Force balance hemispherical resonator gyroscope null drift compensation method and device, electronic equipment and computer readable storage medium

Abstract

The invention discloses a force balance hemispherical resonator gyroscope null drift compensation method and device, electronic equipment and a computer readable storage medium, and the method comprises the steps: setting a hemispherical resonator gyroscope in a force balance mode, pushing a vibration mode azimuth angle to a damping simple vibration shaft, enabling a sensitive shaft of the hemispherical resonator gyroscope to be vertical to the ground, and enabling the sensitive shaft to face upwards, changing the environment temperature of the hemispherical resonator gyroscope, the method comprises the following steps: acquiring circuit temperatures, actually measured resonant frequencies and zero-offset output measured values of a gyroscope in real time, constructing a regression model according to each circuit temperature and the corresponding actually measured resonant frequencies and zero-offset output measured values, solving the regression model to obtain fitting parameters, and substituting the fitting parameters into a zero-offset output compensation model to obtain a zero-offset compensation model. And calculating according to the zero offset output compensation model to obtain a compensated zero offset output value. The amplification factor difference of the circuit is reflected by the sampling temperature of the circuit, the zero drift is estimated and compensated by the two characteristics at the same time, and the compensated gyroscope can basically inhibit the influence of the zero drift.

Description

Technical Field

[0001] The present invention relates to the field of inertial technology, and in particular to a method and device for compensating zero drift of a force-balanced hemispherical resonant gyroscope, an electronic device, and a computer-readable storage medium. Background Art

[0002] The hemispherical resonant gyroscope in force balance mode is an angular rate sensor used in the field of inertial navigation. Zero drift is a key factor in measuring the accuracy of the gyroscope, and the influence of temperature on the structural parameters and measurement and control circuit of the gyroscope is an important cause of zero drift.

[0003] The hemispherical resonator gyroscope mainly relies on the vibration of the second antinode of the hemispherical resonator for angular velocity sensitivity. It is made of fused quartz glass material with a high quality factor. The physical properties of the resonator, such as elastic modulus, density, thickness, radius and Poisson's ratio, have a strong correlation with the temperature of the resonator. These factors will cause the resonant frequency, damping coefficient and frequency splitting coefficient of the resonator to change, thus causing the zero drift of the resonator.

[0004] The main control circuit of the hemispherical resonant gyroscope is mainly divided into the detection circuit and the drive circuit. Its components are greatly affected by temperature. Changes in the temperature of the environment will cause changes in the amplification factors of the detection circuit and the drive circuit, causing the zero-bias output in the force balance mode to drift.

[0005] The existing hemispherical resonant gyroscope zero drift compensation model often starts from the single dimension of the resonant frequency, and solves the complex regression model by piecewise polynomial fitting method, BP neural network method, or particle swarm optimization algorithm. The final compensation model has the disadvantages of poor repeatability, large compensation residual, and large amount of calculation, and is not practical in engineering. Summary of the invention

[0006] In view of the problems in the background technology, the present invention proposes a method for compensating zero drift of a force-balanced hemispherical resonator gyroscope, in which the resonant frequency of the resonator reflects the difference in the physical state of the resonator, and the circuit sampling temperature reflects the difference in the amplification factor of the circuit. These two characteristics are used to estimate and compensate for the zero drift at the same time, and the compensated gyroscope can basically suppress the influence of the zero drift; accordingly, the present invention also provides an apparatus for implementing the compensation method, an electronic device for executing the method, and a computer-readable storage medium.

[0007] The present invention adopts the following technical solutions:

[0008] A method for compensating zero drift of a force-balanced hemispherical resonant gyroscope comprises the following steps:

[0009] Step 1: Set the HRG in the force balance mode and push the vibration mode azimuth to the damped simple vibration axis, and make the sensitive axis of the HRG vertical to the ground and upward.

[0010] Step 2: Change the ambient temperature of the hemispherical resonant gyroscope and collect the circuit temperature T of the hemispherical resonant gyroscope in real time, as well as the measured resonant frequency f and zero bias output measurement value corresponding to each circuit temperature T.

[0011] Step 3: Based on the circuit temperature T of each hemispherical resonant gyroscope, the measured resonant frequency f corresponding to the circuit temperature T of each hemispherical resonant gyroscope, and the zero bias output measurement value corresponding to each measured resonant frequency f Constructing zero bias output measurements The regression model of the relative resonant frequency f and the circuit temperature T is solved to obtain the fitting parameter A,

[0012] Step 4: Substitute the fitting parameter A into the zero bias output compensation model, and calculate the compensated zero bias output value according to the zero bias output compensation model.

[0013] Optionally, the specific expression of the regression model is:

[0014]

[0015] Among them, the fitting parameter A=[a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ,a 7 ,a 8 ].

[0016] Optionally, the regression model is discretized to obtain a specific expression of the discretized regression model:

[0017]

[0018] Among them, Δf=f(t)-f(t-1) is the measured resonant frequency difference between two consecutive sampling times t, t-1, and ΔT=T(t)-T(t-1) is the circuit temperature difference between two consecutive times t, t-1.

[0019] Optionally, the specific expression of the zero-bias output compensation model is:

[0020]

[0021] Where Ω 地速 is the earth's rotation speed at the latitude of the HRG, and k is the scale factor in the HRG force balance mode.

[0022] Optionally, in step 2, the specific operation of changing the ambient temperature of the hemispherical resonant gyroscope is:

[0023] The ambient temperature of the hemispherical resonant gyroscope was continuously decreased from room temperature to -30°C, then continuously increased from -30°C to 50°C, and then continuously decreased from 50°C to -30°C.

[0024] As a general inventive concept, the present invention also provides a force-balanced hemispherical resonant gyro zero drift compensation device, comprising: an operation module, a temperature control module, a collection module and a solution module.

[0025] The operating module is used to set the hemispherical resonant gyroscope in a force balance mode and push the vibration mode azimuth to the damped simple vibration axis, and make the sensitive axis of the hemispherical resonant gyroscope vertical to the ground and upward.

[0026] The temperature control module is used to change the ambient temperature of the hemispherical resonant gyroscope and transmit it to the acquisition module in real time.

[0027] The acquisition module is used to collect the circuit temperature T of the hemispherical resonant gyroscope in real time, as well as the measured resonant frequency f and zero bias output measurement value of the hemispherical resonant gyroscope corresponding to each circuit temperature T. And transmitted to the solution module and zero bias output module,

[0028] The solution module is used to output the measured value of the zero bias corresponding to each measured resonant frequency f according to the circuit temperature T of each hemispherical resonant gyroscope and the measured resonant frequency f corresponding to the circuit temperature T of each hemispherical resonant gyroscope. Constructing zero bias output measurements A regression model of the relative resonant frequency f and the circuit temperature T is solved to obtain a fitting parameter A, and the fitting parameter A is transmitted to a zero bias output module;

[0029] The zero bias output module is used to substitute the fitting parameters into the zero bias output compensation model, and calculate the compensated zero bias output value according to the zero bias output compensation model.

[0030] Optionally, solve the module to construct the zero-bias output measurement The specific expression of the regression model of the relative resonant frequency f and the circuit temperature T is:

[0031]

[0032] Among them, the fitting parameter A=[a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ,a 7 ,a 8 ].

[0033] Optionally, the solution module discretizes the regression model to obtain a specific expression of the discretized regression model:

[0034]

[0035] Among them, Δf=f(t)-f(t-1) is the measured resonant frequency difference between two consecutive sampling times t and t-1, and ΔT=T(t)-T(t-1) is the temperature difference between two consecutive times t and t-1.

[0036] Optionally, the specific expression of the zero bias output compensation model adopted by the zero bias output module is:

[0037]

[0038] Where Ω 地速 is the earth's rotation speed at the latitude of the HRG, and k is the scale factor in the HRG force balance mode.

[0039] As a general inventive concept, the present invention also provides an electronic device, the device comprising:

[0040] Memory for storing computer programs;

[0041] A processor is used to implement the steps of the above-mentioned force-balanced hemispherical resonant gyroscope zero-drift compensation method when executing the computer program.

[0042] As a general inventive concept, the present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the above-mentioned force-balanced hemispherical resonant gyroscope zero drift compensation method are implemented.

[0043] Compared with the prior art, the advantages of the present invention are:

[0044] The zero drift compensation method of the force-balanced hemispherical resonant gyroscope of the present invention performs temperature cycle continuous testing on the force-balanced mode gyroscope, finds the correlation between the zero drift and the resonant frequency and the temperature of the sampling circuit, establishes a regression fitting model, performs regression solution on the model parameters, substitutes the regression parameters into the compensation model, and realizes the zero drift compensation of the gyroscope. Practice shows that the compensated gyroscope can basically suppress the influence of the zero drift. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to make the present invention more easily understood, the present invention will be described in more detail by referring to the specific embodiments shown in the accompanying drawings. These drawings only depict typical embodiments of the present invention and should not be considered as limiting the scope of protection of the present invention.

[0046] Figure 1 The present invention is a flowchart of a method for compensating a zero drift of a hemispherical resonant gyroscope in a force balance mode according to an embodiment of the present invention.

[0047] Figure 2 4 is a system block diagram of a method for compensating a hemispherical resonant gyroscope zero drift in a force balance mode according to an embodiment of the present invention.

[0048] Figure 3 The figure is a schematic diagram comparing the zero bias output results of a force-balanced hemispherical resonant gyroscope before compensation and after compensation using the method of the present invention. DETAILED DESCRIPTION

[0049] The following describes the implementation modes of the present invention with reference to the accompanying drawings so that those skilled in the art can better understand the present invention and implement it. However, the enumerated embodiments are not intended to limit the present invention. In the absence of conflict, the following embodiments and the technical features in the embodiments may be combined with each other, wherein the same components are represented by the same figure marks.

[0050] Embodiment 1:

[0051] like Figure 1 and Figure 2 As shown, this embodiment provides a method for compensating zero drift of a force-balanced hemispherical resonant gyroscope, comprising the following steps:

[0052] Step 1: Set the HRG in the force balance mode and push the vibration mode azimuth to the damped simple vibration axis, and make the sensitive axis of the HRG vertical to the ground and upward.

[0053] Step 2: Change the ambient temperature of the hemispherical resonant gyroscope and collect the circuit temperature T of the hemispherical resonant gyroscope in real time, as well as the measured resonant frequency f and zero bias output measurement value corresponding to each circuit temperature T.

[0054] Step 3: Based on the circuit temperature T of each hemispherical resonant gyroscope, the measured resonant frequency f corresponding to the circuit temperature T of each hemispherical resonant gyroscope, and the zero bias output measurement value corresponding to each measured resonant frequency f Constructing zero bias output measurements The regression model of the relative resonant frequency f and the circuit temperature T is solved to obtain the fitting parameter A,

[0055] Step 4: Substitute the fitting parameter A into the zero bias output compensation model, and calculate the compensated zero bias output value according to the zero bias output compensation model.

[0056] In this embodiment, the specific expression of the regression model is:

[0057]

[0058] Among them, the fitting parameter A=[a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ,a 7 ,a 8 ].

[0059] In this embodiment, the regression model is discretized to obtain a specific expression of the discretized regression model:

[0060]

[0061] Among them, Δf=f(t)-f(t-1) is the measured resonant frequency difference between two consecutive sampling times t, t-1, and ΔT=T(t)-T(t-1) is the circuit temperature difference between two consecutive times t, t-1.

[0062] In this embodiment, the specific expression of the zero-bias output compensation model is:

[0063]

[0064] Where Ω 地速 is the earth's rotation speed at the latitude of the HRG, and k is the scale factor in the HRG force balance mode.

[0065] In step 2 of this embodiment, the specific operation of changing the ambient temperature of the hemispherical resonant gyroscope is:

[0066] The ambient temperature of the hemispherical resonant gyroscope was continuously decreased from room temperature to -30°C, then continuously increased from -30°C to 50°C, and then continuously decreased from 50°C to -30°C.

[0067] The zero-drift compensation method of a force-balanced hemispherical resonator gyroscope of the present invention uses the resonant frequency of the resonator to characterize the current physical state of the resonator, adds a temperature measurement sensor chip to the circuit to measure the real-time temperature of the circuit, puts the hemispherical resonator gyroscope into a temperature box for continuous temperature change to collect the resonant frequency, circuit temperature and corresponding output zero-drift, establishes a multi-factor fitting model and performs regression compensation parameter calculation, and imports the model into a program to realize zero-drift output compensation.

[0068] At different temperatures, the damping coefficient and frequency splitting coefficient of the resonator will change, and the circuit amplification factor will also change accordingly, which will cause the zero bias of the resonator to drift. The present invention uses the resonant frequency of the resonator to reflect the difference in the physical state of the resonator, and uses the circuit sampling temperature to reflect the difference in the amplification factor of the circuit, and uses these two characteristics to simultaneously estimate and compensate for the zero drift.

[0069] The present invention collects compensation sample data in an uninterrupted variable temperature collection mode, and performs model regression fitting through continuous changes in temperature and resonant frequency, thereby improving the accuracy of model fitting based on a large number of data samples. At the same time, the model has a certain degree of generalization, and can perform zero drift compensation prediction calculations on temperature and frequency combinations that are not included in the training data set, so that the model can be applied to various variable temperature and variable frequency scenarios.

[0070] Specifically, the resonant gyroscope head and circuit are placed in an incubator, the gyroscope sensitive axis is vertically upward (sensitive to the local ground speed, i.e., the local angular velocity of the earth's rotation), and the temperature of the incubator is controlled to vary between -30°C and 50°C. Pushing the azimuth angle controlled by the force balance to the damped simple vibration axis can minimize the impact of damping unevenness on zero drift. Due to the uncertainty of the thermal field and the non-uniformity of temperature transfer, the zero bias output of the gyroscope has a relatively large correlation with the rate of temperature change. Considering the influence of multiple factors such as the resonant frequency change, the resonant frequency change rate, the circuit temperature change, and the circuit temperature change rate, the zero bias output measurement value is established. Regression model of relative resonant frequency f and circuit temperature T

[0071]

[0072] Among them, A=[a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ,a 7 ,a 8 ] is the regression fitting parameter. Discretize the above model to get

[0073]

[0074] Wherein Δf=f(t)-f(t-1) is the frequency deviation between two consecutive sampling points, and ΔT=T(t)-T(t-1) is the circuit temperature difference between two consecutive sampling points.

[0075] After sampling to obtain N sample points, substitute them into the above regression model and perform least square fitting calculation to obtain the regression parameter A.

[0076] Substitute the regression parameter A into the following compensation model to perform zero bias output compensation

[0077]

[0078] Where Ω 地速 is the local ground speed at which the gyroscope is located when sampling high and low temperature changes, and k is the scale factor of the gyroscope force balance mode.

[0079] The following is a specific process of a hemispherical resonant gyroscope using the present invention to achieve zero drift compensation:

[0080] S01. Put the gyroscope into the incubator, put the gyroscope upright so that the sensitive axis of the resonator is vertical to the ground and upward (sensitive to the local ground speed, that is, the local angular velocity of the earth's rotation), turn on the force balance mode and control the vibration angle to the damped simple vibration axis.

[0081] S02. Continuously and slowly change the temperature of the incubator. Set the temperature to -30℃, keep it warm for 2 hours, then raise the temperature to 50℃ for 2 hours, keep it warm for 2 hours, and then lower the temperature to -30℃ for 2 hours. The incubator performs temperature changes in this way, and the temperature of the gyroscope circuit will show a process of continuously decreasing from room temperature to -30℃, then continuously increasing from -30℃ to 50℃, and then continuously decreasing from 50℃ to -30℃.

[0082] S03, real-time continuous acquisition of the resonator resonant frequency, sampling circuit temperature and force balance zero drift output value Until the temperature test is completed.

[0083] S04. Substitute the above collected data set into the zero-bias fitting model, perform least squares regression to calculate the compensation parameters, and obtain the estimated parameter A.

[0084] S05. Substitute the estimated parameters into the zero-bias output compensation model to perform zero-drift compensation on the force balance output force.

[0085] Figure 3 This is a comparison chart of the 100-second average zero bias of the static placement compensation test after sampling compensation regression of the above-mentioned hemispherical gyroscope. The sensitive angular velocity is the local ground speed. It can be seen from the figure that as time changes, the uncompensated hemispherical resonant gyroscope produces a larger zero drift, and the compensated gyroscope can basically suppress the influence of zero drift.

[0086] Embodiment 2:

[0087] This embodiment provides a force-balanced hemispherical resonant gyroscope zero drift compensation device, including: an operation module, a temperature control module, a collection module and a solution module.

[0088] The operating module is used to set the hemispherical resonant gyroscope in a force balance mode and push the vibration mode azimuth to the damped simple vibration axis, and make the sensitive axis of the hemispherical resonant gyroscope vertical to the ground and upward.

[0089] The temperature control module is used to change the ambient temperature of the hemispherical resonant gyroscope and transmit it to the acquisition module in real time.

[0090] The acquisition module is used to collect the circuit temperature T of the hemispherical resonant gyroscope in real time, as well as the measured resonant frequency f and zero bias output measurement value of the hemispherical resonant gyroscope corresponding to each circuit temperature T. And transmitted to the solution module and zero bias output module,

[0091] The solution module is used to output the zero bias measurement value corresponding to each measured resonant frequency f according to the circuit temperature T of each hemispherical resonant gyroscope and the measured resonant frequency f corresponding to the ambient temperature T of each hemispherical resonant gyroscope. Constructing zero bias output measurements Relative resonant frequency f and circuit temperature T regression model, solve the regression model, get the fitting parameter A, and transmit it to the zero bias output module;

[0092] The zero bias output module is used to substitute the fitting parameters into the zero bias output compensation model, and calculate the compensated zero bias output value according to the zero bias output compensation model.

[0093] In this embodiment, the zero bias output measurement value constructed by the solution module is The specific expression of the regression model of the relative resonant frequency f and the circuit temperature T is:

[0094]

[0095] Among them, the fitting parameter A=[a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ,a 7 ,a 8 ].

[0096] In this embodiment, the solution module discretizes the regression model, and obtains the specific expression of the discretized regression model as follows:

[0097]

[0098] Among them, Δf=f(t)-f(t-1) is the measured resonant frequency difference between two consecutive sampling times t, t-1, and ΔT=T(t)-T(t-1) is the circuit temperature difference between two consecutive times t, t-1.

[0099] In this embodiment, the specific expression of the zero-bias output compensation model adopted by the zero-bias output module is:

[0100]

[0101] Where Ω 地速 is the earth's rotation speed at the latitude of the HRG, and k is the scale factor in the HRG force balance mode.

[0102] Embodiment 3:

[0103] This embodiment provides an electronic device, the device comprising:

[0104] Memory for storing computer programs;

[0105] The processor is used to implement the steps of the zero drift compensation method of the force-balanced hemispherical resonant gyroscope of embodiment 1 when executing the above-mentioned computer program.

[0106] Embodiment 4:

[0107] This embodiment 4 provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the zero-drift compensation method of the force-balanced hemispherical resonant gyroscope of embodiment 1 are implemented.

[0108] The embodiments described above are only preferred specific implementations of the present invention. This specification uses the phrases "in one embodiment", "in another embodiment", "in yet another embodiment" or "in other embodiments" to refer to one or more of the same or different embodiments according to the present disclosure. Common changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for compensating zero drift of a force-balanced hemispherical resonant gyroscope, characterized in that: The following steps are involved: Step 1: Set the HRG in the force balance mode and push the vibration mode azimuth to the damped simple vibration axis, and make the sensitive axis of the HRG vertical to the ground and upward. Step 2: Change the ambient temperature of the hemispherical resonant gyroscope, and collect the circuit temperature T of the hemispherical resonant gyroscope in real time, as well as the measured resonant frequency f and zero bias output measurement value of the hemispherical resonant gyroscope corresponding to each circuit temperature T. Step 3: Based on the circuit temperature T of each hemispherical resonant gyroscope, the measured resonant frequency f corresponding to the circuit temperature T of each hemispherical resonant gyroscope, and the zero bias output measurement value corresponding to each measured resonant frequency f Constructing zero bias output measurements The regression model of the relative resonant frequency f and the circuit temperature T is solved to obtain the fitting parameter A, Step 4: Substitute the fitting parameter A into the zero bias output compensation model, and calculate the compensated zero bias output value according to the zero bias output compensation model.

2. The zero drift compensation method of the force-balanced hemispherical resonant gyro according to claim 1, characterized in that: The specific expression of the regression model is: Among them, the fitting parameters A = [a1, a2, a3, a4, a5, a6, a7, a8].

3. The zero drift compensation method of the force-balanced hemispherical resonator gyroscope according to claim 2, characterized in that: The regression model is discretized to obtain the specific expression of the discretized regression model: Among them, Δf=f(t)-f(t-1) is the measured resonant frequency difference between two consecutive sampling times t, t-1, and ΔT=T(t)-T(t-1) is the circuit temperature difference between two consecutive times t, t-1.

4. The zero drift compensation method of the force-balanced hemispherical resonator gyroscope according to claim 3, characterized in that: The specific expression of the zero-bias output compensation model is: Where Ω 地速 is the earth's rotation speed at the latitude of the HRG, and k is the scale factor in the HRG force balance mode.

5. The zero drift compensation method of a force-balanced hemispherical resonant gyro according to any one of claims 1 to 4, characterized in that: In step 2, the specific operation of changing the ambient temperature of the hemispherical resonant gyroscope is: The ambient temperature of the hemispherical resonant gyroscope was continuously decreased from room temperature to -30°C, then continuously increased from -30°C to 50°C, and then continuously decreased from 50°C to -30°C.

6. A force-balanced hemispherical resonant gyro zero drift compensation device, comprising: Operation module, temperature control module, acquisition module and solution module, The operating module is used to set the hemispherical resonant gyroscope in a force balance mode and push the vibration mode azimuth to the damped simple vibration axis, and make the sensitive axis of the hemispherical resonant gyroscope vertical to the ground and upward. The temperature control module is used to change the ambient temperature of the hemispherical resonant gyroscope and transmit it to the acquisition module in real time. The acquisition module is used to collect the circuit temperature T of the hemispherical resonant gyroscope in real time, as well as the measured resonant frequency f and zero bias output measurement value of the hemispherical resonant gyroscope corresponding to each circuit temperature T. And transmitted to the solution module and zero bias output module, The solution module is used to output the measured value of the zero bias corresponding to each measured resonant frequency f according to the circuit temperature T of each hemispherical resonant gyroscope and the measured resonant frequency f corresponding to the circuit temperature T of each hemispherical resonant gyroscope. Constructing zero bias output measurements A regression model of the relative resonant frequency f and the circuit temperature T is solved to obtain a fitting parameter A, and the fitting parameter A is transmitted to a zero bias output module; The zero bias output module is used to substitute the fitting parameters into the zero bias output compensation model, and calculate the compensated zero bias output value according to the zero bias output compensation model.

7. The zero drift compensation device for a force-balanced hemispherical resonant gyro according to claim 6, characterized in that: Zero bias output measurement constructed by solver module The specific expression of the regression model of the relative resonant frequency f and the circuit temperature T is: Among them, fitting parameters A=[a1,a2,a3,a4,a5,a6,a7,a8]; The solution module discretizes the regression model, and obtains the specific expression of the discretized regression model as follows: Among them, Δf=f(t)-f(t-1) is the measured resonant frequency difference between two consecutive sampling times t and t-1, and ΔT=T(t)-T(t-1) is the temperature difference between two consecutive times t and t-1.

8. The zero drift compensation device for a force-balanced hemispherical resonant gyro according to claim 6, characterized in that: The specific expression of the zero-bias output compensation model used by the zero-bias output module is: Where Ω 地速 is the earth's rotation speed at the latitude of the HRG, and k is the scale factor in the HRG force balance mode.

9. An electronic device, characterized in that: The device comprises: Memory for storing computer programs; A processor, configured to implement the steps of the zero drift compensation method of a force-balanced hemispherical resonant gyroscope as claimed in any one of claims 1 to 5 when executing the computer program.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the zero-drift compensation method of a force-balanced hemispherical resonant gyroscope as claimed in any one of claims 1 to 5 are implemented.

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