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

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

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CN113252019A
CN113252019A CN202110522933.7A CN202110522933A CN113252019A CN 113252019 A CN113252019 A CN 113252019A CN 202110522933 A CN202110522933 A CN 202110522933A CN 113252019 A CN113252019 A CN 113252019A
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forward amplification
angle
amplification factor
gyroscope
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解伟男
汪昕杨
孙一为
奚伯齐
伊国兴
王常虹
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Harbin Institute of Technology Shenzhen
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
    • G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
    • G01C19/5705—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces using masses driven in reciprocating rotary motion about an axis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
    • G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
    • G01C19/5776—Signal processing not specific to any of the devices covered by groups G01C19/5607 - G01C19/5719
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/18—Stabilised platforms, e.g. by gyroscope

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Abstract

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

Description

一种前向放大系数不一致时的半球谐振陀螺振型角获取方法A method for obtaining the mode angle of hemispherical resonant gyroscope when the forward amplification factor is inconsistent

技术领域technical field

本发明涉及前向放大系数不一致时的半球谐振陀螺振型角获取方法，属于惯性技术领域。The invention relates to a method for obtaining the mode angle of a hemispherical resonant gyro when the forward amplification coefficients are inconsistent, and belongs to the field of inertial technology.

背景技术Background technique

上世纪60年代，出现了一种新型振动陀螺，半球谐振陀螺。此新型陀螺具备许多优点，例如误差小、工作寿命长、应用领域广等优点。不仅如此，相比于传统机械陀螺，半球谐振陀螺组成部件少，结构简单，其表头仅由二到三件零部件组成，且不易磨损，故障率非常低。半球谐振陀螺的核心部件谐振子是由熔融石英制成的，由于石英玻璃稳定的物理特性，因此谐振子不仅可靠性高、工作寿命长，而且具有极强的抗辐射能力，不易受宇宙射线及高能粒子的干扰，常用于空间飞行器的定姿与导航。综上所述，半球谐振陀螺具有极好的发展前景，对半球谐振陀螺进行研究，有益于惯性技术的发展与创新，可以为我国的深空探测以及其它相关的高科技领域进一步打下良好的基础。In the 1960s, a new type of vibrating gyroscope appeared, the hemispherical resonant gyroscope. This new type of gyroscope has many advantages, such as small error, long working life and wide application fields. Not only that, compared with the traditional mechanical gyroscope, the hemispherical resonant gyroscope has fewer components and a simple structure. The resonator, the core component of the hemispherical resonant gyroscope, is made of fused silica. Due to the stable physical properties of quartz glass, the resonator not only has high reliability and long working life, but also has strong radiation resistance and is not susceptible to cosmic rays and The interference of high-energy particles is often used for attitude determination and navigation of space vehicles. To sum up, the hemispherical resonant gyroscope has excellent development prospects. The research on the hemispherical resonant gyroscope is beneficial to the development and innovation of inertial technology, and can further lay a good foundation for my country's deep space exploration and other related high-tech fields. .

现阶段，半球谐振陀螺主要有力平衡和全角两种工作模式，全角模式是一种新型半球谐振陀螺工作模式，该模式是利用谐振子进动角度与陀螺载体转动角度呈正比这一物理特性，通过对谐振子振型的进动角度的实时解算来读出载体的转动角度，适合于转速较高的场合。全角模式下，通常会对0°和45°电极采集到的信号x、y进行等比例的前向放大，再计算振型的进动角度，但这存在一个值得考虑问题：如果两个信号的放大系数不相等时，那么常用的测角方程就不够精确，计算出来的振型角会与实际的振型角存在不小的误差，解算后读出的载体转动角度与载体实际转角也会存在一定误差，这在高精度应用场合中是不允许存在的情况。At present, the hemispherical resonant gyroscope mainly has two working modes: force balance and full-angle. The full-angle mode is a new working mode of hemispherical resonant gyroscope. The real-time calculation of the precession angle of the harmonic oscillator mode shape can read the rotation angle of the carrier, which is suitable for occasions with high rotation speed. In the full-angle mode, the signals x and y collected by the 0° and 45° electrodes are usually forward amplified in equal proportions, and then the precession angle of the mode shape is calculated, but there is a problem worth considering: if the two signals are When the magnification factor is not equal, the commonly used angle measurement equation is not accurate enough, the calculated mode shape angle will have a large error with the actual mode shape angle, and the rotation angle of the carrier read out after the solution will also be different from the actual rotation angle of the carrier. There is a certain error, which is not allowed in high-precision applications.

综上所述，想要计算出精确的振型角，就必须知道前向放大系数比值k的精确大小。因此，提出一种高精度的辨识方法来辨识出k，是十分必要的。To sum up, if you want to calculate the exact mode angle, you must know the exact size of the forward amplification factor ratio k. Therefore, it is very necessary to propose a high-precision identification method to identify k.

发明内容SUMMARY OF THE INVENTION

本发明的目的是为了解决前向放大系数不一致时半球谐振陀螺无法精确测出载体的角度等信息，降低导航准确率的问题，而提出一种前向放大系数不一致时的半球谐振陀螺振型角获取方法。The purpose of the present invention is to solve the problem that the hemispherical resonant gyroscope cannot accurately measure the information such as the angle of the carrier when the forward amplification factor is inconsistent, and reduce the navigation accuracy, and propose a hemispherical resonant gyroscope mode angle when the forward amplification factor is inconsistent. get method.

载体可以是飞行器、转台等等。The carrier may be an aircraft, a turntable, or the like.

一种前向放大系数不一致时的半球谐振陀螺振型角获取方法具体过程为：The specific process of a hemispherical resonant gyro mode angle acquisition method when the forward amplification factor is inconsistent is as follows:

步骤1：将半球谐振陀螺安装并固定在转台上，使陀螺敏感轴与转台的旋转轴重合；Step 1: Install and fix the hemispherical resonant gyroscope on the turntable so that the sensitive axis of the gyroscope coincides with the rotation axis of the turntable;

步骤2：对半球谐振陀螺上的激励电极施加激励电压进行参数激励，直到谐振子的振动信号幅值不变；Step 2: apply an excitation voltage to the excitation electrodes on the hemispherical resonant gyroscope for parameter excitation until the amplitude of the vibration signal of the resonator remains unchanged;

步骤3：使转台匀速旋转，采集陀螺上0°、45°检测电极检测到的振动信号x、y，同时采集转台角度θr；Step 3: make the turntable rotate at a constant speed, collect the vibration signals x and y detected by the 0° and 45° detection electrodes on the gyro, and simultaneously collect the turntable angle θ r ;

步骤4：利用锁相环生成的参考信号vrc、vrs分别对检测到的振动信号x、y进行解调，得到信号Cx、Sx、Cy、Sy，对信号Cx、Sx、Cy、Sy分别进行低通滤波得到信号Cx'、Sx'、Cy'、Sy'，再对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号；Step 4: Use the reference signals v rc and v rs generated by the phase-locked loop to demodulate the detected vibration signals x and y, respectively, to obtain the signals Cx, Sx, Cy, and Sy. Perform low-pass filtering to obtain signals Cx', Sx', Cy', Sy', and then perform secondary combination of signals Cx', Sx', Cy', Sy' to obtain E, R, S signals;

步骤5：建立考虑前向放大系数比值k的测角方程，基于前向放大系数比值k的测角方程，设计扩展卡尔曼滤波器，并对扩展卡尔曼滤波器进行初始参数设置；Step 5: establish an angle measurement equation considering the forward amplification factor ratio k, design an extended Kalman filter based on the angle measurement equation of the forward amplification coefficient ratio k, and set the initial parameters of the extended Kalman filter;

步骤6：将步骤4得到的E、R、S信号作为扩展卡尔曼滤波器的输入，对前向放大系数比值k进行辨识，滤波结束后输出估计的前向放大系数比值

Figure BDA0003064689020000021
Step 6: Use the E, R, and S signals obtained in step 4 as the input of the extended Kalman filter, identify the forward amplification coefficient ratio k, and output the estimated forward amplification coefficient ratio after filtering.
Figure BDA0003064689020000021

步骤7：将输出的

Figure BDA0003064689020000022
代入步骤5建立的考虑前向放大系数比值k的测角方程，获取前向放大系数不一致时的半球谐振陀螺振型角。Step 7: The output will be
Figure BDA0003064689020000022
Substitute into the angle measurement equation established in step 5 considering the ratio k of the forward amplification factor to obtain the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent.

本发明的有益效果为：The beneficial effects of the present invention are:

传统的测角方程默认前向放大系数是等比例的情况，没有考虑前向放大系数不一致的问题，计算出来的载体的角度等信息就会存在一定误差，降低了陀螺的精度，降低了导航准确率，无法满足高精度的工作场合的需求。The default forward magnification factor of the traditional angle measurement equation is equal to the proportion, and the problem of inconsistent forward magnification factor is not considered. There will be certain errors in the calculated information such as the angle of the carrier, which reduces the accuracy of the gyro and reduces the accuracy of navigation. rate, cannot meet the needs of high-precision workplaces.

本发明提出了一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，首先将半球谐振陀螺固定安装在转台上，使陀螺敏感轴与转台的旋转轴重合，然后对间隔布置在半球谐振陀螺上的激励电极施加激励电压进行参数激励，直到谐振子的振动信号幅值稳定。使转台匀速旋转，采集陀螺上0°、45°检测电极检测到的振动信号x、y，并利用锁相环生成的参考信号vrc、vrs分别对x、y进行解调、低通滤波、二次组合后得到E、R、S信号。基于改进的测角方程，完成扩展卡尔曼滤波器的设计后将步骤4得到的信号E、R、S作为扩展卡尔曼滤波器的输入，对k进行辨识，滤波结束后输出

Figure BDA0003064689020000023
最后将辨识的
Figure BDA0003064689020000024
代入改进的测角方程中，得到精确的测角方程。该方法可以实现前向放大系数比值k的精确辨识，具有很高的精度，辨识的
Figure BDA0003064689020000031
误差小，通过
Figure BDA0003064689020000032
计算得到的陀螺振型角精度高，实现了陀螺的高精度角度测量，精确测出载体的角度信息，提高导航准确率；解决前向放大系数不一致时半球谐振陀螺无法精确测出载体的角度等信息，降低导航准确率的问题。The invention proposes a method for obtaining the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent. First, the hemispherical resonant gyroscope is fixedly installed on the turntable, so that the sensitive axis of the gyroscope is coincident with the rotation axis of the turntable, and then the hemispherical resonant gyroscope is arranged at intervals in the hemisphere. The excitation electrodes on the resonant gyroscope apply excitation voltage for parameter excitation until the amplitude of the vibration signal of the resonator is stable. The turntable is rotated at a constant speed, and the vibration signals x and y detected by the 0° and 45° detection electrodes on the gyro are collected, and the reference signals v rc and v rs generated by the phase-locked loop are used to demodulate and low-pass filter x and y respectively. , E, R, S signals are obtained after the second combination. Based on the improved angle measurement equation, after the design of the extended Kalman filter is completed, the signals E, R, and S obtained in step 4 are used as the input of the extended Kalman filter, k is identified, and output after filtering is completed
Figure BDA0003064689020000023
will eventually be identified
Figure BDA0003064689020000024
Substitute into the improved angle measurement equation to get the accurate angle measurement equation. This method can realize the accurate identification of the forward amplification coefficient ratio k, and has high precision.
Figure BDA0003064689020000031
The error is small, through
Figure BDA0003064689020000032
The calculated gyro mode angle has high precision, realizes the high-precision angle measurement of the gyro, accurately measures the angle information of the carrier, and improves the navigation accuracy; it solves the problem that the hemispherical resonant gyro cannot accurately measure the angle of the carrier when the forward amplification factor is inconsistent, etc. information and reduce the navigation accuracy.

本发明通过理论分析和仿真实验可以看出，本发明提出的一种前向放大系数不一致时的半球谐振陀螺振型角获取方法能够实现全角模式半球谐振陀螺在前向放大系数不一致时的高精度工作，从而广泛应用到需要高精度半球谐振陀螺的高端科技领域中。It can be seen from the theoretical analysis and simulation experiments of the present invention that the method for obtaining the mode angle of the hemispherical resonant gyroscope when the forward amplification coefficients are inconsistent proposed by the present invention can realize the high precision of the full-angle mode hemispherical resonant gyroscope when the forward amplification coefficients are inconsistent. It is widely used in high-end technology fields that require high-precision hemispherical resonant gyroscopes.

附图说明Description of drawings

图1为本发明流程图；Fig. 1 is the flow chart of the present invention;

图2为本发明实施例参数k辨识误差曲线图；Fig. 2 is the parameter k identification error curve diagram of the embodiment of the present invention;

图3为本发明实施例振型角误差曲线图；Fig. 3 is the mode shape angle error curve diagram of the embodiment of the present invention;

图4为半球谐振陀螺上的激励电极布置图。FIG. 4 is an arrangement diagram of excitation electrodes on a hemispherical resonant gyroscope.

具体实施方式Detailed ways

具体实施方式一：结合图1说明本实施方式，本实施方式一种前向放大系数不一致时的半球谐振陀螺振型角获取方法具体过程为：Embodiment 1: This embodiment is described with reference to FIG. 1 . The specific process of a method for obtaining the mode angle of a hemispherical resonant gyroscope when the forward amplification factor is inconsistent in this embodiment is as follows:

本发明的目的是针对于半球谐振陀螺检测回路前向放大系数不相等时测角存在误差的问题，提供一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，提出改进的测角公式，基于此公式建立扩展卡尔曼滤波器，在转动陀螺的同时，对0°和45°电极采集到的振动信号进行解调、低通滤波等处理，得到的信号E、R、S作为扩展卡尔曼滤波器的输入，实现了前向放大系数比值k的辨识，得到精确的测角公式，提高陀螺的测量精度。The purpose of the present invention is to solve the problem of angle measurement errors when the forward amplification coefficients of the detection loops of the hemispherical resonant gyroscope are not equal, to provide a method for obtaining the mode angle of the hemispherical resonant gyroscope when the forward amplification coefficients are inconsistent, and to propose an improved angle measurement method. formula, based on this formula, an extended Kalman filter is established. While rotating the gyro, the vibration signals collected by the 0° and 45° electrodes are demodulated and low-pass filtered, and the obtained signals E, R, and S are used as extended The input of the Kalman filter realizes the identification of the ratio k of the forward amplification factor, and obtains an accurate angle measurement formula, which improves the measurement accuracy of the gyro.

为了达到上述目的，本发明提供了一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，包含：In order to achieve the above object, the present invention provides a method for obtaining the mode angle of the hemispherical resonant gyroscope when the forward amplification coefficients are inconsistent, including:

步骤1：将半球谐振陀螺安装并固定在转台上，使陀螺敏感轴与转台的旋转轴重合；Step 1: Install and fix the hemispherical resonant gyroscope on the turntable so that the sensitive axis of the gyroscope coincides with the rotation axis of the turntable;

步骤2：对半球谐振陀螺上的激励电极施加激励电压进行参数(激励电极施加的信号，如信号的幅值、频率、相位)激励，直到谐振子的振动信号幅值不变；Step 2: apply an excitation voltage to the excitation electrodes on the hemispherical resonant gyroscope to excite parameters (signals applied by the excitation electrodes, such as signal amplitude, frequency, phase) until the vibration signal amplitude of the resonator remains unchanged;

步骤3：使转台匀速旋转，采集陀螺上0°、45°检测电极检测到的振动信号x、y，同时采集转台角度θr；Step 3: make the turntable rotate at a constant speed, collect the vibration signals x and y detected by the 0° and 45° detection electrodes on the gyro, and simultaneously collect the turntable angle θ r ;

步骤4：利用锁相环生成的参考信号vrc、vrs分别对检测到的振动信号x、y进行解调，得到信号Cx、Sx、Cy、Sy，对信号Cx、Sx、Cy、Sy分别进行低通滤波得到信号Cx'、Sx'、Cy'、Sy'，再对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号；Step 4: Use the reference signals v rc and v rs generated by the phase-locked loop to demodulate the detected vibration signals x and y, respectively, to obtain the signals Cx, Sx, Cy, and Sy. Perform low-pass filtering to obtain signals Cx', Sx', Cy', Sy', and then perform secondary combination of signals Cx', Sx', Cy', Sy' to obtain E, R, S signals;

步骤5：建立考虑前向放大系数比值k的测角方程，基于前向放大系数比值k的测角方程，设计扩展卡尔曼滤波器，并对扩展卡尔曼滤波器进行初始参数设置；Step 5: establish an angle measurement equation considering the forward amplification factor ratio k, design an extended Kalman filter based on the angle measurement equation of the forward amplification coefficient ratio k, and set the initial parameters of the extended Kalman filter;

步骤6：将步骤4得到的E、R、S信号作为扩展卡尔曼滤波器的输入，对前向放大系数比值k进行辨识，滤波结束后输出估计的前向放大系数比值

Figure BDA0003064689020000041
Step 6: Use the E, R, and S signals obtained in step 4 as the input of the extended Kalman filter, identify the forward amplification coefficient ratio k, and output the estimated forward amplification coefficient ratio after filtering.
Figure BDA0003064689020000041

步骤7：将输出的

Figure BDA0003064689020000042
代入步骤5建立的考虑前向放大系数比值k的测角方程，获取前向放大系数不一致时的半球谐振陀螺振型角。Step 7: The output will be
Figure BDA0003064689020000042
Substitute into the angle measurement equation established in step 5 considering the ratio k of the forward amplification factor to obtain the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent.

具体实施方式二：本实施方式与具体实施方式一不同的是，所述步骤2中激励电极间隔布置在半球谐振陀螺上。如图4所示。Embodiment 2: The difference between this embodiment and Embodiment 1 is that in the step 2, the excitation electrodes are arranged on the hemispherical resonant gyroscope at intervals. As shown in Figure 4.

其它步骤及参数与具体实施方式一相同。Other steps and parameters are the same as in the first embodiment.

具体实施方式三：本实施方式与具体实施方式一或二不同的是，所述步骤4中利用锁相环生成的参考信号vrc、vrs分别对检测到的振动信号x、y进行解调，得到信号Cx、Sx、Cy、Sy，对信号Cx、Sx、Cy、Sy分别进行低通滤波得到信号Cx'、Sx'、Cy'、Sy'，再对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号；具体过程为：Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that in the step 4, the reference signals v rc and v rs generated by the phase-locked loop are used to demodulate the detected vibration signals x and y respectively. , obtain the signals Cx, Sx, Cy, Sy, perform low-pass filtering on the signals Cx, Sx, Cy, and Sy respectively to obtain the signals Cx', Sx', Cy', Sy', and then filter the signals Cx', Sx', Cy' , Sy' are combined twice to obtain E, R, S signals; the specific process is:

所述利用锁相环生成的参考信号vrc、vrs分别对检测到的振动信号x、y进行解调，得到信号Cx、Sx、Cy、Sy，表达式为：The reference signals v rc and v rs generated by the phase-locked loop are used to demodulate the detected vibration signals x and y, respectively, to obtain signals Cx, Sx, Cy, and Sy, and the expressions are:

Figure BDA0003064689020000043
Figure BDA0003064689020000043

将信号Cx、Sx、Cy、Sy经过低通滤波，分别滤除信号Cx、Sx、Cy、Sy中的二倍频，得到信号Cx'、Sx'、Cy'、Sy'；The signals Cx, Sx, Cy, and Sy are subjected to low-pass filtering to filter out the double frequency in the signals Cx, Sx, Cy, and Sy, respectively, to obtain the signals Cx', Sx', Cy', Sy';

对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号。The signals Cx', Sx', Cy', and Sy' are combined twice to obtain E, R, and S signals.

其它步骤及参数与具体实施方式一或二相同。Other steps and parameters are the same as in the first or second embodiment.

具体实施方式四：本实施方式与具体实施方式一至三之一不同的是，所述对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号，表达式为：Embodiment 4: The difference between this embodiment and one of Embodiments 1 to 3 is that the signals Cx', Sx', Cy', and Sy' are combined twice to obtain the E, R, S signals, and the expression for:

Figure BDA0003064689020000051
Figure BDA0003064689020000051

其它步骤及参数与具体实施方式一至三之一相同。Other steps and parameters are the same as one of the first to third embodiments.

具体实施方式五：本实施方式与具体实施方式一至四之一不同的是，所述参考信号vrc、vrs由正弦信号和余弦信号组成。Embodiment 5: The difference between this embodiment and one of Embodiments 1 to 4 is that the reference signals v rc and v rs are composed of sine signals and cosine signals.

其它步骤及参数与具体实施方式一至四之一相同。Other steps and parameters are the same as one of the first to fourth embodiments.

具体实施方式六：本实施方式与具体实施方式一至五之一不同的是，所述步骤5中建立考虑前向放大系数比值k的测角方程；具体过程为：Embodiment 6: The difference between this embodiment and one of Embodiments 1 to 5 is that in the step 5, an angle measurement equation considering the forward magnification coefficient ratio k is established; the specific process is:

建立考虑前向放大系数比值k的测角方程，该公式能精确描述振型的真实进动角，形式如下：An angle measurement equation considering the ratio k of the forward magnification factor is established, which can accurately describe the true precession angle of the mode shape, and the form is as follows:

Figure BDA0003064689020000052
Figure BDA0003064689020000052

其中，k＝ky/kx，kx为0°电极的前向放大系数，ky为45°电极(确定了0°电极后，逆时针方向45°就是45°电极)的前向放大系数；θreal为半球谐振陀螺振型角真实值。Among them, k= ky /k x , k x is the forward amplification factor of the 0° electrode, and ky is the forward amplification of the 45° electrode (after the 0° electrode is determined, 45° in the counterclockwise direction is the 45° electrode) coefficient; θ real is the real value of the mode angle of the hemispherical resonant gyro.

因此，只要知道参数k，就能直接求得半球谐振陀螺振型角真实值θreal。Therefore, as long as the parameter k is known, the real value θ real of the mode shape angle of the hemispherical resonant gyro can be directly obtained.

其它步骤及参数与具体实施方式一至五之一相同。Other steps and parameters are the same as one of the specific embodiments one to five.

具体实施方式七：本实施方式与具体实施方式一至六之一不同的是，所述步骤5中基于前向放大系数比值k的测角方程，设计扩展卡尔曼滤波器，滤波器选取的模型如下所示：Embodiment 7: The difference between this embodiment and one of Embodiments 1 to 6 is that in the step 5, based on the angle measurement equation of the forward amplification coefficient ratio k, an extended Kalman filter is designed, and the model selected by the filter is as follows shown:

Figure BDA0003064689020000053
Figure BDA0003064689020000053

k(i+1)＝k(i)、c(i+1)＝c(i)是状态方程，为陀螺前向放大系数比值k＝ky/kx以及陀螺进动系数c，这两个参数为不随时间改变的固定值k(i)为前向放大系数比值，c(i)为陀螺进动系数，i为第i个时刻；k(i+1)=k(i), c(i+1)=c(i) are the state equations, which are the ratio of the forward amplification factor of the gyro k= ky /k x and the precession coefficient of the gyro, c. The first parameter is a fixed value that does not change with time k(i) is the ratio of the forward amplification coefficient, c(i) is the gyro precession coefficient, and i is the ith moment;

Figure BDA0003064689020000061
是观测方程，θr为转台转角，v为测量噪声；
Figure BDA0003064689020000061
is the observation equation, θ r is the rotation angle of the turntable, and v is the measurement noise;

所述步骤5中对扩展卡尔曼滤波器进行初始参数设置；具体过程为：In the step 5, initial parameter setting is performed on the extended Kalman filter; the specific process is:

扩展卡尔曼滤波是一种递推算法，扩展卡尔曼滤波器启动时进行初始参数设置，给定初始值，令

Figure BDA0003064689020000062
P0|0＝I；Extended Kalman filter is a recursive algorithm. When the extended Kalman filter is started, initial parameters are set. Given the initial value, let
Figure BDA0003064689020000062
P 0|0 =I;

式中，

Figure BDA0003064689020000063
为前向放大系数比值k的初始估计值，
Figure BDA0003064689020000064
为进动系数c的初始估计值，P0|0为估计误差协方差矩阵的初始值。In the formula,
Figure BDA0003064689020000063
is the initial estimated value of the forward amplification factor ratio k,
Figure BDA0003064689020000064
is the initial estimated value of the precession coefficient c, and P 0|0 is the initial value of the estimated error covariance matrix.

其它步骤及参数与具体实施方式一至六之一相同。Other steps and parameters are the same as one of Embodiments 1 to 6.

具体实施方式八：本实施方式与具体实施方式一至七之一不同的是，所述步骤6中将步骤4得到的E、R、S信号作为扩展卡尔曼滤波器的输入，对前向放大系数比值k进行辨识，滤波结束后输出估计的前向放大系数比值

Figure BDA0003064689020000065
辨识具体步骤如下：Embodiment 8: The difference between this embodiment and one of Embodiments 1 to 7 is that in the step 6, the E, R, and S signals obtained in step 4 are used as the input of the extended Kalman filter, and the forward amplification coefficient is The ratio k is used for identification, and the estimated forward amplification coefficient ratio is output after the filtering is completed.
Figure BDA0003064689020000065
The specific steps for identification are as follows:

S1：对下一时刻的状态估计值进行预测S1: Predict the state estimate value at the next moment

Figure BDA0003064689020000066
Figure BDA0003064689020000066

Figure BDA0003064689020000067
Figure BDA0003064689020000067

式中，

Figure BDA0003064689020000068
为前向放大系数比值k第i个时刻的先验估计值，
Figure BDA0003064689020000069
为前向放大系数比值k第i-1时刻的估计值，
Figure BDA00030646890200000610
为进动系数c第i个时刻的先验估计值，
Figure BDA00030646890200000611
为进动系数c第i-1时刻的估计值；In the formula,
Figure BDA0003064689020000068
is the a priori estimate of the forward amplification factor ratio k at the ith moment,
Figure BDA0003064689020000069
is the estimated value of the forward amplification coefficient ratio k at the i-1th moment,
Figure BDA00030646890200000610
is the a priori estimate of the ith moment of the precession coefficient c,
Figure BDA00030646890200000611
is the estimated value of the precession coefficient c at the i-1th moment;

S2：对下一时刻的估计误差协方差进行预测：S2: Predict the estimated error covariance at the next moment:

Pi|i-1＝Pi-1|i-1 P i|i-1 =P i-1|i-1

式中，Pi|i-1为估计误差协方差矩阵第i时刻的预测值，Pi-1|i-1为估计误差协方差矩阵第i-1时刻的值；In the formula, P i|i-1 is the predicted value of the estimated error covariance matrix at time i, and P i-1|i-1 is the value of the estimated error covariance matrix at time i-1;

S3：判断是否还有信号E、R和S输入扩展卡尔曼滤波器，若有则跳到S4，若无则跳到步骤S9；S3: judge whether there are still signals E, R and S input to the extended Kalman filter, if so, skip to S4, if not, skip to step S9;

S4：对下一时刻的测量矩阵进行预测：S4: Predict the measurement matrix at the next moment:

令

Figure BDA0003064689020000071
make
Figure BDA0003064689020000071

Figure BDA0003064689020000072
Figure BDA0003064689020000072

式中，b为中间变量，Ci为第i个时刻的测量矩阵；In the formula, b is the intermediate variable, and C i is the measurement matrix at the ith moment;

S5：对下一时刻的测量估计值进行预测：S5: Predict the measurement estimate at the next moment:

Figure BDA0003064689020000073
Figure BDA0003064689020000073

其中，

Figure BDA0003064689020000074
为转台转角的估计值；in,
Figure BDA0003064689020000074
is the estimated value of the turntable rotation angle;

S6：对下一时刻的状态增益矩阵进行预测：S6: Predict the state gain matrix at the next moment:

Ki＝Pi|i-1*Ci T*(Ci*Pi|i-1*Ci T+Q)-1 K i =P i|i-1 *C i T *(C i *P i|i-1 *C i T +Q) -1

式中，Q为噪声v的协方差，可取Q＝0.012；*为乘号，Ki为第i个时刻的状态增益矩阵，T为转置；In the formula, Q is the covariance of the noise v, which can be taken as Q=0.01 2 ; * is the multiplication sign, K i is the state gain matrix at the ith moment, and T is the transpose;

S7：对下一时刻的状态估计值进行更新：S7: Update the state estimate value at the next moment:

Figure BDA0003064689020000075
Figure BDA0003064689020000075

式中，

Figure BDA0003064689020000076
为前向放大系数比值k第i个时刻的后验估计值；In the formula,
Figure BDA0003064689020000076
is the posterior estimated value of the ith moment of the forward amplification coefficient ratio k;

S8：对下一时刻的估计误差协方差进行更新，然后跳转到S1；S8: Update the estimated error covariance at the next moment, and then jump to S1;

Pi|i＝(I-KiCi)*Pi|i-1 P i|i =(IK i C i )*P i|i-1

式中，Pi|i为估计误差协方差矩阵第i个时刻的值，I为单位矩阵；In the formula, P i|i is the value at the ith moment of the estimated error covariance matrix, and I is the identity matrix;

S9：滤波结束，输出估计的前向放大系数比值

Figure BDA0003064689020000077
S9: The filtering is over, and the estimated forward amplification factor ratio is output
Figure BDA0003064689020000077

综上，完成了基于考虑前向放大系数比值k的测角方程的扩展卡尔曼滤波器的设计。In conclusion, the design of the extended Kalman filter based on the goniometric equation considering the forward amplification factor ratio k is completed.

其它步骤及参数与具体实施方式一至七之一相同。Other steps and parameters are the same as one of the first to seventh embodiments.

具体实施方式九：本实施方式与具体实施方式一至八之一不同的是，所述步骤7中将输出的

Figure BDA0003064689020000081
代入步骤5建立的考虑前向放大系数比值k的测角方程，获取前向放大系数不一致时的半球谐振陀螺振型角；表达式为：Embodiment 9: The difference between this embodiment and one of Embodiments 1 to 8 is that in the step 7, the output
Figure BDA0003064689020000081
Substitute into the angle measurement equation established in step 5 considering the ratio k of the forward amplification factor, and obtain the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent; the expression is:

Figure BDA0003064689020000082
Figure BDA0003064689020000082

式中，θguji为半球谐振陀螺振型角的估计值。In the formula, θ guji is the estimated value of the mode shape angle of the hemispherical resonant gyroscope.

所述其它步骤及参数与具体实施方式一至八之一相同。The other steps and parameters are the same as those of one of the first to eighth embodiments.

具体实施方式十：本实施方式与具体实施方式一至九之一不同的是，所述前向放大系数不一致由前向放大电路误差、谐振子电极极板面积误差、谐振子电极极板间距误差、谐振子安装偏差中的一种或多种导致；Embodiment 10: The difference between this embodiment and one of Embodiments 1 to 9 is that the inconsistency of the forward amplification factor is caused by the forward amplification circuit error, the area error of the resonator electrode plate, the error of the distance between the resonator electrode plates, Caused by one or more of the harmonic oscillator installation deviations;

所述多种为2种、3种或4种。The plurality is 2, 3 or 4.

其它步骤及参数与具体实施方式一至九之一相同。Other steps and parameters are the same as one of Embodiments 1 to 9.

采用以下实施例验证本发明的有益效果：Adopt the following examples to verify the beneficial effects of the present invention:

实施例一：Example 1:

步骤1，将半球谐振陀螺安装并固定在转台上，使陀螺敏感轴与转台的旋转轴重合；Step 1, install and fix the hemispherical resonant gyroscope on the turntable, so that the sensitive axis of the gyroscope coincides with the rotation axis of the turntable;

步骤2，对间隔布置在半球谐振陀螺上的激励电极施加激励电压进行参数激励，直到谐振子的振动信号幅值稳定；Step 2, applying an excitation voltage to the excitation electrodes arranged at intervals on the hemispherical resonant gyroscope to perform parameter excitation, until the amplitude of the vibration signal of the resonator is stable;

步骤3，使转台以Ωr＝30°/s的速度匀速旋转，设定采样频率为fs＝1000Hz，采样时间为ti＝10s，采集陀螺上0°、45°检测电极检测到的振动信号x、y，同时采集转台角度θr，其中0°检测电极前向放大系数为kx＝2，45°检测电极前向放大系数为ky＝2.2，则k＝ky/kx＝1.1；Step 3: Make the turntable rotate at a constant speed at a speed of Ω r = 30°/s, set the sampling frequency to be fs = 1000 Hz, set the sampling time to be t i = 10s, and collect the vibration signals detected by the 0° and 45° detection electrodes on the gyro x, y, and simultaneously acquire the turntable angle θ r , where the forward magnification factor of the 0° detection electrode is k x =2, and the forward magnification factor of the 45° detection electrode is ky =2.2, then k= ky /k x =1.1 ;

步骤4，利用锁相环生成的参考信号vrc、vrs分别对所述的振动信号x、y进行解调，得到信号Cx、Sx、Cy、Sy，低通滤波后得到Cx'、Sx'、Cy'、Sy'，再进行二次组合，得到E、R、S信号，所述的参考信号vrc、vrs由正弦信号和余弦信号组成；Step 4, using the reference signals v rc and v rs generated by the phase-locked loop to demodulate the vibration signals x and y respectively to obtain the signals Cx, Sx, Cy, and Sy, and obtain Cx', Sx' after low-pass filtering , Cy', Sy', and then perform secondary combination to obtain E, R, S signals, and the reference signals v rc and v rs are composed of sine signals and cosine signals;

步骤5，基于考虑前向放大系数比值k的测角方程，完成扩展卡尔曼滤波器的设计，滤波器模型如下：In step 5, the design of the extended Kalman filter is completed based on the angle measurement equation considering the ratio k of the forward amplification factor. The filter model is as follows:

Figure BDA0003064689020000091
Figure BDA0003064689020000091

并将滤波器初始参数设置为

Figure BDA0003064689020000092
P0|0＝I，测量噪声协方差Q＝0.012。and set the filter initial parameters to
Figure BDA0003064689020000092
P 0|0 =I, measurement noise covariance Q=0.01 2 .

步骤6，将步骤4得到的信号E、R、S作为扩展卡尔曼滤波器的输入，对k进行辨识，滤波结束后输出

Figure BDA0003064689020000093
Step 6, take the signals E, R, S obtained in step 4 as the input of the extended Kalman filter, identify k, and output after the filtering is completed.
Figure BDA0003064689020000093

S1：对下一时刻的状态估计值进行预测S1: Predict the state estimate value at the next moment

Figure BDA0003064689020000094
Figure BDA0003064689020000094

Figure BDA0003064689020000095
Figure BDA0003064689020000095

S2：对下一时刻的估计误差协方差进行预测：S2: Predict the estimated error covariance at the next moment:

Pi|i-1＝Pi-1|i-1 P i|i-1 =P i-1|i-1

S3：判断是否还有实验数据输入，若有则跳到S4，若无则跳到步骤S9；S3: determine whether there is still experimental data input, if so, skip to S4, if not, skip to step S9;

S4：对下一时刻的测量矩阵进行预测：S4: Predict the measurement matrix at the next moment:

令

Figure BDA0003064689020000096
make
Figure BDA0003064689020000096

Figure BDA0003064689020000097
Figure BDA0003064689020000097

S5：对下一时刻的测量估计值进行预测：S5: Predict the measurement estimate at the next moment:

Figure BDA0003064689020000098
Figure BDA0003064689020000098

其中，

Figure BDA0003064689020000099
为转台转角的估计值in,
Figure BDA0003064689020000099
is the estimated value of the turntable rotation angle

S6：对下一时刻的状态增益矩阵进行预测：S6: Predict the state gain matrix at the next moment:

Ki＝Pi|i-1*Ci T*(Ci*Pi|i-1*Ci T+Q)-1 K i =P i|i-1 *C i T *(C i *P i|i-1 *C i T +Q) -1

S7：对下一时刻的状态估计值进行更新：S7: Update the state estimate value at the next moment:

Figure BDA0003064689020000101
Figure BDA0003064689020000101

S8：对下一时刻的估计误差协方差进行更新，然后跳转到S1：S8: Update the estimated error covariance at the next moment, and then jump to S1:

Pi|i＝(I-KiCi)*Pi|i-1*(I-KiCi)T P i|i =(IK i C i )*P i|i-1 *(IK i C i ) T

S9：滤波结束，输出估计的前向放大系数比值

Figure BDA0003064689020000102
S9: The filtering is over, and the estimated forward amplification factor ratio is output
Figure BDA0003064689020000102

仿真结果如图2所示，从图2可以看出扩展卡尔曼滤波器在5秒时辨识误差已趋于平稳，在采样时间里滤波器一共输出了10000个

Figure BDA0003064689020000103
值，取最后辨识的
Figure BDA0003064689020000104
可以得到最终辨识的
Figure BDA0003064689020000105
与实际k的差值约等于2×10-5，可以看出滤波器对k辨识精度很高。The simulation results are shown in Figure 2. It can be seen from Figure 2 that the identification error of the extended Kalman filter has stabilized at 5 seconds, and the filter has output a total of 10,000 samples during the sampling time.
Figure BDA0003064689020000103
value, take the last identified
Figure BDA0003064689020000104
finally identifiable
Figure BDA0003064689020000105
The difference from the actual k is approximately equal to 2×10 -5 , and it can be seen that the filter has high identification accuracy for k.

步骤7，将输出的

Figure BDA0003064689020000106
代入步骤5建立的考虑前向放大系数比值k的测角方程，获取前向放大系数不一致时的半球谐振陀螺振型角；表达式为：Step 7, will output the
Figure BDA0003064689020000106
Substitute into the angle measurement equation established in step 5 considering the ratio k of the forward amplification factor, and obtain the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent; the expression is:

Figure BDA0003064689020000107
Figure BDA0003064689020000107

计算得到估计振型角θguji与真实振型角θreal之间的位置误差，绘制的位置误差曲线如图3；Calculate the position error between the estimated mode shape angle θ guji and the real mode shape angle θ real , and the drawn position error curve is shown in Figure 3;

由图3曲线可知，位置误差范围始终处在[-0.0012°,0.0012°]，该方法估计的振型角θguji具有很高的精度。It can be seen from the curve in Figure 3 that the position error range is always in [-0.0012°, 0.0012°], and the mode shape angle θ guji estimated by this method has high accuracy.

本发明还可有其它多种实施例，在不背离本发明精神及其实质的情况下，本领域技术人员当可根据本发明作出各种相应的改变和变形，但这些相应的改变和变形都应属于本发明所附的权利要求的保护范围。The present invention can also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all It should belong to the protection scope of the appended claims of the present invention.

Claims (10)

1.一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述方法具体过程为：1. a hemispherical resonant gyro mode angle acquisition method when the forward amplification factor is inconsistent, is characterized in that: the method concrete process is: 步骤1：将半球谐振陀螺安装并固定在转台上，使陀螺敏感轴与转台的旋转轴重合；Step 1: Install and fix the hemispherical resonant gyroscope on the turntable so that the sensitive axis of the gyroscope coincides with the rotation axis of the turntable; 步骤2：对半球谐振陀螺上的激励电极施加激励电压进行参数激励，直到谐振子的振动信号幅值不变；Step 2: apply an excitation voltage to the excitation electrodes on the hemispherical resonant gyroscope for parameter excitation until the amplitude of the vibration signal of the resonator remains unchanged; 步骤3：使转台匀速旋转，采集陀螺上0°、45°检测电极检测到的振动信号x、y，同时采集转台角度θr；Step 3: make the turntable rotate at a constant speed, collect the vibration signals x and y detected by the 0° and 45° detection electrodes on the gyro, and simultaneously collect the turntable angle θ r ; 步骤4：利用锁相环生成的参考信号vrc、vrs分别对检测到的振动信号x、y进行解调，得到信号Cx、Sx、Cy、Sy，对信号Cx、Sx、Cy、Sy分别进行低通滤波得到信号Cx'、Sx'、Cy'、Sy'，再对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号；Step 4: Use the reference signals v rc and v rs generated by the phase-locked loop to demodulate the detected vibration signals x and y, respectively, to obtain the signals Cx, Sx, Cy, and Sy. Perform low-pass filtering to obtain signals Cx', Sx', Cy', Sy', and then perform secondary combination of signals Cx', Sx', Cy', Sy' to obtain E, R, S signals; 步骤5：建立考虑前向放大系数比值k的测角方程，基于前向放大系数比值k的测角方程，设计扩展卡尔曼滤波器，并对扩展卡尔曼滤波器进行初始参数设置；Step 5: establish an angle measurement equation considering the forward amplification factor ratio k, design an extended Kalman filter based on the angle measurement equation of the forward amplification coefficient ratio k, and set the initial parameters of the extended Kalman filter; 步骤6：将步骤4得到的E、R、S信号作为扩展卡尔曼滤波器的输入，对前向放大系数比值k进行辨识，滤波结束后输出估计的前向放大系数比值
Figure FDA0003064689010000011
Step 6: Use the E, R, and S signals obtained in step 4 as the input of the extended Kalman filter, identify the forward amplification coefficient ratio k, and output the estimated forward amplification coefficient ratio after filtering.
Figure FDA0003064689010000011
 步骤7：将输出的
Figure FDA0003064689010000012
代入步骤5建立的考虑前向放大系数比值k的测角方程，获取前向放大系数不一致时的半球谐振陀螺振型角。Step 7: The output will be
Figure FDA0003064689010000012
Substitute into the angle measurement equation established in step 5 considering the ratio k of the forward amplification factor to obtain the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent. 2.根据权利要求1所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述步骤2中激励电极间隔布置在半球谐振陀螺上。2 . The method for obtaining the mode angle of the hemispherical resonant gyroscope according to claim 1 , wherein the excitation electrodes are arranged on the hemispherical resonant gyroscope at intervals in the step 2 . 3 . 3.根据权利要求1或2所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述步骤4中利用锁相环生成的参考信号vrc、vrs分别对检测到的振动信号x、y进行解调，得到信号Cx、Sx、Cy、Sy，对信号Cx、Sx、Cy、Sy分别进行低通滤波得到信号Cx'、Sx'、Cy'、Sy'，再对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号；具体过程为：3. the hemispherical resonant gyro mode angle acquisition method when a kind of forward amplification factor is inconsistent according to claim 1 and 2, it is characterized in that: in described step 4, utilize the reference signals vrc , vrs that phase-locked loop generates Demodulate the detected vibration signals x and y respectively to obtain the signals Cx, Sx, Cy, and Sy, and perform low-pass filtering on the signals Cx, Sx, Cy, and Sy to obtain the signals Cx', Sx', Cy', Sy ', and then combine the signals Cx', Sx', Cy', Sy' twice to obtain the E, R, S signals; the specific process is: 所述利用锁相环生成的参考信号vrc、vrs分别对检测到的振动信号x、y进行解调，得到信号Cx、Sx、Cy、Sy，表达式为：The reference signals v rc and v rs generated by the phase-locked loop are used to demodulate the detected vibration signals x and y, respectively, to obtain signals Cx, Sx, Cy, and Sy, and the expressions are:
Figure FDA0003064689010000021
Figure FDA0003064689010000021
 将信号Cx、Sx、Cy、Sy经过低通滤波，分别滤除信号Cx、Sx、Cy、Sy中的二倍频，得到信号Cx'、Sx'、Cy'、Sy'；The signals Cx, Sx, Cy, and Sy are subjected to low-pass filtering to filter out the double frequency in the signals Cx, Sx, Cy, and Sy, respectively, to obtain the signals Cx', Sx', Cy', Sy'; 对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号。The signals Cx', Sx', Cy', and Sy' are combined twice to obtain E, R, and S signals. 4.根据权利要求3所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述对信号Cx'、Sx'、Cy'、Sy'进行二次组合，得到E、R、S信号，表达式为：4. The method for obtaining the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent according to claim 3, characterized in that: the signals Cx', Sx', Cy', Sy' are combined twice, Get E, R, S signals, the expression is:
Figure FDA0003064689010000022
Figure FDA0003064689010000022
 5.根据权利要求4所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述参考信号vrc、vrs由正弦信号和余弦信号组成。5 . The method for obtaining the mode angle of the hemispherical resonant gyroscope when the forward amplification coefficients are inconsistent according to claim 4 , wherein the reference signals v rc and v rs are composed of a sine signal and a cosine signal. 6 . 6.根据权利要求5所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述步骤5中建立考虑前向放大系数比值k的测角方程；具体过程为：6. the hemispherical resonant gyro mode angle acquisition method when a kind of forward amplification factor is inconsistent according to claim 5, it is characterized in that: in described step 5, establish the angle measurement equation considering forward amplification factor ratio k; Concrete process for: 建立考虑前向放大系数比值k的测角方程，形式如下：Establish the angle measurement equation considering the ratio k of the forward magnification factor, the form is as follows:
Figure FDA0003064689010000023
Figure FDA0003064689010000023
 其中，k＝ky/kx，kx为0°电极的前向放大系数，ky为45°电极的前向放大系数；θreal为半球谐振陀螺振型角真实值。Among them, k= ky /k x , k x is the forward magnification factor of the 0° electrode, ky is the forward magnification factor of the 45° electrode; θ real is the real value of the mode angle of the hemispherical resonant gyroscope. 7.根据权利要求6所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述步骤5中基于前向放大系数比值k的测角方程，设计扩展卡尔曼滤波器，滤波器选取的模型如下所示：7. the hemispherical resonant gyro mode angle acquisition method when a kind of forward amplification factor is inconsistent according to claim 6, it is characterized in that: in the described step 5, based on the angle measurement equation of forward amplification factor ratio k, the design extended Karl Mann filter, the model selected by the filter is as follows:
Figure FDA0003064689010000031
Figure FDA0003064689010000031
 k(i+1)＝k(i)、c(i+1)＝c(i)是状态方程，k(i)为前向放大系数比值，c(i)为陀螺进动系数，i为第i个时刻；
Figure FDA0003064689010000032
是观测方程，θr为转台转角，v为测量噪声；k(i+1)=k(i), c(i+1)=c(i) is the state equation, k(i) is the ratio of the forward amplification coefficient, c(i) is the gyro precession coefficient, and i is the the i-th moment;
Figure FDA0003064689010000032
is the observation equation, θ r is the rotation angle of the turntable, and v is the measurement noise; 所述步骤5中对扩展卡尔曼滤波器进行初始参数设置；具体过程为：In the step 5, initial parameter setting is performed on the extended Kalman filter; the specific process is: 扩展卡尔曼滤波器启动时进行初始参数设置，给定初始值，令
Figure FDA0003064689010000033
P0|0＝I；Initial parameter settings are made when the extended Kalman filter is started, given the initial value, let
Figure FDA0003064689010000033
P 0|0 =I; 式中，
Figure FDA0003064689010000034
为前向放大系数比值k的初始估计值，
Figure FDA0003064689010000035
为进动系数c的初始估计值，P0|0为估计误差协方差矩阵的初始值。In the formula,
Figure FDA0003064689010000034
is the initial estimated value of the forward amplification factor ratio k,
Figure FDA0003064689010000035
is the initial estimated value of the precession coefficient c, and P 0|0 is the initial value of the estimated error covariance matrix. 8.根据权利要求7所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述步骤6中将步骤4得到的E、R、S信号作为扩展卡尔曼滤波器的输入，对前向放大系数比值k进行辨识，滤波结束后输出估计的前向放大系数比值
Figure FDA0003064689010000036
辨识具体步骤如下：8. the hemispherical resonant gyro mode angle acquisition method when the forward amplification factor is inconsistent according to claim 7, is characterized in that: in the described step 6, the E, R, S signals obtained in step 4 are used as extended Kalman The input of the filter, the forward amplification coefficient ratio k is identified, and the estimated forward amplification coefficient ratio is output after filtering.
Figure FDA0003064689010000036
The specific steps for identification are as follows: S1：对下一时刻的状态估计值进行预测S1: Predict the state estimate value at the next moment
Figure FDA0003064689010000037
Figure FDA0003064689010000037
Figure FDA0003064689010000038
Figure FDA0003064689010000038
 式中，
Figure FDA0003064689010000039
为前向放大系数比值k第i个时刻的先验估计值，
Figure FDA00030646890100000310
为前向放大系数比值k第i-1时刻的估计值，
Figure FDA00030646890100000311
为进动系数c第i个时刻的先验估计值，
Figure FDA00030646890100000312
为进动系数c第i-1时刻的估计值；In the formula,
Figure FDA0003064689010000039
is the a priori estimate of the forward amplification factor ratio k at the ith moment,
Figure FDA00030646890100000310
is the estimated value of the forward amplification coefficient ratio k at the i-1th moment,
Figure FDA00030646890100000311
is the a priori estimate of the ith moment of the precession coefficient c,
Figure FDA00030646890100000312
is the estimated value of the precession coefficient c at the i-1th moment; S2：对下一时刻的估计误差协方差进行预测：S2: Predict the estimated error covariance at the next moment: Pi|i-1＝Pi-1|i-1 P i|i-1 =P i-1|i-1 式中，Pi|i-1为估计误差协方差矩阵第i时刻的预测值，Pi-1|i-1为估计误差协方差矩阵第i-1时刻的值；In the formula, P i|i-1 is the predicted value of the estimated error covariance matrix at time i, and P i-1|i-1 is the value of the estimated error covariance matrix at time i-1; S3：判断是否还有信号E、R和S输入扩展卡尔曼滤波器，若有则跳到S4，若无则跳到步骤S9；S3: judge whether there are still signals E, R and S input to the extended Kalman filter, if so, skip to S4, if not, skip to step S9; S4：对下一时刻的测量矩阵进行预测：S4: Predict the measurement matrix at the next moment: 令
Figure FDA0003064689010000041
make
Figure FDA0003064689010000041
Figure FDA0003064689010000042
Figure FDA0003064689010000042
 式中，b为中间变量，Ci为第i个时刻的测量矩阵；In the formula, b is the intermediate variable, and C i is the measurement matrix at the ith moment; S5：对下一时刻的测量估计值进行预测：S5: Predict the measurement estimate at the next moment:
Figure FDA0003064689010000043
Figure FDA0003064689010000043
 其中，
Figure FDA0003064689010000044
为转台转角的估计值；in,
Figure FDA0003064689010000044
is the estimated value of the turntable rotation angle; S6：对下一时刻的状态增益矩阵进行预测：S6: Predict the state gain matrix at the next moment: Ki＝Pi|i-1*Ci T*(Ci*Pi|i-1*Ci T+Q)-1 K i =P i|i-1 *C i T *(C i *P i|i-1 *C i T +Q) -1 式中，Q为噪声v的协方差；*为乘号，Ki为第i个时刻的状态增益矩阵，T为转置；In the formula, Q is the covariance of the noise v; * is the multiplication sign, K i is the state gain matrix at the ith moment, and T is the transpose; S7：对下一时刻的状态估计值进行更新：S7: Update the state estimate value at the next moment:
Figure FDA0003064689010000045
Figure FDA0003064689010000045
 式中，
Figure FDA0003064689010000046
为前向放大系数比值k第i个时刻的后验估计值；In the formula,
Figure FDA0003064689010000046
is the posterior estimated value of the ith moment of the forward amplification coefficient ratio k; S8：对下一时刻的估计误差协方差进行更新，然后跳转到S1；S8: Update the estimated error covariance at the next moment, and then jump to S1; Pi|i＝(I-KiCi)*Pi|i-1 P i|i =(IK i C i )*P i|i-1 式中，Pi|i为估计误差协方差矩阵第i个时刻的值，I为单位矩阵；In the formula, P i|i is the value at the ith moment of the estimated error covariance matrix, and I is the identity matrix; S9：滤波结束，输出估计的前向放大系数比值
Figure FDA0003064689010000051
S9: The filtering is over, and the estimated forward amplification factor ratio is output
Figure FDA0003064689010000051
 9.根据权利要求8所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述步骤7中将输出的
Figure FDA0003064689010000052
代入步骤5建立的考虑前向放大系数比值k的测角方程，获取前向放大系数不一致时的半球谐振陀螺振型角；9. The method for obtaining the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent according to claim 8, wherein: in the step 7, the output
Figure FDA0003064689010000052
Substitute into the angle measurement equation established in step 5 considering the ratio k of the forward amplification factor, and obtain the mode angle of the hemispherical resonant gyroscope when the forward amplification factor is inconsistent; 表达式为：The expression is:
Figure FDA0003064689010000053
Figure FDA0003064689010000053
 式中，θguji为半球谐振陀螺振型角的估计值。In the formula, θ guji is the estimated value of the mode shape angle of the hemispherical resonant gyroscope. 10.根据权利要求9所述一种前向放大系数不一致时的半球谐振陀螺振型角获取方法，其特征在于：所述前向放大系数不一致由前向放大电路误差、谐振子电极极板面积误差、谐振子电极极板间距误差、谐振子安装偏差中的一种或多种导致；10. The method for obtaining the mode angle of hemispherical resonant gyro when the forward amplification factor is inconsistent according to claim 9, wherein the inconsistent forward amplification factor is determined by the error of the forward amplification circuit, the area of the resonator electrode plate Caused by one or more of error, resonator electrode plate spacing error, and resonator installation deviation; 所述多种为2种、3种或4种。The plurality is 2, 3 or 4.
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CN119147012A (en) * 2024-11-20 2024-12-17 中国船舶集团有限公司第七〇七研究所 An inertial navigation initial alignment method and system

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