CN101158582A

CN101158582A - A MEMS gyroscope differential measurement method

Info

Publication number: CN101158582A
Application number: CNA2007101763382A
Authority: CN
Inventors: 房建成; 张海鹏; 冯浩楠; 蒋颜玮; 马艳武; 谭丽伟
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2007-10-25
Filing date: 2007-10-25
Publication date: 2008-04-09
Anticipated expiration: 2027-10-25
Also published as: CN100559123C

Abstract

A differential measurement method for MEMS gyroscopes. Two MEMS gyroscopes with similar environmental sensitivity characteristics are selected to form a gyroscope differential pair. The measured rotation axis is parallel and sensitive to the same external input angular velocity. Through testing and calibration experiments, the main parameters of the two gyroscopes and the ratio of the environmental coefficient between the two are determined. In practical applications, the formula is calculated in real time according to the input angular velocity. Calculate the high-precision input angular velocity value. The present invention selects the gyroscopes of the same type and the same processing technology, utilizes the similarity of the response characteristics of the same type of MEMS gyroscopes to environmental factors, and the characteristics of differential installation to suppress output drift, and improves the performance of MEMS gyroscopes by processing the output data of the gyroscopes. The measurement accuracy of the instrument. The invention is applicable to the application fields of various MEMS gyroscopes, and is especially suitable for occasions requiring low cost of the MEMS gyroscope and high output precision of the system.

Description

A MEMS gyroscope differential measurement method

技术领域technical field

本发明属于导航、制导与控制技术领域，特别涉及MEMS振动陀螺仪的应用技术，适用于各种低成本、微小型MEMS振动陀螺仪。The invention belongs to the technical field of navigation, guidance and control, in particular to the application technology of MEMS vibrating gyroscopes, and is suitable for various low-cost, micro-miniature MEMS vibrating gyroscopes.

背景技术Background technique

在科学技术的许多领域，陀螺仪发挥着重要的作用。陀螺仪是一种测量角速度的传感器，其示意图如图1和图2所示，其中图1表示陀螺仪的立体示意图，图2表示陀螺仪的平面示意图，其敏感的角速度的正方向根据右手螺旋原则确定。陀螺仪可以直接测量作用在其敏感轴OA上的外界输入角速度ω_i，也可以通过积分或微分等运算间接测量出其敏感轴转过的角度θ或角加速度β。Gyroscopes play an important role in many fields of science and technology. A gyroscope is a sensor for measuring angular velocity. Its schematic diagrams are shown in Figure 1 and Figure 2. Figure 1 shows a three-dimensional schematic diagram of a gyroscope, and Figure 2 shows a schematic plan view of a gyroscope. The positive direction of its sensitive angular velocity is according to the right-handed spiral The principle is determined. The gyroscope can directly measure the external input angular velocity ω _i acting on its sensitive axis OA, and can also indirectly measure the angle θ or angular acceleration β of its sensitive axis through integral or differential operations.

目前测量空间某条轴角速度的具体方法，都是使陀螺仪敏感轴OA与被测转动轴AX方向平行，并将陀螺仪与被测转动轴固定在一起，如图3所示，当被测转动轴以角速度ω转动时，转动角速度ω就会激励陀螺仪敏感轴OA，使陀螺仪输出代表输入角速度ω的模拟量。陀螺仪的一个典型应用就是组成惯性导航系统的核心部件惯性测量单元。惯性测量单元是导航、制导与控制系统中的一种非常重要的设备。它由三只陀螺仪和三只加速度计组成，按照惯性导航原理的要求，三只陀螺仪的敏感轴在空间两两互相垂直并且分别与对应的三个载体坐标轴平行，测量三个载体坐标轴的输入角速度。惯性测量单元工作时不依赖外界信息，也不向外界辐射能量，不易受到干扰，这一独特优点，使其成为运载体，尤其是航天、航空和航海领域中运载体的一种广泛使用的主要导航方法。At present, the specific method for measuring the angular velocity of a certain axis in space is to make the sensitive axis OA of the gyroscope parallel to the direction of the measured rotation axis AX, and fix the gyroscope and the measured rotation axis together, as shown in Figure 3. When the measured When the rotating shaft rotates at the angular velocity ω, the rotating angular velocity ω will excite the sensitive axis OA of the gyroscope, so that the output of the gyroscope represents the analog quantity of the input angular velocity ω. A typical application of gyroscopes is the inertial measurement unit, the core component of an inertial navigation system. Inertial measurement unit is a very important device in navigation, guidance and control system. It consists of three gyroscopes and three accelerometers. According to the requirements of the inertial navigation principle, the sensitive axes of the three gyroscopes are perpendicular to each other in space and parallel to the corresponding three carrier coordinate axes, and measure the three carrier coordinates. The input angular velocity of the axis. The inertial measurement unit does not rely on external information, does not radiate energy to the outside world, and is not easily disturbed. This unique advantage makes it a widely used main carrier, especially in the fields of aerospace, aviation and navigation. navigation method.

随着科学技术的发展，从工程角度看，更小的器件、更小的结构单元甚至更小的分系统，在许多方面表现出了独特的优势，能满足很多特殊场合和功能的要求。所以，近年来，随着微型制造技术和MEMS技术的发展，新一代MEMS陀螺仪迅速发展起来，它们体积很小、重量很轻、成本很低，具有传统陀螺仪许多无可比拟的优点。由MEMS陀螺仪组成的微小型惯性测量单元，满足了以航天、航空和航海为代表的领域中出现的一大批小型化运载体的非常迫切和突出的需求，例如小型化飞机翼展往往不足一米，有的甚至只有手掌般大，它内部的空间和能够承受的载荷非常有限，这就要求它们的惯性测量单元体积很小、重量很轻。With the development of science and technology, from an engineering point of view, smaller devices, smaller structural units and even smaller subsystems have shown unique advantages in many aspects and can meet the requirements of many special occasions and functions. Therefore, in recent years, with the development of micro-manufacturing technology and MEMS technology, a new generation of MEMS gyroscopes has developed rapidly. They are small in size, light in weight, and low in cost, and have many incomparable advantages of traditional gyroscopes. The micro-miniature inertial measurement unit composed of MEMS gyroscopes meets the very urgent and outstanding needs of a large number of miniaturized carriers in the fields represented by aerospace, aviation and navigation. For example, the wingspan of miniaturized aircraft is often less than one meters, some are even as big as a palm, and the space inside and the load it can bear are very limited, which requires their inertial measurement units to be small in size and light in weight.

虽然，MEMS陀螺仪拥有许多无可比拟的优点，但是按照目前陀螺仪的传统应用方法，依然具有很大的缺点。Although MEMS gyroscopes have many incomparable advantages, according to the current traditional application methods of gyroscopes, they still have great disadvantages.

其一，利用单个MEMS陀螺仪测量某条轴的输入角速度，就难以避免其工作原理、制造工艺和应用方式给MEMS陀螺仪带来的很大的输入角速度测量误差。MEMS陀螺仪的测量误差大致可分为两部分，一部分为确定性误差，一部分为不确定性误差。其中，确定性误差可以利用陀螺仪测试、标定、建模和补偿等处理方法减少其影响，但是不确定误差的影响很难被消除。MEMS陀螺仪的核心敏感元件以及其处理电路部分很容易受到复杂的周围环境的影响，例如温度、电磁、震动、甚至辐射、重力异常、湿度、气压等都可能会影响陀螺仪敏感元件和处理电路的特性，从而影响测量的输出精度。这些影响陀螺仪特性的环境因素，大都不容易准确量化和研究，而且这些因素引起的误差会互相耦合和叠加，使得总误差缺少规律性而表现出较强的随机性，即使严格利用标准的陀螺仪测试、标定、建模和补偿等处理方法处理这些环境因素，对陀螺仪精度的提高也不够明显。First, if a single MEMS gyroscope is used to measure the input angular velocity of a certain axis, it is difficult to avoid the large input angular velocity measurement error brought to the MEMS gyroscope by its working principle, manufacturing process and application method. The measurement error of MEMS gyroscope can be roughly divided into two parts, one part is deterministic error and the other part is uncertain error. Among them, the impact of deterministic errors can be reduced by using gyroscope testing, calibration, modeling and compensation methods, but the impact of uncertain errors is difficult to eliminate. The core sensitive components of the MEMS gyroscope and its processing circuit are easily affected by the complex surrounding environment, such as temperature, electromagnetic, vibration, even radiation, abnormal gravity, humidity, air pressure, etc. may affect the gyroscope sensitive components and processing circuit characteristics, thereby affecting the output accuracy of the measurement. Most of these environmental factors that affect the characteristics of the gyroscope are not easy to accurately quantify and study, and the errors caused by these factors will be coupled and superimposed on each other, making the total error lack regularity and show strong randomness, even if the standard gyroscope is strictly used The processing methods such as instrument testing, calibration, modeling and compensation to deal with these environmental factors are not obvious enough to improve the accuracy of the gyroscope.

其二，由于目前MEMS应用方法受环境因素的影响太大，要想进一步提高惯性器件和导航系统的精度，只有对MEMS陀螺仪的加工工艺提出更高的要求，而改善加工工艺，周期长，难度大，复杂性高，风险大。Second, because the current MEMS application methods are too affected by environmental factors, in order to further improve the accuracy of inertial devices and navigation systems, only higher requirements are put forward for the processing technology of MEMS gyroscopes, and the improvement of processing technology requires a long cycle. Difficulty, complexity, and risk.

总之，目前利用单个MEMS陀螺仪测量某条轴的转动角速度的方法，测量精度会受到周围复杂环境因素的严重影响，而且要想降低这种影响，难度很大，成本很高。In short, the current method of using a single MEMS gyroscope to measure the rotational angular velocity of a certain axis, the measurement accuracy will be seriously affected by the surrounding complex environmental factors, and it is very difficult and costly to reduce this effect.

发明内容Contents of the invention

本发明的目的是：克服现有利用单个MEMS陀螺仪测量某轴转动角速度方法的不足，提供一种利用两个MEMS陀螺仪差测量方法，测量同一转动角速度、提高测量精度的方法。The purpose of the present invention is: to overcome the shortcomings of the existing method of measuring the rotational angular velocity of a certain shaft by using a single MEMS gyroscope, and provide a method for measuring the same rotational angular velocity by using two MEMS gyroscopes to measure the same rotational angular velocity and improve the measurement accuracy.

本发明的技术解决方案是：一种MEMS陀螺仪的差分测量方法，挑选两个环境敏感特性相似性接近的MEMS陀螺仪组成陀螺仪差分对，通过安装使两个MEMS陀螺仪的角速度敏感轴方向相反，并均与同一条被测转动轴平行，敏感同一个外界输入角速度，通过测试、标定试验，确定两个陀螺仪的主要参数以及二者之间的环境系数比值，在实际应用时，按照输入角速度实时解算公式，解算出高精度的输入角速度值。The technical solution of the present invention is: a differential measurement method for MEMS gyroscopes, select two MEMS gyroscopes with similar environmental sensitivity characteristics to form a gyroscope differential pair, and make the angular velocity sensitive axis direction of the two MEMS gyroscopes On the contrary, they are both parallel to the same measured rotation axis and sensitive to the same external input angular velocity. Through testing and calibration experiments, the main parameters of the two gyroscopes and the ratio of the environmental coefficient between the two are determined. In practical applications, according to Input the real-time calculation formula of angular velocity, and calculate the high-precision input angular velocity value.

所述的敏感特性相似性的判定步骤如下：The steps for determining the similarity of sensitive characteristics are as follows:

(1)把待测陀螺仪分为两批，一批正向安装，另一批反向安装，同时进行速率实验，假设正向安装的陀螺仪个数为u个，反向安装的陀螺仪个数为v个，按时间序列t采集试验数据y(t)；(1) Divide the gyroscopes to be tested into two batches, one batch is installed in the forward direction, and the other batch is installed in the reverse direction, and the rate experiment is carried out at the same time, assuming that the number of gyroscopes installed in the forward direction is The number is v, and the test data y(t) is collected according to the time series t;

(2)分别以n阶多项式y(t)＝a₀+a₁t+a₂t²+a₃t³+…+a_n-1t^n-1+a_ntⁿ拟合各个被测陀螺仪的实验数据，得出每个陀螺仪的各阶系数a₀，a₁，a₂，…，a_n-1，a_n；(2) Fit each measured value with n-order polynomial y(t)=a ₀ +a ₁ t+a ₂ t ² +a ₃ t ³ +…+a _n-1 t ^n-1 +a _n t ⁿ From the experimental data of the gyroscope, the coefficients a ₀ , a ₁ , a ₂ ,..., a _n-1 , a _n of each gyroscope are obtained;

(3)将每个正向陀螺仪和每个反向陀螺仪都一一对应共组成u×v个陀螺仪对；(3) Each forward gyroscope and each reverse gyroscope are in one-to-one correspondence to form u×v gyroscope pairs;

(4)以陀螺仪对中的正向陀螺仪的各级拟合系数对应除以反向陀螺仪的各级拟合系数，得出n个拟合系数比值数据，然后求出这n个拟合系数比值数据的方差，将所有u×v个陀螺仪对都进行上述操作，共求出u×v个方差值；(4) Divide the fitting coefficients of the forward gyroscopes in the gyroscope pair by the fitting coefficients of the reverse gyroscopes to obtain n fitting coefficient ratio data, and then calculate the n fitting coefficients Combine the variance of the coefficient ratio data, perform the above operations on all u×v gyroscope pairs, and obtain u×v variance values in total;

(5)u×v个方差中，方差值越小的陀螺仪对，其相似性越接近。(5) Among the u×v variances, the smaller the variance value is, the closer the similarity is to the gyroscope pair.

本发明的原理是：一种MEMS陀螺仪的差分应用方法，挑选两个环境敏感特性相似性接近的MEMS陀螺仪组成陀螺仪差分对，如图4所示，通过安装使两个MEMS陀螺仪的角速度敏感轴OA₁和OA₂方向相反，并均与同一条被测转动轴AX平行，敏感同一个外界输入角速度ω。在图4中，称敏感轴与外界输入角速度同向的陀螺仪为正向陀螺仪，称敏感轴与外界输入角速度反向的陀螺仪为负向陀螺仪。组成陀螺仪差分对的两个MEMS陀螺仪，一般是在同一批MEMS陀螺仪中挑选出来的。同一批MEMS陀螺仪是应用同种原理、在同种加工工艺条件下制作出来的，其环境敏感特性比较相似。然后，利用陀螺仪测试实验精确的测试、标定同一批MEMS陀螺仪，相互比较，挑选出环境敏感特性相似性接近的陀螺仪组成陀螺仪差分对。这样就满足了差分应用方法的要求。The principle of the present invention is: a differential application method of a MEMS gyroscope, select two MEMS gyroscopes with similar environmental sensitive characteristics to form a gyroscope differential pair, as shown in Figure 4, make the two MEMS gyroscopes The angular velocity sensitive axes OA ₁ and OA ₂ have opposite directions, are parallel to the same measured rotation axis AX, and are sensitive to the same external input angular velocity ω. In Figure 4, the gyroscope whose sensitive axis is in the same direction as the external input angular velocity is called a positive gyroscope, and the gyroscope whose sensitive axis is opposite to the external input angular velocity is called a negative gyroscope. The two MEMS gyroscopes that make up the differential pair of gyroscopes are generally selected from the same batch of MEMS gyroscopes. The same batch of MEMS gyroscopes are manufactured using the same principle and under the same processing conditions, and their environmental sensitivity characteristics are relatively similar. Then, use the gyroscope test experiment to accurately test and calibrate the same batch of MEMS gyroscopes, compare them with each other, and select gyroscopes with close similarity in environmental sensitivity characteristics to form a gyroscope differential pair. This satisfies the requirements of the differential application method.

MEMS陀螺仪中温度是环境影响因素中最主要的误差源。实验发现，温度的变化会使MEMS陀螺仪的输出电压发生很大的变化。这主要是因为MEMS陀螺仪的敏感元件是由微加工工艺制作而成，体积非常小，厚度仅有数个微米，长度和宽度也不过几个毫米，温度变化必然引起的热胀冷缩，会使MEMS陀螺仪的敏感元件发生变形，并改变其内部应力分布，从而改变MEMS陀螺仪的动力学特性；另外，温度的变化还会严重的影响信号处理电路的特性，使其内部集成电路的电子元件特性发生温度漂移等变化，从而影响MEMS陀螺仪的电学特性。一般的，当温度升高时，MEMS陀螺仪的输出电压也随之升高，而且，在一定的温度范围里，电压随温度的变化可近似为线性关系。当然也有个别MEMS陀螺仪在微加工过程中形成的结构，使其在温度升高时，输出电压随着降低，对他们则需要选择同样的随着温度升高而输出电压降低的MEMS陀螺仪与之配对，组成陀螺仪差分对。其他误差源的影响分析类似。Temperature is the most important source of error among environmental factors in MEMS gyroscopes. Experiments have found that changes in temperature will greatly change the output voltage of the MEMS gyroscope. This is mainly because the sensitive elements of the MEMS gyroscope are made of micro-machining technology, the volume is very small, the thickness is only a few microns, and the length and width are only a few millimeters. The sensitive components of the MEMS gyroscope deform and change its internal stress distribution, thereby changing the dynamic characteristics of the MEMS gyroscope; in addition, changes in temperature will seriously affect the characteristics of the signal processing circuit, making the electronic components of the internal integrated circuit Changes such as temperature drift in the characteristics will affect the electrical characteristics of the MEMS gyroscope. Generally, when the temperature rises, the output voltage of the MEMS gyroscope also rises accordingly, and, within a certain temperature range, the variation of voltage with temperature can be approximately linear. Of course, there are also individual MEMS gyroscopes formed in the micromachining process, so that when the temperature rises, the output voltage decreases. For them, it is necessary to choose the same MEMS gyroscope and the same MEMS gyroscope whose output voltage decreases as the temperature rises. They are paired to form a differential pair of gyroscopes. The impact analysis of other error sources is similar.

根据陀螺仪的工作原理和测试原理，可得出MEMS陀螺仪输出电压U与输入角速度ω之间的关系式，将输出电压U和可以测试、标定和补偿的n个确定性误差项Wi放在等式的左边，将未知的输入角速度ω和难以测试、标定、补偿的不确定性误差项、以及噪声项放在等式的右边，则等式形式如下：According to the working principle and testing principle of the gyroscope, the relationship between the output voltage U of the MEMS gyroscope and the input angular velocity ω can be obtained, and the output voltage U and n deterministic error items Wi that can be tested, calibrated and compensated are placed in the On the left side of the equation, put the unknown input angular velocity ω and the uncertainty error term that is difficult to test, calibrate, and compensate, and the noise term on the right side of the equation, then the equation is as follows:

$U u - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{wi wi} \cdot \cdot {W W}_{i i} = = K K \cdot \cdot ω ω + + {K K}_{d d} \cdot &Center Dot; D D. + + N N - - - - - - ((11))$

式中：In the formula:

U——某测试时刻陀螺仪的输出电压值U——the output voltage value of the gyroscope at a certain test moment

W_i——测试时刻第i个确定性误差项，i＝1，...，nW _i ——the i-th deterministic error term at the test moment, i=1,...,n

K_wi——第i个确定性误差项的系数，i＝1，...，nK _wi —coefficient of the i-th deterministic error term, i=1,...,n

m——可测试、标定和补偿的确定性误差项的个数m - the number of deterministic error terms that can be tested, calibrated and compensated

ω——测试时刻的输入角速度ω——Input angular velocity at the test moment

K——此陀螺仪的标度因数K——The scale factor of this gyroscope

D——测试时刻不确定性误差项影响量的总和D——The sum of the influence quantity of the uncertainty error term at the time of testing

K_d——不确定性总误差系数，即环境系数K _d ——the total error coefficient of uncertainty, that is, the environmental coefficient

N——测试时的测量噪声N——Measurement noise during test

式(1)等式左边各个参数值均可通过标定等实验方法得到，其中，U为陀螺仪的输出电压，可以由数模转换电路直接得出；W_i可以由相应的传感器测量得出，例如，与加速度有关项中的加速度可由加速度的输出确定；K_wi可以按照测试标准测试并标定出来。式(1)等式右边的陀螺标度因数K可以按照测试标准测试并标定出来；ω为需要精确求取的未知量；D是不确定性误差项影响量的总和，目前尚无有效的手段将其精确量化，是难以把握、难以通过现有手段测试、标定、建模、补偿的量，也是本发明针对的对象；由于D难以量化，使得K_d也难以量化，测量过程中仅能确定K_d·D的值，无法单独确定D或K_d的值；N为测量噪声，近似为白噪声，其数学期望值近似为零，当将一段时间中的大量测量值平均后，N的影响基本可以消除掉。Each parameter value on the left side of the equation (1) can be obtained by calibration and other experimental methods, where U is the output voltage of the gyroscope, which can be directly obtained by the digital-to-analog conversion circuit; W _i can be obtained by measuring the corresponding sensor, For example, the acceleration in items related to acceleration can be determined by the output of the acceleration; K _wi can be tested and calibrated according to the test standard. The gyroscope scale factor K on the right side of the equation (1) can be tested and calibrated according to the test standard; ω is the unknown quantity that needs to be accurately obtained; D is the sum of the influence quantities of the uncertainty error items, and there is no effective means at present Its precise quantification is difficult to grasp, it is difficult to test, calibrate, model, and compensate through existing means, and it is also the object of the present invention; because D is difficult to quantify, K _d is also difficult to quantify, and it can only be determined during the measurement process. The value of K _d D cannot be determined independently of the value of D or K _d ; N is measurement noise, which is approximately white noise, and its mathematical expectation value is approximately zero. When a large number of measured values are averaged over a period of time, the influence of N is basically can be eliminated.

根据右手螺旋原则，如图4所示，当沿着被测转动轴AX有一个输入角速度ω时，则正向陀螺仪的敏感轴OA₁感受到的输入角速度为+ω，而负向陀螺仪的敏感轴OA₂感受到的输入角速度为-ω。为了区别两个陀螺仪的参数，给正向陀螺仪参数标注下标1，给负向陀螺仪参数标注下标2。则根据式(1)得出正向陀螺仪的输入输出关系满足：According to the right-handed spiral principle, as shown in Figure 4, when there is an input angular velocity ω along the measured rotation axis AX, the input angular velocity felt by the sensitive axis OA ₁ of the positive gyroscope is +ω, while the negative gyroscope The input angular velocity felt by the sensitive axis OA ₂ is -ω. In order to distinguish the parameters of the two gyroscopes, the subscript 1 is marked for the positive gyroscope parameters, and the subscript 2 is marked for the negative gyroscope parameters. According to formula (1), the input-output relationship of the forward gyroscope satisfies:

${U u}_{11} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot &Center Dot; {W W}_{11 i i} = = {K K}_{11} \cdot &Center Dot; ω ω + + {K K}_{11 d d} \cdot &Center Dot; {D D.}_{11} + + {N N}_{11} - - - - - - ((22))$

负向陀螺仪的输入输出关系满足：The input-output relationship of the negative gyroscope satisfies:

${U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 i i} = = {K K}_{22} \cdot &Center Dot; ((- - ω ω)) + + {K K}_{22 d d} \cdot &Center Dot; {D D.}_{22} + + {N N}_{22} - - - - - - ((33))$

由于正向陀螺仪和负向陀螺仪在空间距离很近，而且本身体积很小，又固定在一起感受同一个被测转动轴上输入的角速度，所以，有足够的理由近似认为两个陀螺仪所处的外界环境相同，即式(2)中的不确定性误差总量D₁与式(3)中的不确定性误差总量D₂相同，假设为D，则：Since the positive gyroscope and the negative gyroscope are very close in space, and their volume is small, and they are fixed together to feel the angular velocity input on the same measured rotation axis, there are sufficient reasons to approximate the two gyroscopes as The external environment is the same, that is, the total amount of uncertainty error D ₁ in formula (2) is the same as the total amount of uncertainty error D ₂ in formula (3), assuming D, then:

D₁＝D₂＝D (4)D ₁ =D ₂ =D (4)

由式(2)得：From formula (2):

${K K}_{11 d d} \cdot \cdot {D D.}_{11} = = {U u}_{11} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot \cdot {W W}_{11 i i} - - {K K}_{11} \cdot \cdot ω ω - - {N N}_{11} - - - - - - ((55))$

由式(3)得：From formula (3):

${K K}_{22 d d} \cdot &Center Dot; {D D.}_{22} = = {U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 i i} + + {K K}_{22} \cdot \cdot ω ω - - {N N}_{22} - - - - - - ((66))$

在某个已知输入角速度ω下，取一段时间内m个数据作平均，以去除噪声N的影响，U_1j、U_2j分别表示正负陀螺仪第j个电压采样值，N_1j、N_2j分别表示正负陀螺仪第j个采样数据所含噪声，j＝1...m。由式(5)和式(6)得：Under a certain known input angular velocity ω, take m data for a period of time as an average to remove the influence of noise N, U _1j , U _2j represent the positive and negative gyroscope j-th voltage sampling values respectively, N _1j , N _2j Respectively represent the noise contained in the jth sampling data of the positive and negative gyroscopes, j=1...m. From formula (5) and formula (6):

${\overset{- -}{K K}}_{11 d d} = = \frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {K K}_{11 d d} \cdot \cdot {D D.}_{11} = = \frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{11} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot \cdot {W W}_{11 i i} - - {K K}_{11} \cdot \cdot ω ω - - {N N}_{11})) - - - - - - ((77))$

${\overset{- -}{K K}}_{22 d d} = = \frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {K K}_{22 d d} \cdot \cdot {D D.}_{22} = = \frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{22 wi wi} \cdot \cdot {W W}_{22 i i} - - {K K}_{22} \cdot \cdot ω ω - - {N N}_{22})) - - - - - - ((88))$

由环境系数定义可以得到：According to the definition of environmental coefficient, we can get:

$K_{1 d} \approx {\bar{K}}_{1 d}$ $K_{2 d} \approx {\bar{K}}_{2 d}$ (9) $K_{1 d} \approx {\bar{K}}_{1 d}$ $K_{2 d} \approx {\bar{K}}_{2 d}$ (9)

环境系数比值为：The environmental factor ratio is:

${K K}_{bd bd} = = \frac{{K K}_{11 d d}}{{K K}_{22 d d}} \approx \approx \frac{{\overset{- -}{K K}}_{11 d d}}{{\overset{- -}{K K}}_{22 d d}} - - - - - - ((1010))$

考虑到式(4)则有：Considering formula (4), there are:

${K K}_{bd bd} = = \frac{{K K}_{11 d d}}{{K K}_{22 d d}} \approx \approx \frac{{\overset{- -}{K K}}_{11 d d}}{{\overset{- -}{K K}}_{22 d d}} = = \frac{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {K K}_{11 d d} \cdot &Center Dot; D D.}{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {K K}_{22 d d} \cdot &Center Dot; D D.} = = \frac{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {K K}_{11 d d} \cdot &Center Dot; {D D.}_{11}}{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {K K}_{22 d d} \cdot &Center Dot; {D D.}_{22}}$

$= = \frac{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{11 j j} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot &Center Dot; {W W}_{11 i i} - - {K K}_{11} \cdot &Center Dot; ω ω - - {N N}_{11 j j}))}{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{22 j j} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 I I} + + {K K}_{22} \cdot &Center Dot; ω ω - - {N N}_{22 j j}))} - - - - - - ((1111))$

$= = \frac{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{11 j j} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot &Center Dot; {W W}_{11 i i} - - {K K}_{11} \cdot &Center Dot; ω ω)) - - \frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {N N}_{11 j j}}{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{22 j j} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 i i} + + {K K}_{22} \cdot &Center Dot; ω ω)) - - \frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {N N}_{22 j j}}$

考虑到N为测量噪声，近似为白噪声，其数学期望值近似为零，则有：Considering that N is the measurement noise, which is approximately white noise, and its mathematical expectation value is approximately zero, then:

$\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {N N}_{11 j j} = = \frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} {N N}_{22 j j} = = 00 - - - - - - ((1212))$

则有：Then there are:

${K K}_{bd bd} = = \frac{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{11 j j} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot \cdot {W W}_{11 i i} - - {K K}_{11} \cdot \cdot ω ω))}{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{22 j j} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 i i} + + {K K}_{22} \cdot &Center Dot; ω ω))} - - - - - - ((1313))$

在输入角速度ω已知的测试试验中，等式(13)右边各个参数均可确定，故利用上述方法可以测量出环境系数比值 $K_{bd} = \frac{K_{1 d}}{K_{2 d}}$ 的大小。In the test experiment where the input angular velocity ω is known, each parameter on the right side of equation (13) can be determined, so the environmental coefficient ratio can be measured by the above method $K_{bd} = \frac{K_{1 d}}{K_{2 d}}$ the size of.

在陀螺仪实际工作应用时，输入角速度ω在不停的变化，系统最主要的任务就是尽量精确的确定输入角速度ω，由式(10)得：In the practical application of the gyroscope, the input angular velocity ω is constantly changing, and the most important task of the system is to determine the input angular velocity ω as accurately as possible. From formula (10):

K_1d＝K_bd·K_2d (14)K _1d =K _bd ·K _2d (14)

故将式(3)两端同时乘以K_bd，则得：Therefore, multiply both ends of formula (3) by K _bd , then:

${K K}_{bd bd} \cdot \cdot {U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{bd bd} \cdot &Center Dot; {K K}_{22 wi wi} \cdot \cdot {W W}_{22 i i} = = {K K}_{bd bd} \cdot \cdot {K K}_{22} \cdot &Center Dot; ((- - ω ω)) + + {K K}_{bd bd} \cdot \cdot {K K}_{22 d d} \cdot &Center Dot; {D D.}_{22} + + {K K}_{bd bd} \cdot &Center Dot; {N N}_{22} - - - - - - ((1515))$

以式(2)减去式(15)得：Subtract formula (15) from formula (2) to get:

$(({U u}_{11} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot \cdot {W W}_{11 i i})) - - (({K K}_{bd bd} \cdot &Center Dot; {U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{bd bd} \cdot &Center Dot; {K K}_{22 wi wi} \cdot \cdot {W W}_{22 i i})) - - - - - - ((1616))$

$= = (({K K}_{11} + + {K K}_{bd bd} \cdot &Center Dot; {K K}_{22})) \cdot &Center Dot; ω ω + + (({K K}_{11 d d} \cdot \cdot {D D.}_{11} - - {K K}_{bd bd} \cdot \cdot {K K}_{22 d d} \cdot \cdot {D D.}_{22})) + + (({N N}_{11} - - {K K}_{bd bd} \cdot \cdot {N N}_{22}))$

考虑到式(4)的关系，则上式化为：Considering the relationship of formula (4), the above formula becomes:

$(({U u}_{11} - - {Σ Σ}_{i i = = 11}^{N N} {K K}_{11 wi wi} \cdot \cdot {W W}_{11 i i})) - - (({k k}_{bd bd} \cdot \cdot {U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{bd bd} \cdot &Center Dot; {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 i i})) - - - - - - ((1717))$

$= = (({K K}_{11} + + {K K}_{bd bd} \cdot &Center Dot; {K K}_{22})) \cdot &Center Dot; ω ω + + (({K K}_{11 d d} - - {K K}_{bd bd} \cdot &Center Dot; {K K}_{22 d d})) \cdot &Center Dot; D D. + + (({N N}_{11} - - {K K}_{bd bd} \cdot &Center Dot; {N N}_{22}))$

又考虑到式(14)的关系，则上式中D的系数等于0，上式化为：Considering the relationship of formula (14), the coefficient of D in the above formula is equal to 0, and the above formula becomes:

$(({U u}_{11} - - {Σ Σ}_{l l = = 11}^{n no} {K K}_{11 wi wi} \cdot &Center Dot; {W W}_{11 i i})) - - (({K K}_{bd bd} \cdot &Center Dot; {U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{bd bd} \cdot &Center Dot; {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 i i})) = = (({K K}_{11} + + {K K}_{bd bd} \cdot &Center Dot; {K K}_{22})) \cdot &Center Dot; ω ω + + (({N N}_{11} + + {K K}_{bd bd} \cdot &Center Dot; {N N}_{22})) - - - - - - ((1818))$

由式(18)可得出在陀螺仪实际工作应用时，输入角速度ω的实时解算公式为：From formula (18), it can be concluded that the real-time solution formula of the input angular velocity ω is:

$ω ω = = \frac{(({U u}_{11} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot &Center Dot; {W W}_{11 i i})) - - (({K K}_{bd bd} \cdot &Center Dot; {U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{bd bd} \cdot &Center Dot; {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 i i})) - - (({N N}_{11} - - {K K}_{bd bd} \cdot \cdot {N N}_{22}))}{(({K K}_{11} + + {K K}_{bd bd} \cdot \cdot {K K}_{22}))} - - - - - - ((1919))$

公式(19)右边的各个参数中，N₁和N₂为测量噪声，一般近似为高斯分布，在实时导航过程中，有成熟的滤波方法可用来抑制其影响，令：Among the parameters on the right side of formula (19), N ₁ and N ₂ are measurement noises, which are generally approximately Gaussian distribution. In the process of real-time navigation, there are mature filtering methods that can be used to suppress their influence. Let:

${N N}_{c c} = = - - \frac{{N N}_{11} - - {K K}_{bd bd} \cdot \cdot {N N}_{22}}{{K K}_{11} + + {K K}_{bd bd} \cdot \cdot {K K}_{22}} - - - - - - ((2020))$

则N_c也为高斯分布的测量噪声。这样，输入角速度ω的实时解算公式(19)化为：Then N _c is also the measurement noise of Gaussian distribution. In this way, the real-time solution formula (19) of the input angular velocity ω is transformed into:

$ω ω = = \frac{(({U u}_{11} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot \cdot {W W}_{11 i i})) - - (({K K}_{bd bd} \cdot \cdot {U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{bd bd} \cdot &Center Dot; {K K}_{22 wi wi} \cdot \cdot {W W}_{22 i i}))}{(({K K}_{11} + + {K K}_{bd bd} \cdot \cdot {K K}_{22}))} + + {N N}_{c c} - - - - - - ((21 twenty one))$

实时解算公式(21)中，U₁和U₂分别为正向和反向两个MEMS陀螺仪的实时输出电压值，K_bd可利用公式(13)根据测试数据求出，剩下的其他参数均可在导航前利用传统的标准测试方法测试、标定出来。所以利用公式(21)可以在导航过程中实时求出输入角速度ω的值。公式(21)中不含表示测试时刻不确定性误差项影响量的参数D，所以利用以上方法实时求取的输入角速度ω不受环境因素的影响。In the real-time calculation formula (21), U ₁ and U ₂ are the real-time output voltage values of the forward and reverse MEMS gyroscopes respectively, K _bd can be calculated according to the test data by using the formula (13), and the rest All parameters can be tested and calibrated by traditional standard test methods before navigation. Therefore, the value of the input angular velocity ω can be calculated in real time during the navigation process by using the formula (21). Formula (21) does not contain the parameter D that represents the influence of the uncertainty error term at the test time, so the input angular velocity ω calculated in real time by the above method is not affected by environmental factors.

本发明与现有技术相比的优点在于：本发明利用两个MEMS陀螺仪测量同一个被测转动轴上的输入角速度，具有以下两方面的优点：Compared with the prior art, the present invention has the advantages that: the present invention utilizes two MEMS gyroscopes to measure the input angular velocity on the same measured rotating shaft, and has the following two advantages:

(1)本发明采用的陀螺议差分应用方法，使导航系统实际应用时的角速度求取公式里，不含不确定性环境误差因素的影响量，因而可以避免大部分环境因素，例如温度、电磁、震动、甚至辐射、重力异常、湿度、气压等因素造成的测量误差，可大大提高测量精度。(1) The gyroscope differential application method that the present invention adopts makes the angular velocity calculation formula during the actual application of the navigation system not contain the influence amount of the uncertainty environmental error factor, thereby can avoid most environmental factors, such as temperature, electromagnetic , vibration, and even radiation, abnormal gravity, humidity, air pressure and other factors cause measurement errors, which can greatly improve the measurement accuracy.

(2)本发明采用的陀螺议差分应用方法中，组成差分陀螺对的两个陀螺仪的相似性越高，组成导航系统后的导航精度就越能大大提高，这就把目前难度很大的通过改善MEMS陀螺仪加工工艺的方法来提高惯性器件和导航系统精度的问题，转化为了难度不大的通过提高两个陀螺仪相似性的方法来提高惯性器件和导航系统精度的问题。降低了解决问题的难度和成本，提高了导航系统的精度。(2) In the gyroscope differential application method adopted in the present invention, the higher the similarity of the two gyroscopes forming the differential gyroscope pair, the higher the navigation accuracy after the navigation system is formed, which is very difficult at present. The problem of improving the accuracy of inertial devices and navigation systems by improving the processing technology of MEMS gyroscopes has been transformed into the less difficult problem of improving the accuracy of inertial devices and navigation systems by improving the similarity of two gyroscopes. The difficulty and cost of solving the problem are reduced, and the accuracy of the navigation system is improved.

附图说明Description of drawings

图1为MEMS陀螺仪三维立体示意图；Figure 1 is a three-dimensional schematic diagram of a MEMS gyroscope;

图2为MEMS陀螺仪二维平面示意图；Fig. 2 is a two-dimensional schematic diagram of a MEMS gyroscope;

图3为利用单个MEMS陀螺仪测量某被测转动轴的示意图；Fig. 3 is the schematic diagram of utilizing a single MEMS gyroscope to measure a certain rotational axis;

图4为敏感轴垂直安装基准面的微型MEMS陀螺仪对测量角速度示意图，图中：1、正向陀螺仪，2、反向陀螺仪；Figure 4 is a schematic diagram of the measurement of angular velocity of the micro MEMS gyroscope with the sensitive axis vertical to the installation reference plane, in the figure: 1, forward gyroscope, 2, reverse gyroscope;

图5为敏感轴平行安装基准面的微型MEMS陀螺仪对测量角速度示意图，图中：1、正向陀螺仪，2、反向陀螺仪；Figure 5 is a schematic diagram of the measurement of angular velocity of the micro MEMS gyroscope with the sensitive axis parallel to the installation reference plane, in the figure: 1, forward gyroscope, 2, reverse gyroscope;

图6为敏感轴垂直安装基准面的CRS03微型MEMS陀螺仪对测量角速度示意图，其中图6a为主视图，图6b为左视图，图6c为俯视图，图6d为左俯视图，图中：1、正向陀螺仪，2、反向陀螺仪；Figure 6 is a schematic diagram of measuring angular velocity of the CRS03 miniature MEMS gyroscope with the sensitive axis perpendicular to the installation reference plane, wherein Figure 6a is the main view, Figure 6b is the left view, Figure 6c is the top view, and Figure 6d is the left top view, in the figure: 1, front Towards gyroscope, 2. Reverse gyroscope;

图7为敏感轴平行安装基准面的LCG50微型MEMS陀螺仪对测量角速度示意图，其中图7a为主视图，图7b为左视图，图7c为俯视图，图7d为左俯视图，图中：1、正向陀螺仪，2、反向陀螺仪。Fig. 7 is a schematic diagram of measuring angular velocity of the LCG50 miniature MEMS gyroscope with the sensitive axis parallel to the installation reference plane, wherein Fig. 7a is the main view, Fig. 7b is the left view, Fig. 7c is the top view, and Fig. 7d is the left top view. Among the figures: 1. 2. Reverse gyroscope.

具体实施方式Detailed ways

本发明的第一个实施例中MEMS陀螺仪以硅MEMS陀螺仪CRS03为实例。The MEMS gyroscope in the first embodiment of the present invention takes the silicon MEMS gyroscope CRS03 as an example.

首先，取一批硅MEMS陀螺仪CRS03，本实施例取20个，按照常用的陀螺仪测试标准，进行测试实验。测试、标定出MEMS陀螺仪各个重要参数，包括各个确定性误差项以及它们的系数，通常有零偏、零偏稳定性、零偏重复性、标度因数、标度因数不对称度、标度因数的重复性、最大输入角速度、阈值、分辨率、随机游走系数、输入轴失准角、频带宽度等参数。First, take a batch of silicon MEMS gyroscopes CRS03, 20 in this embodiment, and conduct test experiments according to the commonly used gyroscope test standards. Test and calibrate each important parameter of MEMS gyroscope, including various deterministic error items and their coefficients, usually including zero bias, zero bias stability, zero bias repeatability, scale factor, scale factor asymmetry, scale Factor repeatability, maximum input angular velocity, threshold, resolution, random walk coefficient, input axis misalignment angle, frequency bandwidth and other parameters.

其次，将这批MEMS陀螺仪CRS03平均分为两组，每组10个。利用单轴速率转台进行转台试验。通过实验夹具将一组MEMS陀螺仪的敏感轴平行转台自转轴方向向上固定于转台上，将另一组MEMS陀螺仪的敏感轴平行转台自转轴方向向下固定于转台上。在输入角速率范围内，选取多个输入角速率，按照设定的采样频率测试并存储陀螺仪输出数据。Secondly, divide this batch of MEMS gyroscopes CRS03 into two groups, 10 in each group. Turntable tests were performed using a uniaxial rate turntable. Fix the sensitive axis of one group of MEMS gyroscopes parallel to the rotation axis of the turntable upward on the turntable through the experimental fixture, and fix the sensitive axis of the other group of MEMS gyroscopes parallel to the rotation axis of the turntable downward on the turntable. Within the input angular rate range, select multiple input angular rates, test and store the gyroscope output data according to the set sampling frequency.

再次，根据处理的数据选取环境敏感特性相似性最接近的两个MEMS陀螺仪组成陀螺仪差分对。所述的敏感特性相似性的判定步骤如下：Thirdly, according to the processed data, two MEMS gyroscopes with the closest similarity in environmental sensitivity characteristics are selected to form a gyroscope differential pair. The steps for determining the similarity of sensitive characteristics are as follows:

(1)把20个待测陀螺仪分为两批，10个正向安装，10个反向安装，同时进行速率实验，按时间序列t采集试验数据y(t)；(1) Divide 20 gyroscopes to be tested into two batches, 10 are installed in the forward direction, and 10 are installed in the reverse direction, and the speed experiment is carried out at the same time, and the test data y(t) is collected according to the time series t;

(2)分别以4阶多项式y(t)＝a₀+a₁t+a₂t²+a₃t³+a₄t⁴拟合各个被测陀螺仪的实验数据，得出每个陀螺仪的各阶系数a₀，a₁，a₂，a₃，a₄；(2) Fit the experimental data of each gyroscope under test with the 4th order polynomial y(t)=a ₀ +a ₁ t+a ₂ t ² +a ₃ t ³ +a ₄ t ⁴ to obtain the The coefficients of each order of the instrument a ₀ , a ₁ , a ₂ , a ₃ , a ₄ ;

(3)将10个正向陀螺仪和10个反向陀螺仪都一一对应共组成10×10＝100个陀螺仪对；(3) 10 forward gyroscopes and 10 reverse gyroscopes are all in one-to-one correspondence to form 10×10=100 gyroscope pairs;

(4)以陀螺仪对中的正向陀螺仪的各级拟合系数对应除以反向陀螺仪的各级拟合系数，得出5个拟合系数比值数据，然后求出这5个拟合系数比值数据的方差，将所有100个陀螺仪对都进行上述操作，共求出100个方差值；(4) Divide the fitting coefficients of the forward gyroscopes in the gyroscope pair by the fitting coefficients of the reverse gyroscopes to obtain 5 fitting coefficient ratio data, and then calculate the 5 fitting coefficients Combine the variance of the coefficient ratio data, perform the above operations on all 100 gyroscope pairs, and find 100 variance values in total;

(5)100个方差中，方差值越小的陀螺仪对，其相似性越接近。(5) Among the 100 variances, the smaller the variance value is, the closer the similarity is to the gyroscope pair.

最后，将选出的CRS03微硅MEMS陀螺仪对安装在需要测量的载体上，其差分原理示意图如图4所示，具体安装示意图如图6所示，通过安装使两个MEMS陀螺仪的角速度敏感轴方向相反，并均与被测转动轴平行，敏感同一个外界输入角速度，应用公式(21)即可在系统中实时解算出高精度的输入角速度值。Finally, install the selected CRS03 microsilicon MEMS gyroscope pair on the carrier to be measured. The schematic diagram of its differential principle is shown in Figure 4, and the specific installation schematic diagram is shown in Figure 6. Through the installation, the angular velocity of the two MEMS gyroscopes The directions of the sensitive axes are opposite, and they are all parallel to the measured rotation axis. They are sensitive to the same external input angular velocity, and the high-precision input angular velocity value can be calculated in real time in the system by applying the formula (21).

本发明的第二个实施例中MEMS陀螺仪以BEI公司生产的石英MEMS陀螺仪LCG50为例。The MEMS gyroscope in the second embodiment of the present invention takes the quartz MEMS gyroscope LCG50 produced by BEI Company as an example.

此时，陀螺仪的测试实验、标定方法、数据采集、数据处理、陀螺仪对的选取，都与实施例一相同。不同的是，CRS03的角速度敏感轴方向垂直于陀螺仪安装基准面，而LCG50的角速度敏感轴方向平行于陀螺仪安装基准面。At this time, the test experiment, calibration method, data collection, data processing, and selection of gyroscope pairs for the gyroscope are all the same as those in the first embodiment. The difference is that the direction of the angular velocity sensitive axis of CRS03 is perpendicular to the gyroscope installation datum plane, while the direction of the angular velocity sensitive axis of LCG50 is parallel to the gyroscope installation datum plane.

故将选出的LCG50MEMS陀螺仪对安装在需要测量的载体上时，安装方式的差分原理示意图如图5所示，具体安装示意图如图7所示。通过安装使两个MEMS陀螺仪的角速度敏感轴方向相反，并均与被测转动轴平行，敏感同一个外界输入角速度，应用公式(21)在系统中实时解算出高精度的输入角速度值。Therefore, when the selected LCG50MEMS gyroscope pair is installed on the carrier to be measured, the schematic diagram of the differential principle of the installation method is shown in Figure 5, and the specific installation schematic diagram is shown in Figure 7. By installing the angular velocity sensitive axes of the two MEMS gyroscopes in opposite directions, parallel to the measured rotation axis, and sensitive to the same external input angular velocity, the high-precision input angular velocity value can be calculated in real time by applying formula (21) in the system.

Claims

1. a differential measurement method of MEMS gyroscope, is characterized in that comprising the following steps:

(1) Select two MEMS gyroscopes with similar environmental sensitivity characteristics to form a gyroscope differential pair;

(2) By installing, the angular velocity sensitive axes of the two MEMS gyroscopes are in opposite directions, and both are parallel to the same measured rotation axis, and are sensitive to the same external input angular velocity;

(3) Through testing and calibration experiments, the characteristic parameters of the two gyroscopes and the ratio of the environmental coefficient between them are determined. In practical applications, the high-precision input angular velocity value is calculated according to the real-time calculation formula of the input angular velocity.

2. the differential measurement method of a kind of MEMS gyroscope according to claim 1, is characterized in that: the judgment step of described sensitivity characteristic similarity is as follows

(1) Divide the gyroscopes to be tested into two batches, one batch is installed in the forward direction, and the other batch is installed in the reverse direction, and the rate experiment is carried out at the same time, assuming that the number of gyroscopes installed in the forward direction is The number is v, and the test data y(t) is collected according to the time series t;

(2) Fit each measured value with n-order polynomial y(t)=a ₀ +a ₁ t+a ₂ t ² +a ₃ t ³ +…+a _n-1 t ^n-1 +a _n t ⁿ From the experimental data of the gyroscope, the coefficients a ₀ , a ₁ , a ₂ ,..., a _n-1 , a _n of each gyroscope are obtained;

(3) Each forward gyroscope and each reverse gyroscope are in one-to-one correspondence to form u×v gyroscope pairs;

(4) Divide the fitting coefficients of the forward gyroscopes in the gyroscope pair by the fitting coefficients of the reverse gyroscopes to obtain n fitting coefficient ratio data, and then calculate the n fitting coefficients Combine the variance of the coefficient ratio data, perform the above operations on all u×v gyroscope pairs, and obtain u×v variance values in total;

(5) Among the u×v variances, the smaller the variance value is, the closer the similarity is to the gyroscope pair.

3. the differential measurement method of a kind of MEMS gyroscope according to claim 1, is characterized in that: the computing formula of described environmental coefficient ratio _K is:

{K K}_{bd bd} = = \frac{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{11 j j} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot &Center Dot; {W W}_{11 i i} - - {K K}_{11} \cdot \cdot ω ω))}{\frac{11}{m m} {Σ Σ}_{j j = = 11}^{m m} (({U u}_{22 j j} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{22 wi wi} \cdot &Center Dot; {W W}_{22 i i} + + {K K}_{22} \cdot &Center Dot; ω ω))}

Among them, K _bd represents the ratio of environmental coefficients; i represents the serial number of qualitative errors, i=1,...n, n=2~7, j represents the number of data involved in data smoothing each time, j=1,. ..m, m=8～30. U _1j represents the output voltage of the j-th sampling point of the forward gyroscope, U _2j represents the output voltage of the j-th sampling point of the negative gyroscope, and K _1wj represents the deterministic error term coefficient of the j-th sampling point of the forward gyroscope , K _2wj represents the deterministic error term coefficient of the jth sampling point of the negative gyroscope, W _1i represents the i-th deterministic error term at the positive gyroscope test time, W _2i represents the i-th deterministic error term at the negative gyroscope test time The linear error term, K ₁ represents the scaling factor of the positive gyroscope, K ₂ represents the scaling factor of the negative gyroscope, and ω represents the input angular velocity at the test moment.

4. the differential measurement method of a kind of MEMS gyroscope according to claim 1, is characterized in that: described input angular velocity real-time solution formula is:

ω ω = = \frac{(({U u}_{11} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{11 wi wi} \cdot &Center Dot; {W W}_{11 i i})) - - (({K K}_{bd bd} \cdot &Center Dot; {U u}_{22} - - {Σ Σ}_{i i = = 11}^{n no} {K K}_{bd bd} \cdot \cdot {K K}_{22 wi wi} \cdot \cdot {W W}_{22 i i}))}{(({K K}_{11} + + {K K}_{bd bd} \cdot &Center Dot; {K K}_{22}))} + + {N N}_{c c}

where N _c is Gaussian white noise,

N_{c} = - \frac{N_{1} - K_{bd} &Center Dot; N_{2}}{K_{1} + K_{bd} &Center Dot; K_{2}},

_N1 represents the measurement noise during the positive-going gyroscope test, and _N2 represents the measurement noise during the negative-going gyroscope test.