Online error calibration method, device and system for hemispherical resonator gyroscope inertial navigation system and readable storage medium

Abstract

The invention discloses a hemispherical resonator gyroscope inertial navigation system error online calibration method, device and system and a readable storage medium. The method comprises the following steps: establishing a dynamic observation equation of a gain error and a misalignment angle error; adaptively extracting error features of different time scales, and constructing a high-dimensional feature vector; decoupling the gain error and the misalignment angle error to obtain an error estimation value; constructing a dynamic compensation matrix, and correcting and measuring the angular velocity in real time; an online self-correction mechanism of the error compensation model is designed, and a compensation matrix is dynamically adjusted to adapt to dynamic changes of errors; an adaptive time sequence regression model is introduced to predict an error long-term drift trend, and a nonlinear compensation method is combined to actively counteract an error accumulation effect; dynamically adjusting the optimization rate of the compensation matrix through stability analysis; and dynamically optimizing error model parameters based on convergence evaluation of error residual errors. According to the invention, the limitation of a traditional method in a dynamic environment, especially the coupling problem of a gain error and a misalignment angle error, is solved.

Description

Technical Field

[0001] The present invention relates to the field of navigation technology, and in particular to an online calibration method, device, system and readable storage medium for errors of a hemispherical resonant gyro inertial navigation system. Background Art

[0002] With the continuous advancement of modern navigation technology, inertial navigation systems (INS) are increasingly used in military, aerospace, navigation, unmanned driving and other fields. Inertial navigation systems rely on inertial sensors, such as accelerometers and gyroscopes, to monitor and estimate the motion state of objects in real time. Especially in high-precision applications, hemispherical resonant gyroscopes (HRGs), as an important inertial measurement unit, have gradually become a key component in the new generation of navigation systems due to their high measurement accuracy, stability and anti-interference capabilities.

[0003] The HRG measures the angular velocity of rotation by utilizing the relationship between angular velocity and frequency oscillation. Its working principle is based on laser interferometry technology and can provide very accurate angular velocity measurement. Therefore, the HRG is widely used in navigation tasks that require high precision and long-term stability. However, despite its widely recognized high-precision characteristics, there are still a series of challenges, among which the most prominent is the dynamic change of system errors. Due to the influence of various factors, such as temperature fluctuations, long-term operation, mechanical aging, etc., HRG will produce different types of errors, resulting in deviations in its measurement accuracy.

[0004] Among these errors, channel gain error and misalignment angle error are particularly important. Channel gain error mainly refers to the imbalance of sensitivity between various sensor channels, while misalignment angle error refers to the angle error caused by the slight deformation of the internal device of the gyroscope during long-term use or other environmental factors. These two errors not only affect the output of the gyroscope separately, but also couple with each other, resulting in more complex error characteristics.

[0005] Existing error calibration methods usually deal with these two types of errors separately, or rely on relatively static calibration methods, which makes the system's performance in dynamic environments unsatisfactory. Especially in application scenarios that require high precision and long-term stability, traditional calibration methods are limited in effect and cannot effectively deal with complex coupling errors in dynamic changes. Therefore, how to calibrate and compensate for gain error and misalignment angle error in real time and online has become a cutting-edge technical problem in the hemispherical resonant gyro inertial navigation system.

[0006] Therefore, a new online error calibration method is proposed to adapt to the changes of various dynamic errors in real time and compensate them through an adaptive adjustment mechanism, which is the key to improving the overall accuracy and stability of the navigation system. Summary of the invention

[0007] In order to solve the above problems, the present invention provides a method, device, system and readable storage medium for online calibration of errors of a hemispherical resonant gyro inertial navigation system.

[0008] To achieve the above purpose, the technical solution adopted by the present invention is as follows: A method for online calibration of hemispherical resonant gyro inertial navigation system errors, comprising: Step 1: Establish the dynamic observation equations of gain error and misalignment angle error through dynamic multi-scale error mapping; Step 2: Adopt a non-uniform feature extraction algorithm to adaptively extract error features of different time scales and construct a high-dimensional feature vector; Step 3: Decouple the gain error and the misalignment angle error using an adaptive coupled regression algorithm to obtain an error estimate. Step 4: Based on the error estimate, construct a dynamic compensation matrix to correct the measured angular velocity in real time; Step 5: Design an online self-correction mechanism for the error compensation model and dynamically adjust the compensation matrix to adapt to the dynamic changes of the error; Step 6: Introduce an adaptive time series regression model to predict the long-term drift trend of the error, and combine it with a nonlinear compensation method to actively offset the error accumulation effect; Step 7: Dynamically adjust the optimization rate of the compensation matrix through stability analysis; Step 8: Based on the convergence evaluation of the error residual, dynamically optimize the error model parameters.

[0009] Further: Step 1 comprises: Define different time scales to capture short-term dynamic error fluctuations, observe error gradual trends, and analyze long-term cumulative effects; A sliding calculation strategy of multi-scale time windows is constructed to smooth the angular velocity output by the hemispherical resonant gyroscope at each moment and obtain the angular velocity observation values ​​at different time scales. Calculate the multi-scale error gain factor, extract its dynamic characteristics by introducing the time series change rate of the gain error, and introduce the multi-scale misalignment angle error factor to measure the change trend of the misalignment angle error at different time scales and calculate its change rate; A nonlinear tensor error field model is constructed to project the error from the time scale space to the high-dimensional feature space, and a six-dimensional error feature vector containing the gain error and misalignment angle error characteristics is obtained; Based on the feature vector, the error mapping gradient field is defined to describe the variation trend of the error characteristics in time and scale; Based on the above calculation results, a dynamic multi-scale error observation equation is constructed.

[0010] Further: Step 2 includes: Design a time-scale adaptive sampling strategy; Under the time scale, introduce an adaptive sampling factor to dynamically adjust the sampling density according to the error variance; Perform nonlinear transformation on error data; use adaptive nonlinear transformation function to transform errors of different time scales according to the distribution characteristics of error data, enhance the expressiveness of features, and avoid the influence of outliers on modeling by compressing extreme error values; Calculate the statistical moments of the error characteristics; calculate the mean, variance, skewness, and kurtosis of the error at each time scale, construct an error feature vector containing these statistical characteristics, and further extract the statistical characteristics of the error; The error feature vector is orthogonally transformed and standardized, and an improved principal component analysis method is used to introduce a weighted orthogonal transformation of the error statistical moment to eliminate redundant information and correlation in the feature vector and enhance the independence of the feature. The transformed feature vectors are standardized to ensure that they have a uniform scale in different data segments, providing stability and consistency for subsequent error modeling and compensation.

[0011] Further: Step 3 comprises: Based on the relationship between the angular velocity measured by HRG and the true angular velocity, the nonlinear coupling relationship between the gain error and the misalignment angle error is defined, the coupling error mapping function is introduced, and the error observation model is constructed to provide a basis for subsequent decoupling; Adopting adaptive multi-kernel regression method, combined with historical training data points, an error decoupling model is constructed, and the kernel function weights are adjusted through multi-scale weighting strategy to achieve adaptive modeling of error characteristics at different time scales. Define the weight update rules and dynamically adjust the weight of the kernel function based on the regression loss function and learning rate to ensure that the model can adaptively adjust according to the changes in error characteristics and improve the error decoupling accuracy; By solving the regression equation, the estimated values ​​of the gain error and the misalignment angle error are calculated respectively, and the error residual is calculated to measure the decoupling accuracy; if the error residual exceeds the threshold, the kernel weight is adjusted and the model is retrained until the convergence condition is met; Adaptive Kalman filtering is used to dynamically adjust the filter gain according to the noise variance to eliminate high-frequency noise interference, further improve the stability of the error decoupling results, and provide a high-precision error estimate for subsequent error compensation.

[0012] Further: Step 4 includes: Calculate the gain error residual and the misalignment angle error residual to evaluate the accuracy of the current error compensation; Construct an error compensation equation and correct the measured angular velocity through a dynamic compensation matrix. The compensated angular velocity is obtained by subtracting the product of the error correction matrix and the dynamic weight matrix from the original measurement value. The error correction matrix is ​​used to independently compensate for the gain error and the misalignment angle error. Based on the error coupling residual, the compensation strength is adjusted dynamically. The weight of the dynamic weight matrix is ​​adjusted according to the size of the error residual. When the residual is large, the compensation strength is reduced to prevent over-compensation. When the residual is small, the compensation capability is enhanced to improve the system accuracy. The measured angular velocity is corrected by applying a dynamic compensation matrix to obtain the compensated angular velocity. The compensation matrix is ​​adaptively updated at each time step to ensure the accuracy and real-time performance of error compensation. A regularization term is introduced to prevent numerical instability, and the weights are dynamically updated according to the error coupling residual.

[0013] Further: Step 5 comprises: Calculate the error correction residual vector to measure the deviation between the measured data after error compensation and the ideal error model. If the error correction residual vector exceeds the preset threshold, it indicates that the error compensation model has deviations and needs to be self-corrected online. Based on the error correction residual vector, the compensation matrix is ​​corrected by using the incremental error update method. By adjusting the self-correction step size, the update rate of the compensation matrix is ​​controlled to dynamically track the error change trend. Design an adaptive step-size adjustment strategy to dynamically adjust the step size according to the degree of error compensation deviation. When the error deviation is large, increase the step size to speed up the convergence speed. When the error is stable, reduce the step size to avoid oscillation. The sliding window averaging method is introduced to average the compensation matrices at several past moments to smooth out the impact of short-term noise and enhance the stability of error compensation. A complete online self-correction closed loop is formed, including error correction residual calculation, dynamic compensation matrix update, adaptive step size adjustment and long-term trend optimization. The above process is repeated at each time step to ensure continuous self-optimization of the error compensation model.

[0014] Further: Step 6 comprises: Define the error drift state variable vector, including the real-time measurement value of the error and its instantaneous rate of change, which is used to describe the instantaneous state of the current error and serves as the input of the error drift prediction model; A recursive nonlinear regression model is used to recursively update the regression parameters based on the sliding window least squares optimization to predict the error change trend of the future steps; According to the predicted error drift trend, the error compensation matrix is ​​updated and nonlinear compensation coefficients are introduced to actively offset the long-term drift effect of the error; The online self-correction compensation is combined with the prediction compensation, and the final error compensation matrix is ​​constructed through the weighted fusion strategy; A closed-loop mechanism is formed, including real-time error drift state estimation, error drift trend prediction, nonlinear error compensation matrix update, and compensation strategy fusion. Error compensation is continuously optimized through closed-loop feedback.

[0015] Further: Step 7 comprises: Calculate the error correction gain matrix, which is used to measure the state change before and after error compensation. The gain matrix is ​​calculated by the error state variable vector at the current and previous moments, reflecting the effectiveness of error correction; The stability of error compensation is evaluated by the gain change rate. If the gain change rate continues to increase, it indicates that the error correction has a divergent trend. If the gain change rate oscillates within a certain range, it indicates that there is an overshoot phenomenon. Based on the gain change rate, a compensation adjustment factor is introduced to dynamically control the adjustment rate of the compensation matrix; the adjustment factor is calculated by adjusting the step size, stability threshold and sign function to ensure the adaptability of the compensation rate; According to the compensation adjustment factor, the compensation matrix is ​​dynamically optimized. When the gain change rate is too large, the compensation rate is reduced to avoid oscillation. When the gain change rate is too small, the compensation rate is accelerated to improve the system convergence. A closed-loop control mechanism is formed, including real-time calculation of the error correction gain matrix, evaluation of compensation stability, updating of the compensation matrix, and periodic evaluation of the compensation effect. The compensation strategy is dynamically adjusted through closed-loop feedback.

[0016] Further: Step 8 comprises: Define the error residual vector, which represents the residual error after compensation, and is calculated by the difference between the current measurement error and the error corrected by the dynamic compensation matrix; The residual convergence rate indicator is introduced to evaluate the convergence of the error model through the change trend of the Euclidean norm of the error residual vector; if the residual convergence rate continues to approach zero, it indicates that the error model converges well; if it exceeds the set threshold, the adaptive adjustment mechanism is triggered; Based on the outer product of the error residual and the error model prediction value, the error correction gain matrix is ​​dynamically adjusted; through the normalization of the learning step size and the error model norm, the error model parameters are optimized to gradually approach the true error characteristics; The error model is updated according to the adjusted error correction gain matrix to ensure continuous error compensation under different working conditions; A closed-loop feedback control system is formed, including error residual evaluation, adaptive adjustment triggering, dynamic adjustment of error model parameters and continuous iterative feedback.

[0017] Furthermore, the present invention also discloses an online calibration system for hemispherical resonant gyro inertial navigation system errors, comprising: Dynamic multi-scale error observation equation construction module: Through dynamic multi-scale error mapping, dynamic observation equations of gain error and misalignment angle error are established; Non-uniform error feature extraction module: uses a non-uniform feature extraction algorithm to adaptively extract error features of different time scales and construct a high-dimensional feature vector; Error decoupling module: uses adaptive coupled regression algorithm to decouple gain error and misalignment angle error to obtain error estimation value; Dynamic compensation matrix construction module: Based on the error estimation value, the dynamic compensation matrix is ​​constructed to correct the measured angular velocity in real time; Online self-correction mechanism establishment module: Design the online self-correction mechanism of the error compensation model and dynamically adjust the compensation matrix to adapt to the dynamic changes of the error; Error drift prediction and compensation module: Introduces an adaptive time series regression model to predict the long-term drift trend of the error, and combines it with a nonlinear compensation method to actively offset the error accumulation effect; Error compensation stability optimization module: dynamically adjusts the optimization rate of the compensation matrix through stability analysis; Error model adaptation module: Dynamically optimizes error model parameters based on convergence evaluation of error residuals.

[0018] One or more embodiments of this specification provide a device for online calibration of hemispherical resonant gyro inertial navigation system errors, the device comprising at least one processor and at least one memory; The at least one memory is used to store computer instructions; The at least one processor is used to execute at least part of the computer instructions to implement the online calibration method for the hemispherical resonant gyro inertial navigation system error.

[0019] One or more embodiments of the present specification provide a computer-readable storage medium, wherein the storage medium stores computer instructions. When a computer reads the computer instructions in the storage medium, the computer executes the online calibration method for the hemispherical resonant gyro inertial navigation system error.

[0020] Compared with the prior art, the present invention has the following technical advances: The present invention introduces the observation equation of dynamic multi-scale error mapping and the non-uniform error feature extraction algorithm, which can capture the changing trend of system errors under different working conditions in real time and dynamically. This design enables the error compensation system to update the gain error and misalignment angle error in a timely manner during actual operation without relying on static or preset calibration values. Compared with traditional error compensation methods, the system has stronger adaptability and real-time performance, can effectively cope with error fluctuations caused by environmental changes, and improves the stability and accuracy of the navigation system.

[0021] Traditional error calibration methods often compensate for gain error and misalignment angle error separately, ignoring the coupling effect between the two. My method directly models and compensates for the coupling relationship between gain error and misalignment angle error by introducing an adaptive coupling regression algorithm. By dynamically adjusting the parameters in the error model, this method can synchronously calibrate the two errors while the system is running, solving the complex coupling problem between them. This comprehensive compensation method significantly improves the error compensation accuracy of the hemispherical resonant gyroscope, especially in high-precision, high-dynamic change application scenarios, and can effectively reduce the decline in navigation accuracy caused by coupling errors.

[0022] By predicting the error drift trend and designing nonlinear compensation, the system can effectively predict and compensate for the error drift caused by long-term operation, temperature change and other factors. This nonlinear compensation mechanism based on error prediction can automatically adjust the compensation strategy when the system error presents nonlinear changes, thereby improving the accuracy and flexibility of compensation.

[0023] In summary, the present invention not only solves the limitations of traditional methods in dynamic environments, especially the coupling problem of gain error and misalignment angle error, but also improves the accuracy, stability and intelligence level of the hemispherical resonant gyro inertial navigation system through innovative means such as adaptive mechanism, dynamic adjustment and nonlinear compensation. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0025] In the attached picture: Figure 1 The flowcharts are shown in some embodiments of the present invention. DETAILED DESCRIPTION

[0026] The following specific embodiments may be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments. The embodiments of the present invention will be described below in conjunction with the accompanying drawings.

[0027] like Figure 1 As shown, the present invention discloses an online calibration method for a hemispherical resonant gyro inertial navigation system error, comprising: Specifically, step 1 aims to perform hierarchical observation of the angular velocity error output by the hemispherical resonant gyro (HRG) at different time scales through a dynamic multi-scale error mapping method, and use a nonlinear tensor error field model to perform high-dimensional projection of the error characteristics, so as to establish a dynamic error observation equation that can simultaneously characterize the gain error and the misalignment angle error.

[0028] 1.1 Setting error observation windows of different time scales 1.1.1 Selecting three types of time scales In order to ensure the temporal consistency of the error observation data and capture both the short-term error fluctuation and the long-term error drift, the short-term scale is defined , medium time scale , long time scale ,in: Pick: Short time scale , used to capture short-term dynamic errors, such as instantaneous gain error fluctuations; Middle time scale , used to observe the gradual trend of the error; Long time scale , used to analyze the long-term cumulative effects of errors, such as the slow drift of misalignment angle errors.

[0029] 1.1.2 Constructing a sliding calculation strategy for multi-scale time windows In time moment, with different window lengths , , Sliding calculation is performed so that there are three scales of error observation data at each moment, and at the same time: in: It is the raw angular velocity measurement value output by HRG; For the time scale The smoothed angular velocity observed under .

[0030] 1.2 Calculation of multi-scale error gain factor In order to extract the gain error characteristics at different time scales, the error gain factor is introduced , defined as follows: in: is the actual angular velocity that should be measured theoretically; Characterize the gain error at different time scales.

[0031] To further extract the dynamic characteristics of the gain error, calculate the time series change rate of the gain error: Thus, the gain error evolution trend at different time scales is obtained, providing input data for subsequent error decoupling.

[0032] 1.3 Calculation of multi-scale misalignment angle error factors Since the misalignment angle error affects the angular velocity coupling relationship of different axes, it is necessary to introduce a multi-scale misalignment angle error factor , defined as follows: in: , The time scales are Angular velocity components of HRG on different axes after smoothing in the observation window; is the nominal sensor mounting angle; Reflects the changing trend of misalignment angle error under different time scales.

[0033] Similarly, the rate of change of the misalignment angle error is introduced: Used to measure the dynamic change characteristics of misalignment angle error.

[0034] 1.4 Constructing nonlinear tensor error field for error mapping 1.4.1 Error Projection into High-Dimensional Feature Space In order to enhance the decoupling of gain error and misalignment angle error, a nonlinear tensor error field model is introduced to project the error from the time scale space to the high-dimensional feature space: Thus, a six-dimensional error feature vector is obtained, which contains the gain error and misalignment angle error characteristics at different time scales.

[0035] 1.4.2 Calculating the error mapping gradient field Based on high-dimensional error feature vector , define the error mapping gradient field: It is used to describe the changing trend of error characteristics in time and scale and ensure the dynamic consistency of error mapping.

[0036] 1.5 Construction of dynamic multi-scale error observation equation Combining the above error calculations, the final error observation equation is constructed: in: , is the error coupling coefficient matrix (needs subsequent optimization); is the system noise term.

[0037] The error observation equation can simultaneously characterize the gain error and misalignment angle error at different time scales, and provide basic data for subsequent error decoupling and compensation.

[0038] In step 1, this embodiment has constructed a high-dimensional error feature space containing gain error and misalignment angle error characteristics at different time scales based on the dynamic multi-scale error mapping method, and established an error observation equation. However, due to the obvious non-uniform distribution characteristics of the statistical characteristics of the error signal at different time scales, such as high-frequency fluctuations of short-term errors, slow drift of long-term errors, and complex nonlinear coupling of gain errors and misalignment angle errors, it is difficult to obtain error data representation with global consistency by directly using traditional uniform feature extraction methods. Therefore, this step proposes a non-uniform error feature extraction algorithm to extract error features at different time scales in an adaptive manner, and construct a high-dimensional error data feature vector to provide data input for subsequent error decoupling and compensation.

[0039] Specifically, step 2 includes: 2.1 Non-uniform sampling strategy of error characteristics 2.1.1 Using time scale adaptive sampling method In order to improve the timeliness and accuracy of error feature extraction, , , Under this condition, the time scale adaptive sampling factor is introduced , which increases the sampling density on a short time scale and reduces the sampling frequency on a long time scale. The non-uniform sampling window is defined as: in: For time scale The number of sampling points under ; is the adaptive sampling factor, defined as: in, For the time scale The error variance under is used to dynamically adjust the sampling density.

[0040] 2.1.2 Constructing multi-scale non-uniform sampling error signals Based on the above sampling strategy, the error signals at different time scales are non-uniformly sampled to obtain a discrete error sequence: This generates non-uniformly sampled multi-scale error data.

[0041] 2.2 Nonlinear transformation of error eigenvector Since the distribution characteristics of the original error data on different time scales may have a nonlinear relationship, for example, the gain error may present a Gaussian distribution on a short time scale and a skewed distribution on a long time scale, it is necessary to perform a nonlinear transformation on the error data to enhance the expressiveness of the features.

[0042] 2.2.1 Using adaptive nonlinear transformation function Define a nonlinear transformation function: in: , , For adaptive transformation parameters, they can be optimized according to the distribution characteristics of error data; The function is used to compress extreme error values ​​to prevent outliers from affecting the overall error modeling.

[0043] For different time scales , , , respectively calculate the transformed error characteristics: 2.3 Dimensionality reduction and feature fusion of error data 2.3.1 Calculation of statistical moments of error characteristics In order to further extract the statistical characteristics of the error, the mean, variance, skewness, and kurtosis of the error are calculated at each time scale, and the error feature vector is constructed: 2.3.2 Constructing the final error data feature vector The error statistical moments at different time scales are fused to form the final error data feature vector: 2.4 Orthogonal transformation of error data eigenvector Since the feature vector of high-dimensional error data may contain redundant information or correlation between features, in order to enhance the independence of features, the orthogonal transformation method is used to process the feature vector.

[0044] 2.4.1 Improved principal component analysis method On the basis of traditional principal component analysis, the weighted orthogonal transformation of error statistical moment is introduced to define the weighted covariance matrix: in: is the time scale weighting factor; is the mean of the error eigenvector.

[0045] Perform eigendecomposition on the covariance matrix to obtain the principal component matrix: Finally, the error eigenvector is projected into the orthogonal principal component space: 2.5 Standardization of error data feature vector In order to ensure that the error eigenvectors have the same scale in different data segments, so that the subsequent error modeling and compensation methods can have stable convergence, the final eigenvectors are standardized: This completes the construction of the error data feature vector based on the non-uniform error feature extraction algorithm, providing high-quality data input for subsequent error decoupling and compensation.

[0046] In step 2, this embodiment constructs a high-dimensional error data feature vector based on a non-uniform error feature extraction algorithm, which contains key statistical information of gain error and misalignment angle error at multiple scales. However, since these two types of errors have a complex nonlinear coupling relationship in the actual measurement process, it is difficult to effectively decouple the errors by relying solely on linear regression or traditional error modeling methods. Therefore, in this step, this embodiment proposes an adaptive coupling regression algorithm, which adaptively models the coupling relationship between gain error and misalignment angle error and adopts a dynamic weight adjustment strategy to ultimately achieve high-precision decoupling of errors.

[0047] Specifically, step 3 includes: 3.1 Establishing error coupling model Due to the gain error Misalignment Angle Error The angular velocity is measured at different time scales. Therefore, the error observation model can be constructed as follows: in: is the angular velocity measured by HRG; is the true angular velocity; is the gain error; is the misalignment angle error; For noise interference; is the unmodeled error term.

[0048] because and There may be different changing trends on the time scale, and noise interference may introduce nonlinear deviations, so the nonlinear coupling modeling method is used to describe its complex relationship.

[0049] First, define the nonlinear coupling error function: in: is the coupling error mapping function; is the error data feature vector generated in step 2.

[0050] In order to establish a more accurate error mapping relationship, this embodiment introduces an adaptive coupled regression model so that error decoupling can take into account both global error trends and local dynamic changes.

[0051] 3.2 Design of adaptive coupled regression model 3.2.1 Adopting Adaptive Multi-kernel Regression Model In order to accurately describe and The nonlinear coupling relationship between them, this embodiment adopts an adaptive multi-kernel regression method to construct an error decoupling model: in: is the kth kernel function. Common choices include Gaussian kernel, radial basis function (RBF), polynomial kernel, etc. For the Adaptive weights for each core; are historical training data points.

[0052] During the training process, a multi-scale weighted strategy is used to adjust the weights of the kernel function so that the model can adaptively model the error characteristics at different time scales.

[0053] 3.2.2 Adopting dynamic weight adjustment strategy Since the gain error and misalignment angle error contribute differently on different time scales, it is necessary to introduce a dynamic weight adjustment mechanism in the regression process and define the weight update rule as follows: in: is the regression loss function, defined as: is the learning rate, which controls the magnitude of weight adjustment.

[0054] This weight updating strategy ensures that the model can adaptively adjust the contribution of different kernel functions, thereby improving the accuracy of error decoupling.

[0055] 3.3 Error decoupling process After completing the coupling error modeling, this embodiment can achieve decoupling of the gain error and the misalignment angle error through an adaptive multi-kernel regression model.

[0056] 3.3.1 Calculating Gain Error Estimates By solving the regression equation, this embodiment can obtain an estimated value of the gain error: 3.3.2 Calculation of the estimated value of the misalignment angle error Since the gain error and the misalignment angle error are coupled in the regression model, the estimated value of the gain error can be used to further calculate the estimated value of the misalignment angle error: 3.3.3 Calculation of error residuals In order to measure the accuracy of error decoupling, this embodiment defines the error residual: If the error residual If the error exceeds the threshold, the kernel weights are adjusted and the model is retrained until the error meets the convergence condition.

[0057] 3.4 Adaptive Optimization of Error Decoupling Results In order to further improve the stability of error decoupling, this embodiment introduces an adaptive optimization mechanism to correct the error decoupling result. The specific method is as follows: 3.4.1 Using dynamic filter to smooth the error estimate Since the error estimate may be interfered by high-frequency noise, this embodiment uses an adaptive Kalman filter to smooth the estimate: in, It is an adaptive gain, which is dynamically adjusted according to the noise variance.

[0058] 3.5 Error decoupling result output Finally, based on the adaptive coupling regression algorithm, this embodiment obtains high-precision gain error and misalignment angle error estimates and ensures that the error decoupling is stable. The decoupling results are as follows: Gain error estimate: ; Misalignment angle error estimate: ; Error residual: .

[0059] These results serve as input to the subsequent error compensation step, ensuring that the inertial navigation system can perform accurate error correction.

[0060] In step 3, this embodiment completes the nonlinear decoupling of the gain error and the misalignment angle error through the adaptive coupling regression algorithm, and obtains a high-precision error estimate. and , and the residual of the error decoupling is calculated However, in order to effectively compensate for these errors in the inertial navigation system, this embodiment needs to construct a dynamic compensation matrix based on the error coupling residual to correct the measurement data in real time, so that the attitude, position and velocity estimation of the system are more accurate.

[0061] Specifically, step 4 includes: 4.1 Error coupling residual calculation In order to construct the dynamic compensation matrix, this embodiment first defines the error coupling residual vector : in: is the gain error residual; is the residual error of the misalignment angle.

[0062] because It reflects the accuracy of the current error compensation and can therefore be used to dynamically adjust the weight coefficients of the compensation matrix.

[0063] 4.2 Constructing the dynamic compensation matrix 4.2.1 Design error compensation model In an inertial navigation system, the angular velocity is measured Affected by the gain error and the misalignment angle error, this embodiment can construct an error compensation equation: in: is the angular velocity after compensation; is the dynamic compensation matrix.

[0064] To construct , this embodiment uses the error estimate and To make corrections: in: is the identity matrix; is a dynamic weight matrix used to adjust the compensation intensity; is the error correction matrix.

[0065] 4.2.2 Error Correction Matrix Error Correction Matrix The definition is as follows: This matrix represents independent compensation for gain error and misalignment angle error.

[0066] 4.2.3 Dynamic Weight Matrix In order to ensure that the compensation matrix can adapt to the time-varying characteristics of the error, this embodiment introduces a dynamic weight matrix based on the error coupling residual , defined as follows: in: represents the gain error compensation weight; represents the compensation weight of misalignment angle error; is the weight decay factor, which controls how fast the weight changes with the error residual.

[0067] The role of the dynamic weight matrix is ​​to reduce the compensation strength when the error coupling residual is large to prevent over-compensation when the error estimation is inaccurate; when the error residual is small, it enhances the compensation capability and improves the system accuracy.

[0068] 4.3 Calculate the angular velocity after compensation Finally, by applying the dynamic compensation matrix Measuring angular velocity After correction, the present embodiment can obtain the compensated angular velocity: In the actual system, the compensation matrix will be adaptively updated at each time step to ensure the accuracy and real-time performance of error compensation.

[0069] 4.4 Optimization of the error compensation matrix To ensure that the compensation matrix To improve stability and robustness, this embodiment introduces an adaptive optimization mechanism, including: 1. Introducing regularization terms To prevent possible numerical instability during matrix calculation, this embodiment Perform regularization: in is a small regularization factor that prevents the denominator from approaching zero.

[0070] 2. Adaptive weight update In time At this moment, this embodiment updates the weight according to the error coupling residual: in: is the learning rate, which controls the speed of weight update; is the weight gradient, calculated based on the error residual.

[0071] 4.5 Application of Error Compensation Matrix Finally, this embodiment constructs the dynamic compensation matrix Applied to the inertial navigation system, the angular velocity measurements are corrected so that the system can obtain a more accurate attitude estimate. The matrix will be dynamically updated at each time step based on the error coupling residuals, thus ensuring that the inertial navigation system has good error compensation capabilities in long-term operation.

[0072] In step 4, this embodiment constructs a dynamic compensation matrix and uses a dynamic weight adjustment strategy based on error coupling residuals to perform error compensation on the measured angular velocity of the inertial navigation system. However, since the error characteristics may be time-varying during the operation of the system, and the error compensation model may gradually deviate from the true error characteristics due to environmental disturbances, temperature drift and other factors, it is necessary to design an online self-correction mechanism to ensure that the error compensation model can continuously adapt to the dynamic changes of the error, thereby improving the compensation accuracy and the long-term stability of the system.

[0073] Specifically, step 5 includes: 5.1 Error compensation model deviation monitoring In order to detect the accuracy deviation of the error compensation model in real time, this embodiment defines an error correction residual vector (ErrorCorrection Residual) to measure the deviation between the current error compensated measurement data and the ideal error model: in: is the reference error vector, i.e., the standard error pattern obtained based on long-term historical data statistics; is the error vector obtained after current error compensation, defined as: when Exceeds a preset threshold , it indicates that the current error compensation model has been offset and needs to be self-calibrated online.

[0074] 5.2 Adaptive Adjustment of Error Compensation Model In order to correct the deviation of the error compensation model, this embodiment adopts a method based on incremental error update to update the compensation matrix Online adjustments are made to enable it to adaptively approach the optimal compensation state.

[0075] 5.2.1 Dynamic Error Compensation Matrix Update This embodiment uses the error correction residual vector To correct the compensation matrix : in: For the current moment The compensation matrix of To self-correct the step size and control the update rate; As feedback of the compensation error, the error correction capability of the compensation matrix is ​​adjusted.

[0076] The role of this update mechanism is to enable the compensation matrix to dynamically track the error change trend and automatically correct its own error compensation capability.

[0077] 5.3 Adaptive Adjustment of Self-Correction Step Size In order to prevent the error compensation model from being adjusted too fast or too slow, this embodiment designs an adaptive step adjustment strategy so that the update rate of the error compensation can be adaptively optimized according to the error change trend: in: is the weight factor, usually 0.8-0.9, used to smooth the step size change; Reflects the degree of deviation of error compensation. The larger the deviation, the larger the step size and the higher the compensation update rate.

[0078] By this method, the step size The convergence speed can be accelerated when the error changes greatly, and the adjustment amplitude can be reduced when the error is stable, thereby avoiding oscillation of the error compensation model.

[0079] 5.4 Long-term self-correction mechanism of error compensation model In order to ensure the stability of the system in long-term operation, this embodiment introduces a sliding window average self-correction strategy to smooth the adjustment process of the error compensation matrix: in: is the sliding window size, usually 10-20; This formula means that at each time step , to the past The compensation matrix at each moment is averaged to suppress the influence of short-term noise and make the error compensation more stable.

[0080] 5.5 Closed-loop mechanism of online self-correction of error compensation model In order to ensure that the entire error compensation model can be continuously self-optimized, this embodiment constructs a complete online self-correction closed loop: 1. Error correction residual calculation calculate , determine the deviation of the current error compensation model.

[0081] 2. Dynamic compensation matrix update Adjusting the compensation matrix using incremental error updates .

[0082] 3. Adaptive step size adjustment Dynamically adjust the step size based on the error residual size , avoid convergence too fast or too slow.

[0083] 4. Long-term trend optimization Sliding window average smoothing error compensation adjustment is used to prevent error oscillation.

[0084] 5. Continuous self-correction The above process is repeated at each time step so that the error compensation model can be continuously optimized.

[0085] 5.6 Application of online self-correction of error compensation model Ultimately, the online self-correction mechanism of the error compensation model can ensure that the inertial navigation system can continuously optimize the error compensation capability during long-term operation, even in the face of time-varying error characteristics and external disturbances, thereby improving the long-term accuracy and stability of the navigation system.

[0086] In step 5, this embodiment constructs an online self-correction mechanism for the error compensation model to ensure that the error compensation matrix can be dynamically adjusted as the error characteristics change. However, in the actual operation process, the error of the inertial navigation system not only manifests itself as short-term random fluctuations, but also has a long-term drift trend, that is, the error presents a complex nonlinear cumulative effect over time. Therefore, in this step, this embodiment proposes an error drift prediction model based on adaptive time series regression, combined with a nonlinear error compensation method, to achieve long-term trend prediction and nonlinear compensation of the error, so as to further improve the long-term stability and accuracy of the inertial navigation system.

[0087] Specifically, step 6 includes: 6.1 Error drift trend modeling Since the long-term drift trend of the error usually presents nonlinear characteristics, this embodiment introduces a nonlinear time series regression method to establish a prediction model for error drift: 6.1.1 Error Drift State Variable Construction Define the error drift state variable vector: in: , , It is the real-time measurement value of the error in each channel (XYZ direction); , , is the instantaneous rate of change of the error, defined as: The error state variable vector is used to describe the instantaneous state of the current error and can be used as the input of the error drift prediction model.

[0088] 6.2 Error Drift Prediction In order to accurately predict the long-term drift trend of the error, this embodiment proposes an error prediction model based on adaptive time series regression, which uses an improved recursive nonlinear regression method to recursively predict the future The error value of the step.

[0089] 6.2.1 Recursive Nonlinear Regression Model Assume that the long-term variation of the error can be expressed by a nonlinear function To model, this embodiment uses a nonlinear time series regression model for prediction: in: is the regression parameter to be sought; is a Gaussian white noise term, representing random error; is the prediction step length.

[0090] To optimize the regression parameters , this embodiment uses sliding window least squares optimization for recursive update: in: is the learning rate, which controls the update rate of the model; is the sliding window size, usually 10-50; Express Find the gradient.

[0091] The regression model can continuously optimize the prediction capability of error drift during system operation and has good real-time performance.

[0092] 6.3 Nonlinear Error Compensation After predicting the error drift trend, this embodiment needs to design a nonlinear error compensation strategy to actively offset the long-term drift effect of the error.

[0093] 6.3.1 Error compensation matrix update Define the prediction error compensation matrix : in: is the compensation matrix calculated in step 5; is the nonlinear compensation coefficient, which controls the weight of error prediction compensation.

[0094] 6.3.2 Error Compensation Matrix Fusion The final error compensation matrix is ​​determined by the online self-correction compensation (step 5) and the prediction compensation (step 6): in: It is the fusion coefficient, which is generally 0.2-0.5, to balance the contribution of the two compensation methods.

[0095] 6.4 Closed-loop mechanism of error prediction and compensation In order to ensure the stability of error drift prediction and nonlinear compensation, this embodiment constructs a complete closed-loop mechanism: 1. Real-time error drift state estimation: Calculate the error state variable vector , get the instantaneous state of the error.

[0096] 2. Prediction error drift trend based on adaptive time series regression: Nonlinear time series regression model Predicting the future The error change trend of the step.

[0097] 3. Construct nonlinear error compensation matrix And update the compensation parameters: Calculate the prediction error compensation matrix , to compensate for the long-term drift trend of the error.

[0098] 4. Integrate online self-correction compensation and prediction compensation to construct the final error compensation matrix : A weighted fusion strategy is adopted to ensure the stability and adaptability of error compensation.

[0099] 6.5 Application of Error Prediction and Nonlinear Compensation Through this step, the inertial navigation system can actively predict the long-term drift trend of the error during operation and perform nonlinear compensation in advance to reduce the cumulative effect of the error, thereby further improving the accuracy and stability of the navigation system.

[0100] In step 6, this embodiment predicts the error drift trend based on adaptive time series regression and constructs a nonlinear error compensation mechanism, so that the inertial navigation system can actively cope with the long-term changes of the error. However, the compensation matrix Real-time adjustments may introduce new unstable factors, such as: 1. Convergence problem of error compensation - due to the nonlinear characteristics of the error compensation model, the error correction may oscillate or even diverge; 2. Insufficient adaptability to dynamic environments - if the external environment changes suddenly (such as temperature changes, vibration disturbances), the original compensation strategy may no longer be applicable; 3. Adaptive compensation overshoot phenomenon - If the compensation parameters are adjusted too quickly, it may lead to excessive error correction, thus affecting system stability.

[0101] Therefore, in this step, this embodiment designs an error compensation adjustment mechanism based on dynamic stability constraints, and realizes adaptive optimization of the compensation matrix through stability analysis of the error compensation effect, thereby ensuring the convergence of the error compensation process.

[0102] Specifically, step 7 includes: 7.1 Error compensation stability evaluation index In order to quantitatively analyze the stability of error compensation, this embodiment defines the error correction gain matrix , which is used to measure the effectiveness and convergence of error correction: in: is the error state variable vector at the current moment; is the error state variable vector at the previous moment.

[0103] The convergence of the error correction gain matrix can be determined by the gain change rate To measure: like Continuously increasing indicates that the error correction has a divergent trend; if Oscillation within a certain range indicates that there is overshoot in the error correction.

[0104] 7.2 Error compensation dynamic adjustment strategy Based on the error correction gain matrix and gain change rate ,This embodiment proposes an adaptive compensation adjustment strategy to ensure the stability of error compensation by dynamically optimizing ,compensation parameters.

[0105] 7.2.1 Adaptive compensation adjustment function This embodiment introduces a compensation adjustment factor , which is used to control the dynamic adjustment rate of the compensation matrix: in: To adjust the step size, determine how fast the compensation rate changes; is the stability threshold, usually 0.05-0.1; is a sign function used to determine the trend of the gain change rate.

[0106] The final error compensation matrix is ​​updated as: when If too large, reduce , reduce the compensation rate to avoid error correction oscillation; when Over time, increase , speed up the compensation rate and improve the system convergence.

[0107] 7.3 Closed-loop Optimization of Stability Control In order to ensure that the error compensation strategy can remain stable under different working conditions, this embodiment constructs a closed-loop control mechanism: 1. Real-time calculation of error correction gain matrix : Monitor the error state changes before and after error compensation and obtain the gain matrix.

[0108] 2. Calculate the gain change rate Evaluate error compensation stability: If the gain change rate is too large, it means that the error correction has a divergent trend and the compensation rate needs to be reduced; If the gain change rate is too small, it means that the error correction is insufficient and the compensation speed needs to be increased.

[0109] 3. Update the compensation matrix based on the adaptive compensation adjustment function: according to Calculate the compensation adjustment factor , dynamically optimized compensation matrix .

[0110] 4. Periodic error compensation stability evaluation: Set a fixed time window (e.g. 1000 sampling cycles) to evaluate the error compensation effect; If the error compensation does not reach a stable state, adjust and To optimize the compensation adjustment rate.

[0111] 7.4 Practical Application of Dynamic Adjustment of Error Compensation Through this step, the inertial navigation system can autonomously evaluate the stability of error compensation during operation, and dynamically adjust the optimization rate of the compensation matrix to ensure that the error compensation can maintain convergence and robustness in different working environments, thereby further improving the long-term reliability and accuracy of the system.

[0112] In the previous steps, this embodiment has ensured that the error compensation of the inertial navigation system can respond to error changes in real time and make effective corrections through mechanisms such as dynamic compensation matrix (step 4), error drift trend prediction (step 6), and stability analysis and dynamic adjustment (step 7). However, although this embodiment has been able to reduce the error to a certain extent through these strategies, there may still be a gradual inaccuracy of the error model during the long-term operation of the system - for example, the compensation strategy may gradually lose its effectiveness due to factors such as changes in the external environment and system aging. Therefore, the core goal of this step is to achieve adaptive adjustment of the error model through convergence evaluation of the error residual, so as to further improve the robustness and accuracy of the compensation system.

[0113] Specifically, step 8 includes: 8.1 Calculation of Error Residuals and Convergence Analysis First, this embodiment needs to calculate the error residual vector , which represents the residual error after compensation at the current moment, that is: in: is the current measurement error, including gyro error, accelerometer error, etc.; is the real-time dynamic compensation matrix (compensation parameters obtained in the previous steps); is the systematic error in model-based predictions (e.g., estimates based on physics models).

[0114] In order to evaluate the convergence of the error residual, this embodiment introduces the residual convergence rate index , which indicates the changing trend of the error residual: in, is the Euclidean norm of the vector, if If it continues to approach 0, it means that the convergence of the error residual is good and the error compensation effect of the system is gradually becoming stable. If it is greater than the set threshold, it means that the error model has not fully converged and there may be a large residual error, and the error model needs to be further adjusted.

[0115] 8.2 Introduction of Adaptive Adjustment Mechanism Through the analysis of the convergence of the error residual, if the system detects that the error residual has not reached the convergence condition, it is necessary to trigger the adaptive error model adjustment mechanism to dynamically optimize the error model parameters so that the system can continue to maintain a good compensation effect in the new environment.

[0116] 8.2.1 Adaptive Error Model Adjustment Algorithm In order to achieve adaptive adjustment of the error model, this embodiment introduces a dynamic error correction gain matrix , by the error residual and prediction error Analyze the relationship between the error correction gain matrix , and then optimize the compensation effect of the error model. The corrected update formula is as follows: in: is the error correction gain matrix at the current moment; is the error residual vector at the current moment, which represents the difference between the measured error and the compensated error; is the error model prediction value at the current moment, indicating the error calculated based on the system model; To learn the step size, control the amplitude of gain matrix adjustment; is the square norm of the error model vector, which is used to normalize the adjustment amplitude to avoid the adverse effects caused by inconsistent error magnitudes.

[0117] The correction process calculates the outer product between the error residual and the error model and uses the norm of the error model for normalization adjustment, thereby effectively adjusting the error correction gain matrix This allows the system to dynamically optimize the error model over time based on real-time error residuals, ensuring that the system continues to provide accurate error compensation under varying operating conditions.

[0118] 8.2.2 Adjusted Error Model After adaptive adjustment, the error model of the system A re-evaluation is required. In this embodiment, the error model is updated by the following formula: This process enables the error model to be dynamically adjusted according to the latest error residual at each moment and gradually approach the actual error characteristics.

[0119] 8.3 Adaptive Closed-Loop Control The core idea of ​​the adaptive error model adjustment mechanism is to form a closed-loop feedback control system, namely: 1. Error residual evaluation: by calculating And analyze its convergence; 2. Adaptive adjustment trigger: If the residual convergence condition is not met, the error model adjustment is triggered; 3. Dynamically adjust error model parameters: by updating and Optimize error model; 4. Continuous iterative feedback: Repeat the above process until the system converges to a stable error model.

[0120] By introducing an adaptive adjustment mechanism for the convergence of error residuals, the inertial navigation system can perceive the inaccuracy trend of the error model in real time and automatically trigger the dynamic adjustment of the error model, thereby improving the compensation accuracy and optimizing the system response speed. Ultimately, it ensures that the system error gradually approaches zero during long-term operation, thereby ensuring the long-term stability and accuracy of the navigation system.

[0121] On the other hand, the present invention discloses an online calibration system for hemispherical resonant gyro inertial navigation system errors, comprising: Dynamic multi-scale error observation equation construction module: Through dynamic multi-scale error mapping, dynamic observation equations of gain error and misalignment angle error are established; Non-uniform error feature extraction module: uses a non-uniform feature extraction algorithm to adaptively extract error features of different time scales and construct a high-dimensional feature vector; Error decoupling module: uses adaptive coupled regression algorithm to decouple gain error and misalignment angle error to obtain error estimation value; Dynamic compensation matrix construction module: Based on the error estimation value, the dynamic compensation matrix is ​​constructed to correct the measured angular velocity in real time; Online self-correction mechanism establishment module: Design the online self-correction mechanism of the error compensation model and dynamically adjust the compensation matrix to adapt to the dynamic changes of the error; Error drift prediction and compensation module: Introduces an adaptive time series regression model to predict the long-term drift trend of the error, and combines it with a nonlinear compensation method to actively offset the error accumulation effect; Error compensation stability optimization module: dynamically adjusts the optimization rate of the compensation matrix through stability analysis; Error model adaptation module: Dynamically optimizes error model parameters based on convergence evaluation of error residuals.

[0122] On the other hand, the present invention discloses an online calibration device for hemispherical resonant gyro inertial navigation system errors, the device comprising at least one processor and at least one memory; The at least one memory is used to store computer instructions; The at least one processor is used to execute at least part of the computer instructions to implement the online calibration method for the hemispherical resonant gyro inertial navigation system error as described in claims 1-9.

[0123] On the other hand, the present invention discloses a computer-readable storage medium, wherein the storage medium stores computer instructions. When a computer reads the computer instructions in the storage medium, the computer executes the online calibration method for the hemispherical resonant gyro inertial navigation system error as described in claims 1 to 9. Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of protection of the claims of the present invention.

Claims

1. A method for online calibration of hemispherical resonant gyro inertial navigation system error, characterized in that: include: Step 1: Establish the dynamic observation equations of gain error and misalignment angle error through dynamic multi-scale error mapping; Step 2: Adopt a non-uniform feature extraction algorithm to adaptively extract error features of different time scales and construct a high-dimensional feature vector; Step 3: Decouple the gain error and the misalignment angle error using an adaptive coupled regression algorithm to obtain an error estimate. Step 4: Based on the error estimate, construct a dynamic compensation matrix to correct the measured angular velocity in real time; Step 5: Design an online self-correction mechanism for the error compensation model and dynamically adjust the compensation matrix to adapt to the dynamic changes of the error; Step 6: Introduce an adaptive time series regression model to predict the long-term drift trend of the error, and combine it with a nonlinear compensation method to actively offset the error accumulation effect; Step 7: Dynamically adjust the optimization rate of the compensation matrix through stability analysis; Step 8: Based on the convergence evaluation of the error residual, dynamically optimize the error model parameters.

2. The method for online calibration of hemispherical resonant gyro inertial navigation system error according to claim 1, characterized in that: The step 1 comprises: Define different time scales to capture short-term dynamic error fluctuations, observe error gradual trends, and analyze long-term cumulative effects; A sliding calculation strategy of multi-scale time windows is constructed to smooth the angular velocity output by the hemispherical resonant gyroscope at each moment and obtain the angular velocity observation values ​​at different time scales. Calculate the multi-scale error gain factor, extract its dynamic characteristics by introducing the time series change rate of the gain error, and introduce the multi-scale misalignment angle error factor to measure the change trend of the misalignment angle error at different time scales and calculate its change rate; A nonlinear tensor error field model is constructed to project the error from the time scale space to the high-dimensional feature space, and a six-dimensional error feature vector containing the gain error and misalignment angle error characteristics is obtained; Based on the feature vector, the error mapping gradient field is defined to describe the variation trend of the error characteristics in time and scale; Based on the above calculation results, a dynamic multi-scale error observation equation is constructed.

3. The method for online calibration of hemispherical resonant gyro inertial navigation system error according to claim 2 is characterized in that: The step 2 comprises: Design a time-scale adaptive sampling strategy; Under the time scale, introduce an adaptive sampling factor to dynamically adjust the sampling density according to the error variance; Perform nonlinear transformation on error data; use adaptive nonlinear transformation function to transform errors of different time scales according to the distribution characteristics of error data, enhance the expressiveness of features, and avoid the influence of outliers on modeling by compressing extreme error values; Calculate the statistical moments of the error characteristics; calculate the mean, variance, skewness, and kurtosis of the error at each time scale, construct an error feature vector containing these statistical characteristics, and further extract the statistical characteristics of the error; The error feature vector is orthogonally transformed and standardized, and an improved principal component analysis method is used to introduce a weighted orthogonal transformation of the error statistical moment to eliminate redundant information and correlation in the feature vector and enhance the independence of the feature. The transformed feature vectors are standardized to ensure that they have a uniform scale in different data segments, providing stability and consistency for subsequent error modeling and compensation.

4. The method for online calibration of hemispherical resonant gyro inertial navigation system error according to claim 3 is characterized in that: The step 3 comprises: Based on the relationship between the angular velocity measured by HRG and the true angular velocity, the nonlinear coupling relationship between the gain error and the misalignment angle error is defined, the coupling error mapping function is introduced, and the error observation model is constructed to provide a basis for subsequent decoupling; Adopting adaptive multi-kernel regression method, combined with historical training data points, an error decoupling model is constructed, and the kernel function weights are adjusted through multi-scale weighting strategy to achieve adaptive modeling of error characteristics at different time scales. Define the weight update rules and dynamically adjust the weight of the kernel function based on the regression loss function and learning rate to ensure that the model can adaptively adjust according to the changes in error characteristics and improve the accuracy of error decoupling; By solving the regression equation, the estimated values ​​of the gain error and the misalignment angle error are calculated respectively, and the error residual is calculated to measure the decoupling accuracy; if the error residual exceeds the threshold, the kernel weight is adjusted and the model is retrained until the convergence condition is met; Adaptive Kalman filtering is used to dynamically adjust the filter gain according to the noise variance to eliminate high-frequency noise interference, further improve the stability of the error decoupling results, and provide a high-precision error estimate for subsequent error compensation.

5. The method for online calibration of hemispherical resonant gyro inertial navigation system error according to claim 4 is characterized in that: The step 4 comprises: Calculate the gain error residual and the misalignment angle error residual to evaluate the accuracy of the current error compensation; Construct an error compensation equation and correct the measured angular velocity through a dynamic compensation matrix. The compensated angular velocity is obtained by subtracting the product of the error correction matrix and the dynamic weight matrix from the original measurement value. The error correction matrix is ​​used to independently compensate for the gain error and the misalignment angle error. Based on the error coupling residual, the compensation strength is adjusted dynamically. The weight of the dynamic weight matrix is ​​adjusted according to the size of the error residual. When the residual is large, the compensation strength is reduced to prevent over-compensation. When the residual is small, the compensation capability is enhanced to improve the system accuracy. The measured angular velocity is corrected by applying a dynamic compensation matrix to obtain the compensated angular velocity. The compensation matrix is ​​adaptively updated at each time step to ensure the accuracy and real-time performance of error compensation. A regularization term is introduced to prevent numerical instability, and the weights are dynamically updated according to the error coupling residual.

6. The method for online calibration of hemispherical resonant gyro inertial navigation system error according to claim 5, characterized in that: The step 5 comprises: Calculate the error correction residual vector to measure the deviation between the measured data after error compensation and the ideal error model. If the error correction residual vector exceeds the preset threshold, it indicates that the error compensation model has deviations and needs to be self-corrected online. Based on the error correction residual vector, the compensation matrix is ​​corrected by using the incremental error update method. By adjusting the self-correction step size, the update rate of the compensation matrix is ​​controlled to dynamically track the error change trend. Design an adaptive step-size adjustment strategy to dynamically adjust the step size according to the degree of error compensation deviation. When the error deviation is large, increase the step size to speed up the convergence speed. When the error is stable, reduce the step size to avoid oscillation. The sliding window averaging method is introduced to average the compensation matrices at several moments in the past, smoothing the influence of short-term noise and enhancing the stability of error compensation. A complete online self-correction closed loop is formed, including error correction residual calculation, dynamic compensation matrix update, adaptive step size adjustment and long-term trend optimization. The above process is repeated at each time step to ensure continuous self-optimization of the error compensation model.

7. The method for online calibration of hemispherical resonator gyro inertial navigation system error according to claim 6, characterized in that: The step 6 comprises: Define the error drift state variable vector, including the real-time measurement value of the error and its instantaneous rate of change, which is used to describe the instantaneous state of the current error and serves as the input of the error drift prediction model; A recursive nonlinear regression model is used to recursively update the regression parameters based on the sliding window least squares optimization to predict the error change trend of the future steps; According to the predicted error drift trend, the error compensation matrix is ​​updated and nonlinear compensation coefficients are introduced to actively offset the long-term drift effect of the error; The online self-correction compensation is combined with the prediction compensation, and the final error compensation matrix is ​​constructed through the weighted fusion strategy; A closed-loop mechanism is formed, including real-time error drift state estimation, error drift trend prediction, nonlinear error compensation matrix update, and compensation strategy fusion. Error compensation is continuously optimized through closed-loop feedback.

8. The method for online calibration of hemispherical resonant gyro inertial navigation system error according to claim 7, characterized in that: The step 7 comprises: Calculate the error correction gain matrix, which is used to measure the state change before and after error compensation. The gain matrix is ​​calculated by the error state variable vector at the current and previous moments, reflecting the effectiveness of error correction; The stability of error compensation is evaluated by the gain change rate. If the gain change rate continues to increase, it indicates that the error correction has a divergent trend. If the gain change rate oscillates within a certain range, it indicates that there is an overshoot phenomenon. Based on the gain change rate, a compensation adjustment factor is introduced to dynamically control the adjustment rate of the compensation matrix; the adjustment factor is calculated by adjusting the step size, stability threshold and sign function to ensure the adaptability of the compensation rate; According to the compensation adjustment factor, the compensation matrix is ​​dynamically optimized. When the gain change rate is too large, the compensation rate is reduced to avoid oscillation. When the gain change rate is too small, the compensation rate is accelerated to improve the system convergence. A closed-loop control mechanism is formed, including real-time calculation of the error correction gain matrix, evaluation of compensation stability, updating of the compensation matrix, and periodic evaluation of the compensation effect. The compensation strategy is dynamically adjusted through closed-loop feedback.

9. The method for online calibration of hemispherical resonator gyro inertial navigation system error according to claim 7, characterized in that: The step 8 comprises: Define the error residual vector, which represents the residual error after compensation, and is calculated by the difference between the current measurement error and the error corrected by the dynamic compensation matrix; The residual convergence rate indicator is introduced to evaluate the convergence of the error model through the change trend of the Euclidean norm of the error residual vector; if the residual convergence rate continues to approach zero, it indicates that the error model converges well; if it exceeds the set threshold, the adaptive adjustment mechanism is triggered; Based on the outer product of the error residual and the error model prediction value, the error correction gain matrix is ​​dynamically adjusted; through the normalization of the learning step size and the error model norm, the error model parameters are optimized to gradually approach the true error characteristics; The error model is updated according to the adjusted error correction gain matrix to ensure continuous error compensation under different working conditions; A closed-loop feedback control system is formed, including error residual evaluation, adaptive adjustment triggering, dynamic adjustment of error model parameters and continuous iterative feedback.

10. An online calibration device for hemispherical resonant gyro inertial navigation system error, characterized in that: The apparatus comprises at least one processor and at least one memory; The at least one memory is used to store computer instructions; The at least one processor is used to execute at least part of the computer instructions to implement the online calibration method for the hemispherical resonant gyro inertial navigation system error as described in any one of claims 1-9.

11. An online calibration system for hemispherical resonant gyro inertial navigation system error, characterized in that: include: Dynamic multi-scale error observation equation construction module: Through dynamic multi-scale error mapping, dynamic observation equations of gain error and misalignment angle error are established; Non-uniform error feature extraction module: uses a non-uniform feature extraction algorithm to adaptively extract error features of different time scales and construct a high-dimensional feature vector; Error decoupling module: uses adaptive coupled regression algorithm to decouple gain error and misalignment angle error to obtain error estimation value; Dynamic compensation matrix construction module: Based on the error estimation value, the dynamic compensation matrix is ​​constructed to correct the measured angular velocity in real time; Online self-correction mechanism establishment module: Design the online self-correction mechanism of the error compensation model and dynamically adjust the compensation matrix to adapt to the dynamic changes of the error; Error drift prediction and compensation module: Introduces an adaptive time series regression model to predict the long-term drift trend of the error, and combines it with a nonlinear compensation method to actively offset the error accumulation effect; Error compensation stability optimization module: dynamically adjusts the optimization rate of the compensation matrix through stability analysis; Error model adaptation module: Dynamically optimizes error model parameters based on convergence evaluation of error residuals.

12. A computer-readable storage medium, characterized in that: The storage medium stores computer instructions. When the computer reads the computer instructions in the storage medium, the computer executes the online calibration method for the hemispherical resonator gyro inertial navigation system error as described in any one of claims 1 to 9.

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