Static angular velocity filtering method and system based on virtual rotating force

Abstract

The invention provides a static angular velocity filtering method and system based on virtual rotating force, and the method comprises the steps: building a hemispherical resonator gyroscope angular velocity model, and carrying out the discretization of the hemispherical resonator gyroscope angular velocity model, and obtaining a discretized hemispherical resonator gyroscope angular velocity model; establishing a Kalman filtering equation based on the discretized angular velocity model of the hemispherical resonator gyroscope; virtual rotating force is applied to the hemispherical resonator gyroscope, the collected virtual rotating force and standing wave rotating angular velocity at each moment are substituted into the established Kalman filtering equation for filtering, and an angular velocity observation value is obtained; and performing moving average on the angular velocity observation value in a complete period to obtain a final angular velocity output value. By applying the technical scheme provided by the invention, the technical problem that the output angular velocity error of the full-angle-mode hemispherical resonator gyroscope is difficult to calibrate accurately in the prior art is solved.

Description

Technical Field

[0001] This invention relates to the field of hemispherical resonant gyroscope technology, and in particular to a static angular velocity filtering method and system based on virtual rotational force. Background Technology

[0002] A hemispherical resonator gyroscope is a novel type of gyroscope that uses the circumferential precession of a standing wave from a hemispherical harmonic oscillator to sense the angular motion of a carrier. In full-angle mode, the hemispherical resonator gyroscope can effectively measure angular velocities over a wide range. During operation, the hemispherical resonator gyroscope generates standing wave precession. Errors such as damping inhomogeneity and frequency fragmentation cause circumferential drift of the standing wave, resulting in drift errors related to the azimuth angle of the harmonic oscillator. These errors accumulate over long-term missions, affecting the accuracy of navigation calculations.

[0003] Due to the operating characteristics of hemispherical resonant gyroscopes, their drift error exhibits periodic variation. To suppress the impact of this periodic drift on output accuracy, the angular velocity can be integrated over the entire period, thereby averaging the drift error. Based on the fundamental principle of hemispherical resonant gyroscopes, a virtual rotational force with certain characteristics can be applied, causing the standing wave mode shape to precess continuously during operation. This transforms the drift error into a periodic variation. Since the errors cancel each other out, the integral result exhibits a mean of 0 within the period, significantly reducing the time accumulation of errors and improving the stability and measurement accuracy of the gyroscope. During the rotation of the driving standing wave, an additional angular velocity component is introduced into the angular velocity output of the hemispherical resonant gyroscope. This component is also sensed by the resonator; therefore, a certain filtering method is needed to improve accuracy when calculating the actual external input angular velocity. Summary of the Invention

[0004] This invention provides a static angular velocity filtering method and system based on virtual rotational force, which can solve the technical problem that it is difficult to accurately calibrate the output angular velocity error of a full-angle mode hemispherical resonator gyroscope in the prior art.

[0005] According to one aspect of the present invention, a static angular velocity filtering method based on virtual rotational force is provided, the method comprising:

[0006] A hemispherical resonant gyroscope angular velocity model is established, and the hemispherical resonant gyroscope angular velocity model is discretized to obtain the discretized hemispherical resonant gyroscope angular velocity model.

[0007] Kalman filter equations are established based on the discrete hemispherical resonant gyroscope angular velocity model.

[0008] A virtual rotational force is applied to the hemispherical resonant gyroscope. The virtual rotational force and the standing wave rotational angular velocity collected at each moment are substituted into the established Kalman filter equation for filtering to obtain the angular velocity observation value.

[0009] The final angular velocity output value is obtained by performing a moving average of the angular velocity observations over a complete cycle.

[0010] Furthermore, the established hemispherical resonant gyroscope angular velocity model is as follows:

[0011]

[0012] In the above formula, Ω represents the angular velocity of the gyroscope standing wave, k is the Blain coefficient, and Ω is the external input angular velocity. For the harmonic oscillator with non-uniform damping, θ τ θ is the angle between the damping angle of the resonator and the x-axis of the electrode, θ is the azimuth angle of the standing wave, k0 is the voltage scaling factor corresponding to the virtual rotating voltage, and Vs is the actively applied virtual rotating force.

[0013] Furthermore, the discretized hemispherical resonant gyroscope angular velocity model is as follows:

[0014]

[0015] In the above formula, The numbers are t0, t1, ..., t in sequence. n The standing wave rotation angular velocities obtained by differential acquisition at time points, Ω(t0), Ω(t1), ..., Ω(t n The values ​​are t0, t1, ..., t in sequence. n The angular velocities input from the external environment at each time point, θ(t0), θ(t1), ..., θ(t2) n The values ​​are t0, t1, ..., t obtained from the calculation. n The standing wave azimuth angle at time t0, Vs(t0), Vs(t1), ..., Vs(t2) n The values ​​are t0, t1, ..., t in sequence. n Virtual rotational forces actively applied at each moment, k0(t0), k0(t1), ..., k0(t n The values ​​are t0, t1, ..., t in sequence. n The voltage scale factor corresponding to the virtual rotational force at any given moment.

[0016] Furthermore, the established Kalman filter equation is as follows:

[0017] X k / k-1 =AX k-1 +u,

[0018] Z k =H k X k +w,

[0019]

[0020] In the above formula, X k / k+1 Let X be the predicted state variable from time k to time k+1, A be the state transition matrix, and X be the predicted state variable. k-1 Let Z be the state vector at time k-1, u be the system noise, and Z be the... k Let H be the observation vector at time k. k Let X be the observation parameter matrix at time k. k Let I be the state vector at time k, w be white noise, and I be the state vector at time k. 2*2 It is a 2x2 identity matrix. For t k The standing wave rotation angular velocity Vs(t) obtained by differential acquisition at time t k ) for t k The virtual rotational force actively applied at all times, k0(t) k ) for t k The voltage scaling factor corresponding to the virtual rotational force at any given time, Ω(t) k ) for t k The angular velocity input from the external environment at any given time, θ(t) k ) represents the calculated t k The azimuth of the standing wave at any given moment.

[0021] Furthermore, applying a virtual rotational force to the hemispherical resonant gyroscope includes:

[0022] Determine the amplitude of the standard voltage applied by the virtual rotational force;

[0023] A positive standard voltage is applied during the first half of each cycle, and a negative standard voltage is applied during the second half of each cycle.

[0024] According to another aspect of the present invention, a static angular velocity filtering system based on virtual rotational force is provided, the system comprising a model building unit, a Kalman filtering unit, and a moving average unit;

[0025] The model building unit is used to build a hemispherical resonant gyroscope angular velocity model and discretize the hemispherical resonant gyroscope angular velocity model to obtain the discretized hemispherical resonant gyroscope angular velocity model.

[0026] The Kalman filter unit is used to establish the Kalman filter equation based on the discrete hemispherical resonant gyroscope angular velocity model; a virtual rotational force is applied to the hemispherical resonant gyroscope, and the virtual rotational force and standing wave rotational angular velocity collected at each moment are substituted into the established Kalman filter equation for filtering to obtain the angular velocity observation value;

[0027] The moving average unit is used to perform a moving average of the angular velocity observations over a complete cycle to obtain the final angular velocity output value.

[0028] The present invention provides a static angular velocity filtering method and system based on virtual rotational force. This method utilizes the basic principle of hemispherical resonant gyroscopes, modulates the angular velocity output of the hemispherical resonant gyroscope by applying a certain virtual rotational force, eliminates angular velocity errors related to azimuth angle by using filtering methods, and extracts external angular velocity input under static conditions. This can effectively improve the accuracy of static angular velocity measurement by hemispherical resonant gyroscopes, thereby improving the angular velocity output accuracy of hemispherical resonant gyroscopes in certain scenarios. Attached Figure Description

[0029] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0030] Figure 1 A flowchart illustrating a static angular velocity filtering method based on virtual rotational force according to a specific embodiment of the present invention is shown.

[0031] Figure 2 A virtual rotational force waveform diagram provided according to a specific embodiment of the present invention is shown. Detailed Implementation

[0032] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0034] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0035] like Figure 1 As shown, a static angular velocity filtering method based on virtual rotational force is provided according to a specific embodiment of the present invention. The method includes:

[0036] A hemispherical resonant gyroscope angular velocity model is established, and the hemispherical resonant gyroscope angular velocity model is discretized to obtain the discretized hemispherical resonant gyroscope angular velocity model.

[0037] Kalman filter equations are established based on the discrete hemispherical resonant gyroscope angular velocity model.

[0038] A virtual rotational force is applied to the hemispherical resonant gyroscope. The virtual rotational force and the standing wave rotational angular velocity collected at each moment are substituted into the established Kalman filter equation for filtering to obtain the angular velocity observation value.

[0039] The final angular velocity output value is obtained by performing a moving average of the angular velocity observations over a complete cycle.

[0040] This configuration provides a static angular velocity filtering method based on virtual rotational force. This method utilizes the basic principle of a hemispherical resonant gyroscope (BRG), applying a certain virtual rotational force to modulate the BRG's angular velocity output. A filtering method is then used to eliminate angular velocity errors related to azimuth angles, extracting the external angular velocity input under static conditions. This effectively improves the accuracy of static angular velocity measurement by the BRG, thereby enhancing the angular velocity output accuracy of the BRG in certain scenarios. Compared with existing technologies, the technical solution of this invention solves the technical problem of difficulty in accurately calibrating the output angular velocity error of full-angle mode hemispherical resonant gyroscopes in existing technologies.

[0041] Furthermore, in this embodiment of the invention, based on the fundamental principle of a hemispherical resonant gyroscope, the angular velocity model of the hemispherical resonant gyroscope is established by solving the corresponding variable equations as follows:

[0042]

[0043] In the above formula, Ω represents the angular velocity of the gyroscope standing wave, k is the Blain coefficient, and Ω is the external input angular velocity. For the harmonic oscillator with non-uniform damping, θ τ θ is the angle between the damping angle of the resonator and the x-axis of the electrode, θ is the azimuth angle of the standing wave, k0 is the voltage scaling factor corresponding to the virtual rotating voltage, and Vs is the actively applied virtual rotating force.

[0044] This invention performs filtering and solution based on the above angular velocity model, and discretizes the above angular velocity model to obtain the discretized hemispherical resonant gyroscope angular velocity model as follows:

[0045]

[0046] In the above formula, The numbers are t0, t1, ..., t in sequence. n The standing wave rotation angular velocities obtained by differential acquisition at time points, Ω(t0), Ω(t1), ..., Ω(t n The values ​​are t0, t1, ..., t in sequence. n The angular velocities input from the external environment at each time point, θ(t0), θ(t1), ..., θ(t2) n The values ​​are t0, t1, ..., t obtained from the calculation. n The standing wave azimuth angle at time t0, Vs(t0), Vs(t1), ..., Vs(t2) n The values ​​are t0, t1, ..., t in sequence. n Virtual rotational forces actively applied at each moment, k0(t0), k0(t1), ..., k0(t n The values ​​are t0, t1, ..., t in sequence. n The voltage scaling factor corresponding to the virtual rotational force at each instant. In other words, discretization yields the set of differential equations satisfied by the hemispherical resonant gyroscope system at every instant.

[0047] Furthermore, this invention uses Kalman filtering to estimate the corresponding angular velocity parameters. Kalman filtering is a linear minimum variance estimator that can estimate parameters in real time. Currently, Kalman filtering is widely used as an estimation theory in various fields. In this embodiment of the invention, the Kalman filter equation established based on the above-discrete differential equation system is as follows:

[0048] X k / k-1 =AX k-1 +u,

[0049] Z k =H k X k +w,

[0050] Input the collected data according to the following rules:

[0051]

[0052] In the above formula, X k / k+1 Let X be the predicted state variable from time k to time k+1, A be the state transition matrix, and X be the predicted state variable. k-1 Let Z be the state vector at time k-1, u be the system noise, and Z be the... k Let H be the observation vector at time k. k Let X be the observation parameter matrix at time k. k Let I be the state vector at time k, w be white noise, and I be the state vector at time k. 2*2 It is a 2x2 identity matrix. For t k The standing wave rotation angular velocity Vs(t) obtained by differential acquisition at time t k ) for t k The virtual rotational force actively applied at all times, k0(t) k ) for t k The voltage scaling factor corresponding to the virtual rotational force at any given time, Ω(t) k ) for t k The angular velocity input from the external environment at any given time, θ(t) k ) represents the calculated t k The azimuth of the standing wave at any given moment.

[0053] The method for calculating the state variable X is as follows:

[0054] State prediction in one step:

[0055] Covariance matrix one-step prediction: P k / k-1 =A*P k-1 *A T +Q k ;

[0056] Filter gain calculation:

[0057] State estimation:

[0058] Estimate the covariance matrix:

[0059] in, This represents the state quantity at time k predicted based on the state quantity at time k-1 and the state transition model; it is also called the one-step predicted state quantity. P represents the state quantity at time k-1. k / k-1The covariance matrix at time k-1, predicted by the state transition model, is also called the one-step predicted covariance matrix, P. k-1 Let Q represent the covariance matrix at time k-1 obtained by filtering. k Let K represent the system noise at time k. k R represents the Kalman filter gain at time k. k This represents the observation noise at time k. P represents the state quantity at time k. k This represents the covariance matrix at time k obtained through filtering. Based on the discretized hemispherical resonant gyroscope angular velocity model and the established Kalman filter equation, this invention applies a virtual rotational force and processes the data. In this embodiment, applying a virtual rotational force to the hemispherical resonant gyroscope includes: determining the amplitude of the standard voltage applied for the virtual rotational force; applying a positive standard voltage in the first half of each cycle and applying a negative standard voltage in the second half of each cycle.

[0060] To gain a further understanding of the present invention, the filtering method of the present invention will be described in detail below with reference to embodiments.

[0061] In this embodiment of the invention, experimental verification was conducted based on a self-developed hemispherical resonant gyroscope prototype. When a virtual control voltage of 2V was applied, the standing wave could achieve a continuous rotation of nearly 90° azimuth angle within 50 seconds, indicating that this voltage amplitude can provide sufficient driving capability to achieve a significant azimuth angle modulation effect while ensuring system stability. Therefore, 2V was selected as the standard voltage amplitude for applying the virtual rotational force.

[0062] Furthermore, to achieve periodic excitation and optimize parameter identification performance, the virtual rotating voltage is designed as a symmetrical square wave signal with a period of 100 seconds: a +2V positive voltage is applied for the first 50 seconds of each period, driving the standing wave to rotate clockwise; for the next 50 seconds, a -2V reverse voltage is applied, causing the standing wave to rotate in the opposite direction, thus forming a symmetrical and repeatable excitation mode. This design helps eliminate the effects of system error drift and zero bias, effectively separates sensitive parameters related to structural asymmetry, and significantly improves the accuracy and convergence speed of parameter identification.

[0063] The virtual rotational force Vs(t) collected at each moment n ), standing wave rotation angular velocity Substituting the Kalman filter equation above, we can calculate the angular velocity observations including the error. This observation not only reflects the true external angular velocity input, but also superimposes error components related to the standing wave azimuth angle caused by errors such as uneven damping, frequency fragmentation, and circuit gain asymmetry, especially the equivalent angular velocity drift caused by damping asymmetry.

[0064] To effectively suppress the impact of such periodic errors, this invention performs whole-cycle smoothing on the calculated angular velocity sequence. Specifically, utilizing the periodic characteristics excited by the virtual rotational force, the angular velocity data within a complete cycle (100 seconds) is averaged, causing the error terms strongly correlated with the azimuth angle to exhibit symmetrical or opposite characteristics in the positive and negative half-cycles, thus canceling each other out during the averaging process. This method significantly reduces the impact of azimuth angle-related errors on the angular velocity output without requiring precise modeling of all error sources, thereby improving the stability and accuracy of the measurement.

[0065] According to another aspect of the present invention, a static angular velocity filtering system based on virtual rotational force is provided, the system comprising a model building unit, a Kalman filtering unit, and a moving average unit;

[0066] The model building unit is used to build a hemispherical resonant gyroscope angular velocity model and discretize the hemispherical resonant gyroscope angular velocity model to obtain the discretized hemispherical resonant gyroscope angular velocity model.

[0067] The Kalman filter unit is used to establish the Kalman filter equation based on the discrete hemispherical resonant gyroscope angular velocity model; a virtual rotational force is applied to the hemispherical resonant gyroscope, and the virtual rotational force and standing wave rotational angular velocity collected at each moment are substituted into the established Kalman filter equation for filtering to obtain the angular velocity observation value;

[0068] The moving average unit is used to perform a moving average of the angular velocity observations over a complete cycle to obtain the final angular velocity output value.

[0069] In summary, this invention provides a static angular velocity filtering method and system based on virtual rotational force. This method utilizes the fundamental principle of a hemispherical resonant gyroscope (BRG), modulates the angular velocity output of the BRG by applying a certain virtual rotational force, and uses a filtering method to eliminate angular velocity errors related to the azimuth angle, extracting the external angular velocity input under static conditions. This effectively improves the accuracy of static angular velocity measurement by the BRG, thereby improving the angular velocity output accuracy of the BRG in certain scenarios. Compared with existing technologies, the technical solution of this invention can solve the technical problem of difficulty in accurately calibrating the output angular velocity error of a full-angle mode hemispherical resonant gyroscope in existing technologies.

[0070] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0071] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0072] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A static angular velocity filtering method based on virtual rotational force, characterized in that, The method includes: A hemispherical resonant gyroscope angular velocity model is established, and the hemispherical resonant gyroscope angular velocity model is discretized to obtain the discretized hemispherical resonant gyroscope angular velocity model. Kalman filter equations are established based on the discrete hemispherical resonant gyroscope angular velocity model. A virtual rotational force is applied to the hemispherical resonant gyroscope. The virtual rotational force and the standing wave rotational angular velocity collected at each moment are substituted into the established Kalman filter equation for filtering to obtain the angular velocity observation value. The final angular velocity output value is obtained by performing a moving average of the angular velocity observations over a complete cycle.

2. The method according to claim 1, characterized in that, The established hemispherical resonant gyroscope angular velocity model is as follows: In the above formula, Ω represents the angular velocity of the gyroscope standing wave, k is the Blain coefficient, and Ω is the external input angular velocity. For the harmonic oscillator with non-uniform damping, θ τ θ is the angle between the damping angle of the resonator and the x-axis of the electrode, θ is the azimuth angle of the standing wave, k0 is the voltage scaling factor corresponding to the virtual rotating voltage, and Vs is the actively applied virtual rotating force.

3. The method according to claim 1 or 2, characterized in that, The discretized hemispherical resonant gyroscope angular velocity model is as follows: In the above formula, The numbers are t0, t1, ..., t in sequence. n The standing wave rotation angular velocities obtained by differential acquisition at time points, Ω(t0), Ω(t1), ..., Ω(t n The values ​​are t0, t1, ..., t in sequence. n The angular velocities input from the external environment at each time point, θ(t0), θ(t1), ..., θ(t2) n The values ​​are t0, t1, ..., t obtained from the calculation. n The standing wave azimuth angle at time t0, Vs(t0), Vs(t1), ..., Vs(t2) n The values ​​are t0, t1, ..., t in sequence. n Virtual rotational forces actively applied at each moment, k0(t0), k0(t1), ..., k0(t n The values ​​are t0, t1, ..., t in sequence. n The voltage scale factor corresponding to the virtual rotational force at any given moment.

4. The method according to claim 3, characterized in that, The established Kalman filter equation is as follows: X k / k-1 =AX k-1 +u, Z k =H k X k +w, A=I 2*2 、 H k =[Vs(t k )1], In the above formula, X k / k+1 Let X be the predicted state variable from time k to time k+1, A be the state transition matrix, and X be the predicted state variable. k-1 Let Z be the state vector at time k-1, u be the system noise, and Z be the... k Let H be the observation vector at time k. k Let X be the observation parameter matrix at time k. k Let I be the state vector at time k, w be white noise, and I be the state vector at time k. 2*2 It is a 2x2 identity matrix. For t k The standing wave rotation angular velocity Vs(t) obtained by differential acquisition at time t k ) for t k The virtual rotational force actively applied at all times, k0(t) k ) for t k The voltage scaling factor corresponding to the virtual rotational force at any given time, Ω(t) k ) for t k The angular velocity input from the external environment at any given time, θ(t) k ) represents the calculated t k The azimuth of the standing wave at any given moment.

5. The method according to any one of claims 1 to 4, characterized in that, Applying a virtual rotational force to a hemispherical resonant gyroscope includes: Determine the amplitude of the standard voltage applied by the virtual rotational force; A positive standard voltage is applied during the first half of each cycle, and a negative standard voltage is applied during the second half of each cycle.

6. A static angular velocity filtering system based on virtual rotational force, characterized in that, The system includes a model building unit, a Kalman filtering unit, and a moving average unit; The model building unit is used to build a hemispherical resonant gyroscope angular velocity model and discretize the hemispherical resonant gyroscope angular velocity model to obtain a discretized hemispherical resonant gyroscope angular velocity model. The Kalman filter unit is used to establish the Kalman filter equation based on the discrete hemispherical resonant gyroscope angular velocity model; a virtual rotational force is applied to the hemispherical resonant gyroscope, and the virtual rotational force and standing wave rotational angular velocity collected at each moment are substituted into the established Kalman filter equation for filtering to obtain the angular velocity observation value; The moving average unit is used to perform a moving average of the angular velocity observations over a complete cycle to obtain the final angular velocity output value.

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