overcome these challenges, in recent years, deep learning technology has been introduced into the error compensation field of MEMS IMU. By training a deep learning model, the measurement error of MEMS IMU can be predicted and compensated, thereby improving the accuracy of measurement data. This method not only can handle complex nonlinear relationships, but also can extract useful feature information from a large amount of data, providing a new solution for error calibration of low-precision SINS.

[0004] Traditional initial alignment methods mainly rely on optimal estimation of attitude, and these methods usually use unit quaternions to describe the rotation matrix. However, this description method will cause the measurement equation to be nonlinear, increasing the complexity of the nonlinear filter processing, and the sensor error is difficult to accurately estimate. In contrast, the special orthogonal group is more intuitive in attitude representation, which can avoid the problems of non-uniqueness and singularity. When constructing the system model, the initial alignment model based on Lie group description can realize one-step accurate alignment of the initial attitude matrix.

[0005] In order to solve the problems existing in the process of self-alignment of low-precision SINS and further improve the performance of initial alignment, the application proposes a deep learning assisted Lie group filtering algorithm by learning from the properties of Lie group and the advantages of deep learning. A neural network model is designed and constructed using a gated recurrent unit (GRU) to calibrate and compensate the measurement errors of low-precision SINS. An initial alignment model is established based on Lie group description, and a variational Bayesian Lie group filtering algorithm is proposed to process various errors in the alignment model. The experiment conducted on a turntable device proves the feasibility of the algorithm, which can be used as a self-alignment method for low-precision SINS. SUMMARY

[0006] The self-alignment algorithm of low-precision SINS in the shaking state has high research significance and application value. Since the carrier is easily affected by various interference factors during the initial alignment process, the effectiveness of the algorithm is also higher. The purpose of the application is to solve the problems existing in the current low-precision SINS self-alignment method: (1) The application introduces a deep learning method to design a neural network structure for calibration and compensation of low-precision SINS measurement errors, which can improve the measurement accuracy. (2) The application describes the initial alignment matrix by Lie group, which avoids the singular value problem of Euler angle method and the nonlinearity and non-uniqueness problem of quaternion method, and can be used for self-alignment at any initial angle.

[0007] The deep learning assisted variational Bayesian Lie group filtering self-alignment method for low-precision SINS is implemented by the following steps:

[0008] Step (1): The SINS (SINS) performs system preheating preparation, starts the system, and obtains the longitude λ, latitude L, and local gravity acceleration projection g in the navigation system of the carrier position n Basic information, collect the rotation angular rate information of the carrier system relative to the inertial system output by the gyroscope in the inertial measurement unit (IMU) in the carrier system And the acceleration information f of the carrier system acceleration meter output b .

[0009] Step (2): Use the sliding window technology to divide the gyroscope measurement data into time series data sets, and use the GRU-based neural network model created by the application to compensate the gyroscope measurement data errors.

[0010] The application designs an end-to-end neural network model based on GRU, which takes the original measurement data of the gyroscope as input and outputs the data after error compensation. The system consists of three core parts: data preprocessing, neural network model, and loss function.

[0011] In the data preprocessing stage, first, the data standardization processing is performed, which normalizes all data based on the mean and standard deviation of the original data, ensuring that all input data is within the same scale range. Subsequently, the sliding window technique is used to divide the standardized data into time series data sets. Given the time-dependent nature of gyroscope errors and their cumulative characteristics, the choice of window size must consider both error characteristics and computational efficiency. The present invention selects a window size of 10 and sets the sliding step size to 1. The continuous measurement data of the gyroscope is divided into multiple time series sequences, with the sequence form being:

[0012] s=[x1,x2,x3…,x N ](N=10)#(1)

[0013] where x i (i=1,2…N) represents the measured angular velocity of the gyroscope's three axes, and the label of each data set is the 11th data y N+1 collected by a high-precision device, thereby constructing a time series data set suitable for neural network training.

[0014] The core neural network part uses GRU to build an end-to-end neural network. The measured data of the gyroscope is directly used as the network input, and the output is the gyroscope data after prediction and error compensation. The internal mechanism of the GRU network can deeply mine the complex error patterns hidden in the gyroscope measurement data and automatically perform efficient error compensation. The estimation of the gyroscope error-free data is represented as:

[0015]

[0016] where is the measured angular velocity of the gyroscope, is the angular velocity estimate output by the neural network, and f(·) is a function defined by the neural network.

[0017] The loss function is used to measure the accuracy of the prediction results by calculating the deviation or difference between the predicted error-free gyroscope data and the reference data, quantifying the prediction performance of the neural network model. During the training process, the loss function can monitor and evaluate the prediction accuracy of the model in real time, and optimize and adjust the model parameters through the backpropagation algorithm to ensure that the model can more accurately capture the error patterns of the gyroscope and output more accurate error-free measurement data. The loss function is defined as:

[0018]

[0019] where is the predicted value output by the neural network, and y is the corresponding data label.

[0020] Step (3): Preprocessing the error-compensated data, and establishing a linear alignment system model based on Lie group differential equation.

[0021] The coordinate system in the detailed description of the method is defined as follows:

[0022] The earth-centered coordinate system e is selected with the center of the earth as the origin, the X-axis is located in the equatorial plane and points to the prime meridian from the center of the earth, the Z-axis points to the geographic north pole from the center of the earth, and the X-axis, the Y-axis and the Z-axis form a right-handed coordinate system and rotate with the earth rotation;

[0023] The earth-centered inertial coordinate system i is selected with the center of the earth as the origin, the X-axis is located in the equatorial plane and points to the vernal equinox from the center of the earth, the Z-axis points to the geographic north pole from the center of the earth, and the X-axis, the Y-axis and the Z-axis form a right-handed coordinate system;

[0024] The navigation coordinate system n is selected as the geographic coordinate system in the method, with the center of gravity of the carrier as the origin and aligned with the east-north-up coordinate axes, the X-axis coincides with the east direction (E), the Y-axis coincides with the north direction (N), and the Z-axis coincides with the up direction (U);

[0025] The carrier coordinate system b represents the coordinate system in which the output of the inertial sensor in the strapdown inertial navigation system is located, with the center of gravity of the carrier as the origin, the X-axis, the Y-axis and the Z-axis respectively point to the right along the carrier transverse axis, point to the front along the longitudinal axis, and point to the up along the vertical axis;

[0026] The initial navigation coordinate system n(0) represents the navigation coordinate system when the strapdown inertial navigation system is started and remains stationary relative to the inertial space during the entire alignment process;

[0027] The initial carrier coordinate system b(0) represents the carrier coordinate system when the strapdown inertial navigation system is started and remains stationary relative to the inertial space during the entire alignment process;

[0028] The error navigation coordinate system n' is obtained by the attitude estimation algorithm.

[0029] Based on the properties of Lie group and the output of low-precision SINS, an initial alignment model based on Lie group description is established:

[0030] According to the characteristics of the strapdown inertial navigation system, the alignment problem in the motion state can be converted into the attitude estimation problem of the carrier, the attitude transformation matrix represents the rotation between the navigation coordinate system n and the carrier coordinate system b, this matrix is a 3x3 orthogonal matrix and the determinant is equal to 1, which exactly meets the properties of the three-dimensional special orthogonal group SO(3) in Lie group, and constitutes the three-dimensional rotation group SO(3):

[0031]

[0032] where R ∈ SO(3) denotes an element in the three-dimensional rotation group SO(3) used to represent the attitude transformation matrix, denotes a 3x3 vector space, the superscript T denotes the transpose of a matrix, I denotes a three-dimensional identity matrix, and det(R) denotes the determinant of the matrix R;

[0033] The alignment problem in the sway state is converted into the estimation problem of the attitude transformation matrix R of the body described by the Lie group. According to the real-time attitude matrix decomposition chain rule based on the Lie group description, the attitude matrix to be solved is decomposed into three matrix products in the time domain: The decomposition in the time domain is in the form of three matrix products:

[0034]

[0035] where t denotes time, denotes the attitude matrix of the initial navigation coordinate system relative to the navigation coordinate system at time t, and the initial attitude matrix denotes the attitude matrix of the initial body coordinate system relative to the initial navigation coordinate system, denotes the attitude matrix of the body coordinate system at time t relative to the initial body coordinate system;

[0036] According to the kinematic characteristics and the Lie group differential equation, the attitude matrix and The update differential equation changing with time is:

[0037]

[0038] where denotes the attitude matrix of the initial body coordinate system relative to the current body coordinate system, denotes the projection of the rotation angular rate of the navigation coordinate system relative to the inertial coordinate system in the navigation coordinate system, denotes the projection of the rotation angular rate of the body coordinate system relative to the inertial coordinate system output by the gyroscope in the body coordinate system, and the symbol (·x) denotes the operation of converting a three-dimensional vector into an anti-symmetric matrix, and the operation rule is as follows:

[0039]

[0040] The iterative update equations of the attitude matrices and can be obtained by discretizing formulas (6) and (7):

[0041]

[0042] According to formulas (5)-(10), and can be calculated in real time from the IMU sensor data, and the solution of Only need The value of represents the initial attitude matrix, which does not change with time, and is a constant attitude matrix; therefore, the solution of the attitude matrix in the motion state during the alignment process is converted into the solution of the initial attitude matrix based on Lie group;

[0043] The sway base does not exist in the translation of the body, so the IMU directly measures the gravity acceleration under the carrier system, and the observation equation is established through the gravity:

[0044]

[0045] where g b represents the gravity acceleration under the carrier system, and g n represents the gravity acceleration under the navigation coordinate system.

[0046] Considering the influence of sensor output error, the relationship between the measured values of the gyroscope and the accelerometer and the true values is represented as:

[0047]

[0048] where represents the output of the gyroscope, represents the output of the accelerometer, δω represents the measurement noise of the gyroscope, and δg represents the measurement noise of the accelerometer.

[0049] Integrate both sides of formula (12):

[0050]

[0051] In summary, the initial attitude matrix is simply denoted as R, and the initial alignment model based on Lie group is represented as:

[0052]

[0053] Step (4): In order to solve the error problem in the initial alignment process of low-precision SINS, especially the state-related noise in model (16), a Lie group filtering method based on variational Bayes is proposed.

[0054] Since the initial attitude matrix R of the state quantity is a time-invariant matrix, the one-step prediction of the state is:

[0055]

[0056] The one-step prediction covariance is:

[0057] P k|k-1 = Pk-1|k-1 (18)

[0058] In the absence of error, β and the predicted vector This is the same vector in the n-system. However, due to estimation errors, the estimated rotation matrix... And the actual rotation matrix R k There are discrepancies between them, which should be compensated for using the following formula:

[0059]

[0060] Most existing methods are based on Lie group differential equations for compensation, and employ... or As the new information ε, there are some problems with this approach. According to the properties of Lie groups, ε should be the rotation Lie algebra corresponding to the compensated rotation matrix, but neither of these representations is correct. The corresponding rotation Lie algebra will cause a decrease in estimation accuracy. Therefore, based on the definition that the error Lie algebra is the rotation vector, the innovation ε can be obtained. k The precise definition of:

[0061] ε k =θl (20)

[0062]

[0063] Where θ represents the rotation angle of the rotation vector, and l represents the rotation axis of the rotation vector.

[0064] The measurement residual error matrix is ​​as follows:

[0065] S k =HP k|k-1 H T +B k (twenty three)

[0066] Among them, B k This refers to the measurement noise covariance matrix. Due to internal and external factors, sensors have significant errors, and the sensor output noise is coupled with state variables, making noise estimation difficult. In this case, using a single, fixed measurement noise covariance matrix will degrade the filter's performance.

[0067] Therefore, this method adjusts B using a variational Bayesian approach. k To adaptively estimate the statistical characteristics of measurement noise, a suitable prior distribution for the measurement noise needs to be selected. In Bayesian statistics, the Inverse Wissaud distribution can be used. e The Wishart (IW) distribution describes the distribution of the measurement noise covariance:

[0068]

[0069] where μ denotes the degree of freedom parameter, U denotes the scale matrix, d denotes the dimension of the measurement noise covariance matrix B and the scale matrix U, and Γ(·) is the gamma function.

[0070] The estimation of the unknown variable is actually an approximate approximation of the posterior distribution P(B k |α 1：k ) when the nonlinear posterior distribution is difficult to obtain. When the nonlinear posterior distribution is difficult to obtain, the variational Bayesian method can achieve an approximate approximation of P(B k |α 1：k ) by constructing a simple variational distribution. The KL divergence is used to measure the difference between two probability models:

[0071]

[0072] where Q(B k ) denotes the approximate posterior distribution.

[0073]

[0074] Let the second term after the equal sign of formula (26) be:

[0075]

[0076] The KL divergence between the two probability models is minimized, which is equivalent to maximizing L[Q(B k )]. Next, take L[Q(B k )] as the objective function. At the same time, the measurement noise covariance matrix has the spatial structure of non-negativity and symmetry. The concept of manifold is applied to process the specific geometric structure of the measurement noise covariance matrix, and the natural gradient with respect to the variational parameter is derived.

[0077] The natural gradient is a gradient that takes into account the geometric structure of the parameter space, and the natural gradient of the variational parameter is:

[0078]

[0079] where denotes the standard gradient, and the Fisher information matrix I F describes the local geometric structure of the variational parameter, and is defined as:

[0080]

[0081] Next, the natural gradients of the scale matrix U and the degree of freedom parameter μ are derived respectively. First, the gradient of the objective function is:

[0082]

[0083] where,

[0084]

[0085] The partial derivatives of the parameters in the variational distribution are respectively:

[0086]

[0087] where,

[0088]

[0089] The natural gradient of the pseudo-scale matrix U and the degree of freedom parameter μ is respectively calculated as:

[0090]

[0091] The updating process of the parameters is:

[0092]

[0093] R(·) represents the mapping from the vector space to the manifold space, which ensures that the updated value still remains on the manifold, and the specific calculation is:

[0094]

[0095] According to the properties of the IW distribution, if A ~ IW(A; γ, Ψ), when λ > d + 1:

[0096] E[A -1 ]=(λ-d-1)Ψ -1 (39)

[0097] Then the updated value of the measurement noise covariance matrix is represented as:

[0098]

[0099] In summary, the measurement noise covariance matrix can be estimated in real time and adaptively. The filter gain matrix is:

[0100] K k =P k|k-1 H k T S k -1 (41)

[0101] The updating equation of the attitude estimation is:

[0102]

[0103] The covariance matrix of the attitude estimation is:

[0104] Pk|k = (I - K k H k )P k|k-1 (43)

[0105] In each step of filtering, the is taken as the estimate of and combined with (5), (6) and (7), the optimal estimate of the attitude matrix at each discrete time can be obtained.

[0106] Step (5): Solve the attitude matrix required by the navigation system, so as to complete the alignment process in the sway state.

[0107] According to the attitude change matrix and information obtained in the previous steps, the navigation attitude matrix can be solved through formula (5), and the alignment of the low-precision SINS in the sway state is completed.

[0108] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0109] (1) The present application fuses deep learning method, and regards the measurement data of the gyroscope in MEMS IMU as a time sequence. On this basis, a neural network model based on GRU is designed and constructed, which is used for error compensation of the measurement data of the gyroscope in MEMS IMU, so as to improve the accuracy and reliability of the data.

[0110] (2) The present application designs a novel Lie group filtering algorithm based on variational Bayesian method, which is specially designed for various error problems existing in the self-alignment model based on the sway base, especially the state-dependent noise. The algorithm dynamically and adaptively adjusts the measurement noise covariance matrix, significantly reduces the interference of the measurement noise on the system performance, and improves the accuracy and stability of the self-alignment. BRIEF DESCRIPTION OF DRAWINGS

[0111] Figure 1 is a flow chart of a strapdown inertial navigation system.

[0112] Figure 2 is a neural network model diagram

[0113] Figure 3 is a comparison diagram of angular velocity error compensation.

[0114] Figure 4 is an alignment result diagram. DETAILED DESCRIPTION

[0115] The application is a deep learning assisted variational Bayesian Lie group filtering self-alignment method for low precision SINS, and the specific implementation steps of the application will be described in detail below in combination with the system flowchart of the application.

[0116] The beneficial effects of the application are as follows:

[0117] (1) Under the following experimental conditions, the gyro error compensation method based on deep learning is experimented:

[0118] In step (1), a three-axis turntable is used as an experimental platform, and MEMSIMU is installed on the platform, and the system is preheated. 15 minutes of static gyroscope and turntable angular velocity data are collected, 80% of which are used as a training data set, and the remaining 20% are used as a test data set.

[0119] In step (2), the constructed static training data set is input into the neural network model designed in the application, and the system model is as shown in Figure 2 , the model is trained. After the model training is completed, the application is performed on the static test data set to verify its performance. The result of the angular velocity error compensation is as shown in Figure 3 .

[0120] (2) Under the following experimental conditions, the variational Bayesian based Lie group filtering self-alignment method is experimented:

[0121] In step (1), the dynamic experimental conditions are set, the heading angle of the turntable is set to rotate at a constant speed of 5° / s in the range of 0° to 360°, the pitch angle is set to swing at a speed of 5° / s in the range of -80° to 80°, and the roll angle is kept stationary. Collect 15 minutes of gyroscope and turntable angular velocity data and turntable attitude change trajectory to construct a dynamic data set. The dynamic data after error compensation is used for alignment experiment.

[0122] In step (1), the initial geographic position is: east longitude 118°, north latitude 40°;

[0123] In step (1), the sensor output frequency is 200Hz;

[0124] In step (3), the earth rotation angular rate is 7.2921158e -5 rad / s;

[0125] In step (3), the time interval T is 0.01s;

[0126] In step (4), the initial value of the Lie group filtering algorithm is

[0127] The method experiment results are as follows:

[0128] The 600s experiment is performed, and the estimation error of the attitude angle is taken as the measurement index, and the experimental results are as shown in Figure 4 It can be seen from the figure that the pitch attitude is aligned at about 65s and converges to 0.05°; the roll attitude is aligned at about 55s and converges to 0.04°; and the heading attitude is aligned at about 139s and converges to 0.39°. From the experimental results, it can be known that the method can quickly and effectively complete the self-alignment task of the low-precision SINS in the shaking state.

[0129] The application proposes and implements a deep learning assisted variational Bayesian Lie group filtering self-alignment method for low-precision SINS. According to the measurement characteristics of MEMS IMU, a lightweight deep learning model is designed and implemented. The model does not need any external auxiliary equipment to calibrate and compensate the sensor error. The strategy can effectively learn the complex nonlinear error patterns existing in the low-precision SINS inertial sensor, thereby significantly improving the accuracy of the gyroscope measurement data. In addition, the application also designs an adaptive Lie group filtering algorithm to solve the state-dependent error problem in the self-alignment model on the shaking base. The algorithm uses the variational Bayesian method to adjust the measurement noise covariance matrix. The self-alignment method proposed by the application is suitable for low-precision SINS and effectively improves the stability and reliability of the navigation system.

[0130] The above description is only the preferred embodiment of the application and is not used to limit the application. It should be pointed out that for ordinary skilled persons in the art, several improvements and modifications can be made without departing from the principles of the application, and these improvements and modifications should be considered as the protection scope of the application.

Claims

1. A deep learning-assisted variational Bayesian Lie group filtering self-alignment method for low-precision SINS, characterized in that, This method is implemented through the following steps: Step (1): The SINS strapdown inertial navigation system performs system warm-up preparation, starts the system, and obtains the longitude of the carrier's location. ,latitude Projection of local gravitational acceleration in the navigation system Basic information: The projection of the rotational angular rate information of the carrier system relative to the inertial frame, output by the gyroscope in the inertial measurement unit (IMU), onto the carrier system. and the acceleration information of the load system output by the accelerometer ; Step (2): Use the sliding window technique to divide the gyroscope measurement data into time series datasets, and use a GRU-based neural network model to perform error compensation on the gyroscope measurement data; Design an end-to-end neural network model based on GRU, taking the raw measurement data of the gyroscope as input and outputting the data after error compensation; The neural network model consists of three core parts: data preprocessing, the neural network model, and the loss function. Step (3): Preprocess the error-compensated data and establish a linear alignment system model based on the Lie group differential equation. Step (4): To address the errors and state-related noise encountered during the initial alignment of low-precision SINS, a Lie group filtering method based on variational Bayes is proposed. Step (5): Solve for the attitude matrix required by the navigation system. This completes the alignment process while the object is swaying. Based on the attitude change matrix obtained in the previous steps , and Information is used to solve the navigation attitude matrix and complete the alignment of low-precision SINS under swaying conditions; Estimating unknown variables is actually estimating the posterior distribution. When a nonlinear posterior distribution is difficult to obtain, the variational Bayesian method can achieve an approximate approximation by constructing a simple variational distribution. An approximate approximation; KL divergence is used to measure the difference between two probability models: （25）， in, This represents an approximate posterior distribution; （26）， Let the second term after the equals sign in formula (26) be: （27）， Minimizing the KL divergence between two probability models is equivalent to... Maximum, then The objective function is defined as follows: The measurement noise covariance matrix has a non-negativity and symmetric spatial structure. The concept of manifolds is applied to handle the specific geometric structure of the measurement noise covariance matrix, and the natural gradient with respect to the variational parameters is derived. The natural gradient is a gradient that takes into account the geometric structure of the parameter space. The natural gradient of the variational parameter is: （28）， in, Represents the standard gradient, Fisher information matrix The local geometry describing the variational parameters is defined as: （29）， Next, we derive the natural gradients of the scaling matrix U and the degree-of-freedom parameter μ, respectively. First, the gradient of the objective function is: （30）， in, （31）， Take the partial derivatives with respect to the parameters in the variational distribution: （32）， in, , （33）， The natural gradients of the pseudo-scaling matrix U and the degree-of-freedom parameter μ are calculated as follows: （34）， （35）， The parameter update process is as follows: （36）， （37）， This represents a mapping from a vector space to a manifold space, ensuring that the updated values ​​remain on the manifold. The specific computation is as follows: （38）， According to the properties of the IW distribution, if ,when hour: （39）， The updated value of the measurement noise covariance matrix is ​​then expressed as: （40）， In summary, it can adaptively estimate the measurement noise covariance matrix in real time; the filter gain matrix is: （41）， The attitude estimation update equation is: （42）， The covariance matrix for attitude estimation is: （43）， In each step of filtering, As By combining the estimated values ​​with (5), (6) and (7), the attitude matrix at each discrete time step can be obtained. The optimal estimate.

2. The deep learning-assisted variational Bayesian Lie group filtering self-alignment method for low-precision SINS as described in claim 1, characterized in that, In step (2), during the data preprocessing stage, data standardization is first performed. Based on the mean and standard deviation of the original data, all data are normalized to ensure that all input data are within the same scale range. Subsequently, the standardized data is divided into time-series datasets using a sliding window technique. Given the time-series dependence and cumulative characteristics of gyroscope errors, the selection of the window size needs to comprehensively consider error characteristics and computational efficiency. The window size is selected as 10, and the sliding step size is set to 1. The continuous measurement data of the gyroscope is divided into multiple time-series sequences, with the sequence form as follows: （1）， in, This represents the measured angular velocity of the three axes of the gyroscope. The label for each data set indicates that it is the 11th data set acquired by the high-precision equipment. This allows for the construction of a time-series dataset suitable for neural network training. The core neural network component employs a GRU to construct an end-to-end neural network. It directly uses gyroscope measurement data as network input, while the output is the gyroscope data after prediction and error compensation. The internal mechanism of the GRU network can deeply mine the complex error patterns hidden in the gyroscope measurement data and automatically perform efficient error compensation. The estimation of error-free gyroscope data is represented as follows: （2）， in, It is the angular velocity measured by the gyroscope. It is the estimated angular velocity output by the neural network. It is a function defined by a neural network; The loss function measures the accuracy of prediction results. It quantifies the predictive performance of the neural network model by calculating the deviation or difference between the predicted error-free gyroscope data and the reference data. During training, the loss function monitors and evaluates the model's prediction accuracy in real time, optimizing and adjusting model parameters through backpropagation to ensure the model can more accurately capture the gyroscope's error patterns and output error-free measurement data closer to the true values. The loss function is defined as: （3）， in, It is the predicted value output by the neural network. These are the corresponding data tags.

3. The deep learning-assisted variational Bayesian Lie group filtering self-alignment method for low-precision SINS according to claim 1, characterized in that, In step (3), the coordinate system is defined as follows: The Earth coordinate system e is set with the Earth's center as the origin. The X-axis lies in the equatorial plane and points from the Earth's center to the Prime Meridian. The Z-axis points from the Earth's center to the geographic North Pole. The X-axis, Y-axis, and Z-axis form a right-handed coordinate system that rotates with the Earth's rotation. The geocentric inertial coordinate system i takes the Earth's center as the origin, with the X-axis located in the equatorial plane, pointing from the Earth's center to the vernal equinox, and the Z-axis pointing from the Earth's center to the geographic North Pole. The X-axis, Y-axis, and Z-axis constitute a right-handed coordinate system. The navigation coordinate system is n-system. In this method, the navigation coordinate system is selected as the geographic coordinate system, with the center of gravity of the vehicle as the origin, aligned with the East-North-Sky coordinate axis, the X-axis coincides with the East (E), the Y-axis coincides with the North (N), and the Z-axis coincides with the Sky (U). The carrier coordinate system b represents the coordinate system in which the output of the inertial sensor in the strapdown inertial navigation system is located. With the center of gravity of the carrier as the origin, the X-axis, Y-axis and Z-axis point to the right along the horizontal axis of the carrier, forward along the vertical axis and upward along the vertical axis, respectively. The initial navigation coordinate system n(0) represents the navigation coordinate system when the strapdown inertial navigation system is powered on and running, and remains stationary relative to inertial space throughout the alignment process; The initial carrier coordinate system b(0) represents the carrier coordinate system during the startup and operation of the strapdown inertial navigation system, and remains stationary relative to inertial space during the alignment process; Error navigation coordinate system The navigation coordinate system obtained by the attitude estimation algorithm; Combining the properties of Lie groups and the output of low-precision SINS, an initial alignment model based on Lie group description is established: Based on the characteristics of strapdown inertial navigation systems, the alignment problem under motion can be transformed into the attitude estimation problem of the vehicle. The attitude transformation matrix represents the rotation between the navigation coordinate system n and the vehicle coordinate system b. This matrix is ​​a 3×3 orthogonal matrix with a determinant of 1, which perfectly matches the three-dimensional special orthogonal group of Lie groups. The properties of these constitute a three-dimensional rotation group. : (4) ， in, This represents the three-dimensional rotation group used to represent the attitude transformation matrix. The elements in Let R represent a 3×3 vector space, where the superscript T denotes the transpose of the matrix, I denotes the three-dimensional identity matrix, and det(R) represents the determinant of matrix R. The alignment problem under swaying conditions is transformed into a Lie group describing the attitude transformation matrix of the download volume. The estimation problem; based on the chain rule of real-time attitude matrix decomposition based on Lie group description, the attitude matrix to be determined is... In the time domain, it can be decomposed into a product of three matrices: (5) ， in, Indicates time, Indicates the initial navigation coordinate system relative to Attitude matrix of the navigation coordinate system at any time, initial attitude matrix This represents the attitude matrix of the initial vehicle coordinate system relative to the initial navigation coordinate system. express The attitude matrix of the carrier coordinate system relative to the initial carrier coordinate system at any given time; Based on kinematic properties and Lie group differential equations, the attitude matrix... and The time-varying update differential equation is: (6) ， (7) ， in, This represents the attitude matrix of the initial carrier coordinate system relative to the current carrier coordinate system. This represents the projection of the rotational angular rate of the navigation coordinate system relative to the inertial coordinate system onto the navigation coordinate system. This represents the projection of the angular rate of rotation of the carrier coordinate system relative to the inertial coordinate system, as output by the gyroscope, onto the carrier coordinate system. The symbol is... This operation transforms a three-dimensional vector into a skew-symmetric matrix, and the rules are as follows: (8)， Discretizing equations (6) and (7) yields the attitude matrix. and Iterative update equation: (9)， (10)， From formulas (5)-(10), we can obtain that and The solution is obtained from real-time calculations based on IMU sensor data. Only The value; The attitude matrix represents the initial attitude matrix; the attitude matrix during alignment in motion. The problem of solving this problem is transformed into solving the initial pose matrix based on the Lie group description. The problem to be solved; Since the load body on the swaying base does not undergo translational motion, the IMU directly measures the gravitational acceleration under the load system, and the observation equation is established using gravity: （11）， （12）， in, This represents the acceleration due to gravity in a loaded system. This represents the acceleration due to gravity in the navigation coordinate system. Considering the influence of sensor output errors, the relationship between the measured values ​​and the true values ​​of the gyroscope and accelerometer is expressed as follows: （13）， in, This indicates the output of the gyroscope. This indicates the output of the accelerometer. This indicates the measurement noise of the gyroscope. Indicates the measurement noise of the accelerometer; Integrating both sides of equation (12): （14）， （15）， In summary, the initial attitude matrix Abbreviated as The initial alignment model based on the Lie group description is expressed as: （16）。 4. The deep learning-assisted variational Bayesian Lie group filtering self-alignment method for low-precision SINS according to claim 1, characterized in that, In step (4), since the initial attitude matrix of the state variable... It is a time-invariant matrix, and the state is predicted in one step as follows: （17）， The one-step prediction covariance is: （18）， In the absence of error and prediction vector For the same vector in the n-system; however, due to estimation errors, the estimated rotation matrix... and the actual rotation matrix There is a discrepancy between them, which can be compensated for using the following formula: （19）， Based on the definition that the error Lie algebra is the rotation vector, we obtain the new information. The precise definition of: （20）， （21）， （22）， in, This represents the angle of rotation of the vector. The axis of rotation represents the rotation vector; The measurement residual error matrix is ​​as follows: （23）， in, It measures the noise covariance matrix; it is adjusted using the variational Bayesian method. In Bayesian statistics, the inverse Witt-Warshall (IW) distribution is used to describe the distribution of the measurement noise covariance: （24）， in, Represents the degree of freedom parameter. Represents the scale matrix. Represents the measurement noise covariance matrix and scale matrix Dimensions It is a gamma function.

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