CN113252019A - Method for acquiring vibration mode angle of hemispherical resonant gyroscope when forward amplification coefficients are inconsistent - Google Patents

Method for acquiring vibration mode angle of hemispherical resonant gyroscope when forward amplification coefficients are inconsistent Download PDF

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CN113252019A
CN113252019A CN202110522933.7A CN202110522933A CN113252019A CN 113252019 A CN113252019 A CN 113252019A CN 202110522933 A CN202110522933 A CN 202110522933A CN 113252019 A CN113252019 A CN 113252019A
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forward amplification
signals
gyroscope
angle
amplification factor
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CN113252019B (en
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解伟男
汪昕杨
孙一为
奚伯齐
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
    • G01C19/5705—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces using masses driven in reciprocating rotary motion about an axis
    • 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
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/18—Stabilised platforms, e.g. by gyroscope

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Abstract

The invention discloses a method for acquiring a hemispherical resonator gyroscope vibration mode angle when forward amplification factors are inconsistent, and relates to a method for acquiring a hemispherical resonator gyroscope vibration mode angle when forward amplification factors are inconsistent. The invention aims to solve the problems that when the forward amplification factors are inconsistent, the hemispherical resonator gyroscope cannot accurately measure the information such as the angle of a carrier, and the navigation accuracy is reduced. The process is as follows: 1: fixing the gyroscope on the rotary table to enable the gyroscope sensitive shaft to be superposed with the rotary shaft of the rotary table; 2: applying excitation voltage to an excitation electrode on the gyroscope for parameter excitation until the amplitude of a vibration signal of the harmonic oscillator is unchanged; 3: enabling the rotary table to rotate at a constant speed, and collecting vibration signals detected by 0-degree and 45-degree electrodes on the gyroscope and the angle of the rotary table; 4: e, R, S signals are obtained; 5: designing an extended Kalman filter and setting initial parameters; 6: estimating a forward amplification factor ratio; 7: and acquiring the vibration mode angle of the hemispherical resonant gyroscope when the forward amplification coefficients are inconsistent. The invention belongs to the technical field of inertia.

Description

Method for acquiring vibration mode angle of hemispherical resonant gyroscope when forward amplification coefficients are inconsistent
Technical Field
The invention relates to a method for acquiring a vibration mode angle of a hemispherical resonant gyroscope when forward amplification coefficients are inconsistent, and belongs to the technical field of inertia.
Background
In the last 60 th century, a novel vibration gyro, a hemispherical resonance gyro, appeared. The novel gyroscope has many advantages, such as small error, long service life, wide application field and the like. Moreover, compare in traditional mechanical top, hemisphere resonance top component part is few, simple structure, and its gauge outfit is only become by two to three spare parts, and difficult wearing and tearing, and the fault rate is very low. The core component harmonic oscillator of the hemispherical resonance gyroscope is made of fused quartz, and due to the stable physical characteristics of quartz glass, the harmonic oscillator not only has high reliability and long service life, but also has extremely strong radiation resistance, is not easily interfered by cosmic rays and high-energy particles, and is commonly used for attitude determination and navigation of a space vehicle. In conclusion, the hemispherical resonator gyroscope has a good development prospect, is beneficial to the development and innovation of an inertia technology by researching the hemispherical resonator gyroscope, and can lay a good foundation for deep space exploration in China and other related high-tech fields.
At the present stage, the hemispherical resonator gyroscope mainly has two working modes of force balance and full angle, the full angle mode is a novel hemispherical resonator gyroscope working mode, the mode utilizes the physical characteristic that the precession angle of a harmonic oscillator is in direct proportion to the rotation angle of a gyroscope carrier, the rotation angle of the carrier is read out through real-time calculation of the precession angle of the resonance oscillator vibration mode, and the hemispherical resonator gyroscope working mode is suitable for occasions with higher rotation speed. In the full-angle mode, signals x and y acquired by 0 ° and 45 ° electrodes are normally forward amplified in equal proportion, and then the precession angle of the mode shape is calculated, but there is a considerable problem: if the amplification coefficients of the two signals are not equal, a commonly used angle measurement equation is not accurate enough, the calculated vibration mode angle and the actual vibration mode angle have small errors, and the carrier rotation angle read out after calculation and the actual rotation angle of the carrier have certain errors, which is not allowed in high-precision application occasions.
In summary, to calculate the precise mode angle, the precise magnitude of the forward amplification factor ratio k must be known. Therefore, it is necessary to provide a high-precision identification method for identifying k.
Disclosure of Invention
The invention aims to solve the problems that the hemispherical resonator gyroscope cannot accurately measure information such as the angle of a carrier when forward amplification factors are inconsistent and the navigation accuracy is reduced, and provides a method for acquiring the vibration mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent.
The carrier may be an aircraft, a turntable, etc.
The method for acquiring the vibration mode angle of the hemispherical resonator gyroscope when the forward amplification coefficients are inconsistent comprises the following specific processes:
step 1: mounting and fixing the hemispherical resonance gyroscope on a rotary table, and enabling a sensitive axis of the gyroscope to be superposed with a rotary axis of the rotary table;
step 2: applying excitation voltage to an excitation electrode on the hemispherical resonance gyroscope for parameter excitation until the amplitude of a vibration signal of the harmonic oscillator is unchanged;
and step 3: the rotary table is rotated at a constant speed, vibration signals x and y detected by detection electrodes of 0 degree and 45 degrees on the gyroscope are collected, and the angle theta of the rotary table is collected at the same timer；
And 4, step 4: 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;
and 5: establishing an angle measurement equation considering the forward amplification factor ratio k, designing an extended Kalman filter based on the angle measurement equation of the forward amplification factor ratio k, and setting initial parameters of the extended Kalman filter;
step (ii) of6: taking the E, R, S signal obtained in the step 4 as the input of an extended Kalman filter, identifying the forward amplification factor ratio k, and outputting the estimated forward amplification factor ratio after the filtering is finished
Figure BDA0003064689020000021
And 7: to be output
Figure BDA0003064689020000022
And (5) substituting the angle measurement equation which is established in the step (5) and takes the forward amplification factor ratio k into consideration to obtain the vibration mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent.
The invention has the beneficial effects that:
the default forward amplification factor of the traditional angle measurement equation is in an equal proportion, the problem of inconsistent forward amplification factors is not considered, information such as calculated carrier angles and the like has certain errors, the precision of the gyroscope is reduced, the navigation accuracy is reduced, and the requirement of high-precision working occasions cannot be met.
The invention provides a method for acquiring the vibration mode angle of a hemispherical resonant gyroscope when the forward amplification coefficients are inconsistent. The rotary table is rotated at a constant speed, vibration signals x and y detected by 0-degree and 45-degree detection electrodes on the gyroscope are collected, and a reference signal v generated by a phase-locked loop is utilizedrc、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, after the design of the extended Kalman filter is completed, the signal E, R, S obtained in the step 4 is used as the input of the extended Kalman filter to identify k, and the k is output after the filtering is finished
Figure BDA0003064689020000023
To be finally identified
Figure BDA0003064689020000024
And substituting the angle measurement equation into the improved angle measurement equation to obtain an accurate angle measurement equation. The method can realize the accurate identification of the forward amplification factor ratio k, and has high accuracy and identification
Figure BDA0003064689020000031
Small error, pass
Figure BDA0003064689020000032
The calculated gyroscope vibration mode angle has high precision, the high-precision angle measurement of the gyroscope is realized, the angle information of the carrier is accurately measured, and the navigation accuracy is improved; the problem of when the forward amplification factor is inconsistent, the hemisphere resonance gyro can't measure information such as the angle of carrier accurately, reduce the navigation rate of accuracy is solved.
According to theoretical analysis and simulation experiments, the method for acquiring the vibration mode angle of the hemispherical resonant gyroscope when the forward amplification factors are inconsistent can realize high-precision work of the full-angle mode hemispherical resonant gyroscope when the forward amplification factors are inconsistent, and therefore the method is widely applied to the high-end science and technology field needing the high-precision hemispherical resonant gyroscope.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of error in identifying a parameter k according to an embodiment of the present invention;
FIG. 3 is a graph of an error in mode angle for an embodiment of the present invention;
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 the method for acquiring the mode angle of the hemispherical resonator gyroscope in the case of the non-uniform forward amplification factor of the present embodiment is as follows:
the invention aims at solving the problem that the angle measurement has errors when the forward amplification coefficients of the detection loops of the hemispherical resonant gyroscope are not equal, and provides a method for acquiring the vibration mode angle of the hemispherical resonant gyroscope when the forward amplification coefficients are not consistent, and provides an improved angle measurement formula, an extended Kalman filter is established based on the formula, vibration signals acquired by 0-degree and 45-degree electrodes are demodulated, subjected to low-pass filtering and the like while the gyroscope is rotated, and the obtained signal E, R, S is used as the input of the extended Kalman filter, so that the identification of the ratio k of the forward amplification coefficients is realized, the accurate angle measurement formula is obtained, and the measurement accuracy of the gyroscope is improved.
In order to achieve the above object, the present invention provides a method for obtaining a mode angle of a hemispherical resonator gyroscope when forward amplification factors are inconsistent, comprising:
step 1: mounting and fixing the hemispherical resonance gyroscope on a rotary table, and enabling a sensitive axis of the gyroscope to be superposed with a rotary axis of the rotary table;
step 2: applying an excitation voltage to an excitation electrode on the hemispherical resonator gyroscope to carry out parameter (signals applied by the excitation electrode, such as amplitude, frequency and phase of the signals) excitation until the amplitude of the vibration signal of the harmonic oscillator is unchanged;
and step 3: the rotary table is rotated at a constant speed, vibration signals x and y detected by detection electrodes of 0 degree and 45 degrees on the gyroscope are collected, and the angle theta of the rotary table is collected at the same timer；
And 4, step 4: 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;
and 5: establishing an angle measurement equation considering the forward amplification factor ratio k, designing an extended Kalman filter based on the angle measurement equation of the forward amplification factor ratio k, and setting initial parameters of the extended Kalman filter;
step 6: taking the E, R, S signal obtained in the step 4 as the input of an extended Kalman filter, identifying the forward amplification factor ratio k, and outputting the estimated forward amplification factor ratio after the filtering is finished
Figure BDA0003064689020000041
And 7: to be output
Figure BDA0003064689020000042
And (5) substituting the angle measurement equation which is established in the step (5) and takes the forward amplification factor ratio k into consideration to obtain the vibration mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent.
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: the difference between this embodiment and the first or second embodiment is that the reference signal v generated by using the phase-locked loop in the step 4 isrc、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:
the reference signal v generated by using the 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 BDA0003064689020000043
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 BDA0003064689020000051
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: the difference between this embodiment and one of the first to fifth embodiments is that, in the step 5, an angle measurement equation considering the forward amplification factor ratio k is established; the specific process is as follows:
an angle measurement equation considering the forward amplification coefficient ratio k is established, and the equation can accurately describe the real precession angle of the vibration mode and has the following form:
Figure BDA0003064689020000052
wherein k is ky/kx，kxIs the forward amplification factor, k, of the 0 DEG electrodeyA forward amplification factor for a 45 ° electrode (after a 0 ° electrode is determined, a 45 ° electrode is true in the counterclockwise direction); thetarealThe real value of the vibration mode angle of the hemispherical resonance gyroscope is obtained.
Therefore, if the parameter k is known, the true value theta of the vibration mode angle of the hemispherical resonator gyroscope 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 one of the first to sixth embodiments is that, in step 5, an extended kalman filter is designed based on an angle measurement equation of the forward amplification factor ratio k, and a model selected by the filter is as follows:
Figure BDA0003064689020000053
k (i +1) ═ k (i), c (i +1) ═ c (i), are state equations, and are gyro forward amplification factor ratio k ═ ky/kxThe two parameters are fixed values k (i) which do not change along with time, the fixed values are a forward amplification coefficient ratio, c (i) is a gyro precession coefficient, and i is the ith moment;
Figure BDA0003064689020000061
is an observation equation, θrIs the rotating angle of the rotary table, and v is the measurement noise;
in the step 5, initial parameter setting is carried out on the extended Kalman filter; the specific process is as follows:
the extended Kalman filter is a recursion algorithm, and is started to set initial parameters and set initial values to enable the extended Kalman filter to work
Figure BDA0003064689020000062
P0|0＝I；
In the formula,
Figure BDA0003064689020000063
is an initial estimate of the forward amplification factor ratio k,
Figure BDA0003064689020000064
as an initial estimate of the precession coefficient c, P0|0Is the initial value of the estimation error covariance matrix.
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 the first to seventh embodiments is that, in step 6, the E, R, S signal obtained in step 4 is used as an input of the extended kalman filter, the forward amplification factor ratio k is identified, and the estimated forward amplification factor ratio is output after the filtering is finished
Figure BDA0003064689020000065
The identification method specifically comprises the following steps:
s1: predicting a state estimate at a next time
Figure BDA0003064689020000066
Figure BDA0003064689020000067
In the formula,
Figure BDA0003064689020000068
is an a priori estimate of the forward amplification factor ratio k at the ith time,
Figure BDA0003064689020000069
is an estimate of the forward amplification factor ratio k at time i-1,
Figure BDA00030646890200000610
is an a priori estimate of the precession coefficient c at the ith instant,
Figure BDA00030646890200000611
is an estimated value of the precession coefficient c at the i-1 th moment;
s2: predicting the covariance of the estimation error at the next time instant:
Pi|i-1＝Pi-1|i-1
in the formula, 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 a signal E, R and S are input into the extended Kalman filter, if so, jumping to S4, and if not, jumping to the step S9;
s4: and predicting the measurement matrix at the next moment:
order to
Figure BDA0003064689020000071
Figure BDA0003064689020000072
In which b is an intermediate variable, CiA measurement matrix at the ith moment;
s5: and predicting the measurement estimation value of the next moment:
Figure BDA0003064689020000073
wherein,
Figure BDA0003064689020000074
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-1*Ci T*(Ci*Pi|i-1*Ci T+Q)-1
wherein Q is the covariance of noise v, and Q is 0.012(ii) a Is a multiplication number, 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 BDA0003064689020000075
in the formula,
Figure BDA0003064689020000076
the forward amplification factor is a posterior estimated value of the forward amplification factor ratio k at the ith moment;
s8: updating the covariance of the estimation error at the next moment, and then jumping to S1;
Pi|i＝(I-KiCi)*Pi|i-1
in the formula, 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 forward amplification factor ratio is output
Figure BDA0003064689020000077
In conclusion, the design of the extended kalman filter based on the angle measurement equation considering the forward amplification factor ratio k is completed.
Other steps and parameters are the same as those in one of the first to seventh embodiments.
The specific implementation method nine: this embodiment differs from the first to eighth embodiments in that the step 7 outputs
Figure BDA0003064689020000081
Substituting the angle measurement equation which is established in the step 5 and takes the forward amplification factor ratio k into consideration to obtain the vibration mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent; the expression is as follows:
Figure BDA0003064689020000082
in the formula, thetagujiThe estimated value of the vibration mode angle of the hemispherical resonance gyroscope is obtained.
The other steps and parameters are the same as in one of the first to eighth embodiments.
The detailed implementation mode is ten: the difference between the present embodiment and one of the first to ninth embodiments is that the inconsistency of the forward amplification factor is caused by one or more of a forward amplification circuit error, a harmonic oscillator electrode plate area error, a harmonic oscillator electrode plate spacing error, and a harmonic oscillator installation deviation;
the plurality is 2, 3 or 4.
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 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 30 deg/s speed, setting fs as 1000Hz and t as sampling timeiAcquiring vibration signals x and y detected by 0-degree and 45-degree detection electrodes on the gyroscope and acquiring the angle theta of the turntable at the same time for 10srWherein the 0 degree detection electrode forward amplification factor is k x2, 45 DEG detection electrode forward amplification factor kyWhen k is 2.2, k is ky/kx＝1.1；
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;
and 5, finishing the design of the extended Kalman filter based on an angle measurement equation considering the forward amplification coefficient ratio k, wherein the filter model is as follows:
Figure BDA0003064689020000091
and setting initial parameters of the filter to
Figure BDA0003064689020000092
P0|0I, the measurement noise covariance Q is 0.012。
And 6, taking the signal E, R, S obtained in the step 4 as the input of the extended Kalman filter, identifying k, and outputting after the filtering is finished
Figure BDA0003064689020000093
S1: predicting a state estimate at a next time
Figure BDA0003064689020000094
Figure BDA0003064689020000095
S2: predicting the covariance of the estimation error at the next time instant:
Pi|i-1＝Pi-1|i-1
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 BDA0003064689020000096
Figure BDA0003064689020000097
S5: and predicting the measurement estimation value of the next moment:
Figure BDA0003064689020000098
wherein,
Figure BDA0003064689020000099
as an estimate of the angle of rotation of the turntable
S6: predicting the state gain matrix at the next moment:
Ki＝Pi|i-1*Ci T*(Ci*Pi|i-1*Ci T+Q)-1
s7: and updating the state estimation value at the next moment:
Figure BDA0003064689020000101
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
s9: after the filtering is finished, the estimated forward amplification factor ratio is output
Figure BDA0003064689020000102
The simulation result is shown in fig. 2, and it can be seen from fig. 2 that the identification error of the extended kalman filter tends to be stable at 5 seconds, and 10000 filters are output in total in the sampling time
Figure BDA0003064689020000103
Value, last identified
Figure BDA0003064689020000104
Can be finally identified
Figure BDA0003064689020000105
The difference from the actual k is equal to about 2 x 10-5It can be seen that the filter pair k identification precision is very high.
Step 7, output
Figure BDA0003064689020000106
Substituting the angle measurement equation which is established in the step 5 and takes the forward amplification factor ratio k into consideration to obtain the vibration mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent; the expression is as follows:
Figure BDA0003064689020000107
is calculated toTo the estimated mode angle thetagujiAngle theta with true mode shaperealPosition error between, position error curve is drawn as figure 3;
as can be seen from the graph of FIG. 3, the position error range is always within [ -0.0012 ], 0.0012 °]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 forward amplification factors are inconsistent is characterized in that: the method comprises the following specific processes:
step 1: mounting and fixing the hemispherical resonance gyroscope on a rotary table, and enabling a sensitive axis of the gyroscope to be superposed with a rotary axis of the rotary table;
step 2: applying excitation voltage to an excitation electrode on the hemispherical resonance gyroscope for parameter excitation until the amplitude of a vibration signal of the harmonic oscillator is unchanged;
and step 3: the rotary table is rotated at a constant speed, vibration signals x and y detected by detection electrodes of 0 degree and 45 degrees on the gyroscope are collected, and the angle theta of the rotary table is collected at the same timer；
And 4, step 4: 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;
and 5: establishing an angle measurement equation considering the forward amplification factor ratio k, designing an extended Kalman filter based on the angle measurement equation of the forward amplification factor ratio k, and setting initial parameters of the extended Kalman filter;
step 6: taking the E, R, S signal obtained in the step 4 as the input of the extended Kalman filter, and performing the following stepsIdentifying the forward amplification factor ratio k, and outputting the estimated forward amplification factor ratio after the filtering is finished
Figure FDA0003064689010000011
And 7: to be output
Figure FDA0003064689010000012
And (5) substituting the angle measurement equation which is established in the step (5) and takes the forward amplification factor ratio k into consideration to obtain the vibration mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent.
2. The method for obtaining the mode angle of a 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 method for obtaining the mode angle of a hemispherical resonator gyroscope according to claim 1 or 2, wherein the forward amplification factor is inconsistent: 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:
the reference signal v generated by using the 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 FDA0003064689010000021
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 of claim 3, wherein the method for obtaining the mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent 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 FDA0003064689010000022
5. the method of claim 4, wherein the method for obtaining the mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent comprises: the reference signal vrc、vrsIs composed of sine signal and cosine signal.
6. The method of claim 5, wherein the method for obtaining the mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent comprises: in the step 5, an angle measurement equation considering the forward amplification coefficient ratio k is established; the specific process is as follows:
establishing an angle measurement equation considering the forward amplification coefficient ratio k, wherein the form is as follows:
Figure FDA0003064689010000023
wherein k is ky/kx，kxIs the forward amplification factor, k, of the 0 DEG electrodeyForward amplification factor for a 45 ° electrode; thetarealThe real value of the vibration mode angle of the hemispherical resonance gyroscope is obtained.
7. The method of claim 6, wherein the method for obtaining the mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent comprises: in the step 5, an extended kalman filter is designed based on an angle measurement equation of the forward amplification factor ratio k, and a model selected by the filter is as follows:
Figure FDA0003064689010000031
k (i +1) ═ k (i), c (i +1) ═ c (i), are state equations, k (i) is the forward amplification coefficient ratio, c (i) is the gyro precession coefficient, i is the ith time;
Figure FDA0003064689010000032
is an observation equation, θrIs the rotating angle of the rotary table, and v is the measurement noise;
in the step 5, initial parameter setting is carried out on the extended Kalman filter; the specific process is as follows:
setting initial parameters when the extended Kalman filter is started, giving initial values and ordering
Figure FDA0003064689010000033
P0|0＝I；
In the formula,
Figure FDA0003064689010000034
is an initial estimate of the forward amplification factor ratio k,
Figure FDA0003064689010000035
as an initial estimate of the precession coefficient c, P0|0Is the initial value of the estimation error covariance matrix.
8. The method of claim 7, wherein the method for obtaining the mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent comprises: in the step 6, the E, R, S signal obtained in the step 4 is used as the input of the extended kalman filter, the forward amplification factor ratio k is identified, and the estimated forward amplification factor ratio is output after the filtering is finished
Figure FDA0003064689010000036
IdentificationThe method comprises the following specific steps:
s1: predicting a state estimate at a next time
Figure FDA0003064689010000037
Figure FDA0003064689010000038
In the formula,
Figure FDA0003064689010000039
is an a priori estimate of the forward amplification factor ratio k at the ith time,
Figure FDA00030646890100000310
is an estimate of the forward amplification factor ratio k at time i-1,
Figure FDA00030646890100000311
is an a priori estimate of the precession coefficient c at the ith instant,
Figure FDA00030646890100000312
is an estimated value of the precession coefficient c at the i-1 th moment;
s2: predicting the covariance of the estimation error at the next time instant:
Pi|i-1＝Pi-1|i-1
in the formula, 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 a signal E, R and S are input into the extended Kalman filter, if so, jumping to S4, and if not, jumping to the step S9;
s4: and predicting the measurement matrix at the next moment:
order to
Figure FDA0003064689010000041
Figure FDA0003064689010000042
In which b is an intermediate variable, CiA measurement matrix at the ith moment;
s5: and predicting the measurement estimation value of the next moment:
Figure FDA0003064689010000043
wherein,
Figure FDA0003064689010000044
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-1*Ci T*(Ci*Pi|i-1*Ci T+Q)-1
wherein Q is the covariance of the noise v; is a multiplication number, 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 FDA0003064689010000045
in the formula,
Figure FDA0003064689010000046
the forward amplification factor is a posterior estimated value of the forward amplification factor ratio k at the ith moment;
s8: updating the covariance of the estimation error at the next moment, and then jumping to S1;
Pi|i＝(I-KiCi)*Pi|i-1
in the formula, 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 forward amplification factor ratio is output
Figure FDA0003064689010000051
9. The method of claim 8, wherein the method for obtaining the mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent comprises: to be output in said step 7
Figure FDA0003064689010000052
Substituting the angle measurement equation which is established in the step 5 and takes the forward amplification factor ratio k into consideration to obtain the vibration mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent;
the expression is as follows:
Figure FDA0003064689010000053
in the formula, thetagujiThe estimated value of the vibration mode angle of the hemispherical resonance gyroscope is obtained.
10. The method of claim 9, wherein the method for obtaining the mode angle of the hemispherical resonator gyroscope when the forward amplification factors are inconsistent comprises: the inconsistency of the forward amplification coefficients is caused by one or more of a forward amplification circuit error, a harmonic oscillator electrode plate area error, a harmonic oscillator electrode plate distance error and a harmonic oscillator installation deviation;
the plurality is 2, 3 or 4.
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