CN113551660A - Method for acquiring vibration mode angle of hemispherical resonator gyroscope when electrode angle has error - Google Patents

Method for acquiring vibration mode angle of hemispherical resonator gyroscope when electrode angle has error Download PDF

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CN113551660A
CN113551660A CN202110826008.3A CN202110826008A CN113551660A CN 113551660 A CN113551660 A CN 113551660A CN 202110826008 A CN202110826008 A CN 202110826008A CN 113551660 A CN113551660 A CN 113551660A
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angle
electrode
error
signals
moment
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CN113551660B (en
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解伟男
汪昕杨
奚伯齐
王奇
伊国兴
王常虹
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
    • G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
    • G01C19/5776—Signal processing not specific to any of the devices covered by groups G01C19/5607 - G01C19/5719
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The invention discloses a method for acquiring a vibration mode angle of a hemispherical resonator gyroscope when an electrode angle has an error, and relates to the method for acquiring the vibration mode angle of the hemispherical resonator gyroscope when the electrode angle has the error. The invention aims to solve the problem that the hemispherical resonator gyroscope cannot realize accurate measurement of the angle when the angle of the detection electrode has an error, so that the navigation accuracy is low. The process is as follows: 1, mounting and fixing a hemispherical resonant gyroscope on a turntable; 2, performing parameter excitation until the amplitude of the vibration signal of the harmonic oscillator is unchanged; 3, collecting vibration signals and turntable angles detected by 0-degree and 45-degree detection electrodes on the gyroscope; 4 to give E, R, S; 5, establishing an angle measurement equation considering the angle error of the electrode; 6, setting initial parameters of the nonlinear identification algorithm; 7, obtaining an estimated electrode angle error; and 8, acquiring the vibration mode angle of the hemispherical resonant gyroscope when the electrode angle has errors. The invention is used in the technical field of inertia.

Description

Method for acquiring vibration mode angle of hemispherical resonator gyroscope when electrode angle has error
Technical Field
The invention relates to a method for acquiring a vibration mode angle of a hemispherical resonator gyroscope when an electrode angle has an error, and belongs to the technical field of inertia.
Background
A gyroscope is an important inertial element that can be used to detect the angle or angular velocity of a carrier. The hemispherical resonator gyroscope has two mechanical structures of a three-piece set and a two-piece set, wherein the three-piece set of hemispherical resonator gyroscope consists of a harmonic oscillator, an excitation cover and a detection base, and the two-piece set of hemispherical resonator gyroscope consists of the harmonic oscillator and an electrode base. Due to the simple mechanical structure and the physical characteristics of manufacturing materials, the hemispherical resonator gyroscope has the advantages of high detection precision, strong reliability, long service life and the like, and is widely applied to military fields of aerospace, navigation and the like in China at present.
According to the measured angular speed or angle, the hemispherical resonator gyroscope can be divided into two working modes of force balance and full angle, wherein the full angle mode is a novel working mode. The principle of the full-angle mode is that the vibration mode position is detected in real time through 0-degree and 45-degree detection electrodes by utilizing the characteristic that the vibration mode precession angle is in direct proportion to the rotation angle of the gyroscope, and the angular speed of the gyroscope is directly calculated. Ideally, the included angle between the 0-degree electrode and the 45-degree electrode should be 45 degrees, but due to errors in machining and manufacturing, the included angle between the 0-degree electrode and the 45-degree electrode has angle errors
Figure BDA0003173601190000011
I.e. 0 and 45 electrode angle
Figure BDA0003173601190000012
Then, the signals detected by the electrodes are processed by the traditional angle measurement method, and a certain error exists in the calculated vibration mode precession angle, so that the angle measurement precision of the gyroscope is reduced.
In the actual manufacturing process, the error of the machining and manufacturing angle of the detection electrode is inevitable, and in order to improve the angle measurement precision of the gyroscope, a method is needed to inhibit or eliminate the influence caused by the error of the electrode angle. Therefore, it is very useful to provide a method for obtaining the mode angle of a hemispherical resonator gyroscope when there is an error in the electrode angle.
Disclosure of Invention
The invention aims to solve the problem that the hemispherical resonator gyroscope cannot realize accurate measurement of an angle when an error exists in a detection electrode angle, so that the navigation accuracy is low, and provides a method for acquiring the vibration mode angle of the hemispherical resonator gyroscope when the error exists in the electrode angle.
A method for obtaining the vibration mode angle of a hemispherical resonator gyroscope when the electrode angle has errors is characterized in that: the method comprises the following specific processes:
step 1, mounting and fixing a hemispherical resonance gyroscope on a turntable, so that a gyroscope sensitive shaft is superposed with a rotating shaft of the turntable;
step 2, applying excitation voltage to an excitation electrode on the hemispherical resonator gyroscope for parameter excitation until the amplitude of a vibration signal of the harmonic oscillator is unchanged;
step 3, enabling the rotary table to rotate at a constant speed, collecting vibration signals x and y detected by detection electrodes of 0 degrees and 45 degrees on the gyroscope, and simultaneously collecting the angle theta of the rotary tabler；
Step 4, generating reference signal v by using phase-locked looprc、vrsDemodulating the detected vibration signals x and y respectively to obtain signals Cx, Sx, Cy and Sy, performing low-pass filtering on the signals Cx, Sx, Cy and Sy respectively to obtain signals Cx ', Sx', Cy 'and Sy', and performing secondary combination on the signals Cx ', Sx', Cy 'and Sy' to obtain E, R, S signals;
step 5, establishing and considering the electrode angle error
Figure BDA0003173601190000021
The angle measurement equation of (1);
step 6, setting initial parameters of the nonlinear identification algorithm;
step 7, using the E, R, S signal obtained in the step 4 as the input of a nonlinear identification algorithm to correct the angle error of the electrode
Figure BDA0003173601190000022
Identifying to obtain estimated electrode angle error
Figure BDA0003173601190000023
Step 8, identifying the obtained
Figure BDA0003173601190000024
Substituting the considered electrode angle error established in step 5
Figure BDA0003173601190000025
The vibration mode angle of the hemispherical resonator gyroscope when the electrode angle has errors is obtained in the angle measurement equation.
The invention has the beneficial effects that:
the invention firstly installs and fixes the hemispherical resonance gyroscope on the turntable, so that the sensitive axis of the gyroscope is coincided with the rotating axis of the turntable, and then applies excitation voltage to the excitation electrodes which are arranged on the hemispherical resonance gyroscope at intervals for parameter excitation until the amplitude of the vibration signal of the harmonic oscillator is stable. The rotary table is rotated at a constant speed, and vibration signals x and y detected by a detection electrode on the gyro and a rotary table corner theta are collectedrAnd using a reference signal v generated by a phase-locked looprc、vrsAnd demodulating, low-pass filtering and twice combining the x and the y respectively to obtain E, R, S signals. Based on the improved angle measurement equation, selecting proper parameter initial value, and using nonlinear least square method to correct the electrode angle error
Figure BDA0003173601190000026
Identifying to obtain an electrode angle error estimation value
Figure BDA0003173601190000027
Finally will be
Figure BDA0003173601190000028
The method substitutes into the improved angle measurement equation to obtain an accurate angle measurement equation, and the angle measurement accuracy of the gyroscope can be improved. Theoretical analysis and simulation experiments prove that the vibration mode angle of the hemispherical resonator gyroscope is changed when the electrode angle provided by the invention has errorsThe method can realize high-precision acquisition of the vibration mode angle, solves the problem of inaccurate gyro angle measurement caused by electrode angle processing errors, improves the measurement precision of the hemispherical resonant gyro, and improves the navigation accuracy.
Drawings
FIG. 1 is a block diagram of an identification process according to the present invention;
FIG. 2 shows parameters
Figure BDA0003173601190000029
Identifying an error curve graph;
FIG. 3 is a graph of a mode angle error curve;
fig. 4 is a diagram of an arrangement of excitation electrodes on a hemispherical resonator gyroscope.
Detailed Description
The first embodiment is as follows: the present embodiment is described with reference to fig. 1, and a specific procedure of a method for acquiring a hemispherical resonator gyroscope oscillation angle when an electrode angle has an error according to the present embodiment is as follows:
the invention provides a method for acquiring the vibration mode angle of a hemispherical resonator gyroscope when the electrode angle has errors, which is based on an improved angle measurement equation and uses a nonlinear least square method to correct the electrode angle errors
Figure BDA0003173601190000031
And (5) performing identification. The method obtains an accurate angle measurement formula by identifying the angle error of the electrode, thereby calculating the accurate vibration mode angle of the harmonic oscillator and realizing the high-precision angle measurement of the gyroscope. The invention can also realize the identification of the electrode angle error through the nonlinear identification algorithm such as extended Kalman filtering.
Step 1, mounting and fixing a hemispherical resonance gyroscope on a turntable, so that a gyroscope sensitive shaft is superposed with a rotating shaft of the turntable;
step 2, applying excitation voltage to an excitation electrode on the hemispherical resonator gyroscope to carry out parameter (signal applied by the excitation electrode, such as amplitude, frequency and phase of the signal) excitation until the amplitude of the vibration signal of the harmonic oscillator is unchanged;
step 3, enabling the rotary table to rotate at a constant speed, and collecting 0-degree and 45-degree detection electricity on the gyroscopeVibration signals x and y detected by the poles and the angle theta of the rotary table are acquired simultaneouslyr；
Step 4, generating reference signal v by using phase-locked looprc、vrsDemodulating the detected vibration signals x and y respectively to obtain signals Cx, Sx, Cy and Sy, performing low-pass filtering on the signals Cx, Sx, Cy and Sy respectively to obtain signals Cx ', Sx', Cy 'and Sy', and performing secondary combination on the signals Cx ', Sx', Cy 'and Sy' to obtain E, R, S signals;
step 5, establishing and considering the electrode angle error
Figure BDA0003173601190000032
The angle measurement equation of (1);
step 6, setting initial parameters of the nonlinear identification algorithm;
step 7, using the E, R, S signal obtained in the step 4 as the input of a nonlinear identification algorithm to correct the angle error of the electrode
Figure BDA0003173601190000033
Identifying to obtain estimated electrode angle error
Figure BDA0003173601190000034
Step 8, identifying the obtained
Figure BDA0003173601190000035
Substituting the considered electrode angle error established in step 5
Figure BDA0003173601190000036
The vibration mode angle of the hemispherical resonator gyroscope when the electrode angle has errors is obtained in the angle measurement equation.
The second embodiment is as follows: the present embodiment is different from the first embodiment in that the excitation electrodes are arranged on the hemispherical resonator gyro at intervals in step 2. As shown in fig. 4.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: this embodiment and the detailed descriptionIn a difference of equation one or two, the reference signal v generated by the phase-locked loop in step 4 is usedrc、vrsDemodulating the detected vibration signals x and y respectively to obtain signals Cx, Sx, Cy and Sy, performing low-pass filtering on the signals Cx, Sx, Cy and Sy respectively to obtain signals Cx ', Sx', Cy 'and Sy', and performing secondary combination on the signals Cx ', Sx', Cy 'and Sy' to obtain E, R, S signals; the specific process is as follows:
reference signal v generated by means of a phase-locked looprc、vrsDemodulating the detected vibration signals x and y respectively to obtain signals Cx, Sx, Cy and Sy, wherein the expression is as follows:
Figure BDA0003173601190000041
performing low-pass filtering on the signals Cx, Sx, Cy and Sy, and respectively filtering out double frequency in the signals Cx, Sx, Cy and Sy to obtain signals Cx ', Sx', Cy 'and Sy';
the signals Cx ', Sx', Cy ', Sy' are combined twice to obtain E, R, S signals.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment and the first to third embodiments is that the signals Cx ', Sx', Cy ', Sy' are secondarily combined to obtain E, R, S signals, and the expression is:
Figure BDA0003173601190000042
other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: this embodiment differs from one of the first to fourth embodiments in that the reference signal vrc、vrsIs composed of sine signal and cosine signal.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: this implementationIn a manner different from one of the first to fifth embodiments, it is established in the step 5 that the electrode angle error is taken into consideration
Figure BDA0003173601190000043
The angle measurement equation of (1); the specific process is as follows:
establishing consideration of electrode angle error
Figure BDA0003173601190000044
The actual precession angle theta capable of accurately describing the vibration mode is obtained by the angle measurement equationrealThe form is as follows:
Figure BDA0003173601190000051
from the above formula, as long as the parameters are known
Figure BDA0003173601190000052
The true precession angle theta of the vibration mode can be directly obtainedreal。
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment: the difference between this embodiment and the first to sixth embodiments is that, in the step 6, initial parameter setting is performed on the nonlinear identification algorithm; the specific process is as follows:
the nonlinear identification algorithm is a nonlinear least square method or an extended Kalman filtering method;
because the nonlinear least square and the extended Kalman filtering are both recursive algorithms, the initial estimation value of the electrode angle error must be given firstly during starting
Figure BDA0003173601190000053
And estimated initial value of precession coefficient
Figure BDA0003173601190000054
Order to
Figure BDA0003173601190000055
Other steps and parameters are the same as those in one of the first to sixth embodiments.
The specific implementation mode is eight: the difference between this embodiment and one of the first to seventh embodiments is that the E, R, S signal obtained in step 4 is used as the input of the nonlinear identification algorithm in step 7 to correct the electrode angle error
Figure BDA0003173601190000056
Identifying to obtain estimated electrode angle error
Figure BDA0003173601190000057
The specific identification process comprises the following steps:
taking the E, R, S signal obtained in the step 4 as the input of a nonlinear least square method;
s1: calculating a value function of the current time:
Figure BDA0003173601190000058
wherein, thetar(i) The turning angle of the rotary table collected at the moment i;
Figure BDA0003173601190000059
is an estimated value of the precession coefficient at the time i;
Figure BDA00031736011900000510
the estimated value of the electrode angle error at the moment i;
s2: calculating a jacobian matrix of the function at the current moment:
order to
Figure BDA00031736011900000511
Figure BDA00031736011900000512
Wherein b is an intermediate variable; j. the design is a squarer(i) Is Jack at time iA ratio matrix;
s3: calculating identification parameters (estimated values of electrode angle errors) based on the value function of the current time and the Jacobian matrix of the current time
Figure BDA00031736011900000513
And an estimate of the precession coefficient
Figure BDA00031736011900000514
) An increment of the current time;
Figure BDA0003173601190000061
wherein the content of the first and second substances,
Figure BDA0003173601190000062
for the current time electrode angle error estimation
Figure BDA0003173601190000063
An increment of (d); Δ c (i) is the current time precession coefficient estimate
Figure BDA0003173601190000064
An increment of (d);
s4: updating the identification parameters at the next moment:
Figure BDA0003173601190000065
wherein the content of the first and second substances,
Figure BDA0003173601190000066
an electrode angle error estimated value at the moment i + 1;
Figure BDA0003173601190000067
the estimated value of the precession coefficient at the moment i + 1;
s5: judging whether signals E, R and S input exist (input to S1), if so, jumping to S1, and if not, jumping to step S6;
s6: after the identification is finished, outputting the estimated electrode angle error
Figure BDA0003173601190000068
In conclusion, the angle error of the counter electrode is realized
Figure BDA0003173601190000069
And (4) identifying.
Here, the nonlinear least square method is given to the angle error of the electrode
Figure BDA00031736011900000610
And performing identification, and identifying the electrode angle error by adopting other identification algorithms such as extended Kalman filtering and the like.
Other steps and parameters are the same as those in one of the first to seventh embodiments.
The specific implementation method nine: the present embodiment is different from the first to seventh embodiments in that the E, R, S signal obtained in step 4 is used as an input of the optimization algorithm in step 7, and the error of the electrode angle is corrected
Figure BDA00031736011900000611
Identifying to obtain estimated electrode angle error
Figure BDA00031736011900000612
The specific identification process comprises the following steps:
the model selected by extended Kalman Filtering is as follows
Figure BDA00031736011900000613
Wherein the content of the first and second substances,
Figure BDA00031736011900000614
the error of the electrode angle at the moment i + 1; c (i +1) is the value of precession coefficient at the moment i + 1;
Figure BDA00031736011900000615
the measured value of the rotating angle of the rotary table at the moment i +1 is obtained, and v is measurement noise;
taking the E, R, S signal obtained in the step 4 as the input of an extended Kalman filter;
s1: and predicting the state estimation value at the next moment:
Figure BDA0003173601190000071
wherein the content of the first and second substances,
Figure BDA0003173601190000072
as an electrode angle error
Figure BDA0003173601190000073
A priori estimated value at the ith moment;
Figure BDA0003173601190000074
is an estimated value of the ith moment;
Figure BDA0003173601190000075
is a priori estimated value of the precession coefficient c at the ith moment;
Figure BDA0003173601190000076
is a priori estimated value of the precession coefficient c at the ith-1 moment;
s2: predicting the covariance of the estimation error at the next time instant:
Pi|i-1＝Pi-1|i-1
wherein, Pi|i-1To estimate the predicted value, P, of the error covariance matrix at time ii-1|i-1Is the value of the estimated error covariance matrix at the (i-1) th moment;
s3: judging whether experimental data are input, if so, jumping to S4, and if not, jumping to S9;
s4: and predicting the measurement matrix at the next moment:
order to
Figure BDA0003173601190000077
Figure BDA0003173601190000078
Wherein b is an intermediate variable; ciA measurement matrix at the ith moment;
s5: and predicting the measurement estimation value of the next moment:
Figure BDA0003173601190000079
wherein the content of the first and second substances,
Figure BDA00031736011900000710
is an estimated value of the rotating angle of the rotary table;
s6: predicting the state gain matrix at the next moment:
Ki＝Pi|i-1Ci T(CiPi|i-1Ci T+Q)-1
wherein Q is the covariance of the noise v; kiIs a state gain matrix of the ith moment, and T is a transposition;
s7: and updating the state estimation value at the next moment:
Figure BDA0003173601190000081
wherein the content of the first and second substances,
Figure BDA0003173601190000082
as an electrode angle error
Figure BDA0003173601190000083
A posterior estimate at the ith time;
Figure BDA0003173601190000084
is a coefficient of precessionc posterior estimated value of ith moment;
s8: update the estimation error covariance for the next time instant, and then jump to S1:
Pi|i＝(I-KiCi)Pi|i-1(I-KiCi)T
wherein, Pi|iThe value of the ith moment of the error covariance matrix is estimated, and I is an identity matrix;
s9: after the filtering is finished, the estimated electrode angle error is output
Figure BDA0003173601190000085
Other steps and parameters are the same as those in one of the first to seventh embodiments.
The detailed implementation mode is ten: the difference between this embodiment and one of the first to ninth embodiments is that the step 8 is to identify
Figure BDA0003173601190000086
Substituting the considered electrode angle error established in step 5
Figure BDA0003173601190000087
Obtaining the vibration mode angle of the hemispherical resonance gyroscope when the electrode angle has errors in the angle measurement equation; the expression is as follows:
Figure BDA0003173601190000088
other steps and parameters are the same as those in one of the first to ninth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
step 1, mounting and fixing a hemispherical resonance gyroscope on a turntable, so that a gyroscope sensitive shaft is superposed with a rotating shaft of the turntable;
step 2, applying excitation voltage to excitation electrodes arranged on the hemispherical resonance gyroscope at intervals to carry out parameter (signal applied by the excitation electrodes, such as amplitude, frequency and phase of the signal) excitation until the amplitude of the vibration signal of the harmonic oscillator is stable;
step 3, the rotary table is enabled to be in omegarRotating at constant speed of 100 deg/s, setting fs as 1000Hz and t as sampling timeiCollecting vibration signals x and y detected by 0-degree and 45-degree detection electrodes on the gyroscope and collecting the angle theta of the turntable at the same time, wherein the vibration signals x and y are 100sr. The error of the machining and manufacturing angles of the 0-degree electrode and the 45-degree electrode is
Figure BDA0003173601190000089
Step 4, generating reference signal v by using phase-locked looprc、vrsDemodulating the vibration signals x and y respectively to obtain signals Cx, Sx, Cy and Sy, low-pass filtering to obtain Cx ', Sx', Cy 'and Sy', and performing secondary combination to obtain E, R, S signal, the reference signal vrc、vrsThe device consists of a sine signal and a cosine signal;
step 5, establishing and considering the electrode angle error
Figure BDA0003173601190000091
Selecting proper parameter initial value, using nonlinear least square method to measure electrode angle error
Figure BDA0003173601190000092
Identifying, wherein the identification of the electrode angle error can be realized through a nonlinear identification algorithm such as extended Kalman filtering;
selecting the initial value of the identification parameter estimation as
Figure BDA0003173601190000093
The identification method specifically comprises the following steps:
s1: calculating a value function of the current time
Figure BDA0003173601190000094
Wherein, thetarIs the corner of the turntable.
S2: calculating a jacobian matrix of the function at the current moment:
order to
Figure BDA0003173601190000095
Figure BDA0003173601190000096
S3: calculating the increment of the identification parameter at the current moment
Figure BDA0003173601190000097
S4: updating the identification parameters at the next moment:
Figure BDA0003173601190000098
s5: judging whether signals E, R and S input exist, if so, jumping to S1, and if not, jumping to the step S6;
s6: after the identification is finished, outputting the estimated electrode angle error
Figure BDA0003173601190000099
As shown in the following graph, it can be seen from FIG. 2 that the accuracy of the parameters identified by the nonlinear least square method is very high, and 100000 filters are output in total in the simulation time
Figure BDA00031736011900000910
Value, last identified
Figure BDA00031736011900000911
Can be finally identified
Figure BDA00031736011900000912
And reality
Figure BDA00031736011900000913
Is approximately equal to 7.2 x 10-4°。
Step 6, identifying
Figure BDA0003173601190000101
Substituting into the improved angle measurement equation to obtain an accurate angle measurement equation, wherein the expression is as follows:
Figure BDA0003173601190000102
calculating to obtain an estimated vibration mode angle thetagujiAngle theta with true mode shaperealPosition error between, position error curve is plotted as in fig. 3:
the curve shows that the position error range is always in [0 degrees, 0.0015 degrees ]]The method estimated mode shape angle thetagujiWith high accuracy.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (10)

1. A method for obtaining the vibration mode angle of a hemispherical resonator gyroscope when the electrode angle has errors is characterized in that: the method comprises the following specific processes:
step 1, mounting and fixing a hemispherical resonance gyroscope on a turntable, so that a gyroscope sensitive shaft is superposed with a rotating shaft of the turntable;
step 2, applying excitation voltage to an excitation electrode on the hemispherical resonator gyroscope for parameter excitation until the amplitude of a vibration signal of the harmonic oscillator is unchanged;
step 3, enabling the rotary table to rotate at a constant speed, collecting vibration signals x and y detected by detection electrodes of 0 degrees and 45 degrees on the gyroscope, and simultaneously collecting the angle theta of the rotary tabler；
In the step 4, the step of,reference signal v generated by means of a phase-locked looprc、vrsDemodulating the detected vibration signals x and y respectively to obtain signals Cx, Sx, Cy and Sy, performing low-pass filtering on the signals Cx, Sx, Cy and Sy respectively to obtain signals Cx ', Sx', Cy 'and Sy', and performing secondary combination on the signals Cx ', Sx', Cy 'and Sy' to obtain E, R, S signals;
step 5, establishing and considering the electrode angle error
Figure FDA0003173601180000011
The angle measurement equation of (1);
step 6, setting initial parameters of the nonlinear identification algorithm;
step 7, using the E, R, S signal obtained in the step 4 as the input of a nonlinear identification algorithm to correct the angle error of the electrode
Figure FDA0003173601180000012
Identifying to obtain estimated electrode angle error
Figure FDA0003173601180000013
Step 8, identifying the obtained
Figure FDA0003173601180000014
Substituting the considered electrode angle error established in step 5
Figure FDA0003173601180000015
The vibration mode angle of the hemispherical resonator gyroscope when the electrode angle has errors is obtained in the angle measurement equation.
2. The method for obtaining the mode angle of the hemispherical resonator gyroscope according to claim 1, wherein the method comprises: in the step 2, the excitation electrodes are arranged on the hemispherical resonator gyroscope at intervals.
3. The hemispherical resonator gyroscope with errors in electrode angles as claimed in claim 2The method for obtaining the vibration mode angle is characterized by comprising the following steps: the reference signal v generated by using the phase-locked loop in the step 4rc、vrsDemodulating the detected vibration signals x and y respectively to obtain signals Cx, Sx, Cy and Sy, performing low-pass filtering on the signals Cx, Sx, Cy and Sy respectively to obtain signals Cx ', Sx', Cy 'and Sy', and performing secondary combination on the signals Cx ', Sx', Cy 'and Sy' to obtain E, R, S signals; the specific process is as follows:
reference signal v generated by means of a phase-locked looprc、vrsDemodulating the detected vibration signals x and y respectively to obtain signals Cx, Sx, Cy and Sy, wherein the expression is as follows:
Figure FDA0003173601180000021
performing low-pass filtering on the signals Cx, Sx, Cy and Sy, and respectively filtering out double frequency in the signals Cx, Sx, Cy and Sy to obtain signals Cx ', Sx', Cy 'and Sy';
the signals Cx ', Sx', Cy ', Sy' are combined twice to obtain E, R, S signals.
4. The method for obtaining the mode angle of the hemispherical resonator gyroscope according to claim 3, wherein the method further comprises: and performing secondary combination on the signals Cx ', Sx', Cy 'and Sy' to obtain E, R, S signals, wherein the expression is as follows:
Figure FDA0003173601180000022
5. the method for obtaining the mode angle of the hemispherical resonator gyroscope according to claim 4, wherein the method further comprises: the reference signal vrc、vrsIs composed of sine signal and cosine signal.
6. Hemispherical resonance in the presence of errors in the electrode angle of claim 5The method for acquiring the vibration mode angle of the gyroscope is characterized by comprising the following steps: the step 5 establishes the consideration of the electrode angle error
Figure FDA0003173601180000023
The angle measurement equation of (1); the specific process is as follows:
establishing consideration of electrode angle error
Figure FDA0003173601180000024
To obtain the true precession angle theta of the moderealThe form is as follows:
Figure FDA0003173601180000025
7. the method for obtaining the mode angle of a hemispherical resonator gyroscope according to claim 6, wherein the method further comprises: in the step 6, initial parameter setting is carried out on the nonlinear identification algorithm; the specific process is as follows:
the nonlinear identification algorithm is a nonlinear least square method or an extended Kalman filtering method;
given estimated initial value of electrode angle error
Figure FDA0003173601180000026
And estimated initial value of precession coefficient
Figure FDA0003173601180000027
8. The method according to claim 7, wherein the method comprises: in the step 7, the E, R, S signal obtained in the step 4 is used as the input of a nonlinear identification algorithm to the electrode angle error
Figure FDA0003173601180000028
Perform identificationObtaining an estimated electrode angle error
Figure FDA0003173601180000029
The specific identification process comprises the following steps:
taking the E, R, S signal obtained in the step 4 as the input of a nonlinear least square method;
s1: calculating a value function of the current time:
Figure FDA0003173601180000031
wherein, thetar(i) The turning angle of the rotary table collected at the moment i;
Figure FDA0003173601180000032
is an estimated value of the precession coefficient at the time i;
Figure FDA0003173601180000033
the estimated value of the electrode angle error at the moment i;
s2: calculating a jacobian matrix of the function at the current moment:
order to
Figure FDA0003173601180000034
Figure FDA0003173601180000035
Wherein b is an intermediate variable; j. the design is a squarer(i) A Jacobian matrix at the time i;
s3: calculating the increment of the identification parameter at the current moment based on the value function of the current moment and the Jacobian matrix of the current moment;
Figure FDA0003173601180000036
wherein the content of the first and second substances,
Figure FDA0003173601180000037
for the current time electrode angle error estimation
Figure FDA0003173601180000038
An increment of (d); Δ c (i) is the current time precession coefficient estimate
Figure FDA0003173601180000039
An increment of (d);
s4: updating the identification parameters at the next moment:
Figure FDA00031736011800000310
wherein the content of the first and second substances,
Figure FDA00031736011800000311
an electrode angle error estimated value at the moment i + 1;
Figure FDA00031736011800000312
the estimated value of the precession coefficient at the moment i + 1;
s5: judging whether signals E, R and S input exist, if so, jumping to S1, and if not, jumping to the step S6;
s6: after the identification is finished, outputting the estimated electrode angle error
Figure FDA00031736011800000313
9. The method according to claim 7, wherein the method comprises: in the step 7, the E, R, S signal obtained in the step 4 is used as the input of an optimization algorithm to correct the electrode angle error
Figure FDA0003173601180000041
Identifying to obtain estimated electrode angle error
Figure FDA0003173601180000042
The specific identification process comprises the following steps:
the model selected by extended Kalman Filtering is as follows
Figure FDA0003173601180000043
Wherein the content of the first and second substances,
Figure FDA0003173601180000044
the error of the electrode angle at the moment i + 1; c (i +1) is the value of precession coefficient at the moment i + 1; thetar(i+1)The measured value of the rotating angle of the rotary table at the moment i +1 is obtained, and v is measurement noise;
taking the E, R, S signal obtained in the step 4 as the input of an extended Kalman filter;
s1: and predicting the state estimation value at the next moment:
Figure FDA0003173601180000045
wherein the content of the first and second substances,
Figure FDA0003173601180000046
as an electrode angle error
Figure FDA0003173601180000047
A priori estimated value at the ith moment;
Figure FDA0003173601180000048
is an estimated value of the ith moment;
Figure FDA0003173601180000049
is a priori estimated value of the precession coefficient c at the ith moment;
Figure FDA00031736011800000410
is a priori estimated value of the precession coefficient c at the ith-1 moment;
s2: predicting the covariance of the estimation error at the next time instant:
Pi|i-1＝Pi-1|i-1
wherein, Pi|i-1To estimate the predicted value, P, of the error covariance matrix at time ii-1|i-1Is the value of the estimated error covariance matrix at the (i-1) th moment;
s3: judging whether experimental data are input, if so, jumping to S4, and if not, jumping to S9;
s4: and predicting the measurement matrix at the next moment:
order to
Figure FDA00031736011800000411
Figure FDA0003173601180000051
Wherein b is an intermediate variable; ciA measurement matrix at the ith moment;
s5: and predicting the measurement estimation value of the next moment:
Figure FDA0003173601180000052
wherein the content of the first and second substances,
Figure FDA0003173601180000053
is an estimated value of the rotating angle of the rotary table;
s6: predicting the state gain matrix at the next moment:
Ki＝Pi|i-1Ci T(CiPi|i-1Ci T+Q)-1
wherein Q is the co-ordination of the noise vVariance; kiIs a state gain matrix of the ith moment, and T is a transposition;
s7: and updating the state estimation value at the next moment:
Figure FDA0003173601180000054
wherein the content of the first and second substances,
Figure FDA0003173601180000055
as an electrode angle error
Figure FDA0003173601180000056
A posterior estimate at the ith time;
Figure FDA0003173601180000057
is a posterior estimated value of the precession coefficient at the ith moment;
s8: update the estimation error covariance for the next time instant, and then jump to S1:
Pi|i＝(I-KiCi)Pi|i-1(I-KiCi)T
wherein, Pi|iThe value of the ith moment of the error covariance matrix is estimated, and I is an identity matrix;
s9: after the filtering is finished, the estimated electrode angle error is output
Figure FDA0003173601180000058
10. The method for obtaining the mode angle of a hemispherical resonator gyroscope according to claim 8 or 9, wherein the method further comprises: obtained by identification in the step 8
Figure FDA0003173601180000059
Substituting the considered electrode angle error established in step 5
Figure FDA00031736011800000510
Obtaining the vibration mode angle of the hemispherical resonance gyroscope when the electrode angle has errors in the angle measurement equation; the expression is as follows:
Figure FDA00031736011800000511
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