CN113987746A - Hemispherical resonator gyroscope use performance improving method based on collective theory - Google Patents

Abstract

The invention discloses a hemispherical resonator gyroscope usability improving method based on collective theory, which comprises the steps of testing static output data of a hemispherical resonator gyroscope, analyzing the obtained data, establishing a time sequence model of random drift of the data, realizing dynamic identification of model parameters aiming at the characteristic that the model changes along with time, estimating an accurate angular rate signal by using an improved collective filtering algorithm, and realizing suppression of random drift errors, thereby improving the usability of the hemispherical resonator gyroscope, and specifically comprising the steps of establishing a random error model, filtering the random errors and evaluating and analyzing the promotion effect. The method has the advantages that the accuracy and the reliability of inhibiting the random drift can be improved, so that the service performance of the method is obviously improved.

Description

A performance improvement method for hemispheric resonant gyroscope based on set membership theory

technical field

The invention belongs to the technical field of inertial navigation, and in particular relates to a method for improving the use performance of a hemispherical resonant gyroscope based on the set membership theory.

Background technique

Hemispherical resonant gyroscopes have outstanding advantages such as long life, short start-up time, and good long-term stability, so they are highly valued in the fields of satellites, space workstations, and detectors. However, due to the late start of domestic research and the limitation of low technological level, the accuracy is relatively low, and it is difficult to meet the military application requirements of high precision in modern warfare. In order to improve its performance, one idea is to improve its production process, structure and circuit. For example, the patent "Gyroscope and devices with structural components comprising HfO ₂ -TiO ₂ material" (US9719168B2) invented a kind of HfO 2 -TiO 2 material containing HfO ₂ -TiO ₂ material. The hemispherical resonator can have good vibration quality; the patent "Precision Assembly and Detection Device of Hemispherical Resonant Gyroscope" (CN211346826U) can realize the six-dimensional precise adjustment of the relative position and relative angle between the resonator and the electrode base , and can perform closed-loop feedback in real time to improve the adjustment accuracy. This kind of method has a remarkable effect on improving the performance of the gyroscope. However, the method of improving the performance of the gyroscope by this method has high cost, long period and great difficulty. Therefore, based on the existing hardware level, it is of great significance to rapidly improve the performance of the hemispherical resonant gyroscope by means of error modeling and compensation, which is of great significance to expand the application range of the hemispherical resonant gyroscope and provide high-precision inertial navigation for guided weapons. For example, the article "Modeling Analysis of HRG Stochastic Error Based on ARMA-AKF"("Piezoelectric and Acousto-Optics" Volume 39 No. 1) proposed a gyroscope random error based on the autoregressive moving average model and the adaptive Kalman filter model. Error processing method, the patent "A method for suppressing random drift error of vehicle-mounted MEMS gyroscope" (CN111561930A) invented a method for processing random drift error of gyroscope. effective suppression. These methods effectively improve the accuracy of the gyroscope to a certain extent. However, the identification and filtering methods they use have strict requirements on the distribution of noise. In practical applications, the statistical characteristics of gyro noise are often quite complex, changing in real time, and there may even be uncertain statistics such as heteroscedasticity and chaotic noise. The noise of the characteristic makes the probability distribution assumption difficult to be satisfied or the statistical characteristics are difficult to determine. This situation will cause the estimation bias and lead to the instability of the estimator. Therefore, it is necessary to provide a new random error modeling and filtering method to overcome the The defects of the traditional filtering method further improve the performance of the hemispherical resonant gyroscope.

SUMMARY OF THE INVENTION

In view of the above-mentioned problems and the analysis and research on the performance of the hemispherical resonant gyroscope, the purpose of the present invention is to provide a method for improving the performance of the hemispherical resonant gyroscope based on the set membership theory, and to realize the hemispherical resonant gyroscope through the set membership identification and the set membership filtering. It overcomes the limitations of traditional identification and filtering methods, and further improves the performance of hemispheric resonant gyroscopes on the basis of existing hardware.

The technical scheme adopted in the present invention is:

A method for improving the performance of a hemispherical resonant gyroscope based on the set membership theory, including the following steps:

Step 1: Build a random error model;

Step 2: Random error filtering;

Step 3: Evaluation and analysis of improvement effect

The estimation result obtained in step 2 is all possible sets of the true angular velocity to which the hemispherical resonant gyroscope is sensitive. The shape of the set is an ellipsoid, and the center of the ellipsoid is used as the point estimation result to analyze the drift suppression situation, and the root mean square of the estimation result is used. Error and bias instability are indicators that characterize the drift of the hemispherical resonant gyroscope; the improvement factor is used to describe the effect of improving the accuracy of the gyroscope, and the improvement factor is defined as:

Among them, Index ₁ represents the random error index after suppression, and Index ₀ represents the random error index before suppression.

Preferably, in step 1, the static output data of the hemispherical resonant gyroscope is collected, the error model of the sample data is established by the time series analysis method after the data is preprocessed, and the model parameters are identified by the set membership identification method to obtain the hemispherical resonant gyroscope. The random error model based on the assumption of bounded noise includes the following steps:

Step 101: Data Preprocessing

After collecting the output data of the hemispherical resonant gyroscope in a static state, the 3σ criterion is used to eliminate the gross errors, and the unit root test method is used to test the stationarity of the output data sequence; if the test result is a non-stationary sequence, the data is subjected to differential processing:

y′ _k =y _k+1 -y _k

Among them, y _k is the original output data, y' _k is the differenced data, and the unit root test method is used to test the stationarity of the differenced data. If the test result is a stationary sequence, the data preprocessing ends; if the result is not If the sequence is stationary, continue to perform differential processing until the unit root test result is a stationary sequence;

Step 102: Determine the model order

Firstly, the autocorrelation feature and partial correlation feature analysis of the preprocessed data sequence is carried out to determine the model structure, and then the Bayesian information criterion is used to determine the order;

Step 103: Model parameter identification

The specific model equation is given according to the model structure and order, and it is converted into the form of a generalized regression model; the boundary of the noise is obtained through the observation data, and the initial value of the model parameters is set; finally, the bound ellipsoid is adaptively constrained The least squares method is used to dynamically identify the model parameters, and an ellipsoid containing a feasible set of parameters is obtained. The center of the ellipsoid is used as the estimated parameter of the model to establish the final error model.

Preferably, in step 102, the Bayesian information criterion function is expressed as:

为残差序列；p为模型阶次；则In the formula: N is the sample length;

is the residual sequence; p is the model order; then

The minimum value of BIC is obtained through the search of the above formula, then i is the order of the AR part, reducing the order of the MA part, and repeating this process, the final model order can be determined.

Preferably, it is characterized in that the specific operation steps of step 103 include:

(1) Establish a random error time series model ARMA:

Among them, y _k gyro drift sequence, n is the AR model order, m is the MA model order, a _i and b _j are undetermined model parameters, and w _k is the additive measurement noise with zero mean;

Convert a random error time series model to a generalized regression model:

Among them, Φ is the time series and noise matrix, θ is the undetermined parameter vector; if w _k is bounded, it satisfies |w _k | ² <γ ² ;

At the same time, it is assumed that the initial value of the parameter to be identified belongs to an ellipsoid:

为椭球的中心，M₀为正定矩阵，定义了椭球的形状；in,

is the center of the ellipsoid, M ₀ is a positive definite matrix, which defines the shape of the ellipsoid;

(2) Then use the outsourcing ellipsoid to approximate the parameter feasible set, and the ellipsoid containing the parameter feasible set can be obtained recursively through the following process

λ_k≥0，后续步骤中以参数可行集的椭球中心作为模型参数。in,

λ _k ≥ 0, in the subsequent steps, the ellipsoid center of the parameter feasible set is used as the model parameter.

Preferably, in step 2, the established random error model is used to transform and obtain the space state equation of the hemispherical resonant gyroscope, and the angular rate is estimated by the set membership filtering algorithm to suppress the random error and improve the use accuracy of the gyroscope. The specific operation steps include:

Step 201: Establish a space state equation

After establishing the time series analysis model of the sample data, establish a linear dynamic system described by the state space equation, select the system state x _k , and determine the state transition matrix F _k , the measurement matrix H _k and the noise according to the model parameters and the system state x _k Drive the matrix G _k to establish the space state equation of the random drift of the hemispherical resonant gyroscope:

x _k =F _k-1 x _k-1 +G _k-1 w _k-1

z _k =H _k x _k +v _k

Set the process noise w _k and measurement noise v _k to be unknown but bounded and belong to the set of ellipsoids appropriate to the noise level:

Among them, Q _k and R _k are known positive definite matrices, which are the shape description matrices of the noise ellipsoid set;

Let the initial state belong to a specific ellipsoid:

为椭球的中心，P₀为正定矩阵；in,

is the center of the ellipsoid, and P ₀ is a positive definite matrix;

Step 202: Set membership filtering process

为上一时刻估计得到的椭球集；Assume

The ellipsoid set estimated for the previous moment;

为椭球的中心，P_k-1定义了椭球的形状，并满足正定性，σ_k-1为大于0的标量；in,

is the center of the ellipsoid, P _k-1 defines the shape of the ellipsoid, and satisfies positive definiteness, σ _k-1 is a scalar greater than 0;

之后得到椭球

同时过程噪声椭球

通过线性变换

后转换为

而估计目标

即为这两个椭球Minkowski和的外定界椭球，其求解过程如下：by linear transformation

Then get the ellipsoid

Simultaneous Process Noise Ellipsoid

by linear transformation

converted to

while the estimated target

It is the outer bounding ellipsoid of the Minkowski sum of the two ellipsoids, and the solution process is as follows:

σ _k|k-1 =σ _k-1

Among them, p _k ∈(0, +∞), using the minimum trace criterion to optimize the parameters, we get

使其同时包含量测值和量测噪声确定的集合

以及时间更新所得的椭球集合

为了提高算法的收敛特性和跟踪能力，采用改进的加权策略来更新椭球集合：In the measurement update phase, the goal of the algorithm is to find an optimal ellipsoid

make it contain both the measured value and the set determined by the measurement noise

and the collection of ellipsoids resulting from the time update

In order to improve the convergence characteristics and tracking ability of the algorithm, an improved weighting strategy is used to update the ellipsoid set:

的求解过程如下：Among them, z _k is the measured value, and the undetermined parameter q _k ≥ 0, through transformation, we get

The solution process is as follows:

残差

in,

residual

In order to improve the stability of the estimated boundary, the parameter optimization method is improved, that is, the optimal parameters are obtained by minimizing σ _k , and the specific solution process of the parameters is obtained by derivation:

时，其最优值为下式的解：when

When , its optimal value is the solution of the following formula:

时，该式无解，此时取0为参数最优值；when

When , the formula has no solution, at this time, take 0 as the optimal value of the parameter;

The updated state ellipsoid contains a high-precision estimation of the input angular rate, so as to suppress the random error of the hemispherical resonant gyroscope and improve the performance.

Beneficial effects of the present invention:

Based on the set membership estimation theory, the invention realizes the online dynamic modeling of the random error signal by adopting the recursive bounded ellipsoid adaptive constraint least square method to identify the parameters of the random error model of the hemispherical resonant gyroscope. By optimizing the weighting strategy and parameter solving method of measurement update, an improved set membership filtering method is realized. This method only requires the noise to be bounded, but does not require the specific distribution of the noise in the boundary, and does not need to know its statistical properties. , which can overcome the defects of the traditional state filtering method; the tracking and stability performance of the filtering method are improved by a new weighting strategy and optimization criterion; in addition, the method can obtain the strict uncertainty boundary constraints of the estimated state. Therefore, applying the proposed identification and filtering method based on the set membership theory to the random error processing of the hemispheric resonant gyroscope can improve the accuracy and reliability of suppressing random drift, thereby significantly improving its use accuracy, and the improvement effect is better than traditional filtering methods.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

FIG. 1 is a schematic block diagram of the performance improvement method of the hemispherical resonant gyroscope based on the set membership theory of the present invention.

Figure 2 shows a graph of the original sequence sample data.

Figure 3 shows the time series graph of the output data after preprocessing.

Figure 4 shows the result of parameter identification of the random error model of the hemispherical resonant gyroscope.

Figure 5 shows the result of random error filtering of the hemispherical resonant gyroscope.

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. The components of the embodiments of the invention generally described and illustrated in the drawings herein may be arranged and designed in a variety of different configurations.

Thus, the following detailed description of the embodiments of the invention provided in the accompanying drawings are not intended to limit the scope of the invention as claimed, but are merely representative of selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

This embodiment specifically provides a method for improving the use performance of a hemispherical resonant gyroscope based on the set membership theory, as shown in FIG. 1 , including the following steps:

Step 1: Build a random error model

Collect the static output data of the hemispherical resonant gyroscope, after preprocessing the data, the error model of the sample data is established by the time series analysis method, and the model parameters are identified by the set membership identification method, and the random error of the hemispherical resonant gyroscope based on the assumption of bounded noise is obtained. model, which includes the following steps:

Step 101: Data Preprocessing

After collecting the output data of the hemispherical resonant gyroscope in a static state, the 3σ criterion is used to eliminate the gross errors, and the unit root test method is used to test the stationarity of the output data sequence; if the test result is a non-stationary sequence, the data is subjected to differential processing:

y′ _k =y _k+1 -y _k

Among them, y _k is the original output data, y' _k is the differenced data, and the unit root test method is used to test the stationarity of the differenced data. If the test result is a stationary sequence, the data preprocessing ends; if the result is not If the sequence is stationary, continue to perform differential processing until the unit root test result is a stationary sequence;

Step 102: Determine the model order

Firstly, the autocorrelation feature and partial correlation feature analysis of the preprocessed data sequence is carried out to determine the model structure, and then the Bayesian information criterion is used to determine the order;

The Bayesian information criterion function is expressed as:

为残差序列；p为模型阶次；则In the formula: N is the sample length;

is the residual sequence; p is the model order; then

The minimum value of BIC is obtained through the above search, then i is the order of the AR part, reduce the order of the MA part, and repeat the process to determine the final model order

Step 103: Model parameter identification

The specific model equation is given according to the model structure and order, and it is converted into the form of a generalized regression model; the noise boundary is obtained through the observation data, and the initial value of the model parameters is set; finally, the adaptive ellipsoid is used to adapt The constrained least squares method is used to dynamically identify the model parameters, and the ellipsoid containing the feasible set of parameters is obtained, and the ellipsoid center is used as the estimated parameter of the model to establish the final error model;

(1) Establish a random error time series model ARMA:

Among them, y _k gyro drift sequence, n is the AR model order, m is the MA model order, a _i and b _j are undetermined model parameters, and w _k is the additive measurement noise with zero mean;

Convert a random error time series model to a generalized regression model:

Among them, Φ is the time series and noise matrix, and θ is the parameter vector to be determined; if w _k is bounded, it satisfies |w _k | ² <γ ² ; at the same time, it is assumed that the initial value of the parameter to be identified belongs to an ellipsoid:

为椭球的中心，M₀为正定矩阵，定义了椭球的形状；in,

is the center of the ellipsoid, M ₀ is a positive definite matrix, which defines the shape of the ellipsoid;

(2) Then use the outsourcing ellipsoid to approximate the parameter feasible set, and the ellipsoid containing the parameter feasible set can be obtained recursively through the following process

λ_k≥0，后续步骤中以参数可行集的椭球中心作为模型参数；in,

λ _k ≥ 0, in the subsequent steps, the ellipsoid center of the parameter feasible set is used as the model parameter;

Step 2: Random Error Filtering

The random error model established by Tongli is transformed to obtain the space state equation of the hemispherical resonant gyroscope, and the angular rate is estimated by the set membership filtering algorithm to suppress the random error and improve the use accuracy of the gyroscope. The specific operation steps include:

Step 201: Establish a space state equation

After establishing the time series analysis model of the sample data, establish a linear dynamic system described by the state space equation, select the system state x _k , and determine the state transition matrix F _k , the measurement matrix H _k and the noise according to the model parameters and the system state x _k Drive the matrix G _k to establish the space state equation of the random drift of the hemispherical resonant gyroscope:

x _k =F _k-1 x _k-1 +G _k-1 w _k-1

z _k =H _k x _k +v _k

Set the process noise w _k and measurement noise v _k to be unknown but bounded and belong to the set of ellipsoids appropriate to the noise level:

Among them, Q _k and R _k are known positive definite matrices, which are the shape description matrices of the noise ellipsoid set;

Let the initial state belong to a specific ellipsoid:

为椭球的中心，P₀为正定矩阵；in,

is the center of the ellipsoid, and P ₀ is a positive definite matrix;

Step 202: Set membership filtering process

为上一时刻估计得到的椭球集；Assume

The ellipsoid set estimated for the previous moment;

为椭球的中心，P_k-1定义了椭球的形状，并满足正定性，σ_k-1为大于0的标量；in,

is the center of the ellipsoid, P _k-1 defines the shape of the ellipsoid, and satisfies positive definiteness, σ _k-1 is a scalar greater than 0;

之后得到椭球

同时过程噪声椭球

通过线性变换

后转换为

而估计目标

即为这两个椭球Minkowski和的外定界椭球，其求解过程如下：by linear transformation

Then get the ellipsoid

Simultaneous Process Noise Ellipsoid

by linear transformation

converted to

while the estimated target

It is the outer bounding ellipsoid of the Minkowski sum of the two ellipsoids, and the solution process is as follows:

σ _k|k-1 =σ _k-1

Among them, p _k ∈(0, +∞), using the minimum trace criterion to optimize the parameters, we get

使其同时包含量测值和量测噪声确定的集合

以及时间更新所得的椭球集合

为了提高算法的收敛特性和跟踪能力，采用改进的加权策略来更新椭球集合：In the measurement update phase, the goal of the algorithm is to find an optimal ellipsoid

make it contain both the measured value and the set determined by the measurement noise

and the collection of ellipsoids resulting from the time update

In order to improve the convergence characteristics and tracking ability of the algorithm, an improved weighting strategy is used to update the ellipsoid set:

的求解过程如下：Among them, z _k is the measured value, and the undetermined parameter q _k ≥ 0, through transformation, we get

The solution process is as follows:

残差

in,

residual

In order to improve the stability of the estimated boundary, the parameter optimization method is improved, that is, the optimal parameters are obtained by minimizing σ _k , and the specific solution process of the parameters is obtained by derivation:

时，其最优值为下式的解：when

When , its optimal value is the solution of the following formula:

时，该式无解，此时取0为参数最优值；when

When , the formula has no solution, at this time, take 0 as the optimal value of the parameter;

The updated state ellipsoid contains a high-precision estimation of the input angular rate, so as to suppress the random error of the hemispherical resonant gyroscope and improve the performance.

Step 3: Evaluation and analysis of improvement effect

The estimation result obtained in step 2 is all possible sets of the true angular velocity to which the hemispherical resonant gyroscope is sensitive. The shape of the set is an ellipsoid, and the center of the ellipsoid is used as the point estimation result to analyze the drift suppression situation, and the root mean square of the estimation result is used. The Root mean square error (RMSE) and the Angular random walk (ARW) and Bias instability (BI) obtained by Allan variance analysis are used to characterize the drift of the hemispherical resonant gyroscope. The factor describes the accuracy improvement effect of the gyroscope, and the improvement factor is defined as:

Among them, Index ₁ represents the random error index after suppression, and Index ₀ represents the random error index before suppression.

Taking a hemispherical resonant gyroscope as an example below, the method for detecting the long-term stability of a hemispherical resonant gyroscope will be further described with reference to the accompanying drawings.

The principle of this embodiment is shown in FIG. 1 .

Step 1: Build a random error model

According to the output characteristics of the hemispherical resonant gyroscope, the sampling interval is set to 0.4s, the sampling number is 18000, and the continuous sampling is 2 hours. The sample data obtained from the test are shown in Figure 2.

标准差为σ＝1.3348e-4，根据3σ准则，其输出稳定范围为

超出该稳定范围的值，予以剔除，并以两侧数据的均值代替。然后进行零均值处理和数据转换，得到预处理后的随机误差时间序列如图3所示。The test data is preprocessed, and it can be obtained by calculation. The mean of the sample data is

The standard deviation is σ=1.3348e-4, and according to the 3σ criterion, the output stability range is

Values outside this stable range are eliminated and replaced by the mean of the data on both sides. Then, zero-mean processing and data transformation are performed to obtain the preprocessed random error time series as shown in Figure 3.

The unit root test method is used to test the stationarity of the output data series, and the results meet the stationarity conditions. Then, the autocorrelation and partial correlation characteristics of the preprocessed random errors are analyzed. The autocorrelation shows the tailing property, and the partial correlation shows the truncation property. According to the time series modeling theory, the AR model is used for modeling. Through the Bayesian information criterion (BIC) criterion analysis, the AR(3) model is selected as the model structure of the random error of the hemispherical resonant gyroscope.

In order to improve the modeling accuracy, the time series error model is treated as a linear time-varying system to improve the modeling accuracy, and the real-time recursive parameter identification method is adopted, and the parameter identification and state estimation are carried out simultaneously during data processing. The identification results of the model parameters of the AR(3) model are shown in Figure 4. It can be seen that the identification method can effectively track the changes of the model parameters.

Step 2: Random Error Filtering

P₀＝I，Q_k＝3.0×10^-11I，r²＝1.52×10^-7，

然后使用发明的集员滤波算法估计系统状态，得到包含真实状态的状态可行集，即包含各时刻真实角速率的椭球集，将椭球集的中心作为真实角速率的估计值，减小随机误差。作为对比，同时也进行基于最小二乘法的时间序列建模和基于卡尔曼滤波的随机误差补偿，作为与本发明随机误差补偿结果的对比。When the model parameters are obtained, the model parameters are substituted into the state transition matrix to establish a system equation. The relevant initial parameters are selected as follows:

P ₀ =I, Q _k =3.0×10 ⁻¹¹ I, r ² =1.52×10 ⁻⁷ ,

Then use the invented set membership filtering algorithm to estimate the system state, and obtain the state feasible set containing the real state, that is, the ellipsoid set containing the real angular velocity at each moment, and use the center of the ellipsoid set as the estimated value of the real angular velocity to reduce the random error. As a comparison, time series modeling based on the least squares method and random error compensation based on Kalman filtering are also performed as a comparison with the random error compensation results of the present invention.

Step 3: Evaluation and analysis of improvement effect

The center of the ellipsoid set containing the true angular rate is taken as the point estimation result of the angular rate, as shown in Figure 5. Use its root mean square error and Allan variance analysis to obtain the angle random walk and zero bias instability indicators to characterize the drift size of the hemispherical resonant gyroscope; use the improvement factor to describe the random error suppression effect and gyroscope performance improvement effect, specifically As shown in Table 1:

Table 1 Performance improvement effect

It can be seen from Table 1 that the data after drift suppression has obvious improvements in the three indicators of root mean square error, angle random walk and zero bias instability, especially the root mean square error is reduced by an order of magnitude, It is proved that the random drift of the hemispherical resonant gyroscope has been effectively suppressed, and its performance has been significantly improved; and the improvement effect is obviously better than that of Kalman filtering, especially the improvement factor of RMSE is further improved by about 56% compared with Kalman filtering. Advantages of the present invention.

The above is only used to illustrate the technical solution of the present invention and not to limit it. Other modifications or equivalent replacements made by those of ordinary skill in the art to the technical solution of the present invention, as long as they do not depart from the spirit and scope of the technical solution of the present invention, should be Included within the scope of the claims of the present invention.

Claims (5)

1. A hemispherical resonator gyroscope use performance improving method based on a collective theory is characterized by comprising the following steps:

step 1: establishing a random error model;

step 2: filtering random errors;

and step 3: promotion effect evaluation analysis

The estimation results obtained in the step 2 are all possible sets of the real angular rate to which the hemispherical resonator gyroscope is sensitive, the sets are ellipsoids, the center of each ellipsoid is used as a point estimation result to analyze the drift inhibition condition, and the root mean square error and the zero-bias instability of the estimation results are used for representing the index of the drift size of the hemispherical resonator gyroscope; describing the use precision improvement effect of the gyroscope by using an improvement factor, wherein the improvement factor is defined as:

therein, Index₁Index representing random error after suppression₀Indicating random errors before suppressionAnd (4) a difference index.

2. The method for improving the service performance of the hemispherical resonator gyroscope based on the centralized theory according to claim 1, wherein in the step 1, the method comprises the steps of collecting static output data of the hemispherical resonator gyroscope, preprocessing the data, establishing an error model of sample data by a time series analysis method, and identifying model parameters by using a centralized identification method to obtain a random error model of the hemispherical resonator gyroscope based on a bounded noise hypothesis, and specifically comprises the following steps:

step 101: data pre-processing

After acquiring output data of the hemispherical resonant gyroscope in a static state, performing gross error elimination by using a 3 sigma criterion, and performing stability inspection on an output data sequence by using a unit root inspection method; if the checking result is a non-stationary sequence, carrying out differential processing on the data:

y′_k＝y_k+1-y_k

wherein, y_kIs the raw output data, y'_kFor the data after the difference, carrying out stability test on the data after the difference processing by adopting a unit root test method, and if the test result is a stable sequence, finishing the data preprocessing; if the result is a non-stationary sequence, continuing to perform differential processing until the unit root test result is a stationary sequence;

step 102: determining model order

Firstly, performing autocorrelation characteristic and partial correlation characteristic analysis on a preprocessed data sequence to determine a model structure, and then determining an order by utilizing a Bayesian information criterion;

step 103: model parameter identification

Giving a specific model equation according to the model structure and the order, and converting the specific model equation into a generalized regression model; obtaining the boundary of noise through observation data, and setting the initial value of the model parameter; and finally, carrying out dynamic identification on the model parameters by a bounding ellipsoid adaptive constraint least square method to obtain an ellipsoid containing a feasible set of parameters, and establishing a final error model by taking the center of the ellipsoid as an estimation parameter of the model.

3. The method for improving the performance of the hemispherical resonator gyroscope based on the collective-membership theory as claimed in claim 2, wherein in step 102, the bayesian information criterion function is expressed as:

in the formula: n is the sample length;

is a residual sequence; p is the model order; then

And (4) obtaining the BIC minimum value through the formula search, wherein i is the AR partial order, reducing the MA partial order, and repeating the process to determine the final model order.

4. The method for improving the use performance of the hemispherical resonator gyroscope based on the collective theory as claimed in claim 2, wherein the step 103 comprises the following specific operation steps:

(1) establishing a random error time series model ARMA:

wherein, y_kA gyro drift sequence, n is the order of AR model, m is the order of MA model, a_i、b_jFor the parameters of the model to be determined, w_kThe noise which can be measured and has a mean value of zero is added;

converting the random error time series model into a generalized regression model:

phi is a time sequence and a noise matrix, and theta is a undetermined parameter vector; if w_kIs bounded, satisfies | w_k|²＜γ²；

Meanwhile, the initial value of the parameter to be identified is assumed to belong to an ellipsoid:

wherein,

is the center of an ellipsoid, M₀Defining the shape of an ellipsoid for a positive definite matrix;

(2) and then, approximating the parameter feasible set by utilizing the outer-wrapped ellipsoid, wherein the ellipsoid containing the parameter feasible set can be obtained by recursion through the following process

Wherein,

in the subsequent steps, ginsengThe ellipsoid centers of the feasible sets of numbers serve as model parameters.

5. The method for improving the use performance of the hemispherical resonator gyroscope based on the collective theory as claimed in claim 1, wherein in step 2, the established random error model is used to convert to obtain the space state equation of the hemispherical resonator gyroscope, the collective filtering algorithm is used to estimate the angular rate, suppress the random error and improve the use precision of the gyroscope, and the specific operation steps include:

step 201: establishing a spatial equation of state

After a time series analysis model of sample data is established, a linear dynamic system described by using a state space equation is established, and a system state x is selected_kBased on model parameters and system state x_kDetermining a state transition matrix F_kA measurement matrix H_kSum noise driving matrix G_kAnd thus establishing a space state equation of the random drift of the hemispherical resonator gyroscope:

x_k＝F_k-1x_k-1+G_k-1w_k-1

z_k＝H_kx_k+v_k

process noise w_kAnd the measurement noise v_kSet to be unknown but bounded and belong to a set of ellipsoids adapted to the noise level:

wherein Q is_k、R_kThe known positive definite matrix is a shape description matrix of the noise ellipsoid set;

let the initial state belong to a specific ellipsoid:

wherein,

is the center of an ellipsoid, P₀Is a positive definite matrix;

step 202: collective filtering process

Let ε_k-1Estimating an ellipsoid set obtained for the last moment;

wherein,

is the center of an ellipsoid, P_k-1Define the shape of an ellipsoid and satisfy positive qualitative, σ_k-1A scalar greater than 0;

by linear transformation of F_k-1ε_k-1Then ellipsoid is obtained

Simultaneous process noise ellipsoid

By linear transformation

After conversion into

To estimate a target epsilon_k|k-1Namely the outer bounding ellipsoid of the Minkowski sum of the two ellipsoids, the solving process is as follows:

σ_k|k-1＝σ_k-1

wherein p is_kE (0, infinity), using the minimum trace criterion to optimize the parameters to obtain

In the measurement updating stage, the algorithm aims to find an optimal ellipsoid epsilon_kSo that it contains both the measured values and the set of measured noise determinations

And the ellipsoid set epsilon obtained by time updating_k|k-1In order to improve the convergence property and the tracking capability of the algorithm, an improved weighting strategy is adopted to update the ellipsoid set:

wherein z is_kFor measured values, the undetermined parameter q_kNot less than 0, by conversion to epsilon_kThe solution process of (2) is as follows:

wherein,

residual error

To improve the stability of the estimated boundaries, the parameter optimization method is improved, i.e. by minimizing σ_kObtaining the optimal parameters, and obtaining a parameter concrete solving process through derivation:

when in use

Then, the optimal value is the solution of the following formula:

when in use

When the formula is not solved, 0 is taken as the optimal value of the parameter;

the state ellipsoid after measurement and update comprises high-precision estimation of the input angular rate, so that the suppression of random errors of the hemispherical resonator gyroscope and the improvement of the use performance are realized.

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