Hemispherical resonator gyroscope inertial navigation system position switching alignment method

Abstract

The invention provides a hemispherical resonator gyroscope inertial navigation system position switching alignment method, which comprises the following steps: establishing an angular rate error equation, and determining a change rule between angular velocity fluctuation caused by a frequency difference between damping non-uniformity and a frequency main axis and a standing wave azimuth angle; installing the hemispherical resonator gyroscope inertial navigation system on a rotary table, and driving the rotary table to rotate at a fixed rate to obtain an angular rate error characteristic curve; determining a standing wave azimuth angle switching scheme in a coarse alignment stage; in the coarse alignment stage, the gyroscope is set to be in a standing wave azimuth angle switching state, the angular rate of the gyroscope and the specific force vector of the accelerometer in a position stable state before and after switching are collected, and an angular rate average value and a specific force vector average value are obtained respectively; and calculating an initial attitude matrix based on the angular rate average value and the specific force vector average value. By applying the technical scheme of the invention, the technical problem that drift caused by non-uniform frequency and non-uniform damping distribution cannot be effectively compensated in the prior art is solved.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, and more particularly to a position switching alignment method for a hemispherical resonant gyroscope inertial navigation system. Background Technology

[0002] A hemispherical resonant gyroscope consists of two parts: a hemispherical fused silica resonator and a planar electrode. It measures the angular rate of base rotation by measuring the circumferential precession of the four antinodes on the lip of the hemispherical resonator. Structurally, a hemispherical resonant gyroscope eliminates the need for a high-speed rotor and moving supports, and features a wide signal bandwidth, high reliability, and low cost.

[0003] The drift of a hemispherical resonant gyroscope is mainly caused by circumferential frequency non-uniformity and harmonic oscillator damping non-uniformity. Its drift is related to the circumferential position of the standing wave of the four antinodes, affecting the system alignment and navigation accuracy. There is currently no effective solution. Summary of the Invention

[0004] This invention provides a position switching alignment method for a hemispherical resonant gyroscope inertial navigation system, which can solve the technical problem in the prior art that it is impossible to effectively compensate for drift caused by non-uniform frequency and non-uniform damping distribution.

[0005] According to one aspect of the present invention, a position switching alignment method for a hemispherical resonant gyroscope inertial navigation system is provided. The hemispherical resonant gyroscope inertial navigation system includes a hemispherical resonant gyroscope and an accelerometer. The method includes:

[0006] Establish the angular rate error equation, and determine the variation law between the angular velocity fluctuation and the standing wave azimuth angle caused by damping inhomogeneity and frequency difference between the principal frequency axis based on the angular rate error equation.

[0007] A hemispherical resonant gyroscope inertial navigation system is installed on a turntable, and the turntable is driven to rotate at a fixed rate to obtain the angular rate error characteristic curve.

[0008] The standing wave azimuth switching scheme for the coarse alignment stage is determined based on the variation law and the angular rate error characteristic curve.

[0009] During the coarse alignment stage, the gyroscope is set to stand wave azimuth angle switching state according to the determined standing wave azimuth angle switching scheme, and the angular rate of the gyroscope and the specific force vector of the accelerometer are collected under the stable position state before and after the switching.

[0010] The collected angular velocities and force vectors are accumulated and then averaged over time to obtain the average angular velocity and the average force vector.

[0011] The initial attitude matrix is ​​calculated based on the average angular rate and the average force vector.

[0012] Furthermore, the angular rate error equation is:

[0013]

[0014] In the above formula, θ represents the angle. Let θ represent the angular velocity, and Δω represent the frequency difference between the two principal axes ω1 and ω2. Assuming ω1 > ω2, then θ ω This represents the azimuth angle of the frequency axis where ω2 is located. Let τ1 and τ2 represent the damping non-uniformity, and let τ1 and τ2 represent the decay time constants of the two principal damping axes. Assuming τ1 < τ2, then θ τ denoted by τ1, a represents the azimuth angle of the damping axis, q represents the orthogonality, k represents the gyroscope precession factor, and Ω represents the external input angular velocity.

[0015] Furthermore, according to the angular rate error equation, the variation law between the angular velocity fluctuation caused by the frequency difference between the damping inhomogeneity and the frequency principal axis and the standing wave azimuth angle is as follows: the angular velocity fluctuation caused by the frequency difference between the damping inhomogeneity and the frequency principal axis exhibits a periodic 90° sine and cosine periodic variation with the standing wave azimuth angle.

[0016] Furthermore, based on the variation law and the angular rate error characteristic curve, the standing wave azimuth angle switching scheme for the coarse alignment stage is determined as follows: two standing wave azimuth angles that are symmetrically spaced 45° apart are selected as the two switching positions.

[0017] Furthermore, the initial attitude matrix is ​​calculated based on the average angular rate and the average force vector using the following formula:

[0018]

[0019] In the above formula, Let g represent the initial attitude matrix, g represent the gravitational acceleration, and ω represent the initial attitude matrix. ie The value represents the Earth's rotational angular velocity, L represents latitude, and f represents the Earth's rotational angular velocity. x ,f y ,f z The values ​​ω represent the average values ​​of the x-axis, y-axis, and z-axis accelerometer output force vectors acquired during the coarse alignment process, respectively. x ,ω y ,ω z The values ​​represent the average values ​​of the x-axis gyroscope output angular rate, y-axis gyroscope output angular rate, and z-axis gyroscope output angular rate collected during the coarse alignment process, respectively.

[0020] Furthermore, the method also includes: during the fine alignment stage, setting the gyroscope to normal state and using velocity matching based on Kalman filtering for fine alignment.

[0021] The present invention provides a method for position switching alignment of a hemispherical resonant gyroscope inertial navigation system. This method analyzes the angular rate error of the hemispherical resonant gyroscope, establishes an angular rate error equation, and obtains the relationship between the angular rate error and the standing wave azimuth angle by combining the angular rate error characteristic curve, thereby determining the standing wave azimuth angle switching scheme. The drift of the gyroscope is modulated by driving the standing wave to rotate to the angular position before and after the switching, thereby improving the alignment accuracy. Attached Figure Description

[0022] 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.

[0023] Figure 1 A block diagram illustrating the basic working principle of a position switching alignment method for a hemispherical resonant gyroscope inertial navigation system according to a specific embodiment of the present invention is shown. Detailed Implementation

[0024] 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.

[0025] 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.

[0026] 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.

[0027] The drift caused by circumferential frequency non-uniformity and harmonic oscillator damping non-uniformity is related to the circumferential position of the standing wave of the four antinode vibration, and is expressed as a sine and cosine form of the standing wave rotation angle. Therefore, this invention considers analyzing the angular rate error characteristics of the hemispherical resonant gyroscope, studying the relationship between the angular rate error and the azimuth angle of the standing wave, and modulating the drift of the gyroscope by driving the standing wave to a symmetrical angular position, effectively reducing the error caused by the standing wave drift, thereby improving the alignment accuracy.

[0028] According to a specific embodiment of the present invention, a position switching alignment method for a hemispherical resonant gyroscope inertial navigation system is provided. The hemispherical resonant gyroscope inertial navigation system includes a hemispherical resonant gyroscope and an accelerometer. The method includes:

[0029] Establish the angular rate error equation, and determine the variation law between the angular velocity fluctuation and the standing wave azimuth angle caused by damping inhomogeneity and frequency difference between the principal frequency axis based on the angular rate error equation.

[0030] A hemispherical resonant gyroscope inertial navigation system is installed on a turntable, and the turntable is driven to rotate at a fixed rate to obtain the angular rate error characteristic curve.

[0031] The standing wave azimuth switching scheme for the coarse alignment stage is determined based on the variation law and the angular rate error characteristic curve.

[0032] During the coarse alignment stage, the gyroscope is set to stand wave azimuth angle switching state according to the determined standing wave azimuth angle switching scheme, and the angular rate of the gyroscope and the specific force vector of the accelerometer are collected under the stable position state before and after the switching.

[0033] The collected angular velocities and force vectors are accumulated and then averaged over time to obtain the average angular velocity and the average force vector.

[0034] The initial attitude matrix is ​​calculated based on the average angular rate and the average force vector.

[0035] This configuration provides a method for position switching alignment of a hemispherical resonant gyroscope inertial navigation system. This method analyzes the angular rate error of the hemispherical resonant gyroscope, establishes an angular rate error equation, and combines this with the angular rate error characteristic curve to obtain the relationship between the angular rate error and the standing wave azimuth angle. This allows for the determination of the standing wave azimuth angle switching scheme. By driving the standing wave to rotate to the angular positions before and after the switching, the gyroscope drift is modulated, thereby improving alignment accuracy. Compared with existing technologies, the technical solution of this invention can solve the technical problem that existing technologies cannot effectively compensate for drift caused by frequency non-uniformity and damping distribution non-uniformity.

[0036] In this embodiment of the invention, an angular rate error equation is established by analyzing the angular rate error of a hemispherical resonant gyroscope. Specifically, the damping sources of the hemispherical gyroscope include thermoelastic damping, surface damping, anchor point damping, and environmental damping, which cause the vibration of the resonator to decay. Due to the inhomogeneity of the fused silica material, the inhomogeneity of the surface damage layer during processing, and the inhomogeneity of the metal film surface adhesion, the damping distribution at various points along the circumference of the hemispherical resonator is uneven, forming two damping principal axes spaced 45° apart with different damping coefficients. Limited by the processing precision of the resonator and the inhomogeneity of the density of the fused silica material, there is a problem of uneven distribution of parameters such as the resonator mass, Young's modulus, and wall thickness along the circumference, leading to frequency splitting in the hemispherical resonator, forming two frequency principal axes spaced 45° apart. When the antinodes are located on the two frequency principal axes, one resonant frequency is the highest, and the other resonant frequency is the lowest.

[0037] Considering the two types of error terms mentioned above, the dynamic equation of the hemispherical harmonic oscillator is as follows:

[0038]

[0039] Where x represents the output signal of electrode x, and y represents the output signal of electrode y. Let x represent the first and second derivatives, respectively. Let k represent the first and second derivatives of y, respectively. xx k yy Let k represent the resonant frequencies of the harmonic oscillator at electrodes x and y, respectively. xy k yx D represents the coupling terms at the resonant frequencies of the harmonic oscillator at electrodes x and y, respectively. xx D yy D represents the damping coefficients of the harmonic oscillator at the x and y electrodes, respectively. xy D yx Let f represent the coupling terms of the harmonic oscillator damping at electrodes x and y, respectively. x f y These represent the forces applied to the x and y electrodes, respectively; k represents the gyroscope precession factor; and Ω represents the external input angular velocity. The specific expressions are as follows:

[0040] k xx =ω 2 -ωΔωcos4θ ω ,k yy =ω 2 +ωΔωcos4θ ω

[0041] k xy =k yx =-ωΔωsin4θ ω

[0042]

[0043] The meanings of each variable are as follows:

[0044]

[0045] In the above formula, ω1 and ω2 represent the resonant frequencies of the two principal axes. Due to frequency fragmentation, the two frequencies are not equal. Assuming ω1 > ω2, then θ ω Let θ represent the azimuth angle of the frequency axis where ω2 is located; τ1 and τ2 represent the decay time constants of the two damping principal axes. Assuming τ1 < τ2, then θ τ This represents the azimuth angle of the damping axis where τ1 is located.

[0046] By using the "average method" to solve the motion parameters of the elliptical trajectory in the dynamic equation containing the error term over one oscillation cycle of the harmonic oscillator, the angular rate error equation can be obtained as follows:

[0047]

[0048] In the above formula, θ represents the angle. Let ω represent the angular velocity, Δω represent the frequency difference between the two principal axes ω1 and ω2, a represent the amplitude, and q represent orthogonality. This indicates uneven damping.

[0049] According to the standing wave azimuth rate of change equation, -kΩ represents the portion generated by the angular velocity of the sensitive carrier. Furthermore, the measured angular velocity introduces an error term due to damping inhomogeneity and frequency fragmentation. Damping inhomogeneity... The presence of [variable name] causes an error term in the angular velocity that is periodically related to the standing wave azimuth angle, with the magnitude of the fluctuation depending on the position of the damping axis; the presence of the frequency difference Δω causes an error term in the angular velocity that is periodically related to the standing wave azimuth angle, with the magnitude of the fluctuation depending on the position of the stiffness axis. Since q is suppressed near 0 during operation, the angular velocity error term caused by frequency fragmentation is much smaller than the angular velocity error term caused by damping inhomogeneity. In other words, in this embodiment of the invention, the variation law between the angular velocity fluctuation caused by the two error sources of damping inhomogeneity and the frequency difference between the frequency principal axes, as determined by the angular rate error equation, and the standing wave azimuth angle is as follows: the angular velocity fluctuation caused by damping inhomogeneity and the frequency difference between the frequency principal axes exhibits a periodic 90° sine and cosine periodic variation with the standing wave azimuth angle.

[0050] Based on the above embodiments, in this embodiment of the invention, the standing wave azimuth angle switching scheme for the coarse alignment stage, determined based on the variation law and angular rate error characteristic curve, is as follows: two standing wave azimuth angles symmetrically spaced 45° apart are selected as two switching positions. By averaging the angular rates of the two standing wave positions differing by 45°, the standing wave offset error can be effectively reduced, thereby improving the alignment accuracy.

[0051] After determining the standing wave azimuth angle switching scheme, the hemispherical resonant gyroscope inertial navigation system is installed on the turntable, and the turntable is driven to rotate at a fixed rate to establish the relationship between the standing wave azimuth angle and angular velocity, that is, to obtain the angular rate error characteristic curve. Using the angular rate error characteristic of the hemispherical resonant gyroscope, two angles symmetrically separated by 45 degrees are selected.

[0052] In the coarse alignment stage, the gyroscope is set to two angle switching states. The standing wave azimuth angle of the hemispherical resonant gyroscope is switched at two angles with a phase difference of 45°. The gyroscope output (angular rate) and accelerometer output (specific force vector) of the two stable positions after the switching are collected. The gyroscope angular rate information and accelerometer specific force information are accumulated. Then, the accumulated values ​​are averaged over time. The average result is used to perform coarse alignment calculation. The initial attitude matrix of the inertial navigation system is obtained through the following calculation.

[0053] Attitude matrix The method for obtaining the coordinate system from the vehicle coordinate system to the navigation coordinate system is as follows:

[0054] Take the Earth's gravitational acceleration vector in the navigation coordinate system as Earth's rotational angular velocity vector is Additionally, construct vectors

[0055] Similarly, take the specific force vector in the carrier coordinate system. and angular velocity vector Constructing vectors The attitude matrix can be obtained from this. The expression is as follows:

[0056]

[0057] In the above formula The acceleration-force vector obtained and averaged during the coarse alignment process. replace, The gyroscope angular rate vector obtained and averaged during the coarse alignment process. By substitution, the attitude matrix can be obtained. The expression is as follows:

[0058]

[0059] because Since it is an orthogonal matrix, the initial attitude matrix can be obtained:

[0060]

[0061] In other words, the initial attitude matrix is ​​calculated based on the average angular velocity and the average force vector using the following formula:

[0062]

[0063] In the above formula, Let g represent the initial attitude matrix, g represent the gravitational acceleration, and ω represent the initial attitude matrix. ie The value represents the Earth's rotational angular velocity, L represents latitude, and f represents the Earth's rotational angular velocity. x ,f y ,f z The values ​​ω represent the average values ​​of the x-axis, y-axis, and z-axis accelerometer output force vectors acquired during the coarse alignment process, respectively. x ,ω y ,ω z The values ​​represent the average values ​​of the x-axis gyroscope output angular rate, y-axis gyroscope output angular rate, and z-axis gyroscope output angular rate collected during the coarse alignment process, respectively.

[0064] Furthermore, the method also includes: during the fine alignment stage, setting the gyroscope to normal state and using velocity matching based on Kalman filtering for fine alignment.

[0065] The main steps of the position switching alignment method for the hemispherical resonant gyroscope inertial navigation system provided by this invention can be referred to... Figure 1The basic working principle block diagram is shown, and the specific implementation methods of each step have been described in detail in the foregoing embodiments, and will not be described in detail here. Those skilled in the art will understand that this example is merely an application of the position switching alignment method for the hemispherical resonant gyroscope inertial navigation system provided by this invention, and does not constitute any limitation thereof.

[0066] In summary, this invention provides a position switching alignment method for a hemispherical resonant gyroscope inertial navigation system. This method analyzes the angular rate error of the hemispherical resonant gyroscope, establishes an angular rate error equation, and combines the angular rate error characteristic curve to obtain the relationship between the angular rate error and the standing wave azimuth angle. This allows for the determination of the standing wave azimuth angle switching scheme. By driving the standing wave to rotate to the angular positions before and after the switching, the drift of the gyroscope is modulated, thereby improving alignment accuracy. Compared with existing technologies, the technical solution of this invention can solve the technical problem that existing technologies cannot effectively compensate for drift caused by frequency non-uniformity and damping non-uniformity.

[0067] 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.

[0068] 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.

[0069] 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 method for position switching and alignment of a hemispherical resonant gyroscope inertial navigation system, characterized in that, The hemispherical resonant gyroscope inertial navigation system includes a hemispherical resonant gyroscope and an accelerometer, and the method includes: Establish the angular rate error equation, and determine the variation law between the angular velocity fluctuation and the standing wave azimuth angle caused by damping inhomogeneity and frequency difference between the principal frequency axis based on the angular rate error equation. A hemispherical resonant gyroscope inertial navigation system is mounted on a turntable, and the turntable is driven to rotate at a fixed rate to obtain the angular rate error characteristic curve. Based on the aforementioned variation pattern and the aforementioned angular rate error characteristic curve, a standing wave azimuth angle switching scheme for the coarse alignment stage is determined. During the coarse alignment stage, the gyroscope is set to stand wave azimuth angle switching state according to the determined standing wave azimuth angle switching scheme, and the angular rate of the gyroscope and the specific force vector of the accelerometer are collected under the stable position state before and after the switching. The collected angular velocities and force vectors are accumulated and then averaged over time to obtain the average angular velocity and the average force vector. The initial attitude matrix is ​​calculated based on the average angular rate and the average force vector.

2. The method according to claim 1, characterized in that, The angular rate error equation is: In the above formula, θ represents the angle. Let θ represent the angular velocity, and Δω represent the frequency difference between the two principal axes ω1 and ω2. Assuming ω1 > ω2, then θ ω This represents the azimuth angle of the frequency axis where ω2 is located. Let τ1 and τ2 represent the damping non-uniformity, and let τ1 and τ2 represent the decay time constants of the two principal damping axes. Assuming τ1 < τ2, then θ τ denoted by τ1, a represents the azimuth angle of the damping axis, q represents the orthogonality, k represents the gyroscope precession factor, and Ω represents the external input angular velocity.

3. The method according to claim 1 or 2, characterized in that, The variation law between the angular velocity fluctuation caused by damping inhomogeneity and the frequency difference between the main frequency axis and the standing wave azimuth angle, as determined by the angular rate error equation, is as follows: the angular velocity fluctuation caused by damping inhomogeneity and the frequency difference between the main frequency axis exhibits a periodic 90° sine and cosine periodic variation with the standing wave azimuth angle.

4. The method according to claim 3, characterized in that, Based on the aforementioned variation pattern and the aforementioned angular rate error characteristic curve, the standing wave azimuth angle switching scheme for the coarse alignment stage is determined as follows: two standing wave azimuth angles that are symmetrically spaced 45° apart are selected as two switching positions.

5. The method according to claim 4, characterized in that, The initial attitude matrix is ​​calculated based on the average angular rate and the average force vector using the following formula: In the above formula, Let g represent the initial attitude matrix, g represent the gravitational acceleration, and ω represent the initial attitude matrix. ie The value represents the Earth's rotational angular velocity, L represents latitude, and f represents the Earth's rotational angular velocity. x ,f y ,f z The values ​​ω represent the average values ​​of the x-axis, y-axis, and z-axis accelerometer output force vectors acquired during the coarse alignment process, respectively. x ,ω y ,ω z The values ​​represent the average values ​​of the x-axis gyroscope output angular rate, y-axis gyroscope output angular rate, and z-axis gyroscope output angular rate collected during the coarse alignment process, respectively.

6. The method according to any one of claims 1 to 5, characterized in that, The method further includes: during the fine alignment stage, setting the gyroscope to normal state and using velocity matching based on Kalman filtering for fine alignment.

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