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

Hemispherical resonator gyroscope use performance improving method based on collective theory Download PDF

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CN113987746A
CN113987746A CN202111116062.5A CN202111116062A CN113987746A CN 113987746 A CN113987746 A CN 113987746A CN 202111116062 A CN202111116062 A CN 202111116062A CN 113987746 A CN113987746 A CN 113987746A
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沈强
汪立新
李�灿
刘洁瑜
李新三
吴宗收
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Rocket Force University of Engineering of PLA
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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

Hemispherical resonator gyroscope use performance improving method based on collective theory
Technical Field
The invention belongs to the technical field of inertial navigation, and particularly relates to a hemispherical resonator gyroscope usability improving method based on an ensemble theory.
Background
The hemispherical resonator gyroscope has the outstanding advantages of long service life, short starting time, good long-term stability and the like, so the hemispherical resonator gyroscope is highly valued in the fields of satellites, space workstations, detectors and the like. However, due to the limitations of late domestic research and initiation and low process level, the precision is relatively low, and the requirement of high-precision military application in modern war is difficult to meet. One idea is to improve the production process, structure and circuit of the product in order to improve the performance, such as "Gyroscope and devices with structural components comprising HfO2-TiO2Material "(US 9719168B2) invented a kind of material containing HfO2-TiO2The material of the hemispherical harmonic oscillator has good vibration quality; the patent 'a hemisphere resonance top precision adjustment and detection device' (CN211346826U) can realize the six-dimensional degree of freedom precision adjustment of relative position and relative angle between harmonic oscillator and electrode base to can carry out closed-loop feedback in real time, improve the adjustment precision. The method has obvious effect on improving the performance of the gyroscope, but the method for improving the performance of the gyroscope by the method has high cost, long period and great difficulty. Therefore, based on the existing hardware level, the use performance of the hemispherical resonator gyroscope is rapidly improved in an error modeling compensation mode, and the method has important significance for expanding the application range of the hemispherical resonator gyroscope and providing high-precision inertial navigation for guided weapons. For example, in the text of ARMA-AKF-based HRG random error modeling analysis (piezoelectric and acousto-optic 39 Vol. No. 1), a gyroscope random error processing method based on an autoregressive moving average model and an adaptive Kalman filtering model is provided, and in the patent, "a method for restraining random drift errors of a vehicle-mounted MEMS gyroscope" (CN111561930A), a method for processing random drift errors of a gyroscope is provided, and interference noise is processed by time sequence modeling and multiple Kalman filteringThe sound is effectively suppressed. The methods effectively improve the precision of the gyroscope to a certain extent. However, the identification and filtering methods adopted by them have strict requirements on noise distribution, and in practical applications, the statistical characteristics of gyro noise are often quite complex and change in real time, and even noise with uncertain statistical characteristics such as variance and chaotic noise may exist, so that probability distribution assumptions are difficult to meet or statistical characteristics are difficult to determine, and this situation may cause estimation deviation and cause instability of an estimator.
Disclosure of Invention
Aiming at the problems and the analysis and research on the performance of the semi-spherical resonance gyroscope, the invention aims to: the utility model provides a hemispherical resonator gyroscope performance promotion method based on collective theory, realizes hemispherical resonator gyroscope's random error modeling and compensation through collective identification and collective filtering, overcomes the limitation of traditional identification and filtering method, further improves hemispherical resonator gyroscope's performance on current hardware basis.
The technical scheme adopted by the invention is as follows:
a hemispherical resonator gyroscope service performance improving method based on a set member theory comprises 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:
Figure BDA0003275360680000021
therein, Index1Index representing random error after suppression0Indicating a random error indicator prior to suppression.
Preferably, in step 1, collecting the 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 member identification method to obtain a random error model of the hemispherical resonator gyroscope based on a bounded noise hypothesis, specifically comprising 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＝yk+1-yk
wherein, ykIs 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.
Preferably, in step 102, the bayesian information criterion function is expressed as:
Figure BDA0003275360680000031
in the formula: n is the sample length;
Figure BDA0003275360680000032
is a residual sequence; p is the model order; then
Figure BDA0003275360680000033
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.
Preferably, the specific operation steps of step 103 include:
(1) establishing a random error time series model ARMA:
Figure BDA0003275360680000041
wherein, ykA gyro drift sequence, n is the order of AR model, m is the order of MA model, ai、bjFor the parameters of the model to be determined, wkThe 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:
Figure BDA0003275360680000042
phi is a time sequence and a noise matrix, and theta is a undetermined parameter vector; if wkIs that the material is bounded by the surface,satisfy | wk|2＜γ2；
Meanwhile, the initial value of the parameter to be identified is assumed to belong to an ellipsoid:
Figure BDA0003275360680000043
wherein,
Figure BDA0003275360680000044
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
Figure BDA0003275360680000045
Figure BDA0003275360680000046
Figure BDA0003275360680000047
Figure BDA0003275360680000048
Wherein,
Figure BDA0003275360680000049
Figure BDA00032753606800000410
λkand more than or equal to 0, and taking the center of an ellipsoid of the parameter feasible set as a model parameter in the subsequent step.
Preferably, in step 2, the established random error model is used to convert to obtain a space state equation of the hemispherical resonator gyroscope, the angular rate is estimated through the collective filtering algorithm, the random error is suppressed, and the use precision of the gyroscope is improved, 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 selectedkBased on model parameters and system state xkDetermining a state transition matrix FkA measurement matrix HkSum noise driving matrix GkAnd thus establishing a space state equation of the random drift of the hemispherical resonator gyroscope:
xk＝Fk-1xk-1+Gk-1wk-1
zk＝Hkxk+vk
process noise wkAnd the measurement noise vkSet to be unknown but bounded and belong to a set of ellipsoids adapted to the noise level:
Figure BDA0003275360680000051
Figure BDA0003275360680000052
wherein Q isk、RkThe known positive definite matrix is a shape description matrix of the noise ellipsoid set;
let the initial state belong to a specific ellipsoid:
Figure BDA0003275360680000053
wherein,
Figure BDA0003275360680000054
is the center of an ellipsoid, P0Is a positive definite matrix;
step 202: collective filtering process
Is provided with
Figure BDA00032753606800000513
Estimating an ellipsoid set obtained for the last moment;
Figure BDA0003275360680000055
wherein,
Figure BDA0003275360680000056
is the center of an ellipsoid, Pk-1Define the shape of an ellipsoid and satisfy positive qualitative, σk-1A scalar greater than 0;
by linear transformation
Figure BDA0003275360680000057
Then ellipsoid is obtained
Figure BDA0003275360680000058
Simultaneous process noise ellipsoid
Figure BDA0003275360680000059
By linear transformation
Figure BDA00032753606800000510
After conversion into
Figure BDA00032753606800000511
To estimate the target
Figure BDA00032753606800000512
Namely the outer bounding ellipsoid of the Minkowski sum of the two ellipsoids, the solving process is as follows:
Figure BDA0003275360680000061
σk|k-1＝σk-1
Figure BDA0003275360680000062
wherein p iskE (0, infinity), using the minimum trace criterion to optimize the parameters to obtain
Figure BDA0003275360680000063
In the measurement updating stage, the algorithm aims to find an optimal ellipsoid
Figure BDA0003275360680000064
To include both measured values and a set of measured noise determinations
Figure BDA0003275360680000065
And time updated set of ellipsoids
Figure BDA0003275360680000066
In order to improve the convergence property and the tracking capability of the algorithm, an improved weighting strategy is adopted to update the ellipsoid set:
Figure BDA0003275360680000067
wherein z iskFor measured values, the undetermined parameter qkNot less than 0, by conversion to
Figure BDA0003275360680000068
The solution process of (2) is as follows:
Figure BDA0003275360680000069
Figure BDA00032753606800000610
Figure BDA00032753606800000611
wherein,
Figure BDA00032753606800000612
residual error
Figure BDA00032753606800000613
To improve the stability of the estimated boundaries, the parameter optimization method is improved, i.e. by minimizing σkObtaining the optimal parameters, and obtaining a parameter concrete solving process through derivation:
when in use
Figure BDA00032753606800000614
Then, the optimal value is the solution of the following formula:
Figure BDA00032753606800000615
when in use
Figure BDA00032753606800000616
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.
The invention has the beneficial effects that:
the method is based on the collective estimation theory, and realizes the online dynamic modeling of random error signals by adopting the bounding ellipsoid self-adaptive constraint least square method with recursive property to identify the parameters of the random error model of the hemispherical resonator gyroscope. An improved centralized filtering method is realized by optimizing a weighting strategy and a parameter solving method for measurement updating, the method only requires that the noise is bounded, does not require specific distribution of the noise in the boundary, does not need to know the statistical characteristics, and can overcome the defects of the traditional state filtering method; the tracking and stability performance of the filtering method is improved through a new weighting strategy and an optimization criterion; furthermore, the method may obtain a strict uncertainty boundary constraint for the estimated state. Therefore, the identification and filtering method based on the set member theory is used for processing the random error of the hemispherical resonator gyroscope, the accuracy and the reliability of restraining the random drift can be improved, the use precision of the hemispherical resonator gyroscope is obviously improved, and the improvement effect is superior to that of the traditional filtering method.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic block diagram illustrating a performance improvement method for a hemispherical resonator gyroscope based on collective theory according to the present invention.
Fig. 2 is a diagram of original sequence sample data.
FIG. 3 is a time series diagram of the output data after preprocessing.
FIG. 4 is a diagram showing the result of identifying parameters of a random error model of a hemispherical resonator gyroscope.
FIG. 5 is a graph showing the random error filtering results of the hemispherical resonator gyroscope.
Detailed Description
In order to make the objects, 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 drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment specifically provides a method for improving the use performance of a hemispherical resonator gyroscope based on an ensemble theory, as shown in fig. 1, the method includes the following steps:
step 1: establishing a random error model
The method comprises the following steps of collecting static output data of the hemispherical resonator gyroscope, preprocessing the data, establishing an error model of sample data through a time sequence analysis method, identifying model parameters by using a centralized member identification method, and obtaining a random error model of the hemispherical resonator gyroscope based on bounded noise hypothesis, wherein the random error model 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＝yk+1-yk
wherein, ykIs 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;
the Bayesian information criterion function is expressed as:
Figure BDA0003275360680000091
in the formula: n is the sample length;
Figure BDA0003275360680000092
is a residual sequence; p is the model order; then
Figure BDA0003275360680000093
Obtaining BIC minimum value by the above formula search, if i is AR partial order, reducing MA partial order, repeating the process to determine final model order
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; 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;
(1) establishing a random error time series model ARMA:
Figure BDA0003275360680000094
wherein, ykA gyro drift sequence, n is the order of AR model, m is the order of MA model, ai、bjFor the parameters of the model to be determined, wkThe 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:
Figure BDA0003275360680000095
where Φ is the time series and the noise matrixTheta is a undetermined parameter vector; if wkIs bounded, satisfies | wk|2＜γ2(ii) a Meanwhile, the initial value of the parameter to be identified is assumed to belong to an ellipsoid:
Figure BDA0003275360680000101
wherein,
Figure BDA0003275360680000102
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
Figure BDA0003275360680000103
Figure BDA0003275360680000108
Figure BDA0003275360680000104
Figure BDA0003275360680000105
Wherein,
Figure BDA0003275360680000106
Figure BDA0003275360680000107
λkmore than or equal to 0, and taking the center of an ellipsoid of the parameter feasible set as a model parameter in the subsequent step;
step 2: random error filtering
The method is characterized by comprising the following steps of utilizing an established random error model, obtaining a space state equation of the hemispherical resonator gyroscope through conversion, estimating an angular rate through an ensemble filtering algorithm, restraining random errors, and improving the use precision of the gyroscope, wherein the specific operation steps comprise:
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 selectedkBased on model parameters and system state xkDetermining a state transition matrix FkA measurement matrix HkSum noise driving matrix GkAnd thus establishing a space state equation of the random drift of the hemispherical resonator gyroscope:
xk＝Fk-1xk-1+Gk-1wk-1
zk＝Hkxk+vk
process noise wkAnd the measurement noise vkSet to be unknown but bounded and belong to a set of ellipsoids adapted to the noise level:
Figure BDA0003275360680000111
Figure BDA0003275360680000112
wherein Q isk、RkThe known positive definite matrix is a shape description matrix of the noise ellipsoid set;
let the initial state belong to a specific ellipsoid:
Figure BDA0003275360680000113
wherein,
Figure BDA0003275360680000114
is the center of an ellipsoid, P0Is a positive definite matrix;
step 202: collective filtering process
Is provided with
Figure BDA0003275360680000115
Estimating an ellipsoid set obtained for the last moment;
Figure BDA0003275360680000116
wherein,
Figure BDA0003275360680000117
is the center of an ellipsoid, Pk-1Define the shape of an ellipsoid and satisfy positive qualitative, σk-1A scalar greater than 0;
by linear transformation
Figure BDA0003275360680000118
Then ellipsoid is obtained
Figure BDA0003275360680000119
Simultaneous process noise ellipsoid
Figure BDA00032753606800001110
By linear transformation
Figure BDA00032753606800001111
After conversion into
Figure BDA00032753606800001112
To estimate the target
Figure BDA00032753606800001113
Namely the outer bounding ellipsoid of the Minkowski sum of the two ellipsoids, the solving process is as follows:
Figure BDA00032753606800001114
σk|k-1＝σk-1
Figure BDA00032753606800001115
wherein p iskE (0, infinity), using the minimum trace criterion to optimize the parameters to obtain
Figure BDA00032753606800001116
In the measurement updating stage, the algorithm aims to find an optimal ellipsoid
Figure BDA00032753606800001117
To include both measured values and a set of measured noise determinations
Figure BDA00032753606800001118
And time updated set of ellipsoids
Figure BDA00032753606800001119
In order to improve the convergence property and the tracking capability of the algorithm, an improved weighting strategy is adopted to update the ellipsoid set:
Figure BDA0003275360680000121
wherein z iskFor measured values, the undetermined parameter qkNot less than 0, by conversion to
Figure BDA0003275360680000122
The solution process of (2) is as follows:
Figure BDA0003275360680000123
Figure BDA0003275360680000124
Figure BDA0003275360680000125
wherein,
Figure BDA0003275360680000126
residual error
Figure BDA0003275360680000127
To improve the stability of the estimated boundaries, the parameter optimization method is improved, i.e. by minimizing σkObtaining the optimal parameters, and obtaining a parameter concrete solving process through derivation:
when in use
Figure BDA0003275360680000128
Then, the optimal value is the solution of the following formula:
Figure BDA0003275360680000129
when in use
Figure BDA00032753606800001210
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.
And step 3: promotion effect evaluation analysis
The estimation result obtained in the step 2 is all possible sets of the real Angular rate to which the hemispherical resonator gyroscope is sensitive, the shape of the set is an ellipsoid, the center of the ellipsoid is used as a point estimation result to analyze the drift suppression condition, and the indexes of the drift size of the hemispherical resonator gyroscope are represented by using the Root Mean Square Error (RMSE) of the estimation result and the Angle Random Walk (ARW) and the zero Bias Instability (BI) obtained by Allan variance analysis; describing the use precision improvement effect of the gyroscope by using an improvement factor, wherein the improvement factor is defined as:
Figure BDA00032753606800001211
therein, Index1Index representing random error after suppression0Indicating a random error indicator prior to suppression.
The following further describes a method for detecting the long-term stability of a hemispherical resonator gyroscope by taking a hemispherical resonator gyroscope as an example and combining the accompanying drawings.
The principle of this embodiment is shown in fig. 1.
Step 1: establishing a random error model
According to the output characteristic of the hemispherical resonator gyroscope, the sampling interval is set to be 0.4s, the sampling number is 18000, and 2 hours of continuous sampling are carried out. The sample data obtained by the test is shown in FIG. 2.
Test data is preprocessed and calculated to obtain the average value of sample data
Figure BDA0003275360680000131
The standard deviation is 1.3348e-4, and the output stability range is 1.3348e-4 according to the 3 sigma criterion
Figure BDA0003275360680000132
Values outside the stable range are eliminated and replaced by the mean of the two side data. Then, zero-mean processing and data conversion are performed to obtain a preprocessed random error time sequence as shown in fig. 3.
And performing stationarity test on the output data sequence by using a unit root test method, wherein the result accords with stationarity conditions. And then, analyzing the self-correlation characteristic and the partial correlation characteristic of the preprocessed random error, wherein the self-correlation presents a trailing property, the partial correlation presents a truncation property, and according to a time series modeling theory, an AR model is adopted for modeling. And (3) selecting an AR (3) model as a model structure of the hemispherical resonant gyroscope random error through Bayesian Information Criterion (BIC) criterion analysis.
In order to improve the modeling precision, the time series error model is used as a linear time-varying system to be processed so as to improve the modeling precision, and a real-time recursion parameter identification method is adopted to synchronously carry out parameter identification and state estimation during data processing. The identification results of the model parameters of the AR (3) model are shown in fig. 4. It can be seen that the identification method can effectively track the change of the model parameters.
Step 2: random error filtering
And substituting the model parameters into the state transition matrix while obtaining the model parameters to establish a system equation, wherein the related initial parameters are selected as follows:
Figure BDA0003275360680000141
P0＝I，Qk＝3.0×10-11I，r2＝1.52×10-7，
Figure BDA0003275360680000142
then, the system state is estimated by using the set membership filtering algorithm to obtain a state feasible set containing a real state, namely an ellipsoid set containing the real angular rate at each moment, and the center of the ellipsoid set is used as an estimated value of the real angular rate to reduce random errors. As comparison, time series modeling based on the least square method and random error compensation based on Kalman filtering are carried out at the same time, and the comparison with the random error compensation result is carried out.
And step 3: promotion effect evaluation analysis
The center of the set of ellipsoids containing the true angular rate is taken as the point estimation result of the angular rate, as shown in fig. 5. Using the index of the drift size of the hemispherical resonator gyroscope represented by angle random walk and zero-bias instability obtained by the root mean square error and Allan variance analysis; the suppression effect of random errors and the gyroscope performance improvement effect described by the improvement factor are specifically shown in table 1:
TABLE 1 Performance enhancement Effect
Figure BDA0003275360680000143
As can be seen from table 1, the data after the drift suppression are significantly improved in three indexes of root mean square error, angle random walk and zero-bias instability, and particularly, the root mean square error is reduced by one order of magnitude, which proves that the random drift of the hemispherical resonator gyro is effectively suppressed, and the service performance of the hemispherical resonator gyro is significantly improved; and the improvement effect is obviously superior to the Kalman filtering result, particularly the improvement factor of the RMSE is further improved by about 56 percent relative to the Kalman filtering, and the advantages of the invention are proved.
The above description is only for the purpose of illustrating the technical solutions of the present invention and not for the purpose of limiting the same, and other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention should be covered within the scope of the claims of the present invention without departing from the spirit and scope of the technical solutions 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:
Figure FDA0003275360670000011
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＝yk+1-yk
wherein, ykIs 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:
Figure FDA0003275360670000021
in the formula: n is the sample length;
Figure FDA0003275360670000022
is a residual sequence; p is the model order; then
Figure FDA0003275360670000023
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:
Figure FDA0003275360670000024
wherein, ykA gyro drift sequence, n is the order of AR model, m is the order of MA model, ai、bjFor the parameters of the model to be determined, wkThe 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:
Figure FDA0003275360670000025
phi is a time sequence and a noise matrix, and theta is a undetermined parameter vector; if wkIs bounded, satisfies | wk|2＜γ2；
Meanwhile, the initial value of the parameter to be identified is assumed to belong to an ellipsoid:
Figure FDA0003275360670000031
wherein,
Figure FDA0003275360670000032
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
Figure FDA0003275360670000033
Figure FDA0003275360670000034
Figure FDA0003275360670000035
Figure FDA0003275360670000036
Wherein,
Figure FDA0003275360670000037
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 selectedkBased on model parameters and system state xkDetermining a state transition matrix FkA measurement matrix HkSum noise driving matrix GkAnd thus establishing a space state equation of the random drift of the hemispherical resonator gyroscope:
xk＝Fk-1xk-1+Gk-1wk-1
zk＝Hkxk+vk
process noise wkAnd the measurement noise vkSet to be unknown but bounded and belong to a set of ellipsoids adapted to the noise level:
Figure FDA0003275360670000041
Figure FDA0003275360670000042
wherein Q isk、RkThe known positive definite matrix is a shape description matrix of the noise ellipsoid set;
let the initial state belong to a specific ellipsoid:
Figure FDA0003275360670000043
wherein,
Figure FDA0003275360670000044
is the center of an ellipsoid, P0Is a positive definite matrix;
step 202: collective filtering process
Let εk-1Estimating an ellipsoid set obtained for the last moment;
Figure FDA0003275360670000045
wherein,
Figure FDA0003275360670000046
is the center of an ellipsoid, Pk-1Define the shape of an ellipsoid and satisfy positive qualitative, σk-1A scalar greater than 0;
by linear transformation of Fk-1εk-1Then ellipsoid is obtained
Figure FDA0003275360670000047
Simultaneous process noise ellipsoid
Figure FDA0003275360670000048
By linear transformation
Figure FDA0003275360670000049
After conversion into
Figure FDA00032753606700000410
To estimate a target epsilonk|k-1Namely the outer bounding ellipsoid of the Minkowski sum of the two ellipsoids, the solving process is as follows:
Figure FDA00032753606700000411
σk|k-1＝σk-1
Figure FDA00032753606700000412
wherein p iskE (0, infinity), using the minimum trace criterion to optimize the parameters to obtain
Figure FDA00032753606700000413
In the measurement updating stage, the algorithm aims to find an optimal ellipsoid epsilonkSo that it contains both the measured values and the set of measured noise determinations
Figure FDA00032753606700000414
And the ellipsoid set epsilon obtained by time updatingk|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:
Figure FDA0003275360670000051
wherein z iskFor measured values, the undetermined parameter qkNot less than 0, by conversion to epsilonkThe solution process of (2) is as follows:
Figure FDA0003275360670000052
Figure FDA0003275360670000053
Figure FDA0003275360670000054
wherein,
Figure FDA0003275360670000055
residual error
Figure FDA0003275360670000056
To improve the stability of the estimated boundaries, the parameter optimization method is improved, i.e. by minimizing σkObtaining the optimal parameters, and obtaining a parameter concrete solving process through derivation:
when in use
Figure FDA0003275360670000057
Then, the optimal value is the solution of the following formula:
Figure FDA0003275360670000058
when in use
Figure FDA0003275360670000059
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.
CN202111116062.5A 2021-09-23 2021-09-23 Hemispherical resonator gyroscope use performance improving method based on collective theory Pending CN113987746A (en)

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