Error self-calibration method of hemispherical resonator gyroscope

Abstract

The invention discloses an error self-calibration method of a hemispherical resonator gyroscope. The error self-calibration method comprises the following steps: realizing mapping and transition between modals; identifying and eliminating transient errors generated in the mode switching process; the error compensation process is optimized, and the adaptive capacity of the system to complex dynamic changes is enhanced; the control parameters of the gyroscope in different modes are automatically adjusted; the correction of an error mode is optimized, and the output precision is improved; transient errors are recognized and eliminated in real time, and system output signals are smoothed; constructing a mode switching decision support and prediction algorithm, judging a mode switching opportunity, predicting an error after switching and compensating the error in advance; system control and calibration parameters are adjusted in real time; layered optimization is carried out on errors of different modal hierarchies; and error self-learning and system optimization are realized by combining adaptive learning and a global optimization strategy. According to the method, the transient error problem caused in the mode switching process can be effectively solved, and global optimization and error correction can be carried out in real time.

Description

Technical Field

[0001] The invention relates to the technical field of hemispherical resonant gyroscopes, and in particular to an error self-calibration method for a hemispherical resonant gyroscope. Background Art

[0002] As a high-precision inertial measurement device, the Hemisphere Resonant Gyroscope (HRG) is widely used in aerospace, navigation, military and other fields, especially in tasks that require long-term stable operation and provide high-precision data. Compared with traditional gyroscopes, HRGs have higher sensitivity and lower energy consumption, so they are increasingly used in modern high-precision positioning and navigation systems. However, as the application field of HRGs continues to expand, the error characteristics of the system are gradually emerging. Especially in high-dynamic and complex working environments, system errors will affect its stability and accuracy, becoming a technical problem that needs to be solved urgently.

[0003] During the operation of the hemispherical resonant gyroscope, the main sources of error include manufacturing errors, environmental changes (such as temperature, humidity, pressure, etc.), and internal electrical noise. In order to ensure the long-term high-precision performance of the gyroscope, error compensation and self-calibration mechanisms become key. Most of the current error compensation methods rely on model adjustments in static and dynamic environments to improve the accuracy of the gyroscope by detecting errors in real time and making corrections. However, due to the rapid change in the working state of the gyroscope when the mode is switched, traditional error compensation algorithms often find it difficult to effectively deal with the transient errors caused by this change.

[0004] Mode switching is an inevitable part of the working process of the hemispherical resonant gyroscope. Especially under different working conditions and mission requirements, the gyroscope needs to switch between different operating modes (such as operating frequency, oscillation mode, etc.) to meet different measurement requirements. However, mode switching is often accompanied by sudden changes and adjustments in system parameters, which will cause obvious transient errors in a short period of time and affect the output signal of the gyroscope. This error usually manifests as short-term fluctuations or instability. In severe cases, it may even cause the accuracy of the gyroscope output to decrease, thereby affecting the performance of the entire navigation system.

[0005] Therefore, how to effectively reduce the transient error during mode switching and ensure the smooth transition of the gyro in different working modes has become an important challenge in the current hemispherical resonant gyro error calibration technology. Summary of the invention

[0006] In order to solve the above problems, the present invention provides an error self-calibration method for a hemispherical resonant gyroscope.

[0007] To achieve the above purpose, the technical solution adopted by the present invention is as follows: On the one hand, the present invention discloses an error self - calibration method for a hemispherical resonant gyroscope, including: Step 1: Implement the mapping and transition between modes through an adaptive mode mapping algorithm; Step 2: Use a non - stationary error elimination network to identify and eliminate the transient errors generated during the mode switching process; Step 3: Based on the mode feedback back - propagation compensation algorithm, optimize the error compensation process and enhance the system's adaptive ability to complex dynamic changes; Step 4: Introduce a multi - dimensional time - domain mode self - regulation control algorithm to automatically adjust the control parameters of the gyroscope in different modes; Step 5: Generate an error correction signal through a generative adversarial network to optimize the correction of error patterns and improve the output accuracy; Step 6: Design an adaptive transient error clustering and smoothing algorithm to real - time identify and eliminate transient errors and smooth the system output signal; Step 7: Construct a mode switching decision - making support and prediction algorithm to judge the mode switching timing, predict the errors after switching and compensate in advance; Step 8: Through a closed - loop feedback mechanism, real - time adjust the system control and calibration parameters; Step 9: Design a mode - level hierarchical error optimization algorithm to hierarchically optimize the errors at different mode levels; Step 10: Introduce a global multi - mode error self - learning and optimization algorithm, combine the adaptive learning and global optimization strategies to achieve error self - learning and system optimization.

[0008] Furthermore: The said Step 1 includes: Collect real - time vibration data through the sensor array of the gyroscope, including electrode excitation signals, acceleration data, and angular velocity data; sample and pre - process the collected signals, and retain the key signal frequency bands; Perform time - frequency analysis on the signals using the short - time Fourier transform, map the signals to the time - frequency plane, extract the frequency components, their amplitudes, and phase information at each moment, and based on the spectral peak extraction algorithm of the time - frequency diagram, identify the key mode features and record the spectral changes during mode switching; Design an adaptive mode mapping matrix, calculate the similarity between the current mode and the previous mode, use the cosine similarity as a metric, the mapping matrix records the transformation rules between modes, each element represents the mapping strength between modes, and is dynamically updated according to real - time data; Introduce an incremental learning strategy, use the incremental least - squares method to adjust the mapping matrix, and fine - tune the mapping matrix according to the new mode features to ensure timely adaptation during mode switching; Through continuous update of the adaptive mapping matrix, use a time-series-based prediction model to predict the mode switching information at the next moment, and adjust the electrode excitation signal in advance to achieve a smooth transition; During the mode switching process, combine the synergistic effects of the adaptive mode mapping matrix and the prediction model to adjust the electrode drive signal in real time, reduce the transient error, and ensure a smooth transition of the mode switching.

[0009] Further: The step 2 includes: Based on the mode information output by the adaptive mode mapping algorithm, collect the error signals during the mode switching process, including angular velocity, acceleration, and electrode signals, calculate the error between the output signal and the ideal value, and remove low-frequency noise and long-term drift through a high-pass filter to focus on high-frequency transient errors; Perform a short-time Fourier transform on the real-time error signal to analyze the spectral characteristics of the error and its changing trend over time; further use the empirical mode decomposition method to decompose the error signal into intrinsic mode functions to analyze the error components at multiple scales and accurately identify the non-stationary errors caused by mode switching; Use a long short-term memory network to model the error signal, capture the long-term dependence relationship of the error, adaptively adjust the weights according to the error characteristics after mode switching, and predict and eliminate non-stationary errors in real time; Based on the learning results of the long short-term memory network, design an error compensation network to generate a compensation signal to eliminate transient errors; the network structure of the error compensation network includes an input layer, an LSTM module, an error prediction layer, and a compensation output layer; use the Adam optimization algorithm to train the ECN to minimize the mean square error between the predicted error and the actual error; Apply the compensation signal generated by the error compensation network to the gyroscope control system to adjust the electrode excitation signal in real time to eliminate transient errors; introduce a feedback mechanism to compare the compensated signal with the target output, further correct and optimize the compensation signal, and the feedback update formula is based on the real-time monitoring of the error; Regularly evaluate the accuracy of error elimination, calculate the error elimination rate by comparing the error between the model prediction value and the actual output; if the set threshold is not reached, continue to optimize the parameters of the error compensation network until the error elimination rate meets the requirements to ensure high stability and high precision of the system output.

[0010] Further: The step 3 includes: Based on the output data of the adaptive mode mapping algorithm and the non-stationary error elimination network, define a feedback signal; the feedback signal combines the characteristic changes during mode switching and the compensation signal of the error elimination network: Introduce a mode coupling model to describe the interaction between different modes and the error generation mechanism, and deduce the compensation amount through the inverse matrix of the mode coupling matrix; Adopt an incremental learning mechanism to dynamically update the backstepping compensation parameters according to the error signal during the mode switching process; Generate a compensation drive signal according to the real-time updated compensation amount and apply it to the gyroscope control system to correct the error in the output signal; Evaluate the backstepping compensation result through a feedback adjustment algorithm and optimize the compensation parameters according to the new feedback signal; After each mode switching, compare the error between the compensated output signal and the target signal, calculate the error elimination rate. When the error elimination rate reaches the preset threshold, the compensation process is completed to ensure the high precision and stability of the system output.

[0011] Furthermore: Step 4 includes: Collect multi-dimensional signals from the gyroscope system, including angular velocity, acceleration, control electrode signals, and feedback signals; use wavelet transform or short-time Fourier transform to extract time-frequency domain features of the signals, analyze the frequency, phase, and amplitude changes during the mode switching process, and capture the mode conversion features; Combined with the output of the non-stationary error elimination network, analyze the time-domain change trend of the error, extract the time-domain error change rate, and based on the error dynamics, extract the mode self-adjustment parameters to describe the error characteristics of the system output in different modes; Construct a multi-dimensional time-domain adaptive control model, dynamically adjust the control signal according to the mode self-adjustment parameters, and achieve error compensation in different modes by adjusting the gain; Introduce a feedback control strategy, use PID control to optimize the adjustment process, and ensure the sensitivity of the system to dynamic errors and the reduction of steady-state errors; Regularly evaluate the parameters of the mode self-adjustment control, use genetic algorithm or particle swarm optimization algorithm to optimize the gain matrix and adjustment coefficients, define the fitness function as the error elimination rate, and through iterative optimization, adjust the control signal to achieve the best compensation effect; Evaluate the system performance by comparing the error elimination rates of the target output and the actual output, continuously adjust the control gain and feedback parameters, and gradually increase the error elimination rate.

[0012] Furthermore: Step 5 includes: Construct a generative adversarial network, including a generator and a discriminator. The generator generates data that approximates the real error correction signal from the input features, and the discriminator distinguishes the difference between the generated signal and the real signal; Collect the control signals and error signals after mode feedback backstepping compensation and multi-dimensional time-domain self-adjustment control as the input features of the adversarial network, and construct a high-dimensional input feature vector through the fusion of time-domain, frequency-domain, and mode features; The design generator is a deep neural network, including a convolutional layer, a fully connected layer, and an activation function. The generator learns the relationship between the input features and the error correction signal, and generates the error correction signal. The discriminator is a deep neural network that outputs a binary classification probability value to judge the authenticity of the signal. The discriminator optimizes the network parameters by maximizing the discriminant loss function. By alternately optimizing the generator and the discriminator, the generator generates a correction signal close to the real signal, and the discriminator continuously improves the judgment accuracy. The training process is based on the gradient update of the generator and the discriminator until the generator can generate correction signals that are difficult to distinguish. After the training is completed, the generator generates an error correction signal according to the input signal features and applies it to the gyroscope control system. During the real-time operation of the system, the error correction signal is continuously updated through the GAN.

[0013] Further: Step 6 includes: Design an error fluctuation detector. Based on the transient response characteristics of the time-domain and frequency-domain signals, determine whether the error is a transient error. The identification criterion is whether the change amount and change rate of the error exceed the set threshold, so as to screen out the transient error segments from the system output. Adopt a clustering algorithm based on dynamic time warping to classify the transient error segments. Extract the error segment features through the sliding window method, including time-domain changes, frequency-domain features, and modal states, and classify the error segments with similar dynamic responses into one category. For different clustering groups, design an adaptive weighted smoothing filter, which is dynamically adjusted according to the error change amplitude to suppress fluctuations and maintain signal smoothness. For the multi-modal characteristics of the system, introduce a dynamic smoothing strategy based on modal switching. According to the modal switching signal, recalculate the smoothing factor and clustering strategy. Evaluate the performance of the smoothing algorithm by comparing the difference between the smoothed error correction signal and the actual output signal. If the fluctuation of the error correction signal does not reach the predetermined threshold, adjust the clustering and smoothing strategies according to the evaluation results to optimize the error correction process.

[0014] Further: Step 7 includes: By real-time monitoring the system state and external environmental factors, analyze the triggering conditions of modal switching. When the change amount of the system state or the change amount of the external environment exceeds the set threshold, it is determined that the modal switching condition is met. Based on the historical modal switching data and the current system state, design a prediction model based on machine learning. The model extracts features and trains to predict whether modal switching is required at the next moment and gives the optimal switching time. Combine the modal feedback backstepping compensation algorithm and the adaptive transient error clustering and smoothing algorithm to predict the error after modal switching and take compensation measures in advance. Adopt a multimodal optimization algorithm to dynamically adjust the system control parameters to adapt to the new modal state, and optimize the control parameters by evaluating the system performance.

[0015] Furthermore: Step 8 includes: Construct a closed-loop feedback system, including an error sampling module, a real-time calibration adjustment module, and a calibration effect feedback module; the error sampling module monitors the system output signal in real time, evaluates the error level, the calibration adjustment module dynamically adjusts the system parameters according to the error information, and the calibration effect feedback module evaluates the system performance after adjustment to form a closed-loop adjustment mechanism; The error sampling module collects the system output error. After preprocessing, combined with a non-stationary error elimination network, it ensures the accuracy of the feedback signal; through error comparison and correction, it dynamically adjusts the calibration parameters using an adaptive adjustment algorithm; Based on the error feedback mechanism, adopt an adaptive fuzzy logic control algorithm, combined with the modal switching and error correction requirements, to intelligently adjust the system parameters. The input of the fuzzy controller is the real-time error, modal switching information and its change rate, and the output is the optimized control parameters; After each calibration adjustment, evaluate the calibration effect through the feedback loop and transfer the result to the error sampling module; if the error after calibration does not reach the predetermined threshold, the system continues to adjust the parameters until the accuracy requirement is met: Adopt a long-term stability monitoring algorithm to monitor the system performance indicators, prevent over-calibration or loss of stability under different environmental conditions, and ensure that the system maintains the optimal state during long-term operation by dynamically optimizing the feedback loop.

[0016] Furthermore: Step 9 includes: Construct a hierarchical error optimization framework, divide the system error into multiple levels according to different stages of modal switching; each modal level corresponds to a specific error structure, and the framework includes modal level division, hierarchical error correction module, and global error optimization module; Analyze the error characteristics under different modes and construct an error model; Adopt a hierarchical adaptive particle swarm optimization algorithm to optimize the modal error layer by layer; Update the modal parameters according to the optimization results. The error correction module corrects the error of the modal level according to the new control parameters, and performs iterative optimization through error sampling and feedback; Integrate the optimization results of each modal level, and perform global error optimization through a multi-objective optimization algorithm to ensure the overall performance of the system during multi-modal switching; Evaluate the effectiveness of the optimization results through an error verification module; if the error does not reach the predetermined accuracy standard, re-execute the optimization process to form an iterative feedback mechanism and gradually approach the optimal solution.

[0017] Further: The step 10 includes: Construct a global multi-modal error self-learning and optimization framework, including a multi-modal error learning module, a global feedback learning network, and an adaptive error optimization mechanism; this framework dynamically identifies and processes errors in different modalities based on real-time data streams and feedback mechanisms; Adopt an adaptive neural network regression model, which is trained through historical error data and real-time feedback information to generate a non-linear error function; Based on the error self-learning module, construct a global feedback learning network, fuse error data in different modalities, generate a globally optimized error correction strategy, and dynamically adjust the control strategy under real-time environmental feedback; Through a multi-objective optimization algorithm, realize error interaction and collaborative correction between different modalities, and balance the errors of each modality based on the selection strategy of Pareto optimal solutions; Introduce a dynamic update mechanism, collect error data in real-time and feedback it to the global learning network, and dynamically adjust the optimization parameters through online learning to ensure the minimization of system errors during modality switching; Evaluate the effectiveness of the optimization results through an error verification module. If the error does not reach the predetermined accuracy standard, re-execute the optimization process to form an iterative feedback mechanism and gradually approach the optimal solution.

[0018] On the other hand, the present invention discloses an error self-calibration device for a hemispherical resonator gyroscope, including: a modal adaptive mapping module: realizing mapping and transition between modalities through an adaptive modal mapping algorithm; A non-stationary error elimination module: using a non-stationary error elimination network to identify and eliminate transient errors generated during modality switching; A modal feedback backstepping compensation module: optimizing the error compensation process based on a modal feedback backstepping compensation algorithm to enhance the adaptive ability of the system to complex dynamic changes; A multi-dimensional time-domain modal self-regulation control module: introducing a multi-dimensional time-domain modal self-regulation control algorithm to automatically adjust the control parameters of the gyroscope in different modalities; An error correction generation module: generating an error correction signal through a generative adversarial network to optimize the correction of error patterns and improve the output accuracy; An adaptive transient error clustering and smoothing module: designing an adaptive transient error clustering and smoothing algorithm to identify and eliminate transient errors in real-time and smooth the system output signal; A modal switching decision support and prediction module: constructing a modal switching decision support and prediction algorithm to judge the timing of modal switching, predict the error after switching, and compensate in advance; A feedback loop self-calibration module: adjusting the system control and calibration parameters in real-time through a closed-loop feedback mechanism; Modal Hierarchical Stratified Error Optimization Module: Design a modal hierarchical stratified error optimization algorithm to perform stratified optimization on errors at different modal levels; Global Multimodal Error Self-Learning and Optimization Module: Introduce a global multimodal error self-learning and optimization algorithm, combine adaptive learning and global optimization strategies to achieve error self-learning and system optimization.

[0019] Compared with the prior art, the technical progress achieved by the present invention lies in: By introducing a global multimodal error self-learning and optimization algorithm, the present invention enables the hemispherical resonant gyroscope to adaptively learn error characteristics and perform dynamic adjustment under different working modes. The system can continuously self-correct during long-term operation. Through the input and feedback learning of real-time data streams, the error compensation strategy is optimized in real time. Especially during the mode switching process, the error model can quickly self-update based on historical data and the current state, thereby effectively coping with the error fluctuations caused by mode switching. This self-learning ability is the key to solving the problem that traditional methods cannot effectively handle sudden errors.

[0020] Traditional error compensation methods for hemispherical resonant gyroscopes often have difficulty handling transient errors during mode switching because these errors usually cause severe fluctuations in the system output within a short period of time, affecting accuracy and stability. The modal feedback backstepping compensation algorithm and non-stationary error elimination network and other technologies of the present invention can efficiently compensate for and eliminate transient errors during the mode switching process. Through multimodal error learning and optimization, the system can automatically perform error backstepping and adjustment at the moment of mode switching, thereby minimizing the impact of transient errors on the output signal and maintaining the stable output of the gyroscope.

[0021] By introducing a multi-dimensional time-domain modal self-regulation control algorithm and a modal hierarchical stratified error optimization algorithm, the present invention can perform error optimization at the global level, coordinate the error impacts between different modes, and ensure the balance and optimization between each mode. During the mode switching process, the system does not ignore the errors of any mode, but realizes the dynamic adjustment of the errors of each mode through a global optimization mechanism, further improving the stability and accuracy of the system in a complex environment.

[0022] With the help of an error correction generation algorithm based on a generative adversarial network, the present invention can generate a more accurate error correction model through an adversarial training strategy. This model can respond to system errors in real time and effectively correct transient errors during mode switching. The introduction of the generative adversarial network makes the error correction process more accurate and avoids problems such as over-correction or insufficient correction that may be caused by traditional models. The feedback mechanism enables the gyroscope to continuously adapt to changes in the external environment through continuous error detection and optimization, further enhancing its error correction ability during long-term operation.

[0023] The modal switching decision support and prediction algorithm and the adaptive transient error clustering and smoothing algorithm can predict and make decisions on the error compensation strategy in real time for each modal switch. By analyzing and clustering the error patterns in historical data, the system can make a pre-judgment before modal switching, automatically adjust the operating parameters, and ensure the timeliness and accuracy of error correction. Through this series of innovative algorithms, the gyroscope can efficiently handle the transient errors and modal switching under different environments, improving its response speed and accuracy.

[0024] In the present invention, the combination of the feedback loop self-calibration algorithm and the global multi-modal error self-learning and optimization algorithm ensures stable transition between all modes and error minimization. Even in a complex dynamic environment, the system can maintain the optimal working state through an efficient feedback loop and a global optimization strategy, avoiding any performance degradation caused by modal switching. This global optimization strategy ensures the long-term stable operation of the hemispherical resonant gyro under variable working conditions, further improving its accuracy and reliability.

[0025] In summary, the present invention can not only effectively solve the transient error problem caused during modal switching, but also perform global optimization and error correction in real time. Brief Description of the Drawings

[0026] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention.

[0027] In the drawings: Figure 1 is a flowchart of the present invention. Detailed Embodiments

[0028] The following specific embodiments can be combined with each other. The same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present invention will be described below in conjunction with the drawings.

[0029] As Figure 1 shown, the present invention discloses an error self-calibration method for a hemispherical resonant gyro, including: The goal of specific step 1 is to achieve efficient mapping between modes, enabling the gyroscope to quickly identify and adapt to new vibration characteristics during modal switching and smoothly transition. To achieve this goal, the adaptive modal mapping algorithm combines multi-dimensional signal analysis, time-frequency feature extraction, and a dynamic learning mechanism. The specific steps are as follows: 1. Signal acquisition and preliminary data processing First, through the sensor array of the gyroscope, real-time vibration data is collected, including electrode excitation signals, acceleration data, angular velocity data, etc. To extract modal features, in this embodiment, high-precision sampling and preprocessing of the signals are required to remove noise and low-frequency interference. A band-pass filter can be used to filter the signals to retain the key signal frequency bands. 2. Time-frequency Feature Extraction and Modal Analysis To identify and distinguish different modes, the short-time Fourier transform is used to perform time-frequency analysis on the signals. The short-time Fourier transform maps the original signal to the time-frequency plane to obtain the distribution of the signal in time and frequency:

[0030] where, is the original signal, is the window function, is the time-frequency distribution. Through the short-time Fourier transform, the frequency components of the signal at each moment and their corresponding amplitude and phase information can be obtained.

[0031] Next, based on the spectral peak extraction algorithm for the time-frequency diagram, key modal features (such as frequency peaks, bandwidths, etc.) can be extracted from the time-frequency diagram, and the spectral changes at each modal transition are recorded. These features will be used for subsequent modal mapping.

[0032] 3. Preliminary Construction of Modal Mapping To achieve effective mapping between modes, an adaptive modal mapping matrix needs to be designed. After each modal transition, the time-frequency features of the current mode and the features of the previous mode are recorded, and the similarity between them is calculated. The similarity measure can use the cosine similarity, and the formula is as follows:

[0033] where, and are two modal feature vectors respectively, and the dot product calculates their similarity, and are the norms of the feature vectors.

[0034] Based on the similarity measure, in this embodiment, a modal mapping matrix can be constructed. This matrix records the conversion rules between modes. Specifically, each element of the matrix represents the mapping strength from mode to mode . This mapping matrix will be dynamically updated according to the real-time data to make it adaptively change.

[0035] 4. Adaptive Learning Mechanism and Modal Mapping Update To ensure the adaptability of the mapping, this embodiment introduces an incremental learning strategy. Each time a modality switch occurs, the incremental least squares method is used to adjust the mapping matrix. The incremental least squares method can fine-tune the mapping matrix according to the new modality features. The specific update rules are as follows:

[0036] where, is the learning rate, is the feature difference vector between the current modality and the previous modality. This update strategy can ensure that the mapping matrix can be adjusted in a timely manner according to new data during modality switching.

[0037] 5. Modality Switch Prediction and Mapping Output Through the continuous update of the adaptive mapping matrix, this embodiment can predict the conversion relationship between the current modality and the next modality each time a modality switch occurs, so as to adjust the electrode excitation signal in advance and achieve a smoother transition. This prediction process can perform a regression analysis through historical data and apply a time series-based prediction model (such as LSTM or RNN) to predict the modality switching information at the next moment, so as to provide a more accurate pre-adjustment signal.

[0038] The basic structure of this prediction model is:

[0039] where, is the input feature vector at the current moment, are the parameters of the model, is the modality prediction value at the next moment.

[0040] 6. Modality Transition and Output Correction During the modality switching process, through the collaborative action of the adaptive modality mapping matrix and the prediction model, the electrode drive signal is adjusted in real time to achieve a smooth transition between modalities. Specifically, the mapping matrix gives the relationship between modalities, and the prediction model provides the switching time point and the modality features after switching, so that the system can dynamically adjust the electrode signal according to the mapping relationship and the prediction result, minimizing the transient error to the greatest extent.

[0041] This step can achieve fast mapping and transition between modalities, not only being able to sense modality changes in real time, but also pre-adjusting the system working state during the modality switching process to avoid the influence of transient errors on the gyroscope output. In specific implementation, through time-frequency feature extraction and an adaptive learning mechanism, the system can efficiently adjust the electrode excitation signal to ensure a smooth transition during the modality switching process.

[0042] Specifically, step 2 includes: In step 1, an adaptive modal mapping algorithm is designed in this embodiment. Its core function is to identify and map the transitions between different modes in real time, ensuring that the system can transition smoothly and reduce the generation of errors when switching modes. Based on this premise, the goal of step 2 is to further identify and eliminate the transient errors generated during the mode switching process through a non-stationary error elimination network, ensuring the stability and accuracy of the gyroscope output.

[0043] 1. Real-time error acquisition and preprocessing First, based on the modal information and signal mapping output by the adaptive modal mapping algorithm, this embodiment needs to collect the errors during each mode switching process. These errors usually manifest as transient fluctuations in frequency, amplitude, or phase. Especially during mode transitions, this embodiment collects the output signals of the system in real time (including angular velocity, acceleration, and electrode signals, etc.) and calculates the error between the output signal and the ideal value. The error signal is passed through a high-pass filter to remove low-frequency noise and long-term drift, so as to focus on the high-frequency transient errors caused by mode switching.

[0044] 2. Time-series error modeling and feature extraction Through the acquisition of real-time error signals, this embodiment first uses the short-time Fourier transform to perform time-frequency analysis on the error signals. In this way, this embodiment can not only determine the spectral characteristics of the errors, but also understand the trend of the errors changing with time. For example, the transient errors during mode switching usually cause significant changes in frequency and amplitude, and the short-time Fourier transform can reveal this time-varying characteristic.

[0045] Furthermore, this embodiment uses the empirical mode decomposition method for the error signals to perform multi-scale time-series analysis, decomposing the complex error signals into a series of intrinsic mode functions (IMFs). Each intrinsic mode function represents the error components at different scales and has good resolution, which can help to more accurately identify the non-stationary errors brought by mode switching. The decomposition process of the intrinsic mode function is as follows:

[0046] Among them, is the error signal, is the th intrinsic mode function, is the residual.

[0047] 3. Dynamic learning of non-stationary error features To make the error compensation adaptive and efficient, this embodiment uses a Recurrent Neural Network (RNN) for error modeling. Specifically, this embodiment employs a Long Short-Term Memory network (LSTM) to capture the long-term dependencies of error signals. When dealing with non-stationary time series data, LSTM can effectively avoid the problem of gradient vanishing or explosion, enabling the model to learn the complex time series features during the mode switching process.

[0048] Through the dynamic learning of error signals, the LSTM network can adaptively adjust its weights according to the error characteristics after mode switching, thereby predicting and eliminating non-stationary errors in real time.

[0049] 4. Error Compensation Network Design and Optimization Based on the learning results of the LSTM network, this embodiment designs an Error Compensation Network (ECN), whose goal is to generate a compensation signal according to the predicted error characteristics to eliminate the transient errors generated during mode switching. The ECN network structure includes an input layer, an LSTM module, an error prediction layer, and a compensation output layer. The formula for generating the compensation signal is as follows:

[0050] where, is the error signal, are the parameters of the ECN network, is the compensation signal.

[0051] To optimize the effect of the error compensation network, this embodiment trains the ECN network by the gradient descent method (such as the Adam optimization algorithm) to minimize the loss function between the predicted error and the actual error. The loss function uses the Mean Squared Error (MSE):

[0052] where, is the actual error, is the predicted error, is the number of samples.

[0053] 5. Non-stationary Error Elimination and Feedback Mechanism Once the ECN network generates a compensation signal, this compensation signal will be applied to the control system of the gyroscope to adjust the electrode excitation signal in real time to eliminate the transient errors caused by mode switching. Meanwhile, this embodiment introduces a feedback mechanism to feedback the compensated signal into the system to compare the difference between the corrected output and the target output, thereby further correcting and optimizing the compensation signal.

[0054] The update formula of the feedback mechanism is as follows:

[0055] Wherein, is the current control signal, the adaptive modal mapping algorithm is the learning rate, is the target output, is the current output.

[0056] 6. Real-time evaluation and update of error cancellation effect To ensure the effect of error cancellation, the system regularly evaluates the accuracy of error cancellation. In this embodiment, by comparing the error between the model prediction value and the actual output, the error cancellation rate is calculated:

[0057] When the error cancellation rate reaches the set threshold, the system will stop the update of error compensation. Otherwise, continue to optimize the error cancellation effect by adjusting the parameters of the ECN.

[0058] Through the above steps, the non-stationary error cancellation network can effectively identify and eliminate the transient errors introduced during the mode switching process. Based on the dynamic learning of LSTM and the optimization of the error compensation network, the non-stationary error cancellation network can adaptively adjust the electrode drive signal to achieve real-time and high-precision error cancellation. Through the feedback mechanism and real-time error evaluation, the system can continuously optimize and maintain high stability and high precision of the output.

[0059] Specifically, step 3 includes: In step 1, in this embodiment, the adaptive modal mapping algorithm is used to complete the modal identification and transition mapping during the mode switching process, providing the system with a real-time understanding between different modes; in step 2, the non-stationary error cancellation network effectively identifies and eliminates the transient errors generated during the mode switching process. Based on these technical foundations, the goal of step 3 is to further optimize the error compensation process through the modal feedback backstepping compensation algorithm. Especially when the system encounters complex dynamic changes, by adjusting the compensation strategy in real time through feedback, the adaptive ability of the system to unknown or sudden modal errors is enhanced. This algorithm combines the ideas of feedback control, reverse inference, and dynamic optimization to ensure that the output of the gyroscope remains accurate even in a dynamic environment.

[0060] 1. Design of modal feedback mechanism The modal feedback mechanism is the basis of this algorithm, aiming to adjust the compensation signal of the system through real-time feedback on modal changes. To efficiently capture the impact of modal changes on errors, in this embodiment, the feedback signal is first defined based on the output data of the adaptive modal mapping algorithm and the non-stationary error cancellation network. In this process, the feedback signal will be adjusted in real time by combining the characteristic changes during mode switching (such as transient changes in frequency, amplitude, and phase) and the compensation signal of the error cancellation network.

[0061] When defining the feedback signal, set the modal feedback amount is the deviation between the error signal and the ideal target after modal switching. The calculation formula for the feedback signal is:

[0062] where is the target signal, is the current output signal, is the feedback signal.

[0063] 2. Establishment of the backstepping compensation mechanism The backstepping compensation mechanism adjusts the compensation signal through the feedback signal to eliminate the error caused by modal switching. In this process, this embodiment assumes that the output of the gyroscope is controlled by the coupling effect of multiple modes. Therefore, it is necessary to back-calculate the compensation amount based on modal characteristics (such as frequency and phase, etc.) and apply it to the control signal.

[0064] To achieve backstepping compensation, this embodiment introduces a modal coupling model, which describes the interaction between different modes and the error generation mechanism. Assuming that the gyroscope output error can be back-calculated and corrected through the coupling relationship between each mode, then the compensation amount can be calculated by the following formula:

[0065] where is the matrix describing the modal coupling relationship, is its inverse matrix, and this matrix is obtained from previous experimental data or dynamically calculated through an incremental learning method.

[0066] 3. Real-time update of the backstepping compensation algorithm To enable the compensation algorithm to adjust according to real-time changes, this embodiment introduces an incremental learning mechanism to dynamically update the backstepping compensation parameters based on the error signal during modal switching. Incremental learning allows the system to update the backstepping compensation strategy in a timely manner when facing new modal switches, ensuring a tight correlation between the compensation signal and the real-time error.

[0067] Based on the LMS (Least Mean Square) algorithm, the compensation update formula is designed as:

[0068] where is the learning rate, which controls the update speed and accuracy of the system, is the feedback signal at the current moment.

[0069] 4. Generation and application of the error compensation signal Through the compensation amount updated in real time , the system will generate compensation drive signals and apply them to the control system of the gyroscope to correct the errors in the output signals. These compensation drive signals will guide the electrode excitation signals to ensure the accuracy of the gyroscope output.

[0070] The specific process of generating the compensation signal is as follows:

[0071] Among them, is the actual control signal, is the reference control signal, is the compensation signal generated by the modal feedback backstepping compensation algorithm.

[0072] 5. Real-time feedback regulation and error minimization To improve the accuracy and stability of the feedback mechanism, the system will regularly evaluate the results of the backstepping compensation through the feedback adjustment algorithm and further optimize the compensation parameters according to the new feedback signals. Through repeated iteration and update, the compensation signals will be continuously adjusted until the error is minimized.

[0073] The feedback adjustment algorithm is based on the optimization objective - minimizing the error loss function , and its formula is:

[0074] Among them, T is the length of the time window, and are the target output and the current output respectively, and the loss function \(\mathcal{L}\) is continuously optimized to ensure the minimization of the error.

[0075] 6. Evaluation of compensation effect during modal transition To ensure the effectiveness of the backstepping compensation during the modal switching process, the system will perform real-time evaluation of the compensation effect after each modal switching. The evaluation process will compare the error between the compensated output signal and the target signal, and quantify the compensation effect through the error elimination rate:

[0076] When the error elimination rate reaches the preset threshold, the system considers that the compensation is accurate enough and the backstepping compensation process can be completed.

[0077] The modal feedback backstepping compensation algorithm can achieve efficient and accurate error correction during modal switching by introducing a dynamic compensation method based on the feedback mechanism. Through real-time feedback of modal errors, backstepping compensation, and incremental learning adjustment, the system can adaptively adjust the compensation signal to maximize the elimination of transient errors caused by modal switching. The dynamic optimization and real-time update of the compensation signal enable this algorithm to not only handle traditional error compensation problems but also cope with non-stationary errors in complex dynamic environments.

[0078] Specifically, step 4 includes: In the previous steps, the adaptive modal mapping algorithm, the non-stationary error elimination network, and the modal feedback backstepping compensation algorithm have successfully identified and eliminated transient errors during modal switching. At the same time, to further improve the system stability and accuracy, the goal of step 4 is to introduce a multi-dimensional time-domain modal self-regulation control algorithm, which will combine multi-dimensional time-domain signal analysis, adaptive regulation strategies, and modal adaptive mechanisms to automatically adjust the control parameters of the gyroscope in different modes, thereby optimizing the overall performance of the system and ensuring its stability and high precision in dynamic working environments.

[0079] 1. Multi-dimensional signal acquisition and modal feature extraction To perform effective control and adjustment in different time-domain modes, this embodiment first needs to collect multi-dimensional signals from the gyroscope system, mainly including angular velocity, acceleration, control electrode signals, and feedback signals, etc. Through the acquisition of these signals, this embodiment can not only track the working state of the gyroscope but also capture the complex dynamic characteristics during modal switching.

[0080] Multi-dimensional time-frequency analysis techniques, such as wavelet transform (WT) or short-time Fourier transform, are used to extract time-frequency domain features of these signals, especially to analyze the spectral components of high-frequency transient changes and modal transitions. By analyzing the changes in frequency, phase, amplitude, etc. of each mode, this embodiment can capture the conversion characteristics between modes and the time-domain behavior of transient errors.

[0081] 2. Time-domain error analysis and extraction of modal self-regulation parameters Through the time-frequency analysis of multi-dimensional signals and combined with the output of the non-stationary error elimination network in the previous steps, this embodiment needs to further analyze the time-domain change trend of errors. In error analysis, the system will real-time evaluate the error dynamics in each mode, especially the change rate of transient errors and its correlation with the modal switching process.

[0082] On this basis, this embodiment adopts an adaptive modal control strategy to extract modal self-regulation parameters from the change rate of time-domain errors. These parameters are used to describe the error characteristics of the system output in different modes and the corresponding adjustment requirements. The definition of modal self-regulation parameters is:

[0083] Among them, is the current output signal, is the target signal, is the adjustment parameter for the change of time-domain error, is the adjustment coefficient to control the adjustment sensitivity.

[0084] 3. Design of Multidimensional Time-Domain Adaptive Control Model Based on the above error analysis, in this embodiment, a multidimensional time-domain adaptive control model is constructed. This model can not only identify the error dynamics after mode switching in real time, but also adjust the mode control parameters to cope with the changes in different modes.

[0085] Specifically, the multidimensional time-domain adaptive control model is based on the aforementioned mode self-adjusting parameter , and dynamically adjusts the control signal during the mode switching process. The update formula of the control signal is as follows:

[0086] Among them, is the original control signal, is the time-domain error adjustment parameter, is the control gain matrix. By adjusting , in this embodiment, the error compensation effect in each mode can be flexibly controlled.

[0087] 4. Feedback Control of Mode Self-Adjusting Mechanism In order to further enhance the stability and adaptive ability of the system, the mode self-adjusting mechanism will introduce a feedback control strategy. By real-time monitoring the error and system response after mode switching, the system can dynamically adjust the gain of the control signal and optimize the adjustment parameter through the feedback loop.

[0088] Specifically, in this embodiment, PID control (Proportional-Integral-Differential control) is used to optimize the adjustment process of the control signal. The feedback control formula is as follows:

[0089] Among them, is the error signal, is the proportional gain, is the integral gain, is the differential gain, is the final control signal. This feedback mechanism ensures the sensitivity of the system to dynamic errors and can also reduce the steady-state error.

[0090] 5. Real-Time Optimization and Adjustment of Multidimensional Time-Domain Self-Adjusting Control To further optimize the control effect of the system, the multi-dimensional time-domain self-regulating control algorithm will regularly evaluate and optimize the parameters of the modal self-regulating control. During the optimization process, the system uses a genetic algorithm or a particle swarm optimization algorithm (PSO) to optimize the gain matrix according to the current time-domain error and the feedback control signal. and the adjustment coefficient .

[0091] The fitness function of the genetic algorithm is defined as:

[0092] By continuously iteratively optimizing the gain matrix and the adjustment coefficient, the system can continuously adjust the control signal to achieve the best error compensation effect.

[0093] 6. System Performance Evaluation and Self-Regulating Effect Confirmation During the implementation of the multi-dimensional time-domain self-regulating control algorithm, the system will continuously evaluate its performance, especially the error elimination rate and stability. By continuously adjusting the control gain and feedback parameters, the system will gradually increase the error elimination rate until the target accuracy is reached. The calculation method of the error elimination rate is the same as described above, and the compensation effect is evaluated by comparing the difference between the target output and the actual output.

[0094] The multi-dimensional time-domain modal self-regulating control algorithm can achieve efficient real-time regulation by combining multi-dimensional signal acquisition, time-domain error analysis, modal self-regulation, and feedback control mechanisms, and optimize the performance of the gyroscope system in a dynamic environment. Through real-time feedback and gain optimization, the multi-dimensional time-domain modal self-regulating control algorithm can effectively handle complex errors during the modal switching process and ensure that the gyroscope can maintain high precision and high stability in different working modes.

[0095] Specifically, step 5 includes: In steps 1 to 4, this embodiment has completed the design of links such as modal adaptive mapping, non-stationary error elimination, modal feedback backstepping compensation, and multi-dimensional time-domain self-regulating control. The combination of these technologies provides a relatively accurate error compensation mechanism for the gyroscope system. However, due to the complexity and dynamic changes of the system, the existing compensation methods may still have limitations when dealing with more complex or unknown error patterns. Therefore, the focus of step 5 is to introduce a generative adversarial network (GAN) and construct an error correction generation algorithm based on the generative adversarial network. This algorithm will combine the potential of the generative adversarial network and automatically predict and correct more complex and difficult-to-model error patterns through the generated error correction model, thereby further optimizing the output accuracy of the gyroscope.

[0096] 1. Basic Architecture Design of the Generative Adversarial Network A generative adversarial network (GAN) consists of two main components: a generator and a discriminator. The task of the generator is to generate data that approximates the true error correction signal from random noise or known input features, while the task of the discriminator is to distinguish the difference between the correction signal output by the generator and the true correction signal. In the application of this embodiment, the goal of the generator is to generate an effective error correction model, and the discriminator is used to evaluate the quality of the error correction signal.

[0097] The objective functions of the generator G and the discriminator D can be optimized by minimizing the following adversarial loss:

[0098] where is the true error correction signal, is the error correction signal generated by the generator, is the discriminator, is the generator.

[0099] 2. Preparation of Input Data and Construction of Error Features To effectively train the generative adversarial network, this embodiment needs to prepare rich input data. These data should come from all aspects of steps 1 to 4, especially the control signals and error signals after modal feedback backstepping compensation and multi-dimensional time-domain self-regulation control. These signals will constitute the input features of the GAN and serve as the input vectors of the generator.

[0100] In this step, this embodiment particularly focuses on the construction of error features, that is, by performing deep feature extraction on the output error of the gyroscope, a high-dimensional feature vector that can describe the system state is obtained. Through time-domain feature extraction, frequency-domain feature analysis, and the fusion of modal features, this embodiment can provide rich input data for the GAN, such as:

[0101] where is the input feature vector at time and contains the output signal, the change rate of the output signal, frequency-domain features, and feedback signals.

[0102] 3. Design of the Generator and Generation of Error Correction The task of the generator is to generate an accurate error correction signal by learning the relationship between the input feature and the known error correction signal. For this purpose, this embodiment designs the generator as a deep neural network (DNN), and its network structure includes multiple convolutional layers, fully connected layers, and activation functions to be able to extract effective error correction features from complex input data.

[0103] The output of the generator is the correction signal and is generated through the following network structure:

[0104] where are the parameters of the generator network, is the deep network function of the generator, and the output is the generated error correction signal.

[0105] 4. Design and Training of the Discriminator The task of the discriminator is to judge the difference between the generated error correction signal and the true correction signal, and to prompt the generator to generate a more real and effective correction signal. The discriminator is also a deep neural network (DNN), whose structure is similar to that of the generator, but its output is a binary classification probability value indicating whether the signal is a true signal.

[0106] The training objective of the discriminator is to optimize the network parameters by maximizing the following discriminant loss function:

[0107] Through this loss function, the discriminator can identify the difference between the true signal and the generated signal, thus promoting the training of the generator towards the goal of generating a more real error correction signal.

[0108] 5. Generative Adversarial Training and Error Correction Optimization Through generative adversarial training, the generator and the discriminator will be continuously optimized alternately. The generator gradually learns to generate more and more accurate error correction signals, while the discriminator improves the judgment accuracy by identifying the differences. This process is carried out through adversarial training until the correction signal generated by the generator is almost indistinguishable from the true signal.

[0109] The specific training process is as follows:

[0110]

[0111] where and are the learning rates of the generator and the discriminator respectively, and are the gradients of the generator and the discriminator respectively.

[0112] 6. Error Correction Generation and Real-time Update After the GAN training is completed, the generator can generate accurate error correction signals according to the input signal characteristics and apply it to the control system of the gyroscope. This correction signal will be combined with the other aforementioned compensation signals to achieve more precise output control.

[0113] During the real-time operation of the system, updates for error correction generated by the generative adversarial network will continue to be carried out to ensure that the system can continuously perform effective error correction in new modalities or environmental changes.

[0114] By introducing the generative adversarial network, this embodiment can provide an error correction generation algorithm for the gyroscope system. The generator generates precise error correction signals, and the discriminator evaluates the generation results to optimize the error correction process. This algorithm can not only handle complex and unknown error patterns but also adaptively optimize the compensation signals in a dynamic environment, thus significantly improving the output accuracy and system stability of the gyroscope.

[0115] Specifically, step 6 includes: implementation of the adaptive transient error clustering and smoothing algorithm In the previous steps, this embodiment has established an efficient error compensation and correction mechanism through a series of steps such as the modal adaptive mapping algorithm, non-stationary error elimination network, modal feedback backstepping compensation algorithm, multi-dimensional time-domain modal self-regulation control algorithm, and the error correction generation algorithm based on the generative adversarial network. However, in practical applications, especially in scenarios where modal switching and system state changes are relatively frequent, transient errors (such as errors caused by switching instants or sudden changes in sensor data) may still affect the system performance and weaken the accuracy of the output results. Therefore, the goal of step 6 is to design an adaptive transient error clustering and smoothing algorithm to identify and eliminate transient errors in real time and smooth the system output signal, thereby improving the performance of the gyroscope in complex dynamic environments.

[0116] 1. Definition and identification of transient errors First, in the adaptive transient error clustering and smoothing algorithm, this embodiment first needs to define and identify the transient errors of the system. Transient errors usually manifest as severe fluctuations within a short period and may be caused by the following situations: modal switching, sudden changes in system vibration, external interference, etc. To effectively identify transient errors, this embodiment designs an error fluctuation detector. Based on the transient response characteristics of time-domain and frequency-domain signals, the following criteria are combined to determine whether the error is a transient error. The transient error judgment criteria are as follows:

[0117] Among them, is the change amount of the error, is the error change rate, and are the set thresholds.

[0118] The purpose of transient error detection is to identify those error segments from the output signal of the system that do not conform to the normal variation pattern and have a drastic change. These error segments will be used as inputs for subsequent clustering and smoothing processes.

[0119] 2. Error Clustering and Dynamic Grouping Once the transient error segments are identified, this embodiment needs to classify these error segments through a clustering algorithm for better subsequent smoothing. To this end, this embodiment adopts a clustering algorithm based on dynamic time warping (DTW), which can cluster errors with similar dynamic response characteristics together by measuring the time dynamic characteristics of the error segments.

[0120] The steps of the clustering algorithm include: 1. Error segment extraction: The detected transient error segments are segmented by the sliding window method to obtain the characteristics of each error segment.

[0121] 2. Feature extraction: The characteristics of each error segment include the time-domain variation of the error, the frequency-domain characteristics, and the current modal state of the system.

[0122] 3. Clustering: Use the clustering algorithm based on dynamic time warping (DTW) to classify the extracted error segments to obtain multiple error clustering groups with similar characteristics.

[0123] The goal of clustering is to identify transient errors with similar dynamic patterns and classify them into a group, so as to design a suitable smoothing method according to the clustering results.

[0124] 3. Adaptive Smoothing Processing and Error Correction According to the error clustering results, for different error groups, this embodiment adopts an adaptive smoothing algorithm for error correction and signal smoothing. The core idea of this smoothing algorithm is to design an adaptive weighted smoothing filter for each clustering group, dynamically adjust the filtering parameters according to the characteristics of the group, so that the system can effectively eliminate transient errors while maintaining the smoothness and timeliness of the signal.

[0125] The specific smoothing process can be realized by the weighted moving average method, and the formula is as follows:

[0126] Where, is the smoothed error correction signal, is the current correction signal, is the correction signal at the previous moment, is the adaptive smoothing factor, and its value is automatically adjusted according to the dynamic characteristics of the clustering group.

[0127] Adaptive smoothing factor It is dynamically adjusted according to the error change amplitude of the group. When the error changes violently, reduce , increase the weight of the signal at the previous moment to suppress excessive fluctuations; when the error changes relatively smoothly, increase , enhance the weight of the current correction signal to quickly adapt to the system state.

[0128] 4. Multi-modal smoothing strategy For multiple modal states that may exist in the system (for example, the working mode switch of the gyroscope), the smoothing strategy needs to be further adjusted. In the multi-modal state, the characteristics of the transient error may have different dynamic performances with the change of the mode. Therefore, this embodiment introduces a dynamic smoothing strategy based on mode switching to dynamically adjust the parameters in the smoothing algorithm according to the mode switching signal of the system.

[0129] Specifically, the modal state is obtained through the aforementioned modal adaptive mapping algorithm. Whenever the system undergoes a mode switch, the smoothing algorithm will recalculate the smoothing factor and clustering strategy according to the current modal characteristics, so as to ensure the accuracy of the error correction signal in different modes.

[0130] 5. Smoothing effect evaluation and error correction feedback Finally, in order to ensure the effectiveness of the adaptive transient error clustering and smoothing algorithm, this embodiment designs a real-time feedback evaluation mechanism. This mechanism evaluates the performance of the smoothing algorithm by comparing the difference between the smoothed error correction signal and the actual output signal. If the fluctuation of the error correction signal still exists, the system will adjust the clustering and smoothing strategies according to the evaluation results to continuously optimize the error correction process.

[0131] The error correction feedback can be quantitatively evaluated in the following way:

[0132] Among them, is the actual output error, is the corrected error after smoothing, is the evaluation window size.

[0133] Through the adaptive transient error clustering and smoothing algorithm, this embodiment can effectively identify and eliminate the transient error in the system, and use the dynamic clustering and adaptive smoothing strategy to realize the smoothing and optimization of the error correction signal. This algorithm can not only respond to the impact brought by the transient error in real time, but also continuously provide high-precision and stable output signals for the gyroscope in the context of system state and mode changes, thereby improving the reliability and performance of the entire system.

[0134] Specifically, step 7 includes: In the above steps, in this embodiment, an efficient error self-calibration system has been constructed through a series of steps such as the modal adaptive mapping algorithm, non-stationary error elimination network, modal feedback backstepping compensation algorithm, multi-dimensional time-domain modal self-regulation control algorithm, error correction generation algorithm based on generative adversarial network, and adaptive transient error clustering and smoothing algorithm, and remarkable results have been achieved in aspects such as error correction, transient error suppression, and smoothing. However, the modal switching itself has a profound impact on the performance and stability of the system. Therefore, how to achieve intelligent decision support and accurate prediction of modal switching, enabling the system to flexibly respond to the switching of different working modes, so as to ensure continuous accuracy and stability, becomes the goal of this step.

[0135] The modal switching decision support and prediction algorithm aims to intelligently determine when to perform modal switching based on the current state of the system, the trend of modal changes, and external environmental factors, and predict the performance of the system after switching. Through this intelligent decision-making and prediction ability, this embodiment can effectively predict the errors that may be brought about by modal switching and take preventive measures to reduce or eliminate the impact of these errors on the system output.

[0136] 1. Analysis of Modal Switching Trigger Conditions Modal switching is triggered by external conditions, system state changes, or internal control strategies. Therefore, when implementing decision support for modal switching, it is first necessary to deeply analyze the trigger conditions for modal switching. These trigger conditions can be defined according to different sensor signal changes, external disturbances, working mode requirements, or state changes. By real-time monitoring of the system state, the state fluctuations of the system can be detected, and it can be judged whether the conditions for modal switching are met.

[0137] The specific trigger conditions can be determined through a threshold detection and state recognition mechanism, and the formula is as follows: Trigger Condition Judgment:

[0138] Among them, is the change amount of the system state, is the trigger threshold for modal switching, is the change amount of external environmental factors (such as temperature, acceleration, etc.), is the threshold for environmental factors.

[0139] The purpose of this step is to accurately judge the timing of modal switching by analyzing the current system state and external environment, so as to ensure a smooth and efficient switching process.

[0140] 2. Modal Switching Decision Support Algorithm The core task of the modal switching decision support algorithm is to predict the modal switching requirement at the next moment based on the current modal state and historical data of the system, and make a switching decision in advance according to the prediction result. To achieve this, this embodiment designs a modal switching prediction model based on machine learning. This model uses historical modal switching data and system state data as inputs, and through training, an algorithm that can effectively predict the switching timing in various dynamic environments is obtained.

[0141] The specific steps are as follows: Data collection and preprocessing: Collect historical modal switching data from the system (including information such as switching time, environmental factors, system errors, etc.) and current real-time sensor data. Denoise and normalize the data to improve the accuracy of the subsequent model.

[0142] Feature extraction: Extract features from the real-time sensor data that can effectively describe the system state, including but not limited to the amplitude of error fluctuations, modal switching frequency, external environment changes, etc.

[0143] Model training and prediction: Use time series data modeling algorithms such as support vector machine (SVM) or long short-term memory network (LSTM) to train a prediction system that can predict whether a modal switch is required at the next moment based on the current state and historical data, and give the optimal switching timing.

[0144] The prediction formula is as follows:

[0145] Among them, represents whether a modal switch is required at the predicted next moment, is the current system state feature, is the historical modal switching data, are the model parameters obtained through training.

[0146] The output of this prediction model will be used as the basis for decision support to help the system judge whether to perform a modal switch in a timely and accurate manner.

[0147] 3. Error prediction and compensation after modal switching Once the system determines that a modal switch is required according to the decision support algorithm, the next step is to predict the error after the switch and take effective error compensation measures according to the prediction result. To achieve this, this embodiment designs an error prediction model based on modal changes, which can predict the error after the modal switch before the switch and give appropriate compensation strategies.

[0148] To achieve error prediction and compensation, this embodiment combines the aforementioned modal feedback backstepping compensation algorithm and the adaptive transient error clustering and smoothing algorithm. According to the modal switching moments and error change rules in historical data, it predicts the error of the system after switching and takes pre-compensation measures for correction.

[0149] The error prediction model formula is as follows:

[0150] Where, is the predicted error after switching, is the error prediction weight matrix obtained through training, is the current modal state feature.

[0151] In this step, by predicting the error after switching and making early compensation, this embodiment can effectively reduce the instability caused by modal switching.

[0152] 4. Dynamic Optimization after Modal Switching To ensure the stability and accuracy of the system after modal switching, dynamic optimization after modal switching is crucial. In this stage, this embodiment adopts a multi-modal optimization algorithm to dynamically adjust the control parameters of the system to adapt to the new modal state. By continuously evaluating and adjusting the system parameters, it can ensure that the system maintains the optimal working state in the new mode after switching.

[0153] The dynamic optimization is carried out through the following process:

[0154] Where, is the optimal control parameter, is the target output, is the output of the system model based on the current control parameter.

[0155] Through the modal switching decision support and prediction algorithm, this embodiment can intelligently judge the timing of modal switching and predict the error after switching, so as to take compensation measures in advance to ensure the stability and accuracy of the system. This algorithm combines machine learning techniques, error prediction models, and dynamic optimization strategies, and can achieve efficient and stable modal switching management in a complex dynamic environment.

[0156] Specifically, step 8 includes: In the foregoing steps, this embodiment has achieved efficient self-calibration of the hemispherical resonator gyroscope through a series of innovative methods such as mode switching, error compensation, and time-domain adjustment. However, there are still certain errors and uncertainties in operations such as the mode switching process, transient error elimination, and response to external disturbances. This requires the system to perform continuous self-correction and calibration during operation. The goal of the feedback loop self-calibration algorithm is to adjust the control and calibration parameters of the gyroscope system in real time through a closed-loop feedback mechanism, so as to ensure accuracy and stability under long-term operation or complex environments.

[0157] 1. Design of the Feedback Loop Self-Calibration Framework First, design a self-calibration framework. Its core idea is to use real-time errors and system states as inputs, adjust the calibration parameters of the system through a feedback loop, and continuously optimize the system performance. To this end, the designed feedback loop includes an error sampling module, a real-time calibration adjustment module, and a calibration effect feedback module, forming a closed-loop system.

[0158] 1.1 Error Sampling Module: Monitor the output signals of the system in real time, especially the signals related to the gyroscope accuracy. Collect these signals and perform error evaluation to determine the current error level.

[0159] 1.2 Real-Time Calibration Adjustment Module: According to the error information and combined with the current state of the system, adjust the system parameters (such as electrode position, mode frequency, etc.) through an adaptive algorithm.

[0160] 1.3 Calibration Effect Feedback Module: Evaluate the performance of the adjusted system and feedback the results to the error sampling module. If the current error does not reach the predetermined tolerance threshold, the system will continue to adjust the parameters until the best accuracy is achieved.

[0161] The goal of this framework design is to form a dynamic adjustment mechanism to achieve precise error correction under different environmental changes.

[0162] 2. Error Feedback and Dynamic Adjustment Mechanism In the feedback loop, the error feedback mechanism is the key. In this step, the error feedback and dynamic adjustment mechanism will combine the foregoing various error correction methods (such as the modal feedback backstepping compensation algorithm, the adaptive transient error clustering and smoothing algorithm, the non-stationary error elimination network, etc.) to perform feedback correction on the real-time errors. The core idea of this mechanism is to use the error changes during the operation of the system to dynamically adjust the control strategy of the gyroscope to compensate for the errors that the model fails to fully predict or calibrate.

[0163] Specifically, the error feedback mechanism will include the following steps: Error collection and preprocessing: Collect the system output error through sensors and perform denoising processing. For the non-stationary error part, use the non-stationary error elimination network method to eliminate it to ensure the accuracy of the feedback signal.

[0164] Error comparison and correction: Compare the current error with the expected error, and determine the calibration parameters to be adjusted according to the error magnitude and change trend. This process performs parameter correction through an adaptive adjustment algorithm (such as an adjustment algorithm based on modal inversion).

[0165] The error dynamic feedback formula is as follows:

[0166] where, is the system error collected at time ; is the actual output of the system, is the expected output. Through the feedback of the error, the control system can perform necessary calibration.

[0167] 3. Adaptive calibration adjustment algorithm The adaptive calibration adjustment algorithm is based on the aforementioned error feedback and dynamic adjustment mechanism, and performs self-calibration on the system through the optimal control theory. This algorithm dynamically adjusts the calibration parameters of the system (such as modal frequency, sensor gain, etc.) according to the errors and system states collected in real time to minimize the error.

[0168] This embodiment proposes an adjustment algorithm based on adaptive fuzzy logic control. Combining the requirements of modal switching and error correction, it performs intelligent adjustment. The basic idea of this algorithm is to automatically adjust the control parameters according to the fuzzy rules of the current error of the system, so that the system can quickly respond and correct the error. The input of the adaptive fuzzy controller is the real-time error, modal switching information and their change rates, and the output is the optimized control parameters.

[0169] The design formula of the fuzzy controller is as follows:

[0170] where, is the control parameter after adaptive adjustment, is the fuzzy control gain matrix, is the current error, is the error change rate, is the current system state characteristic.

[0171] 4. Real-time feedback of calibration effect After each calibration adjustment, the system will evaluate the calibration effect through a feedback loop and pass the evaluation results to the error sampling module. This mechanism ensures the effectiveness of the calibration and can evaluate and optimize the system performance after each adjustment. The effect evaluation is performed using the following formula:

[0172] in, is the error after calibration, For adjusting the control parameters, through this formula, this embodiment can continuously track the system accuracy and make real-time adjustments.

[0173] 5. Closed-loop system optimization and long-term stability In the process of continuous error feedback and adaptive calibration, the stability of the system is gradually enhanced. In order to ensure that the system always remains in the optimal state during long-term operation, a long-term stability monitoring algorithm is adopted. This algorithm optimizes the feedback loop by monitoring system performance indicators (such as error convergence rate, control parameter changes, etc.) to prevent the system from "over-calibration" or "loss of stability" under different environmental conditions.

[0174] The stability monitoring algorithm formula is as follows:

[0175] in, As an indicator of long-term stability, To adjust the parameters, this indicator is used to evaluate the stability of the system in long-term operation and ensure that the calibration process does not cause the performance of the system to degrade.

[0176] Through the feedback loop self-calibration algorithm, this embodiment achieves the goal of continuously optimizing the performance of the gyroscope during its operation. The algorithm realizes real-time error evaluation and dynamic parameter adjustment through a closed-loop feedback mechanism, and adopts methods such as adaptive fuzzy control and long-term stability monitoring to ensure the accuracy and stability of the system during operation. In this step, the gyroscope system can automatically adjust the control strategy according to real-time feedback in different working modes, thereby minimizing the impact caused by changes in the external environment, transient errors, and mode switching.

[0177] Specifically, step 9 includes: In the foregoing steps, in this embodiment, various technical means have been used to solve problems such as mode switching, error compensation, transient error correction, and feedback loop calibration, further improving the overall accuracy and stability of the hemispherical resonator gyroscope. However, with the increase in system complexity and changes in external environmental factors, traditional error correction methods may not take into account the interaction effects between error characteristics and hierarchical structures in different modes. Therefore, in this context, the goal of the modal hierarchical error optimization algorithm is to further improve the accuracy performance of the system in various working modes by optimizing the relationship between different modes and their hierarchical structures.

[0178] 1. Design of Hierarchical Error Optimization Framework First, a hierarchical error optimization framework needs to be designed. Based on different stages of mode switching, the errors of the entire system are divided into multiple levels for optimization. Each mode (or mode switching) corresponds to a specific error structure, and these error structures are either independent or intertwined with each other, and need to be optimized separately according to the characteristics of each level.

[0179] The framework of hierarchical error optimization includes the following parts: Modal Hierarchical Division: According to the working principle and mode switching characteristics of the gyroscope, the error levels in different modes are determined, and the error characteristics of each modal level can be modeled through empirical formulas, experimental data, or simulation models.

[0180] Hierarchical Error Correction Module: A dedicated error correction module is designed for each modal level to specifically eliminate errors at different levels. This module combines the spatial characteristics, time-domain characteristics, and frequency-domain characteristics of the errors to achieve targeted optimization.

[0181] Global Error Optimization Module: This module integrates the optimization results of each modal level and performs overall error optimization on the system. During the global optimization process, a multi-objective optimization algorithm is used to ensure the minimum error during multi-modal switching.

[0182] 2. Modal Hierarchical Error Analysis In this stage, in this embodiment, it is first necessary to deeply analyze the errors of the gyroscope in different working modes. The errors of each mode have different characteristics. For example, some modes may introduce larger frequency errors, while some modes may generate transient errors due to external vibration effects. These different error characteristics require this embodiment to construct corresponding error models according to the mode types.

[0183] Assume that in mode the error can be expressed as:

[0184] where is modal the error under is modal the actual output under is the expected output under this mode.

[0185] Under different modal levels, the error characteristics may exhibit different dynamic changes, such as the oscillation frequency and amplitude of the error, and may even involve more complex non-linear phenomena. In order to accurately capture and optimize these errors, it is necessary to accurately model each modal level and incorporate an error model related to environmental factors during the modeling process.

[0186] 3. Hierarchical Optimization Process After completing the error analysis, this embodiment enters the hierarchical process of modal level error optimization. This process optimizes the error layer by layer through a multi-level optimization algorithm to ensure that the errors under different modes can be effectively compensated.

[0187] The optimization process of each modal level can be described as a constrained optimization problem, the goal of which is to minimize the modal error while following the constraints of the system. For this purpose, a hierarchical adaptive particle swarm optimization algorithm is adopted, which combines the traditional particle swarm optimization (PSO) and the hierarchical optimization strategy. Through the hierarchical particle swarm optimization process, it gradually approaches the optimal solution of the error.

[0188] The optimization goal of the hierarchical adaptive particle swarm optimization algorithm can be expressed as:

[0189] where is the total number of modes, and are the weight coefficients of mode , is the modal error, is the optimized control parameter. This optimization goal takes into account the balance between error minimization and parameter changes, thus achieving optimal error compensation.

[0190] 4. Modal Level Error Correction and Parameter Update During the optimization process, the error correction module will update the modal parameters according to the optimization results, such as modal frequency, sensor gain, etc. After each optimization is completed, the error correction module will correct the error of the modal level according to the new control parameter. To ensure the effectiveness of the correction, error sampling and feedback will be performed again after the correction, and the optimization will be continuously iterated.

[0191] 5. Global Error Optimization and Adjustment After the optimization of all modal levels is completed, the global error optimization stage is entered. Through the global error optimization module, the overall error of the system level is adjusted by combining the optimization results of each modal level. Global optimization uses a multi-objective optimization algorithm to comprehensively consider the trade-offs and interactions between various modes, ensuring the minimization of errors during different mode switches.

[0192] The global error optimization formula is:

[0193] Where, is the control parameter after global adjustment, is the global optimization weight coefficient.

[0194] 6. Result Verification and Iterative Update Finally, after multi-level error optimization and global optimization, the effectiveness of the optimization results is verified through the error verification module. If the error does not meet the predetermined accuracy standard, the optimization process is restarted to gradually approach the optimal solution. This process forms an iterative feedback mechanism to ensure that the system always maintains accuracy under different working conditions.

[0195] The modal-level hierarchical error optimization algorithm divides the system error into different modal levels and finely adjusts each level through a multi-level adaptive particle swarm optimization algorithm, achieving the minimization of errors during the mode switching process of the hemispherical resonator gyroscope system.

[0196] Specifically, step 10 includes: In the foregoing steps, several key technologies such as hierarchical optimization and correction of multi-modal errors, transient error compensation, and feedback loop self-calibration have been successfully implemented. However, although each modal level and local optimization scheme have been effectively processed, in the face of complex and dynamically changing working environments and unknown environmental disturbances, traditional error correction methods still face certain challenges because a single optimization model cannot handle the intertwined error patterns between multiple modes and cannot adapt in a timely manner to sudden changes in the working state of the gyroscope. To overcome this problem, this embodiment designs an innovative global multi-modal error self-learning and optimization algorithm, which combines an adaptive learning and global optimization strategy to achieve error self-learning and system optimization in a complex dynamic environment, thereby further improving the accuracy and stability of the hemispherical resonator gyroscope.

[0197] 1. Design of the Global Self-Learning Framework The core idea of the global multi-modal error self-learning and optimization algorithm is to construct an error optimization framework that can self-learn in real time. This framework can not only dynamically identify and process errors in different modalities, but also continuously update and optimize parameters through real-time data streams and feedback mechanisms. Specifically, the algorithm designs a multi-modal error learning module, a global feedback learning network, and an adaptive error optimization mechanism, and combines these modules to form a global self-learning system.

[0198] This system relies on real-time data input. It can not only identify errors in the current modality, but also adjust its own learning process according to the conversion between modalities and external interference factors to adapt to changes in the system state.

[0199] 2. Construction of the error self-learning module The error self-learning module is the basis of the entire global multi-modal error self-learning and optimization algorithm. It analyzes the error data generated by the system, identifies and constructs an error model. Different from traditional error modeling methods, this embodiment uses an adaptive neural network regression model, which can automatically generate a non-linear error function based on the input data and continuously optimize and adjust itself over time.

[0200] The training process of this adaptive neural network regression model introduces historical error data and real-time feedback information, and continuously adjusts its weight coefficients to optimize the error compensation process of each modality.

[0201] 3. Global error optimization and learning network Based on the error self-learning module, the global feedback learning network fuses and optimizes the error data of different modalities to generate a globally optimized error correction strategy. The goal of the global error optimization network is to identify error patterns in all modality switches and dynamic changes and make timely optimization adjustments.

[0202] The global learning network combines reinforcement learning (RL) and deep learning (DL) to gradually adjust and update the control strategy under real-time environmental feedback.

[0203] 4. Cooperative mechanism of multi-modal error self-learning and global optimization After realizing error self-learning and global optimization, the global multi-modal error self-learning and optimization algorithm realizes error interaction and cooperative correction between different modalities through a multi-modal adaptive cooperation mechanism. This mechanism adjusts the optimization strategy of each modality in real time through the interaction of the errors and optimization results of each modality, and ensures the minimization of the global error during modality switching.

[0204] This collaborative mechanism relies on a multi-objective optimization algorithm (MOEA), which weighs and adjusts various errors at the global level. Through a selection strategy based on Pareto optimal solutions, the balance of errors in each mode is achieved, thus avoiding the over-optimization of a certain mode from overly affecting the overall stability of the system.

[0205] 5. Dynamic Update and Error Correction Feedback As the system continues to operate, the error correction feedback module will collect error data in real time and input it into the global learning network for retraining. Through this online learning method, the global multi-modal error self-learning and optimization algorithm can dynamically adapt to changes in the environment and working conditions, continuously update the optimization parameters, and ensure the minimization of system errors at each mode switch.

[0206] The global multi-modal error self-learning and optimization algorithm realizes real-time error self-learning and global optimization of the hemispherical resonator gyroscope system in a complex dynamic environment by combining adaptive neural networks, reinforcement learning, and multi-objective optimization algorithms. This algorithm can effectively identify the error characteristics in different modes and, through continuous optimization and adjustment, ensure the accuracy performance and stability of the system during multi-mode switching, thereby significantly improving the comprehensive performance and adaptive ability of the system.

[0207] On the other hand, the present invention discloses an error self-calibration device for a hemispherical resonator gyroscope, including: a modal adaptive mapping module: realizing the mapping and transition between modes through an adaptive modal mapping algorithm; a non-stationary error elimination module: using a non-stationary error elimination network to identify and eliminate transient errors generated during mode switching; a modal feedback backstepping compensation module: optimizing the error compensation process based on a modal feedback backstepping compensation algorithm to enhance the adaptive ability of the system to complex dynamic changes; a multi-dimensional time-domain modal self-regulation control module: introducing a multi-dimensional time-domain modal self-regulation control algorithm to automatically adjust the control parameters of the gyroscope in different modes; an error correction generation module: generating an error correction signal through a generative adversarial network to optimize the correction of error patterns and improve the output accuracy; an adaptive transient error clustering and smoothing module: designing an adaptive transient error clustering and smoothing algorithm to identify and eliminate transient errors in real time and smooth the system output signal; a modal switching decision support and prediction module: constructing a modal switching decision support and prediction algorithm to judge the timing of mode switching, predict the errors after switching, and compensate in advance; a feedback loop self-calibration module: adjusting the system control and calibration parameters in real time through a closed-loop feedback mechanism; Modal Hierarchical Stratification Error Optimization Module: Design a modal hierarchical stratification error optimization algorithm to perform hierarchical optimization on errors at different modal levels; Global Multi-modal Error Self-learning and Optimization Module: Introduce a global multi-modal error self-learning and optimization algorithm, combine adaptive learning and global optimization strategies to achieve error self-learning and system optimization.

[0208] Finally, it should be noted that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A method for self-calibration of an error of a hemispherical resonant gyroscope, characterized in that: include: Step 1: Use the adaptive modal mapping algorithm to achieve mapping and transition between modes; Step 2: Use a non-stationary error elimination network to identify and eliminate transient errors generated during mode switching; Step 3: Based on the modal feedback backstepping compensation algorithm, optimize the error compensation process and enhance the system's adaptive ability to complex dynamic changes; Step 4: Introduce a multi-dimensional time-domain modal self-adjustment control algorithm to automatically adjust the control parameters of the gyroscope in different modes; Step 5: Generate an error correction signal through a generative adversarial network to optimize the correction of the error pattern and improve the output accuracy; Step 6: Design an adaptive transient error clustering and smoothing algorithm to identify and eliminate transient errors in real time and smooth the system output signal; Step 7: Construct a mode switching decision support and prediction algorithm to determine the timing of mode switching, predict the error after switching and compensate in advance; Step 8: Adjust system control and calibration parameters in real time through a closed-loop feedback mechanism; Step 9: Design a modal hierarchical error optimization algorithm to perform hierarchical optimization on the errors at different modal levels; Step 10: Introduce the global multimodal error self-learning and optimization algorithm, combine adaptive learning and global optimization strategy, and realize error self-learning and system optimization.

2. The error self-calibration method of a hemispherical resonant gyroscope according to claim 1, characterized in that: The step 1 comprises: Collect real-time vibration data through the sensor array of the gyroscope, including electrode excitation signals, acceleration data, and angular velocity data; sample and pre-process the collected signals to retain key signal frequency bands; Use short-time Fourier transform to perform time-frequency analysis on the signal, map the signal to the time-frequency plane, extract the frequency component and its amplitude and phase information at each moment, identify key modal features based on the spectrum peak extraction algorithm of the time-frequency diagram, and record the spectrum changes when the mode switches; Design an adaptive modal mapping matrix to calculate the similarity between the current mode and the previous mode, using cosine similarity as a metric. The mapping matrix records the transformation rules between modes, and each element represents the mapping strength between modes, and is dynamically updated according to real-time data. Introducing an incremental learning strategy, using the incremental least squares method to adjust the mapping matrix, fine-tuning the mapping matrix according to the new modal features to ensure timely adaptation when the modality is switched; By continuously updating the adaptive mapping matrix, the mode switching information at the next moment is predicted using a prediction model based on a time series, and the electrode excitation signal is adjusted in advance to achieve a smooth transition. During the mode switching process, the synergistic effect of the adaptive mode mapping matrix and the prediction model is combined to adjust the electrode drive signal in real time to reduce the transient error and ensure a smooth transition of the mode switching.

3. The error self-calibration method of a hemispherical resonant gyroscope according to claim 2, characterized in that: The step 2 comprises: Based on the modal information output by the adaptive modal mapping algorithm, the error signal during the mode switching process is collected, including angular velocity, acceleration and electrode signal, the error between the output signal and the ideal value is calculated, and the low-frequency noise and long-term drift are removed through a high-pass filter to focus on the high-frequency transient error; Perform short-time Fourier transform on the real-time error signal to analyze the spectral characteristics of the error and its changing trend over time; further use the empirical mode decomposition method to decompose the error signal into intrinsic mode functions, analyze the error components at multiple scales, and accurately identify the non-stationary errors caused by mode switching; The error signal is modeled using a long short-term memory network to capture the long-term dependency of the error, and the weight is adaptively adjusted according to the error characteristics after mode switching to predict and eliminate non-stationary errors in real time. Based on the learning results of the long short-term memory network, an error compensation network is designed to generate compensation signals to eliminate transient errors. The network structure of the error compensation network includes an input layer, an LSTM module, an error prediction layer, and a compensation output layer. The Adam optimization algorithm is used to train the ECN to minimize the mean square error between the predicted error and the actual error. The compensation signal generated by the error compensation network is applied to the gyroscope control system to adjust the electrode excitation signal in real time to eliminate transient errors. A feedback mechanism is introduced to compare the compensated signal with the target output to further correct and optimize the compensation signal. The feedback update formula is based on real-time monitoring of the error. Regularly evaluate the accuracy of error elimination, and calculate the error elimination rate by comparing the error between the model prediction value and the actual output; if the set threshold is not reached, continue to optimize the error compensation network parameters until the error elimination rate meets the requirements to ensure high stability and high accuracy of the system output.

4. The error self-calibration method of a hemispherical resonant gyroscope according to claim 3, characterized in that: The step 3 comprises: Based on the output data of the adaptive mode mapping algorithm and the non-stationary error elimination network, the feedback signal is defined; the feedback signal combines the characteristic changes during mode switching and the compensation signal of the error elimination network: The modal coupling model is introduced to describe the interaction between different modes and the error generation mechanism, and the compensation amount is inferred through the inverse matrix of the modal coupling matrix; Adopting incremental learning mechanism, the backstepping compensation parameters are dynamically updated according to the error signal during mode switching; Generate a compensation drive signal based on the real-time updated compensation amount and apply it to the gyro control system to correct the error in the output signal; Evaluate the back-thrust compensation results through the feedback adjustment algorithm and optimize the compensation parameters according to the new feedback signal; After each mode switching, the error between the compensated output signal and the target signal is compared, and the error elimination rate is calculated. When the error elimination rate reaches the preset threshold, the compensation process is completed, ensuring the high accuracy and stability of the system output.

5. The error self-calibration method of a hemispherical resonant gyroscope according to claim 4, characterized in that: The step 4 comprises: Collect multi-dimensional signals from the gyroscope system, including angular velocity, acceleration, control electrode signal and feedback signal; use wavelet transform or short-time Fourier transform to extract time-frequency domain features of the signal, analyze the frequency, phase and amplitude changes during mode switching, and capture the mode conversion characteristics; Combined with the output of the non-stationary error elimination network, the time domain variation trend of the error is analyzed, the time domain error variation rate is extracted, and based on the error dynamics, the modal self-adjustment parameters are extracted to describe the error characteristics of the system output under different modes; Construct a multi-dimensional time-domain adaptive control model, dynamically adjust the control signal according to the modal self-adjustment parameters, and achieve error compensation under different modes by adjusting the gain; Introducing feedback control strategy and using PID control to optimize the regulation process to ensure the system's sensitivity to dynamic errors and the reduction of steady-state errors; Regularly evaluate the parameters of modal self-regulation control, use genetic algorithm or particle swarm optimization algorithm to optimize the gain matrix and adjustment coefficient, the fitness function is defined as the error elimination rate, and adjust the control signal through iterative optimization to achieve the best compensation effect; By comparing the error elimination rate between the target output and the actual output, the system performance is evaluated, and the control gain and feedback parameters are continuously adjusted to gradually improve the error elimination rate.

6. The error self-calibration method of a hemispherical resonant gyroscope according to claim 5, characterized in that: The step 5 comprises: Construct a generative adversarial network, including a generator and a discriminator. The generator generates data that approximates the true error correction signal from the input features, and the discriminator distinguishes the difference between the generated signal and the true signal; The control signal and error signal after modal feedback backstepping compensation and multi-dimensional time domain self-regulation control are collected as the input features of the adversarial network, and a high-dimensional input feature vector is constructed by fusing the time domain, frequency domain and modal features; The generator is designed as a deep neural network, which includes convolutional layers, fully connected layers and activation functions. The generator learns the relationship between the input features and the error correction signal and generates the error correction signal. The discriminator is a deep neural network that outputs binary classification probability values ​​to determine the authenticity of the signal. The discriminator optimizes the network parameters by maximizing the discriminant loss function. By alternately optimizing the generator and the discriminator, the generator generates a correction signal close to the real signal, and the discriminator continuously improves the judgment accuracy; the training process is based on the gradient update of the generator and the discriminator until the generator can generate a correction signal that is difficult to distinguish; After training is completed, the generator generates an error correction signal based on the input signal characteristics and applies it to the gyroscope control system; during real-time operation, the system continues to update the error correction signal through GAN.

7. The error self-calibration method of a hemispherical resonant gyroscope according to claim 6, characterized in that: The step 6 comprises: An error fluctuation detector is designed to determine whether the error is a transient error based on the transient response characteristics of time domain and frequency domain signals. The identification criteria are whether the change amount and change rate of the error exceed the set threshold, thereby filtering out transient error fragments from the system output. A clustering algorithm based on dynamic time warping is used to classify transient error fragments. The characteristics of error fragments, including time domain changes, frequency domain characteristics and modal states, are extracted through the sliding window method, and error fragments with similar dynamic responses are grouped together. For different clustering groups, an adaptive weighted smoothing filter is designed, which is dynamically adjusted according to the error variation to suppress fluctuations and maintain signal smoothness. Aiming at the multimodal characteristics of the system, a dynamic smoothing strategy based on mode switching is introduced. According to the mode switching signal, the smoothing factor and clustering strategy are recalculated; The performance of the smoothing algorithm is evaluated by comparing the difference between the smoothed error correction signal and the actual output signal. If the fluctuation of the error correction signal does not reach the predetermined threshold, the clustering and smoothing strategies are adjusted according to the evaluation results to optimize the error correction process.

8. The error self-calibration method of a hemispherical resonant gyroscope according to claim 7, characterized in that: The step 7 comprises: By real-time monitoring of system status and external environmental factors, the triggering conditions for mode switching are analyzed. When the change in system status or external environment exceeds the set threshold, it is determined that the mode switching conditions are met. Based on historical mode switching data and current system status, a prediction model based on machine learning is designed. Through feature extraction and training, the model predicts whether mode switching is needed at the next moment and gives the optimal switching time. Combine the modal feedback backstepping compensation algorithm and the adaptive transient error clustering and smoothing algorithm to predict the error after mode switching and take compensation measures in advance; A multi-modal optimization algorithm is used to dynamically adjust system control parameters to adapt to new modal states, and control parameters are optimized by evaluating system performance.

9. The error self-calibration method of a hemispherical resonant gyroscope according to claim 8, characterized in that: The step 8 comprises: Construct a closed-loop feedback system, including an error sampling module, a real-time calibration adjustment module, and a calibration effect feedback module; the error sampling module monitors the system output signal in real time and evaluates the error level; the calibration adjustment module dynamically adjusts the system parameters according to the error information; and the calibration effect feedback module evaluates the performance of the adjusted system, thus forming a closed-loop regulation mechanism; The error sampling module collects the system output error, and after preprocessing, combines it with the non-stationary error elimination network to ensure the accuracy of the feedback signal; through error comparison and correction, the calibration parameters are dynamically adjusted using the adaptive adjustment algorithm; Based on the error feedback mechanism, an adaptive fuzzy logic control algorithm is used to intelligently adjust system parameters in combination with mode switching and error correction requirements. The input of the fuzzy controller is the real-time error, mode switching information and its change rate, and the output is the optimized control parameters. After each calibration adjustment, the calibration effect is evaluated through the feedback loop and the result is passed to the error sampling module; if the error after calibration does not reach the predetermined threshold, the system continues to adjust the parameters until the accuracy requirements are met: A long-term stability monitoring algorithm is used to monitor system performance indicators to prevent over-calibration or loss of stability under different environmental conditions. By dynamically optimizing the feedback loop, the system is ensured to maintain the optimal state during long-term operation.

10. The error self-calibration method of a hemispherical resonant gyroscope according to claim 9, characterized in that: The step 9 comprises: A hierarchical error optimization framework is constructed to divide the system error into multiple levels according to the different stages of mode switching. Each modal level corresponds to a specific error structure. The framework includes modal level division, hierarchical error correction module and global error optimization module. Analyze the error characteristics under different modes and build an error model; Adopt hierarchical adaptive particle swarm optimization algorithm to optimize modal error layer by layer; The modal parameters are updated according to the optimization results. The error correction module corrects the errors at the modal level according to the new control parameters and performs iterative optimization through error sampling and feedback. Integrate the optimization results of each modal level, perform global error optimization through a multi-objective optimization algorithm, and ensure the overall performance of the system in multi-modal switching; The effectiveness of the optimization results is evaluated through the error verification module; if the error does not reach the predetermined accuracy standard, the optimization process is re-executed to form an iterative feedback mechanism to gradually approach the optimal solution.

11. The error self-calibration method of a hemispherical resonant gyroscope according to claim 10, characterized in that: The step 10 comprises: Construct a global multimodal error self-learning and optimization framework, which includes a multimodal error learning module, a global feedback learning network, and an adaptive error optimization mechanism. This framework dynamically identifies and processes errors in different modes based on real-time data streams and feedback mechanisms. Adopting adaptive neural network regression model, training through historical error data and real-time feedback information, a nonlinear error function is generated; Based on the error self-learning module, a global feedback learning network is constructed to integrate error data of different modes, generate a globally optimized error correction strategy, and dynamically adjust the control strategy under real-time environmental feedback; Through the multi-objective optimization algorithm, the error interaction and coordinated correction between different modes are realized, and the errors of each mode are balanced based on the selection strategy of Pareto optimal solution; A dynamic update mechanism is introduced to collect error data in real time and feed it back to the global learning network. Through online learning, the optimization parameters are dynamically adjusted to ensure that the system error is minimized when the mode is switched. The effectiveness of the optimization results is evaluated through the error verification module. If the error does not reach the predetermined accuracy standard, the optimization process is re-executed to form an iterative feedback mechanism to gradually approach the optimal solution.

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