A gyro temperature drift intelligent modeling and compensation method based on meta learning

Abstract

This invention relates to a meta-learning-based intelligent modeling and compensation method for gyroscope temperature drift, belonging to the field of inertial sensing and intelligent navigation. Addressing the complex temperature drift characteristics of fiber optic gyroscopes, this invention first constructs a database of gyroscope temperature drift under different temperatures and input angular velocities. Secondly, in the offline stage, by combining least-squares analytical solutions with neural network learning residuals, gyroscope temperature drift is modeled as a structured function driven by both angular velocity features and environmental parameters. Then, a meta-learning strategy is used to train the feature extraction network and the parameterization network to obtain an initial model with generalization capabilities across temperature conditions. Finally, in the online stage, the model is rapidly adapted using a small sample size, and Kalman filtering is used to fine-tune the model parameters, achieving real-time estimation and compensation of gyroscope temperature drift. This invention improves the accuracy of gyroscope error estimation and compensation in complex environments, effectively enhancing the navigation performance of inertial navigation systems.

Description

Technical Field

[0001] This invention belongs to the field of inertial navigation and intelligent sensing, and relates to a meta-learning-based intelligent modeling and compensation method for gyroscope temperature drift. It realizes adaptive estimation and compensation of fiber optic gyroscope temperature drift under different ambient temperatures, thereby improving the navigation performance of inertial navigation systems in complex dynamic temperature environments. Background Technology

[0002] Fiber optic gyroscopes, as angular velocity sensors based on the Sagnac effect, have been widely used in inertial navigation fields such as autonomous driving and marine mapping due to their significant advantages, including being all-solid-state, having no moving parts, fast startup, and a large dynamic range. However, fiber optic gyroscopes are extremely sensitive to changes in ambient temperature. The thermal expansion and contraction of the fiber optic ring, the Schuylkov effect, and the thermal sensitivity of optical components can cause significant zero-bias drift and scaling factor errors. This temperature drift is nonlinear, time-varying, and hysteretic; without accurate compensation, it will accumulate over time and lead to a severe decrease in navigation accuracy. Therefore, establishing a high-precision temperature drift model and performing real-time compensation is a key technology for improving the performance of fiber optic gyroscopes.

[0003] Existing temperature drift compensation methods are mainly divided into two categories: one is the traditional physical modeling method, which usually uses polynomial fitting or temperature gradient models and determines the model coefficients using the least squares method. This type of method has clear physical meaning and low computational cost, but it is difficult to accurately characterize complex nonlinear features; the other is the data-driven method based on neural networks. This type of method has strong fitting ability, but it has shortcomings in practical applications, such as insufficient generalization ability, lack of physical constraints and interpretability, and weak online adaptive ability.

[0004] Existing research has proposed several improvement methods. For example, Chinese patent CN114254487B proposes a method based on piecewise polynomial fitting. This method uses wavelet thresholding for noise reduction preprocessing to establish a piecewise compensation model with temperature change and temperature gradient as independent variables, and then calculates the coefficients using the least squares method. While this method is computationally fast and easy to implement, its model structure is fixed (mainly relying on the cubic and gradient terms of temperature), limiting its ability to fit high-order nonlinearities or drift components with complex hysteresis characteristics. Chinese patent CN103499345B discloses a compensation method based on wavelet analysis and a BP neural network, which uses wavelets to separate the trend term and then uses a BP network to fit the temperature trend. However, BP neural networks suffer from slow convergence and are prone to getting trapped in local minima. Furthermore, this method is purely data-driven and heavily relies on the distribution of a specific dataset; when the test and training environments differ significantly, the model's generalization ability is poor.

[0005] Therefore, designing a drift compensation method that retains the stability and interpretability of the physical model, possesses the nonlinear fitting capability of deep learning, and can adapt to different temperature environments is a technical challenge that urgently needs to be solved in the field of inertial navigation. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention proposes a meta-learning-based intelligent modeling and compensation method for gyroscope temperature drift, constructing a database of gyroscope temperature drift under different temperatures and input angular velocities. In the offline stage, by combining least-squares analytical solutions with neural network learning residuals, gyroscope temperature drift is modeled as a structured function driven by both angular velocity features and environmental parameters. A meta-learning strategy is employed to train the feature extraction network and the parameterization network to obtain an initial model with generalization capabilities across temperature conditions. In the online stage, the model is rapidly adapted using limited sample data, and Kalman filtering is used to fine-tune the model parameters, achieving real-time estimation and compensation of gyroscope temperature drift.

[0007] To achieve the above objectives, the technical solution adopted by this invention is as follows: a method for intelligent modeling and compensation of gyroscope temperature drift based on meta-learning, the implementation steps of which are as follows:

[0008] Step 1: Construct a gyroscope temperature drift modeling database, specifically implemented as follows:

[0009] First, the output angular velocity of the three-axis gyroscope was collected under different temperature and input angular velocity conditions. and temperature variables ;

[0010] Before constructing the temperature drift modeling database, the raw temperature data and gyroscope output angular velocity data are processed by moving average to suppress high-frequency noise interference; then the gyroscope output angular velocity and the set input angular velocity are... The difference is used to obtain the corresponding temperature drift data. Based on smoothed temperature data, environmental characteristic parameters are constructed, including temperature, temperature square term, temperature cube term, and temperature gradient; angular velocity data is output from a smoothed three-axis gyroscope. With the constructed environmental characteristic parameters As input features to the model, the corresponding three-axis gyroscope temperature drift As output labels, construct gyroscope temperature drift modeling samples;

[0011] Secondly, in order to achieve cross-temperature generalization, this invention divides the database according to temperature ranges. The task consists of several independent subtasks with varying distributions. Each subtask corresponds to all rotational speed data at a specific temperature point or within a narrow temperature range. Within each subtask, the samples are further divided into an adaptation set and a query set. The adaptation set is randomly selected from the current temperature task. The sample set consists of 100 sample points; the query set is formed by sampling from the remaining sample points in the subtask.

[0012] Finally, the input features and output labels are standardized to eliminate the influence of different units on the model training process, thus completing the construction of the gyroscope temperature drift modeling database.

[0013] Step 2: Establish analytical solutions containing least squares. Learning residuals with neural networks The hybrid model represents the gyroscope temperature drift as a structured function driven by both angular velocity and environmental parameters, as specifically implemented below:

[0014] Establish a hybrid model that incorporates the least squares analytical solution and the residuals learned by the neural network:

[0015] ;

[0016] Among them, feature extraction network Angular velocity output by gyroscope As input, the output is the drift characteristics related to angular motion; based on the angular motion characteristics and temperature drift observations, the analytical solution of the drift parameters is obtained using the least squares method. ; Parameterized network Based on environmental parameters As input, the output is used to correct the residuals of the analytical solution.

[0017] This enables the modeling of gyroscope temperature drift as a structured function driven by the separation of angular motion features and environmental features, and combines the least squares analytical solution with neural network residual learning.

[0018] Step 3: In the offline phase, design a meta-learning strategy for the feature extraction network. With parameterized networks Training is performed to obtain an initial model with generalization ability across temperature conditions, specifically implemented as follows:

[0019] a) Inner loop task adaptation: Sampling from the task distribution includes The fitness set of each sample is used to output angular motion features through a feature extraction network. Combined with temperature drift observations First, the analytical benchmark solution of the drift parameters is calculated using the least squares method. :

[0020] ;

[0021] Using a parameterized network to predict residual parameters based on environmental characteristics Construct the final drift parameter estimates:

[0022] ;

[0023] Based on the adaptation set, the parameters of the parameterized network are fine-tuned using gradient descent to minimize the inner loop loss function. The inner loop loss function includes a mean squared error term and a normalized residual regularization term:

[0024] ;

[0025] The first term is the mean squared error, and the second term is the normalized residual regularization term, used to constrain the magnitude of the residual parameters relative to the analytical benchmark solution. Describing the Frobenius norm, This is the regularization coefficient for the inner loop. It is a tiny amount;

[0026] b) External circulation joint update:

[0027] Using a fine-tuned parameterized network, inference and prediction are performed on the query set. First, a feature extraction network outputs features, and then the least-squares analytical solution for the training set is computed. To prevent numerical divergence, we normalize and truncate the values:

[0028] when hour;

[0029] in, This is a globally preset upper limit threshold for amplitude. Then, it is combined with the residual output from the parameterized network. The final drift parameter estimate is obtained. and the final parameters Apply a global threshold constraint:

[0030] when hour;

[0031] In a single training iteration, multiple sampled subtasks are traversed, and the single-task outer loop loss is calculated based on the query set for each subtask. The losses of all sampled tasks are then summed and averaged to construct a global meta-loss function.

[0032] ;

[0033] in The first term represents the prediction mean square error, and the second term represents the soft constraint regularization term for the residual parameters. This is the regularization coefficient for the outer loop;

[0034] Finally, the gradient is calculated based on the meta-loss function, and the parameters of the feature extraction network and the parameterization network are jointly updated.

[0035] Step 4: In the online phase, use a small amount of sample data to test the parameterized network. In-task adaptive updates are performed, and the temperature drift parameters are corrected using the least-squares analytical solution. The obtained temperature drift parameters are used as initial values ​​to introduce a Kalman filter for online estimation and fine-tuning of the drift parameters, achieving real-time estimation and compensation of gyroscope temperature drift. The specific implementation is as follows:

[0036] a) In-task adaptation

[0037] Collect a small number of adaptive samples under the current operating conditions and calculate the least-squares analytical solution of the drift parameters. The parameterized network is then fine-tuned using gradient descent with adaptive samples to obtain the adapted residual parameters. .right Apply a hard constraint on the relative amplitude if its norm exceeds preset ratio Then, scaling and truncation will be performed:

[0038] when hour;

[0039] Then synthesize parameters And by applying a global threshold constraint, the drift parameter estimates are obtained. .

[0040] b) Online estimation and fine-tuning of the Kalman filter;

[0041] A Kalman filter for the drift parameter is established, and the state equation and measurement equation are defined as follows:

[0042] ; ;

[0043] in, for The drift parameters to be estimated at time (i.e., the aforementioned drift parameters) Expanded column vectors); for Real-time feature vectors output by the feature extraction network at each step The constructed observation matrix; for The temperature drift measurement at any given moment is obtained by subtracting the reference angular velocity provided by the auxiliary sensor from the angular velocity output by the gyroscope at the current moment. For process noise, its covariance matrix is ​​denoted as... , For measuring noise, its covariance matrix is ​​denoted as... .

[0044] The drift parameter estimates obtained in step a) The state estimation vector assigned to the Kalman filter This serves as the initial state for online estimation; simultaneously, the state covariance matrix is ​​initialized. Process noise covariance matrix and measurement noise covariance matrix The Kalman filtering process is as follows:

[0045] ; ; ; ; ;

[0046] in, This indicates a one-step prediction of the state; Represents the filter gain matrix; This represents the one-step prediction error covariance matrix; This represents the estimation error covariance matrix. The drift parameters are estimated and fine-tuned online using a Kalman filter, and the fine-tuned drift parameters are then used as the output. With real-time feature vectors Perform inner product calculations to determine the final temperature drift prediction value and compensate the gyroscope output in real time.

[0047] Compared with existing technologies, the present invention has the following advantages:

[0048] (1) Existing methods for compensating temperature drift in fiber optic gyroscopes often struggle to balance model interpretability and nonlinear fitting capabilities, and their generalization performance deteriorates significantly when applied across temperature ranges. To address this issue, this invention proposes a structured meta-learning modeling method based on physical mechanism constraints. This method organically couples prior physical knowledge with the advantages of data-driven modeling to construct a structured drift model; and utilizes a two-layer optimization strategy of meta-learning to obtain an initial model with generalization capabilities across temperature conditions. This approach not only significantly improves the model's rapid adaptation capability across different temperature ranges but also enhances its interpretability and stability.

[0049] (2) This invention proposes a composite drift estimation strategy that integrates prior prediction and online correction, organically combining a structured meta-learning network with a Kalman filter. Existing technologies typically rely solely on network output or filtering algorithms, making it difficult to simultaneously address complex nonlinearities and dynamic temperature drift. This invention utilizes a network model to provide prior drift prediction and employs a Kalman filter to fuse real-time measurement information for online estimation and dynamic fine-tuning of the prediction results. This collaborative mechanism achieves real-time closed-loop correction of temperature drift errors, significantly improving the navigation accuracy of fiber optic gyroscopes under complex dynamic conditions. Attached Figure Description

[0050] Figure 1 This is a flowchart of a method for intelligent modeling and compensation of gyroscope temperature drift based on meta-learning, as described in this invention.

[0051] Figure 2 This shows how the meta-loss function changes with the number of iterations during offline training.

[0052] Figure 3 The curves show a comparison of the temperature drift prediction errors of the three methods. Detailed Implementation

[0053] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0054] The method of this invention is specifically implemented as follows:

[0055] Step 1: Construct a gyroscope temperature drift modeling database, specifically implemented as follows:

[0056] First, the output angular velocity of the three-axis gyroscope was collected under different temperature and input angular velocity conditions. and temperature variables ;

[0057] Before constructing the temperature drift modeling database, the raw temperature data and gyroscope output angular velocity data are processed by moving average to suppress high-frequency noise interference; then the gyroscope output angular velocity and the set input angular velocity are... The difference is used to obtain the corresponding temperature drift data. Based on smoothed temperature data, environmental characteristic parameters are constructed, including temperature, temperature square term, temperature cube term, and temperature gradient; angular velocity data is output from a smoothed three-axis gyroscope. With the constructed environmental characteristic parameters As input features to the model, the corresponding three-axis gyroscope temperature drift As output labels, construct gyroscope temperature drift modeling samples;

[0058] Secondly, in order to achieve cross-temperature generalization, this invention divides the database according to temperature ranges. The task consists of several independent subtasks with varying distributions. Each subtask corresponds to all rotational speed data at a specific temperature point or within a narrow temperature range. Within each subtask, the samples are further divided into an adaptation set and a query set. The adaptation set is randomly selected from the current temperature task. The sample set consists of 100 sample points; the query set is formed by sampling from the remaining sample points in the subtask.

[0059] Finally, the input features and output labels are standardized to eliminate the influence of different units on the model training process, thus completing the construction of the gyroscope temperature drift modeling database.

[0060] Step 2: Establish analytical solutions containing least squares. Learning residuals with neural networks The hybrid model represents the gyroscope temperature drift as a structured function driven by both angular velocity and environmental parameters, as specifically implemented below:

[0061] Establish a hybrid model that incorporates the least squares analytical solution and the residuals learned by the neural network:

[0062] ;

[0063] Among them, feature extraction network Angular velocity output by gyroscope As input, the output is the drift characteristics related to angular motion; based on the angular motion characteristics and temperature drift observations, the analytical solution of the drift parameters is obtained using the least squares method. ; Parameterized network Based on environmental parameters As input, the output is used to correct the residuals of the analytical solution.

[0064] This enables the modeling of gyroscope temperature drift as a structured function driven by the separation of angular motion features and environmental features, and combines the least squares analytical solution with neural network residual learning.

[0065] Step 3: In the offline phase, design a meta-learning strategy for the feature extraction network. With parameterized networks Training is performed to obtain an initial model with generalization ability across temperature conditions, specifically implemented as follows:

[0066] a) Inner loop task adaptation: Sampling from the task distribution includes The fitness set of each sample is used to output angular motion features through a feature extraction network. Combined with temperature drift observations First, the analytical benchmark solution of the drift parameters is calculated using the least squares method. :

[0067] ;

[0068] Using a parameterized network to predict residual parameters based on environmental characteristics Construct the final drift parameter estimates:

[0069] ;

[0070] Based on the adaptation set, the parameters of the parameterized network are fine-tuned using gradient descent to minimize the inner loop loss function. The inner loop loss function includes a mean squared error term and a normalized residual regularization term:

[0071] ;

[0072] The first term is the mean squared error, and the second term is the normalized residual regularization term, used to constrain the magnitude of the residual parameters relative to the analytical benchmark solution. Describing the Frobenius norm, This is the regularization coefficient for the inner loop. It is a tiny amount;

[0073] b) External circulation joint update:

[0074] Using a fine-tuned parameterized network, inference and prediction are performed on the query set. First, a feature extraction network outputs features, and then the least-squares analytical solution for the training set is computed. To prevent numerical divergence, we normalize and truncate the values:

[0075] when hour;

[0076] in, This is a globally preset upper limit threshold for amplitude. Then, it is combined with the residual output from the parameterized network. The final drift parameter estimate is obtained. and the final parameters Apply a global threshold constraint:

[0077] when hour;

[0078] In a single training iteration, multiple sampled subtasks are traversed, and the single-task outer loop loss is calculated based on the query set for each subtask. The losses of all sampled tasks are then summed and averaged to construct a global meta-loss function.

[0079] ;

[0080] in The first term represents the prediction mean square error, and the second term represents the soft constraint regularization term for the residual parameters. This is the regularization coefficient for the outer loop;

[0081] Finally, the gradient is calculated based on the meta-loss function, and the parameters of the feature extraction network and the parameterization network are jointly updated.

[0082] Step 4: In the online phase, use a small amount of sample data to test the parameterized network. In-task adaptive updates are performed, and the temperature drift parameters are corrected using the least-squares analytical solution. The obtained temperature drift parameters are used as initial values ​​to introduce a Kalman filter for online estimation and fine-tuning of the drift parameters, achieving real-time estimation and compensation of gyroscope temperature drift. The specific implementation is as follows:

[0083] a) In-task adaptation;

[0084] Collect a small number of adaptive samples under the current operating conditions and calculate the least-squares analytical solution of the drift parameters. The parameterized network is then fine-tuned using gradient descent with adaptive samples to obtain the adapted residual parameters. .right Apply a hard constraint on the relative amplitude if its norm exceeds preset ratio Then, scaling and truncation will be performed:

[0085] when hour;

[0086] Then synthesize parameters And by applying a global threshold constraint, the drift parameter estimates are obtained. .

[0087] b) Online estimation and fine-tuning of the Kalman filter;

[0088] A Kalman filter for the drift parameter is established, and the state equation and measurement equation are defined as follows:

[0089] ; ;

[0090] in, for The drift parameters to be estimated at time (i.e., the aforementioned drift parameters) Expanded column vectors); for Real-time feature vectors output by the feature extraction network at each step The constructed observation matrix; for The temperature drift measurement at any given moment is obtained by subtracting the reference angular velocity provided by the auxiliary sensor from the angular velocity output by the gyroscope at the current moment. For process noise, its covariance matrix is ​​denoted as... , For measuring noise, its covariance matrix is ​​denoted as... .

[0091] The drift parameter estimates obtained in step a) The state estimation vector assigned to the Kalman filter This serves as the initial state for online estimation; simultaneously, the state covariance matrix is ​​initialized. Process noise covariance matrix and measurement noise covariance matrix The Kalman filtering process is as follows:

[0092] ; ; ; ; ;

[0093] in, This indicates a one-step prediction of the state; Represents the filter gain matrix; This represents the one-step prediction error covariance matrix; This represents the estimation error covariance matrix. The drift parameters are estimated and fine-tuned online using a Kalman filter, and the fine-tuned drift parameters are then used as the output. With real-time feature vectors Perform inner product calculations to determine the final temperature drift prediction value and compensate the gyroscope output in real time.

[0094] Example:

[0095] To verify the effectiveness of the method proposed in this invention, a temperature drift acquisition and compensation experiment was designed across the entire temperature range, and the experimental results are presented.

[0096] The fiber optic gyroscope to be tested was fixed on a temperature-controlled turntable. The temperature test range was set from -20℃ to +60℃, including various operating conditions such as temperature rise and constant temperature hold. Simultaneously, the gyroscope was designed to rotate around the z-axis at different angular velocities (…). , The gyroscope rotates. It collects the raw output angular velocity data (50Hz) from the gyroscope, temperature data from the internal temperature sensor, and high-precision angular velocity information from the encoder.

[0097] Because the fiber optic gyroscope output contains high-frequency quantization noise, the raw data is first preprocessed using a moving average filter. Then, the acquired long-sequence data is divided into multiple sub-tasks according to different temperature ranges (each range is 10°C). For each sub-task, data is randomly sampled... A subset of sample points is used as the adaptation set for inner loop updates and to simulate fast adaptation during the online phase. The remaining data is used as the query set for evaluating model performance and outer loop updates. Model training uses the Adam optimizer with a total of 100 iterations. The learning rate is , The learning rate is The inner loop iterates 10 steps for each task, with a learning rate of [missing information]. The global amplitude threshold is set to 10, and the residual relative ratio is set to 0.05.

[0098] Figure 2 This demonstrates how the global meta-loss function changes with the number of iterations during offline meta-training. It can be seen that the loss function decreases rapidly in the early stages of training and then stabilizes after approximately 80 iterations, proving that the model training has good convergence. The model with epoch=80 is selected and validated on the test set. Figure 3 The temperature drift prediction error comparison curves of the three methods on test set 6 are presented visually. Among them, the DAIML method and ECOA-MAML method showed large spikes and fluctuations at some sampling points. The prediction error fluctuation amplitude of the proposed method is significantly smaller than that of the comparison methods, indicating that it has higher robustness in dynamic temperature environments.

[0099] To quantify the performance of different error compensation methods, we compared them with the Domain Adversarial Invariant Meta-Learning Method (DAIML) and the Meta-Learning Method Based on Enhanced Long-Nosed Raccoon Optimization Algorithm (ECOA-MAML), and used the root mean square error (RMSE) as a metric. () is used as an evaluation indicator. Specifically defined as:

[0100] ;

[0101] in This represents the error estimate; This is the true value of the error; The data size represents the amount of data in the test set. Table 1 shows the statistical information on the prediction errors of the three methods across multiple test sets.

[0102] Table 1. Statistical information on residuals from error estimation using different methods

[0103] unit: The proposed method DAIML ECOA-MAML Test set 1 Test Set 2 Test Set 3 Test Set 4 Test Set 5 Test Set 6

[0104] Table 1 As a core metric, the performance of various error estimation and compensation methods was quantitatively evaluated on six different test sets. The results show that the proposed method performs better on these six test sets. All metrics are significantly better than the other two methods. Specifically, using test set 6 (50℃ environment, input angular velocity is...) For example, the method of the present invention... for Compared to the DAIML method It reduced by approximately 11.29%, compared to the ECOA-MAML method. This represents a reduction of approximately 17.66%. This fully validates that the meta-learning strategy constrained by physical mechanisms, combined with online fine-tuning of Kalman filtering, can significantly improve the temperature drift compensation accuracy of fiber optic gyroscopes under dynamic conditions.

[0105] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes will be obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method for intelligent modeling and compensation of gyroscope temperature drift based on meta-learning, characterized in that, Includes the following steps: Step 1: Construct a gyroscope temperature drift modeling database. Under different temperatures and different input angular velocities, collect the output angular velocities of the three-axis gyroscope. Environment variables and the corresponding temperature drift data ,in The three-axis gyroscope outputs angular velocity. This refers to the temperature of the three-axis gyroscope. and These represent the square term, cube term, and temperature gradient, respectively. This refers to the temperature-dependent drift error of a three-axis gyroscope. Step 2: Establish analytical solutions containing least squares. Learning residuals with neural networks The hybrid model represents the gyroscope temperature drift as a structured function driven by both angular velocity and environmental parameters. ; Step 3: In the offline phase, design a meta-learning strategy for the feature extraction network. With parameterized networks Training is performed to obtain an initial model that can generalize across temperature conditions; Step 4: In the online phase, use a small amount of sample data to test the parameterized network. In-task adaptive updates are performed, and the temperature drift parameters are corrected by combining the least squares analytical solution. The obtained temperature drift parameters are used as initial values ​​to introduce the Kalman filter, and the drift parameters are estimated and fine-tuned online to realize the real-time estimation and compensation of gyroscope temperature drift.

2. The intelligent modeling and compensation method for gyroscope temperature drift based on meta-learning as described in claim 1, characterized in that, In step 1, a gyroscope temperature drift modeling database is constructed. First, the output angular velocity of the three-axis gyroscope is collected under different temperatures and different input angular velocities. and temperature variables ; Before constructing the temperature drift modeling database, the raw temperature data and gyroscope output angular velocity data are processed by moving average to suppress high-frequency noise interference; then the gyroscope output angular velocity and the set input angular velocity are... The difference is used to obtain the corresponding temperature drift data. Based on smoothed temperature data, environmental characteristic parameters are constructed, including temperature, temperature square term, temperature cube term, and temperature gradient; angular velocity data is output from a smoothed three-axis gyroscope. With the constructed environmental characteristic parameters As input features to the model, the corresponding three-axis gyroscope temperature drift As output labels, construct gyroscope temperature drift modeling samples; Secondly, the database is divided into temperature ranges. The task consists of several independent subtasks with varying distributions; each subtask corresponds to all rotational speed data at a specific temperature point or within a narrow temperature range; within each subtask, the samples are further divided into an adaptation set and a query set; the adaptation set is randomly selected from the current temperature task. The query set is composed of sample points; the query set is formed by sampling from the remaining sample points in the subtask. Finally, the input features and output labels are standardized to eliminate the influence of different units on the model training process, thus completing the construction of the gyroscope temperature drift modeling database.

3. The intelligent modeling and compensation method for gyroscope temperature drift based on meta-learning as described in claim 1, characterized in that, In step 2, the gyroscope temperature drift is represented as a structured function driven by both angular velocity and environmental parameters: ； Among them, feature extraction network by As input, the output is the drift characteristics related to angular motion; based on the angular motion characteristics and temperature drift observations, the analytical solution of the drift parameters is obtained using the least squares method. ; Parameterized network Based on environmental parameters As input, the output is a residual correction of the analytical solution; This enables the modeling of gyroscope temperature drift as a structured function driven by the separation of angular motion features and environmental features, and combines the least squares analytical solution with neural network residual learning.

4. The intelligent modeling and compensation method for gyroscope temperature drift based on meta-learning as described in claim 1, characterized in that, In step 3, during the offline phase, a meta-learning strategy is designed for the feature extraction network. With parameterized networks The training is performed as follows: a) Inner loop task adaptation: Sampling from the task distribution includes The fitness set of each sample is used to output angular motion features through a feature extraction network. Combined with temperature drift observations First, the analytical benchmark solution of the drift parameters is calculated using the least squares method. : ； Using a parameterized network to predict residual parameters based on environmental characteristics Construct the final drift parameter estimates: ； Based on the adaptation set, the parameters of the parameterized network are fine-tuned using gradient descent to minimize the inner loop loss function. The inner loop loss function includes a mean squared error term and a normalized residual regularization term: ； The first term is the mean squared error, and the second term is the normalized residual regularization term, used to constrain the magnitude of the residual parameters relative to the analytical benchmark solution. Describing the Frobenius norm, This is the regularization coefficient for the inner loop. It is a tiny amount; b) External circulation joint update: Using a fine-tuned parameterized network, inference and prediction are performed on the query set; firstly, the feature extraction network outputs features and the least-squares analytical solution of the training set is calculated. To prevent numerical divergence, we normalize and truncate the values: when hour, in, A globally preset upper limit threshold for amplitude; Then, the residual output by the parameterized network is combined The final drift parameter estimate is obtained. and the final parameters Apply a global threshold constraint: when hour, In a single training iteration, multiple sampled subtasks are traversed, and the single-task outer loop loss is calculated based on the query set for each subtask. The losses of all sampled tasks are then summed and averaged to construct a global meta-loss function. ； in The first term represents the prediction mean square error, and the second term represents the soft constraint regularization term for the residual parameters. This is the regularization coefficient for the outer loop; Finally, the gradient is calculated based on the meta-loss function, and the parameters of the feature extraction network and the parameterization network are jointly updated.

5. The intelligent modeling and compensation method for gyroscope temperature drift based on meta-learning as described in claim 1, characterized in that, Step 4 is implemented as follows: a) In-task adaptation; Collect a small number of adaptive samples under the current operating conditions and calculate the least-squares analytical solution of the drift parameters. The parameterized network is then fine-tuned using gradient descent with adaptive samples to obtain the adapted residual parameters. ;right Apply a hard constraint on the relative amplitude if its norm exceeds preset ratio Then, scaling and truncation will be performed: when hour; Then synthesize parameters And by applying a global threshold constraint, the drift parameter estimates are obtained. ; b) Online estimation and fine-tuning of the Kalman filter; A Kalman filter for the drift parameter is established, and the state equation and measurement equation are defined as follows: ； ； in, for The drift parameters to be estimated at any given time; for Real-time feature vectors output by the feature extraction network at each step The constructed observation matrix; for The temperature drift measurement at any given moment is obtained by subtracting the reference angular velocity provided by the auxiliary sensor from the angular velocity output by the gyroscope at the current moment. For process noise, its covariance matrix is ​​denoted as... , For measuring noise, its covariance matrix is ​​denoted as... ; The drift parameter estimates obtained in step a) The state estimation vector assigned to the Kalman filter This serves as the initial state for online estimation; simultaneously, the state covariance matrix is ​​initialized. Process noise covariance matrix and measurement noise covariance matrix The Kalman filtering process is as follows: ； in, This indicates a one-step prediction of the state; Represents the filter gain matrix; This represents the one-step prediction error covariance matrix; This represents the estimation error covariance matrix; the drift parameters are estimated and fine-tuned online using a Kalman filter, and the fine-tuned drift parameters are then used as output. With real-time feature vectors Perform inner product calculations to determine the final temperature drift prediction value and compensate the gyroscope output in real time.

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