CN106342175B

CN106342175B - A kind of data fusion method that improves Gyro Precision

Info

Publication number: CN106342175B
Application number: CN201010047241.3A
Authority: CN
Inventors: 常洪龙; 薛亮; 袁广民; 苑伟政; 姜澄宇
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2010-01-14
Filing date: 2010-01-14
Publication date: 2013-11-13
Anticipated expiration: 2030-01-14

Abstract

The invention discloses a data fusion method for improving the precision of a gyroscope, which belongs to the field of sensor measurement. This method uses multiple gyroscopes of the same type to form an array sensitive to the angular rate in the same direction, designs an optimal estimation filter based on a simplified noise model, performs fusion filtering of multiple angular rate signals, and establishes a measurement through noise correlation analysis. The noise-related covariance matrix is used to solve the analytical solution of the Riccati equation, and the angular rate estimation discrete Kalman filter recurrence equation is obtained, which realizes the optimal estimation of the angular rate and improves the accuracy. The effects of the invention are as follows: 1) The accuracy of the gyroscope is improved by adopting the method of multi-sensor array data fusion, which breaks through the bottleneck of improving the accuracy in the traditional method. 2) The simplification of the gyro error model reduces the filtering dimension and improves the real-time performance of the system. 3) The analytical solution of the steady-state value of the estimated variance of the filter greatly simplifies the implementation of the filter, and the optimal estimation of the angular rate can be realized only by one cycle of the recursive equation.

Description

A Data Fusion Method for Improving Gyroscope Accuracy

技术领域technical field

本发明涉及一种提高陀螺精度的数据融合方法，属于传感器测量领域。The invention relates to a data fusion method for improving the precision of a gyroscope, which belongs to the field of sensor measurement.

背景技术Background technique

基于微机电技术的微机械陀螺具有体积小、功耗低、价格低、寿命长及可批量生产等优点，非常适合于构建微型化、低成本的惯性导航与制导系统。然而，微机械陀螺的精度与传统陀螺相比相差较远，严重限制了在航空航天高端领域中的应用。通过改进陀螺敏感结构、加工工艺、接口检测电路等提高信噪比的传统方法，很难较大幅度提高微机械陀螺的精度，且无法从根本上改善陀螺的漂移特性。采用多传感器数据融合技术，利用最优估计理论设计融合算法可以实现陀螺漂移的估计补偿，利用传感器自身达到随机误差的自补偿校准，提高精度。即利用多个陀螺组成阵列，设计最优估计滤波算法，对陀螺阵列多个测量信息滤波加权处理，得到一个高精度的陀螺信号，称之为“虚拟陀螺”。专利号为US2003/0187623的美国专利“High accuracy inertial sensors from inexpensive components，2003”提出了对多个单个陀螺组成的阵列信号滤波处理提高陀螺精度的方法。该方法通过多个一般精度的微机械陀螺组成阵列，算法设计中将陀螺信号建模为真实角速率、角度随机游走ARW和偏置漂移三部分，其中偏置漂移由速率随机游走RRW噪声驱动；将真实角速率和陀螺偏置漂移列为状态对其估计，利用噪声信号之间的相关性建立系统噪声和量测噪声协方差阵，求解连续卡尔曼滤波方程获得滤波估计方差的解析解，设计卡尔曼滤波器对多个量测值进行滤波，得到输入角速度的最优估计，从而提高陀螺精度。此方法虽然能够大幅度提高微机械陀螺的精度，但也存在一些不足：首先，对于低精度的微机械陀螺，其随机误差主要表现为角度随机游走白噪声，尤其对于短时内的应用环境速率随机游走噪声所占比重很小，将其建模为真实角速率、角度随机游走ARW和偏置漂移三部分增大了滤波器的维数，增加了计算负担，不利于虚拟陀螺实时数据处理。其次，增大陀螺阵列的个数将导致黎卡蒂微分方程解析求解的复杂度的增加，不利于滤波算法的实施。另外，申请号为200610104564.5的专利“陀螺的虚拟实现方法，2006”，同样将陀螺误差模型建模为真实角速率、角度随机游走ARW和偏置漂移三部分，算法设计中采用差分法建立了动态滤波模型，即对陀螺阵列多个量测信号进行差分运算来消除真实角速率对建模的影响，估计陀螺偏置漂移，校正各陀螺输出信号，再对校正后的多个陀螺信号取平均，实现动态角速率的估计。这种差分法也存在一定的不足：首先，滤波估计的目的是要获取真实角速率的估计值，而差分处理中消除掉了有用的真实角速率信号，导致估计精度的降低。其次，这种误差模型不利于降低陀螺角度随机游走噪声。Micro-mechanical gyroscopes based on micro-electromechanical technology have the advantages of small size, low power consumption, low price, long life, and mass production, and are very suitable for building miniaturized, low-cost inertial navigation and guidance systems. However, the accuracy of micromachined gyroscopes is far behind that of traditional gyroscopes, which seriously limits the application in high-end aerospace fields. It is difficult to greatly improve the accuracy of micro-mechanical gyroscopes by improving the traditional methods of improving the signal-to-noise ratio such as gyroscope sensitive structure, processing technology, and interface detection circuit, and it is impossible to fundamentally improve the drift characteristics of gyroscopes. Using multi-sensor data fusion technology and using optimal estimation theory to design fusion algorithm can realize the estimation and compensation of gyro drift, and use the sensor itself to achieve self-compensation calibration of random errors and improve accuracy. That is to use multiple gyroscopes to form an array, design the optimal estimation filter algorithm, filter and weight the multiple measurement information of the gyroscope array, and obtain a high-precision gyroscope signal, which is called "virtual gyroscope". The US patent "High accuracy inertia sensors from inexpensive components, 2003" with the patent number US2003/0187623 proposes a method for improving the accuracy of the gyroscope by filtering and processing the array signal composed of multiple single gyroscopes. In this method, multiple general-precision micromechanical gyroscopes are used to form an array. In the algorithm design, the gyroscope signal is modeled as three parts: real angular rate, angle random walk ARW, and bias drift. The bias drift is composed of rate random walk RRW noise Drive; the true angular rate and gyro bias drift are listed as states to estimate them, and the correlation between the noise signals is used to establish the system noise and measurement noise covariance matrix, and the continuous Kalman filter equation is solved to obtain the analytical solution of the estimated variance of the filter , design a Kalman filter to filter multiple measured values, and obtain the optimal estimate of the input angular velocity, thereby improving the accuracy of the gyroscope. Although this method can greatly improve the accuracy of micro-mechanical gyroscopes, there are still some shortcomings: First, for low-precision micro-mechanical gyroscopes, the random error is mainly manifested as angle random walk white noise, especially for short-term application environments The proportion of rate random walk noise is very small. Modeling it as three parts of real angular rate, angle random walk ARW and bias drift increases the dimension of the filter and increases the computational burden, which is not conducive to the real-time performance of the virtual gyroscope. data processing. Secondly, increasing the number of gyro arrays will lead to an increase in the complexity of the analytical solution of the Riccati differential equation, which is not conducive to the implementation of the filtering algorithm. In addition, the patent "Virtual Implementation Method of Gyroscope, 2006" with the application number of 200610104564.5 also modeled the gyroscope error model into three parts: real angular rate, angle random walk ARW and bias drift. The difference method was used in the algorithm design to establish Dynamic filtering model, that is, to perform differential operations on multiple measurement signals of the gyro array to eliminate the influence of the real angular rate on the modeling, estimate the gyro bias drift, correct the output signals of each gyro, and then average the corrected multiple gyro signals , to realize the estimation of the dynamic angular rate. This differential method also has certain deficiencies: First, the purpose of filtering estimation is to obtain the estimated value of the real angular rate, but the useful real angular rate signal is eliminated in the differential processing, resulting in a decrease in estimation accuracy. Second, this error model is not conducive to reducing random walk noise in gyroscope angles.

发明内容Contents of the invention

为了克服现有技术的上述缺陷，本发明提出了一种基于简化噪声模型的提高陀螺精度的数据融合方法，采用同类型规格的N个陀螺组成阵列敏感同一方向的角速率，进行多个角速率信号的滤波合成，实现真实角速率的最优估计，提高精度。In order to overcome the above-mentioned defects of the prior art, the present invention proposes a data fusion method based on a simplified noise model to improve the accuracy of the gyroscope, using N gyroscopes of the same type and specification to form an array sensitive to the angular rate in the same direction, and perform multiple angular rate Filtering and synthesis of signals realizes optimal estimation of true angular rate and improves accuracy.

本发明提出的提高陀螺精度的数据融合方法原理如图1，具体包括以下步骤：The data fusion method principle that the present invention proposes improves gyro precision as shown in Figure 1, specifically comprises the following steps:

第一步：采集陀螺阵列角速率信号。采用N个陀螺组成的阵列检测相同敏感方向的同一个角速率信号，设定陀螺信号采样周期T，通过A/D转换得到N个角速率信号y₁，y₂，…，y_N。The first step: collect the angular rate signal of the gyro array. An array composed of N gyroscopes is used to detect the same angular rate signal in the same sensitive direction, the sampling period T of the gyroscope signal is set, and N angular rate signals y ₁ , y ₂ ,...,y _N are obtained through A/D conversion.

第二步：求取陀螺角度随机游走ARW噪声方差q_n。利用第一步采集的角速率信号y₁，y₂，…，y_N，采用Allan方差法分析N个陀螺随机误差，得到各个陀螺角度随机游走ARW噪声方差，取平均得到q_n。Step 2: Calculate the random walk ARW noise variance q _n of the gyro angle. Using the angular rate signals y ₁ , y ₂ , ..., y _N collected in the first step, the random error of N gyroscopes is analyzed by Allan variance method, and the random walk ARW noise variance of each gyroscope angle is obtained, which is averaged to obtain q _n .

第三步：求取陀螺阵列噪声相关系数ρ。利用第一步采集的角速率信号y₁，y₂，…，y_N，通过相关性分析，求取陀螺阵列角度随机游走ARW噪声之间的相关系数ρ。The third step: Calculate the noise correlation coefficient ρ of the gyroscope array. Using the angular rate signals y ₁ , y ₂ ,..., y _N collected in the first step, through correlation analysis, the correlation coefficient ρ between the angle random walk ARW noise of the gyro array is obtained.

第四步：求取相关协方差矩阵R。利用第二步和第三步获取的ARW噪声方差q_n及相关系数ρ，得到ARW噪声相关协方差矩阵R：Step 4: Obtain the correlation covariance matrix R. Using the ARW noise variance q _n and correlation coefficient ρ obtained in the second and third steps, the ARW noise correlation covariance matrix R is obtained:

第五步：设计数据融合卡尔曼滤波器。卡尔曼滤波器的设计是陀螺阵列数据融合的核心，包括以下子步骤：Step 5: Design data fusion Kalman filter. The design of the Kalman filter is the core of the data fusion of the gyroscope array, including the following sub-steps:

子步骤1：建立陀螺阵列数据融合状态空间模型Sub-step 1: Establish a state-space model for gyroscope array data fusion

将陀螺信号建模为真实角速率ω和角度随机游走噪声n之和，对于N个陀螺组成的阵列，有：The gyroscope signal is modeled as the sum of the true angular rate ω and the angular random walk noise n, for an array of N gyroscopes, there are:

y＝H·ω+v(1)y=H·ω+v(1)

$y the y = = [\begin{matrix} {y the y}_{11} \\ \cdot \cdot \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ {y the y}_{N N} \end{matrix}],, v v = = [\begin{matrix} {n no}_{11} \\ \cdot &Center Dot; \\ \cdot &Center Dot; \\ \cdot \cdot \\ {n no}_{N N} \end{matrix}],, H h = = {[\begin{matrix} 11 \\ \cdot &Center Dot; \\ \cdot \cdot \\ \cdot &Center Dot; \\ 11 \end{matrix}]}_{N N \times \times 11} - - - - - - ((22))$

其中y为多个陀螺量测值组成的向量，v为角度随机游走噪声组成的向量，H为量测矩阵。将ω建模为随机游走过程其中n_ω为真实角速率驱动白噪声。将ω列入状态向量对其估计，建立陀螺阵列数据融合状态空间模型如下：Among them, y is a vector composed of multiple gyro measurement values, v is a vector composed of angular random walk noise, and H is a measurement matrix. Model ω as a random walk process where n _ω is the real angular rate driving white noise. Include ω in the state vector to estimate it, and establish the state-space model of gyroscope array data fusion as follows:

$\{\begin{matrix} X x ((t t)) = = ω ω \\ \overset{\cdot &Center Dot;}{X x} ((t t)) = = 00 \cdot \cdot X x ((t t)) + + w w ((t t)) = = {n no}_{ω ω} \\ y the y ((t t)) = = H h \cdot &Center Dot; X x ((t t)) + + v v ((t t)) \end{matrix} - - - - - - ((33))$

具中X(t)为状态向量，y(t)为量测值向量，系统噪声向量w(t)和量测噪声向量v(t)分别为具有零均值的高斯白噪声，即：E[w(t)]＝0，E[w(t)w^T(t+τ)]＝q_ωδ(τ)，E[v(t)]＝0，E[v(t)v^T(t+τ)]＝Rδ(τ)，q_ω为白噪声n_ω的方差，R为第四步获得的ARW噪声相关协方差矩阵，δ(τ)为Kroneckerδ函数。In the tool, X(t) is the state vector, y(t) is the measurement value vector, the system noise vector w(t) and the measurement noise vector v(t) are Gaussian white noise with zero mean, namely: E[ w(t)]=0, E[w(t)w ^T (t+τ)]=q _ω δ(τ), E[v(t)]=0, E[v(t)v ^T (t +τ)]=Rδ(τ), q _ω is the variance of white noise n _ω , R is the ARW noise correlation covariance matrix obtained in the fourth step, and δ(τ) is the Kroneckerδ function.

子步骤2：求解滤波估计方差稳态值Sub-step 2: Solve the steady-state value of the estimated variance of the filter

对于子步骤1建立的数据融合状态空间模型，则真实角速率估计连续卡尔曼滤波方程为：For the data fusion state-space model established in sub-step 1, the continuous Kalman filter equation for real angular rate estimation is:

$\overset{\cdot \cdot}{\overset{^^}{X x}} ((t t)) = = K K ((t t)) [[y the y ((t t)) - - H h \overset{^^}{X x} ((t t))]] - - - - - - ((44))$

K(t)＝P(t)H^TR^-1 (5)K(t)＝P(t)H ^T R ^-1 (5)

$\overset{\cdot &Center Dot;}{P P} ((t t)) = = {q q}_{ω ω} - - P P ((t t)) {H h}^{T T} {R R}^{- - 11} H h P P ((t t)) - - - - - - ((66))$

其中K(t)和P(t)分别为t时刻状态向量的估计值、滤波增益矩阵及滤波估计方差，H^T为矩阵H的转置矩阵，R^-1为矩阵R的逆矩阵，方程(6)称之为黎卡蒂方程。通过对子步骤1建立的状态空间模型可观测性分析知滤波系统完全可观测，随着滤波时间t的增长，P(t)逐渐的不受初始值的影响并达到稳态值P(∞)，因此只要得到P(∞)就可以得到稳态滤波增益矩阵K(∞)，最终得到状态向量的最优估计，简化滤波器的实施，提高计算速度。in K(t) and P(t) are the estimated value of the state vector at time t, the filter gain matrix and the estimated variance of the filter respectively, H ^T is the transpose matrix of matrix H, R ^-1 is the inverse matrix of matrix R, equation (6 ) is called the Riccati equation. Through the observability analysis of the state space model established in sub-step 1, it is known that the filtering system is completely observable. As the filtering time t increases, P(t) is gradually not affected by the initial value and reaches the steady-state value P(∞) , so as long as P(∞) is obtained, the steady-state filter gain matrix K(∞) can be obtained, and finally the optimal estimation of the state vector can be obtained, which simplifies the implementation of the filter and improves the calculation speed.

黎卡蒂方程的Hamiltonian矩阵M为：The Hamiltonian matrix M of the Riccati equation is:

$M m = = [\begin{matrix} 00 & {H h}^{T T} {R R}^{- - 11} H h \\ {q q}_{ω ω} & 00 \end{matrix}] - - - - - - ((77))$

黎卡蒂方程的解为：P(t)＝A(t)B^-1(t)，其中矩阵A(t)和B(t)满足一阶线性微分方程：The solution of the Riccati equation is: P(t)=A(t)B ^-1 (t), where the matrices A(t) and B(t) satisfy the first-order linear differential equation:

$[\begin{matrix} \overset{\cdot \cdot}{B B} ((t t)) \\ \overset{\cdot \cdot}{A A} ((t t)) \end{matrix}] = = [\begin{matrix} 00 & {H h}^{T T} {R R}^{- - 11} H h \\ {q q}_{ω ω} & 00 \end{matrix}] [\begin{matrix} B B ((t t)) \\ A A ((t t)) \end{matrix}] - - - - - - ((88))$

求解方程(8)，得：Solving equation (8), we get:

$[\begin{matrix} B B ((t t)) \\ A A ((t t)) \end{matrix}] = = {e e}^{M m t t} [\begin{matrix} I I \\ {P P}_{00} \end{matrix}] - - - - - - ((99))$

其中I为单位矩阵，P₀为初始滤波估计方差，定义变量C＝H^TR^-1H，则求解e^Mt得：Among them, I is the identity matrix, P ₀ is the estimated variance of the initial filter, and the variable C=H ^T R ^-1 H is defined, then e ^Mt is solved to get:

${e e}^{M m t t} = = [\begin{matrix} \frac{11}{22} {e e}^{\sqrt{{Cq Q}_{ω ω}} t t} & \frac{\sqrt{C C / / {q q}_{ω ω}}}{22} {e e}^{\sqrt{{Cq Q}_{ω ω}} t t} \\ \frac{\sqrt{{q q}_{ω ω} / / C C}}{22} {e e}^{\sqrt{{Cq Q}_{ω ω}} t t} & \frac{11}{22} {e e}^{\sqrt{{Cq Q}_{ω ω}} t t} \end{matrix}] + + [\begin{matrix} \frac{11}{22} {e e}^{- - \sqrt{{Cq Q}_{ω ω}} t t} & - - \frac{\sqrt{C C / / {q q}_{ω ω}}}{22} {e e}^{- - \sqrt{{Cq Q}_{ω ω}} t t} \\ - - \frac{\sqrt{{q q}_{ω ω} / / C C}}{22} {e e}^{- - \sqrt{{Cq Q}_{ω ω}} t t} & \frac{11}{22} {e e}^{- - \sqrt{{Cq Q}_{ω ω}} t t} \end{matrix}] - - - - - - ((1010))$

因此，滤波估计方差稳态值P(∞)为：Therefore, the steady-state value P(∞) of the estimated variance of the filter is:

$P P ((∞ ∞)) = = ((\sqrt{{q q}_{ω ω} / / C C} + + {P P}_{00})) {((11 + + \sqrt{C C / / {q q}_{ω ω}} {P P}_{00}))}^{- - 11} - - - - - - ((1111))$

子步骤3：求解角速率估计离散卡尔曼滤波递推方程Sub-step 3: Solve the discrete Kalman filter recurrence equation for angular rate estimation

利用子步骤2获取的滤波估计方差稳态值P(∞)，计算稳态滤波增益矩阵K(∞)：Using the steady-state value P(∞) of the estimated variance of the filter obtained in sub-step 2, calculate the steady-state filter gain matrix K(∞):

${K K}_{∞ ∞} = = P P ((∞ ∞)) {H h}^{T T} {R R}^{- - 11} = = ((\sqrt{{q q}_{ω ω} / / C C} + + {P P}_{00})) {((11 + + \sqrt{C C / / {q q}_{ω ω}} {P P}_{00}))}^{- - 11} {H h}^{T T} {R R}^{- - 11} = = {GH GH}^{T T} {R R}^{- - 11} - - - - - - ((1212))$

其中变量则角速率估计连续卡尔曼滤波方程为：where variable Then the angular rate estimation continuous Kalman filter equation is:

$\overset{\cdot \cdot}{\overset{^^}{X x}} ((t t)) = = {K K}_{∞ ∞} [[y the y ((t t)) - - H h \overset{^^}{X x} ((t t))]] = = - - G G C C \overset{\cdot \cdot}{\overset{^^}{X x}} ((t t)) + + {GH GH}^{T T} {R R}^{- - 11} y the y ((t t)) - - - - - - ((1313))$

对连续滤波方程(13)离散化，则角速率估计离散卡尔曼滤波递推方程为：Discretize the continuous filter equation (13), then the angular rate estimation discrete Kalman filter recurrence equation is:

$\overset{^^}{X x} ((k k + + 11)) = = {e e}^{- - G G C C T T} \overset{^^}{X x} ((k k)) + + \frac{11}{C C} ((11 - - {e e}^{- - G G C C T T})) {H h}^{T T} {R R}^{- - 11} y the y ((k k)) - - - - - - ((1414))$

其中和分别为k+1及k时刻的角速率估计值，y(k)为k时刻陀螺阵列输出角速率值。到此完成了卡尔曼滤波器的设计。in and are the estimated values of angular rate at time k+1 and k respectively, and y(k) is the output angular rate value of the gyroscope array at time k. This completes the design of the Kalman filter.

第六步：角速率信号滤波估计。设定初始滤波估计方差P₀＝0，白噪声n_ω的方差q_ω取值为100～1000(°/h)²之间的任一实数，初始状态向量估计值对于第一步中获得的k时刻陀螺角速率信号y₁，y₂，…，y_N组成的向量y(k)＝[y₁，y₂，…，y_N]^T，利用k时刻的角速率估计值及第五步中子步骤3得到的角速率估计离散卡尔曼滤波递推方程(14)，递推得到k+1时刻的角速率估计值返回第一步采集k+1时刻陀螺阵列角速率信号y(k+1)，利用及第五步中的子步骤3估计k+2时刻的角速率估计值依次循环计算。Step 6: Estimation of angular rate signal filtering. Set the initial filtering estimation variance P ₀ =0, the variance q _ω of the white noise n _ω is any real number between 100 and 1000(°/h) ² , and the estimated value of the initial state vector For the vector y(k)=[y ₁ , y ₂ ,...,y _{N ]} ^T of the gyro angular rate signal y ₁ , y ₂ ,..., _y N obtained in the first step at time k, the angle at time k is used rate estimate And the angular rate estimation discrete Kalman filter recursive equation (14) obtained in sub-step 3 in the fifth step, the angular rate estimated value at k+1 time is obtained recursively Go back to the first step to collect the angular rate signal y(k+1) of the gyro array at time k+1, use And sub-step 3 in the fifth step estimates the estimated value of the angular rate at time k+2 Cycle through the calculations sequentially.

本发明的有益效果：1)利用多个陀螺组成阵列，采用数据融合的方法提高陀螺精度，突破了传统方法提高微机械陀螺精度的瓶颈。2)陀螺误差模型的简化，降低了滤波维数，提高了系统实时性。3)滤波估计方差稳态值的解析求解，大大简化了滤波器的实施，只需要一个递推方程的循环就可以实现角速率的最优估计，避免了直接采用卡尔曼滤波离散方程对滤波估计方差和滤波增益的更新计算。The beneficial effects of the present invention: 1) Multiple gyroscopes are used to form an array, and the method of data fusion is used to improve the accuracy of the gyroscope, which breaks through the bottleneck of improving the accuracy of the micromechanical gyroscope in the traditional method. 2) The simplification of the gyro error model reduces the filtering dimension and improves the real-time performance of the system. 3) The analytical solution of the steady-state value of the estimated variance of the filter greatly simplifies the implementation of the filter, and only needs a cycle of the recursive equation to realize the optimal estimation of the angular rate, avoiding the direct use of the discrete equation of the Kalman filter to estimate the filter Updated computation of variance and filter gain.

附图说明Description of drawings

图1是陀螺精度提高数据融合方法原理图Figure 1 is a schematic diagram of the gyroscope precision improvement data fusion method

图2是陀螺精度提高数据融合方法流程图Figure 2 is a flow chart of the gyroscope precision improvement data fusion method

具体实施方式Detailed ways

本实施例采用6个微机械陀螺ADXRS300组成陀螺阵列，实现一个高精度的虚拟陀螺系统，参阅图1，图2，本实施例的数据融合方法具体包括如下步骤：This embodiment adopts 6 micromechanical gyroscopes ADXRS300 to form a gyroscope array to realize a high-precision virtual gyroscope system. Referring to Fig. 1 and Fig. 2, the data fusion method of this embodiment specifically includes the following steps:

第一步：采集陀螺阵列角速率信号。采用6个陀螺的阵列检测相同敏感方向的同一个角速率信号，设定采样周期T＝0.01s，通过A/D转换得到6个陀螺角速率信号y₁，y₂，…，y₆。The first step: collect the angular rate signal of the gyro array. An array of six gyroscopes is used to detect the same angular rate signal in the same sensitive direction, the sampling period is set to T=0.01s, and six gyroscope angular rate signals y ₁ , y ₂ ,...,y ₆ are obtained through A/D conversion.

第二步：求取陀螺角度随机游走ARW噪声方差q_n。利用第一步采集的角速率信号y₁，y₂，…，y₆，采用Allan方差法分析各个陀螺随机误差，得到各个陀螺角度随机游走ARW噪声方差，取平均得到q_n＝370.3²(°/h)²。Step 2: Calculate the random walk ARW noise variance q _n of the gyro angle. Using the angular rate signals y ₁ , y ₂ ,..., y ₆ collected in the first step, the Allan variance method is used to analyze the random error of each gyroscope, and the random walk ARW noise variance of each gyroscope angle is obtained, and the average is obtained q _n =370.3 ² ( °/h) ² .

第三步：求取陀螺阵列噪声相关系数ρ。利用第一步采集的角速率信号y₁，y₂，…，y₆，通过相关性分析，得到陀螺角度随机游走ARW噪声之间的相关系数ρ＝0.01。The third step: Calculate the noise correlation coefficient ρ of the gyroscope array. Using the angular rate signals y ₁ , y ₂ , ..., y ₆ collected in the first step, through correlation analysis, the correlation coefficient ρ=0.01 among the gyro angle random walk ARW noises is obtained.

第五步：设计数据融合卡尔曼滤波器。将陀螺信号建模为真实角速率ω和角度随机游走噪声n之和，真实角速率ω建模为随机游走过程其中n_ω为均值为0方差为q_ω的真实角速率驱动白噪声。将ω列入状态向量对其估计，建立真实角速率最优估计卡尔曼滤波器为：Step 5: Design data fusion Kalman filter. The gyro signal is modeled as the sum of the true angular rate ω and the angular random walk noise n, and the true angular rate ω is modeled as a random walk process where n _ω is the true angular rate drive white noise with a mean of 0 and a variance of q _ω . Put ω into the state vector to estimate it, and establish the optimal estimation Kalman filter of the true angular rate as:

$\overset{^^}{X x} ((k k + + 11)) = = {e e}^{- - G G C C T T} \overset{^^}{X x} ((k k)) + + \frac{11}{C C} ((11 - - {C C}^{- - G G C C T T})) {H h}^{T T} {R R}^{- - 11} y the y ((k k))$

其中和分别为k+1及k时刻的角速率估计值，y(k)为k时刻陀螺阵列输出角速率向量，R^-1为协方差矩阵R的逆矩阵，H^T为量测矩阵的转置矩阵，T为陀螺信号采样周期，变量C＝H^TR^-1H，P₀为初始滤波估计方差。in and are the estimated values of the angular rate at time k+1 and k respectively, y(k) is the output angular rate vector of the gyroscope array at time k, R ^-1 is the inverse matrix of the covariance matrix R, H ^T is the measurement matrix The transpose matrix of , T is the sampling period of the gyro signal, variable C=H ^T R ^-1 H, P ₀ is the estimated variance of initial filtering.

第六步：角速率信号滤波估计。设定初始滤波估计方差P₀＝0，白噪声n_ω的方差q_ω＝100(°/h)²，初始状态向量的估计值对于第一步中获得的k时刻陀螺角速率信号y₁，y₂，…，y₆组成的向量y(k)＝[y₁，y₂，…，t₆]^T，利用k时刻的角速率估计值及第五步中子步骤3得到的角速率估计离散卡尔曼滤波递推方程(14)，递推得到k+1时刻的角速率估计值返回第一步采集k+1时刻陀螺角速率信号y(k+1)，利用及第五步中的子步骤3估计k+2时刻的角速率估计值依次循环计算。Step 6: Estimation of angular rate signal filtering. Set the estimated variance of initial filtering P ₀ =0, the variance q _ω of white noise n _ω =100(°/h) ² , and the estimated value of the initial state vector For the vector y(k)=[y ₁ , y ₂ ,...,t ₆ ] ^T of the gyro angular rate signal y ₁ , y ₂ ,...,y ₆ obtained in the first step at time k, using the angle at time k rate estimate And the angular rate estimation discrete Kalman filter recursion equation (14) obtained in sub-step 3 in the fifth step, the angular rate estimate at k+1 time is obtained recursively Go back to the first step to collect the gyro angular rate signal y(k+1) at time k+1, use And sub-step 3 in the fifth step estimates the estimated value of the angular rate at time k+2 Cycle through the calculations sequentially.

通过实验，6个角度随机游走噪声和速率随机游走噪声分别为370.3°/h及4.14°/h的微机械陀螺ADXRS300，通过数据融合滤波后，得到一个高精度的虚拟陀螺，其中角度随机游走噪声和速率随机游走噪声分别降为1.179°/h及0.1274°/h，精度得到很大提高。Through experiments, the micromechanical gyroscope ADXRS300 with 6 angle random walk noises and rate random walk noises of 370.3°/h and 4.14°/h respectively, after data fusion filtering, obtains a high-precision virtual gyroscope, in which the angles are random The walk noise and rate random walk noise are reduced to 1.179°/h and 0.1274°/h respectively, and the accuracy is greatly improved.

Claims

1. a data fusion method improving gyroscope precision, is characterized in that: comprise the steps:

The first step: collect the angular rate signal of the gyroscope array: use an array composed of N gyroscopes to detect the same angular rate signal in the same sensitive direction, set the gyroscope signal sampling period T, and obtain N angular rate signals y ₁ through A/D conversion ,y ₂ ,...,y _N ;

Step 2: Find the random walk ARW noise variance q _n of the gyro angle: use the angular rate signals y ₁ , y ₂ ,..., y _N collected in the first step, and use the Allan variance method to analyze the random errors of N gyro, and get each Gyro angle random walk ARW noise variance, averaged to get q _n ;

The third step: Calculate the noise correlation coefficient ρ of the gyro array: use the angular rate signals y ₁ , y ₂ , ..., y _N collected in the first step, and through correlation analysis, calculate the angle between the random walk ARW noise of the gyro array The correlation coefficient ρ;

Step 4: Calculate the correlation covariance matrix R: use the ARW noise variance q _n and correlation coefficient ρ obtained in the second and third steps to obtain the ARW noise correlation covariance matrix R:

Step 5: Design data fusion Kalman filter: model the gyroscope signal as the sum of the real angular rate ω and the angle random walk noise n, and model the real angular rate ω as a random walk process Among them, _nω is the real angular rate driving white noise with the mean value of 0 and the variance of _qω ; ω is included in the state vector to estimate it, and the angular rate estimation discrete Kalman filter recursive equation is established as:

\overset{^^}{X x} ((k k + + 11)) = = {e e}^{- - G G C C T T} \overset{^^}{X x} ((k k)) + + \frac{11}{C C} ((11 - - {e e}^{- - G G C C T T})) {H h}^{T T} {R R}^{- - 11} y the y ((k k)) - - - - - - ((11))

in and are the estimated values of the angular rate at time k+1 and k respectively, y(k) is the output angular rate vector of the gyroscope array at time k, R ^-1 is the inverse matrix of the covariance matrix R, H ^T is the measurement matrix The transpose matrix of , T is the sampling period of the gyro signal, variable C＝H ^T R ^-1 H, P ₀ is the estimated variance of initial filtering;

Step 6: Angular rate signal filtering estimation: set the initial filtering estimation variance P ₀ , the variance q _ω of white noise n _ω , and the initial state vector estimation value For the vector y(k)=[y ₁ , y ₂ ,...,y _{N ]} ^T of the gyro angular rate signal y ₁ , y ₂ ,..., _y N obtained in the first step at time k, the angle at time k is used rate estimate And the angular rate estimation discrete Kalman filter recursion equation (1) obtained in the fifth step, the angular rate estimation value at k+1 time is obtained recursively Go back to the first step to collect the angular rate signal y(k+1) of the gyro array at time k+1, use And in the fifth step, the Kalman filter estimates the estimated value of the angular rate at time k+2 The calculation is performed sequentially to realize the optimal estimation of the angular rate and improve the accuracy.

2. A data fusion method for improving gyroscope accuracy as claimed in claim 1, characterized in that: in the sixth step, the initial filtering estimation variance P ₀ is set as P ₀ =0.

3. a data fusion method ^improving gyro precision as claimed in claim 1, is characterized in that: in the described 6th step, the variance q _ω of white noise n _ω takes a value between 100～1000 (°/h) any real number in between.

4. a data fusion method improving gyro precision as claimed in claim 1, is characterized in that: in the described 6th step, initial state vector estimated value set as