CN103411628A

CN103411628A - Processing method for random drift error of MEMS gyroscope

Info

Publication number: CN103411628A
Application number: CN2013103547896A
Authority: CN
Inventors: 俞吉; 周德云; 马云红; 张堃; 黄吉传
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2013-08-14
Filing date: 2013-08-14
Publication date: 2013-11-27
Anticipated expiration: 2033-08-14
Also published as: CN103411628B

Abstract

The invention provides a method for processing random drift errors of MEMS gyroscopes. Firstly, the structure of the RBF neural network is determined, and then learning samples are obtained, and the learning samples are optimized by genetic algorithm (GA) to train the RBF neural network, and finally the random drift error suppression is obtained. The subsequent angular velocity data. Aiming at the random drift error of the MEMS gyroscope, the invention adopts the real-time mean value method to suppress the random drift error, and utilizes the RBF neural network optimized based on the genetic algorithm to control the calculation step size of the real-time mean value method. The invention does not need to model the random drift error, has a small calculation amount, and can conveniently realize the real-time random drift error suppression of the MEMS gyroscope.

Description

A MEMS gyroscope random drift error processing method

技术领域technical field

本发明属于惯性技术领域，特别涉及一种陀螺仪随机漂移误差的处理方法。The invention belongs to the technical field of inertia, in particular to a method for processing random drift errors of gyroscopes.

背景技术Background technique

近年来，微电子机械系统（MEMS）陀螺作为惯性领域一个十分重要的分支，获得了长足的发展。由于它的成本低、尺寸小、重量轻和可靠性高的特性，在低成本惯性系统中得到了越来越广泛的应用。但是，目前MEMS陀螺仪性能还比较低，如何降低MEMS陀螺仪的漂移误差，尤其是其中的随机漂移误差，成为了提高MEMS陀螺仪精度的关键。为了提高MEMS陀螺仪的精度，一方面是不断提高MEMS陀螺仪的器件精度，但是由于受到制造工艺的限制，短期内快速提高器件精度是很难实现的；另一方面就是建立合理的随机漂移误差处理模型，实时抑制MEMS陀螺仪的随机漂移误差。现有MEMS陀螺仪的随机漂移误差处理基本思路是：首先建立误差模型，然后采用一定的滤波技术对其进行估计和补偿。但该思路存在以下几个问题：1.因为MEMS陀螺仪的随机漂移误差的随机特性，很难建立合理的误差模型；2.采用滤波技术，计算量比较大，使用MEMS陀螺仪时的实时性会受到限制。In recent years, microelectromechanical systems (MEMS) gyroscopes, as a very important branch of the inertial field, have made great progress. Due to its low cost, small size, light weight, and high reliability, it is increasingly used in low-cost inertial systems. However, the performance of the MEMS gyroscope is still relatively low at present. How to reduce the drift error of the MEMS gyroscope, especially the random drift error, has become the key to improving the accuracy of the MEMS gyroscope. In order to improve the accuracy of the MEMS gyroscope, on the one hand, it is necessary to continuously improve the device accuracy of the MEMS gyroscope, but due to the limitation of the manufacturing process, it is difficult to quickly improve the device accuracy in the short term; on the other hand, it is necessary to establish a reasonable random drift error Processing models to suppress random drift errors of MEMS gyroscopes in real time. The basic idea of the random drift error processing of the existing MEMS gyroscope is: first establish the error model, and then use a certain filtering technology to estimate and compensate it. However, there are several problems with this idea: 1. Due to the random characteristics of the random drift error of the MEMS gyroscope, it is difficult to establish a reasonable error model; 2. Using filtering technology, the calculation amount is relatively large, and the real-time performance when using the MEMS gyroscope will be restricted.

发明内容Contents of the invention

为了克服现有技术的不足，本发明提供一种MEMS陀螺仪随机漂移误差的处理方法，采用实时均值法来抑制MEMS陀螺仪的随机漂移误差，利用基于遗传算法优化的RBF神经网络控制实时均值法的计算的步长，计算量小，可便捷实现MEMS陀螺仪实时的随机漂移误差抑制。In order to overcome the deficiencies in the prior art, the present invention provides a method for processing random drift errors of MEMS gyroscopes, using the real-time mean value method to suppress the random drift errors of the MEMS gyroscopes, and utilizing the RBF neural network optimized based on genetic algorithm to control the real-time mean value method The calculation step size is small, and the calculation amount is small, which can conveniently realize the real-time random drift error suppression of the MEMS gyroscope.

本发明解决其技术问题所采用的技术方案包括以下步骤：The technical solution adopted by the present invention to solve its technical problems comprises the following steps:

步骤1：设置RBF神经网络为单输入单输出，输入量为x＝[Δw]，Δw为MEMS陀螺仪角速度变化量，输出量为y＝[Y_step]，Y_step为实时均值法的计算步长，径向基向量h＝[h₁ h₂…h_j…h_n]^T，其中h_j为高斯基函数，n为隐含层单元数，Step 1: Set the RBF neural network as single input and single output, the input value is x=[Δw], Δw is the angular velocity change of the MEMS gyroscope, the output value is y=[Y _step ], and Y _step is the calculation step of the real-time mean value method Long, radial basis vector h=[h ₁ h ₂ …h _j …h _n ] ^T , where h _j is the Gaussian base function, n is the number of hidden layer units,

${h h}_{j j} = = exp exp ((- - \frac{{| | | | x x - - {m m}_{j j} | | | |}^{22}}{22 {σ σ}_{j j}^{22}})),, j j = = 1,2 1,2 \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; n no$

式中，x是RBF神经网络的输入量，m_j和σ_j ²分别是RBF神经网络的第j个隐含层单元高斯基函数的中心和方差；In the formula, x is the input quantity of the RBF neural network, m _j and σ _j ² are the center and variance of the Gaussian function of the jth hidden layer unit of the RBF neural network, respectively;

RBF神经网络的权向量W＝[w₁,w₂,…,w_n]^T，The weight vector W of RBF neural network=[w ₁ ,w ₂ ,…,w _n ] ^T ,

则RBF神经网络的输出y＝[Y_step]＝W^Th；得到1-n-1的RBF神经网络初始模型，其中高斯基函数的中心m_j、方差σ_j ²和权向量W的初始值由步骤3中对初始种群解码后数据确定；Then the output of the RBF neural network y=[Y _step ]=W ^T h; the initial model of the RBF neural network of 1-n-1 is obtained, in which the center m _j of the Gaussian function, the variance σ _j ² and the initial value of the weight vector W Determined by the decoded data of the initial population in step 3;

步骤2：将MEMS陀螺仪固定在单轴速率转台上，然后在

范围内，等间隔分别给单轴速率转台输入k个角加速度，在给单轴速率转台输入每一个角加速度的同时采集MEMS陀螺仪输出的角速度和转台输出的角速度，得到k组训练样本；其中是MEMS陀螺仪可以量测的最大角加速度，所述的等间隔

k为采集数据的组数，20≤k≤50；Step 2: Fix the MEMS gyroscope on the single-axis rate turntable, and then

Within the range, input k angular accelerations to the single-axis rate turntable at equal intervals, and collect the angular velocity output by the MEMS gyroscope and the angular velocity output by the turntable while inputting each angular acceleration to the single-axis rate turntable to obtain k groups of training samples; is the maximum angular acceleration that the MEMS gyroscope can measure, and the equal interval

k is the number of groups of collected data, 20≤k≤50;

步骤3：用步骤2得到的训练样本对步骤1得到的RBF神经网络初始模型进行训练，并采用遗传算法对RBF神经网络的高斯基函数的中心、方差和隐含层到输出层的连接权值进行优化，最后得到最优的RBF神经网络，具体包括以下步骤：Step 3: Use the training samples obtained in step 2 to train the initial model of the RBF neural network obtained in step 1, and use the genetic algorithm to modify the center, variance, and connection weights from the hidden layer to the output layer of the Gaussian function of the RBF neural network Carry out optimization, and finally obtain the optimal RBF neural network, specifically including the following steps:

3.1：染色体采用二进制编码，每个染色体的二进制编码均包括n个高斯基函数的中心m_j、n个高斯基函数的方差σ_j ²和n个隐含层到输出层的连接权值W_j，j＝1,2…n；中心m_j、方差σ_j ²、连接权值W_j都采用p位二进制数表示，一个染色体的总长度为3*p*n，4≤p≤8；3.1: Chromosomes are encoded in binary, and the binary encoding of each chromosome includes the center m _j of n Gaussian functions, the variance σ _j ² of n Gaussian functions, and the connection weight W _j of n hidden layers to the output layer , j=1,2...n; center m _j , variance σ _j ² , and connection weight W _j are all represented by p-bit binary numbers, and the total length of a chromosome is 3*p*n, 4≤p≤8;

3.2：种群的初始化，生成初始的N个染色体，30≤N≤80；3.2: Initialization of the population, generating initial N chromosomes, 30≤N≤80;

3.3：染色体解码，将二进制编码的各个染色体的三个部分分别转换为十进制数；3.3: Chromosome decoding, converting the three parts of each chromosome in binary code into decimal numbers;

3.4：计算各个染色体的适应度，具体步骤如下：3.4: Calculate the fitness of each chromosome, the specific steps are as follows:

1）将解码获得的各组染色体对应的高斯基函数的中心m_j和方差σ_j ²，以及隐含层到输出层的连接权值W_j代入RBF神经网络，得到N个RBF神经网络；1) Substitute the center m _j and variance σ _j ² of the Gaussian function corresponding to each group of chromosomes obtained by decoding, and the connection weight W _j from the hidden layer to the output layer into the RBF neural network to obtain N RBF neural networks;

2）使用步骤2中获得的训练样本，根据步骤1）中得到的N个RBF神经网络得到不同的实时均值法的计算步长Y_step，分别采用实时均值法对样本数据进行处理，得到n组抑制随机漂移误差后的角速度数据

2) Using the training samples obtained in step 2, according to the N RBF neural networks obtained in step 1), the calculation step size Y _step of different real-time mean method is obtained, and the real-time mean method is used to process the sample data respectively, and n groups are obtained Angular velocity data after suppressing random drift error

3）计算第j个染色体适应度函数 $f_{j} = \frac{1}{E [(w_{j}^{RT} - w_{j}^{ZT}) * {(w_{j}^{RT} - w_{j}^{ZT})}^{T}]},$ 式中，

为转台输出的角速度；3) Calculate the fitness function of the jth chromosome

f_{j} = \frac{1}{E. [(w_{j}^{RT} - w_{j}^{ZT}) * {(w_{j}^{RT} - w_{j}^{ZT})}^{T}]},

In the formula,

is the angular velocity output by the turntable;

3.5：判断是否达到两个终止条件当中的任意一个，若满足，则将最优染色体对应的数据构成最优RBF神经网络；若不满足，则执行种群演化操作并返回步骤3.3；3.5: Determine whether any one of the two termination conditions is met, and if so, construct the optimal RBF neural network with the data corresponding to the optimal chromosome; if not, execute the population evolution operation and return to step 3.3;

所述的终止条件包括：The termination conditions mentioned include:

(1).种群演化的次数达到预先设定的循环次数NumCycle，50≤NumCycle≤100；(1). The number of population evolution reaches the preset number of cycles NumCycle, 50≤NumCycle≤100;

(2).适应度满足 $f_{j} > \frac{1}{α * E [(w_{j}^{o} - w_{j}^{ZT}) * {(w_{j}^{o} - w_{j}^{ZT})}^{T}]},$ 式中，

为陀螺仪原始输出的角速度，α是一个比例调节系数，0.01≤α＜1；(2). Fitness satisfaction

f_{j} > \frac{1}{α * E. [(w_{j}^{o} - w_{j}^{ZT}) * {(w_{j}^{o} - w_{j}^{ZT})}^{T}]},

In the formula,

is the angular velocity originally output by the gyroscope, α is a proportional adjustment coefficient, 0.01≤α<1;

所述的演化操作包括以下步骤：Described evolution operation comprises the following steps:

1）保留父代种群中适应度前3的个体，直接复制作为子代；然后再利用轮盘赌法对剩余个体进行选择，直到产生N个个体；1) Keep the top 3 individuals with fitness in the parent population and copy them directly as offspring; then use the roulette method to select the remaining individuals until N individuals are produced;

2）根据设定的交叉概率P_c确定染色体是否要交叉，0.4≤P_c≤0.8，交叉算子采用两点交叉法；2) Determine whether the chromosomes are to be crossed according to the set crossover probability P _c , 0.4≤P _c ≤0.8, and the crossover operator adopts the two-point crossover method;

设两条交叉的染色体分别为

和

{PG}_{2} = [A_{1}^{P_{2}}, A_{2}^{P_{2}}, \cdot \cdot \cdot, A_{90}^{P_{2}}],

式中，

和

分别代表对应染色体上的基因；Let the two crossed chromosomes be

and

{PG}_{2} = [A_{1}^{P_{2}}, A_{2}^{P_{2}}, &Center Dot; \cdot &Center Dot;, A_{90}^{P_{2}}],

In the formula,

and

Represent the genes on the corresponding chromosomes respectively;

随机产生两个小于等于90的正整数r₁、r₂，r₁＜r₂，将大于等于r₁且小于等于r₂的染色体段作为互换对象，得到两个新的子代：Randomly generate two positive integers r ₁ and r ₂ less than or equal to 90, r ₁ < r ₂ , and take the chromosome segment greater than or equal to r ₁ and less than or equal to r ₂ as the exchange object, and obtain two new offspring:

${CG CG}_{11} = = [[{A A}_{11}^{{P P}_{11}},, {A A}_{22}^{{P P}_{11}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{{r r}_{11} - - 11}^{{P P}_{11}},, {A A}_{{r r}_{11}}^{{P P}_{22}},, \cdot \cdot \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{{r r}_{22}}^{{P P}_{22}},, {A A}_{{r r}_{22} + + 11}^{{P P}_{11}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{9090}^{{P P}_{11}}]]$

${CG CG}_{22} = = [[{A A}_{11}^{{P P}_{22}},, {A A}_{22}^{{P P}_{22}},, \cdot &Center Dot; \cdot \cdot \cdot &Center Dot;,, {A A}_{{r r}_{11} - - 11}^{{P P}_{22}},, {A A}_{{r r}_{11}}^{{P P}_{11}},, \cdot \cdot \cdot \cdot \cdot &Center Dot;,, {A A}_{{r r}_{22}}^{{P P}_{11}},, {A A}_{{r r}_{22} + + 11}^{{P P}_{22}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{9090}^{{P P}_{22}}]]$

3）根据设定的变异概率P_m确定染色体是否要变异，0.001≤P_m≤0.2，变异算子采用基本变异算子，在染色体上随机挑选一个或多个基因座进行基因值取反；3) Determine whether the chromosome should be mutated according to the set mutation probability P _m , 0.001≤P _m ≤0.2, the mutation operator adopts the basic mutation operator, and randomly selects one or more loci on the chromosome to invert the gene value;

步骤4：实时采集MEMS陀螺仪的输出角速度变化量，输入到步骤3的最优的RBF神经网络，实时获得不同情况下的实时均值的计算步长；然后根据计算步长，采用实时均值法处理MEMS陀螺的原始输出数据，就可以得到随机漂移误差抑制后的角速度数据。Step 4: Collect the output angular velocity variation of the MEMS gyroscope in real time, input it to the optimal RBF neural network in step 3, and obtain the calculation step size of the real-time mean value in different situations in real time; then according to the calculation step size, use the real-time mean value method to process The raw output data of the MEMS gyroscope can be used to obtain the angular velocity data after the random drift error is suppressed.

本发明的有益效果是：本发明针对MEMS陀螺仪的随机漂移误差，采用实时均值法来抑制随机漂移误差，利用基于遗传算法优化的RBF神经网络控制实时均值法的计算步长。本发明不需要对随机漂移误差建模，计算量小，可便捷实现MEMS陀螺仪实时的随机漂移误差抑制。The beneficial effect of the present invention is: the present invention aims at the random drift error of the MEMS gyroscope, adopts the real-time mean value method to restrain the random drift error, and utilizes the RBF neural network optimized based on the genetic algorithm to control the calculation step size of the real-time mean value method. The invention does not need to model the random drift error, has a small calculation amount, and can conveniently realize the real-time random drift error suppression of the MEMS gyroscope.

附图说明Description of drawings

图1是本发明实现方法的流程图；Fig. 1 is the flowchart of the method for realizing the present invention;

图2是RBF神经网络结构示意图Figure 2 is a schematic diagram of the structure of the RBF neural network

图3是MEMS陀螺仪的输出在实时均值法处理前后数据对比图。Figure 3 is a comparison of the output of the MEMS gyroscope before and after the real-time averaging method.

具体实施方式Detailed ways

下面结合附图和实施例对本发明进一步说明，本发明包括但不仅限于下述实施例。The present invention will be further described below in conjunction with the accompanying drawings and embodiments, and the present invention includes but not limited to the following embodiments.

本发明包括以下步骤：The present invention comprises the following steps:

步骤1:确定RBF神经网络结构Step 1: Determine the RBF neural network structure

设置RBF神经网络为单输入单输出（即输入层，输出层单元个数都为1），输入量为x＝[Δw]，Δw为MEMS陀螺仪角速度变化量，输出量为y＝[Y_step]，Y_step为实时均值法的计算步长，径向基向量h＝[h₁ h₂…h_j…h_n]^T，其中h_j为高斯基函数，即：Set the RBF neural network to single input and single output (that is, the number of units in the input layer and output layer is 1), the input value is x=[Δw], Δw is the angular velocity change of the MEMS gyroscope, and the output value is y=[Y _step ], Y _step is the calculation step size of the real-time mean value method, the radial basis vector h=[h ₁ h ₂ …h _j …h _n ] ^T , where h _j is the Gaussian basis function, namely:

${h h}_{j j} = = exp exp ((- - \frac{{| | | | x x - - {m m}_{j j} | | | |}^{22}}{22 {σ σ}_{j j}^{22}})),, j j = = 1,2 1,2 \cdot \cdot \cdot \cdot \cdot \cdot n no - - - - - - ((11))$

式中，x是RBF神经网络的输入量，m_j和σ_j ²分别是RBF神经网络的第j个隐含层单元高斯基函数的中心和方差。In the formula, x is the input quantity of the RBF neural network, m _j and σ _j ² are the center and variance of the Gaussian function of the jth hidden layer unit of the RBF neural network, respectively.

RBF神经网络的权向量为：The weight vector of the RBF neural network is:

W＝[w₁,w₂,…,w_n]^T (2)W＝[w ₁ ,w ₂ ,…,w _n ] ^T (2)

则RBF神经网络的输出为：Then the output of the RBF neural network is:

y＝[Y_step]＝W^Th (3)y=[Y _step ]=W ^T h (3)

得到1-n-1的RBF神经网络初始模型，其中高斯基函数的中心m_j、方差σ_j ²和权向量W的初始值由步骤3中对初始种群解码后数据确定。Obtain the initial model of the 1-n-1 RBF neural network, where the initial values of the center m _j of the Gaussian function, the variance σ _j ² and the weight vector W are determined by the decoded data of the initial population in step 3.

步骤2:获取学习样本Step 2: Get Learning Samples

首先将MEMS陀螺仪通过夹具固定在单轴速率转台上，然后在

（是MEMS陀螺仪可以量测的最大角加速度）范围内，按等间隔（

k为采集数据的组数，一般20≤k≤50），分别给转台输入k个角加速度，在给转台输入每一个角加速度的同时采集MEMS陀螺仪输出的角速度和转台输出的角速度。在完成所有的不同角加速度下的MEMS陀螺仪输出和转台输出的数据采集后，可以得到k组训练样本。First fix the MEMS gyroscope on the single-axis rate turntable through the fixture, and then

( is the maximum angular acceleration that the MEMS gyroscope can measure), within the range of equal intervals (

k is the number of groups of collected data, generally 20≤k≤50), input k angular accelerations to the turntable respectively, and collect the angular velocity output by the MEMS gyroscope and the angular velocity output by the turntable while inputting each angular acceleration to the turntable. After completing the data collection of MEMS gyroscope output and turntable output under all different angular accelerations, k groups of training samples can be obtained.

步骤3:采用遗传算法（GA）优化，训练RBF神经网络Step 3: Use genetic algorithm (GA) to optimize and train the RBF neural network

用步骤2得到的学习样本对步骤1得到的初始RBF神经网络进行训练，并采用遗传算法对RBF神经网络的高斯基函数的中心、方差和隐含层到输出层的连接权值进行优化，最后得到最优的RBF神经网络。Use the learning samples obtained in step 2 to train the initial RBF neural network obtained in step 1, and use the genetic algorithm to optimize the center, variance and connection weights from the hidden layer to the output layer of the Gaussian function of the RBF neural network, and finally Get the optimal RBF neural network.

3.1：染色体采用二进制编码，每个染色体编码包括三个部分，具体定义为：3.1: Chromosomes are coded in binary, and each chromosome code includes three parts, specifically defined as:

单元1：n高斯基函数的中心m_j，j＝1,2…n；Unit 1: center m _j of n Gaussian function, j=1,2...n;

单元2：n个高斯基函数的方差σ_j ²，j＝1,2…n；Unit 2: variance σ _j ² of n Gaussian base functions, j=1,2...n;

单元3：n个隐含层到输出层的连接权值W_j，j＝1,2…n；Unit 3: Connection weight W _j from n hidden layers to output layer, j=1,2...n;

中心m_j、方差σ_j ²、连接权值W_j都采用p位（一般取4≤p≤8）二进制数表示，所以一个染色体的总长度为3*p*n。Center m _j , variance σ _j ² , and connection weight W _j are all represented by p-bit (generally 4≤p≤8) binary numbers, so the total length of a chromosome is 3*p*n.

3.2：种群的初始化，生成初始的N（一般取30≤N≤80）个染色体。3.2: Initialization of the population, generating initial N (generally 30≤N≤80) chromosomes.

3.3：染色体解码，将二进制编码的各个染色体的三个部分分别转换为十进制数。3.3: Chromosome decoding, convert the three parts of each chromosome in binary code into decimal numbers respectively.

1）将3.3中解码获得的各组染色体对应的高斯基函数的中心m_j和方差σ_j ²，以及隐含层到输出层的连接权值W_j代入RBF神经网络，可以得到N个RBF神经网络。1) Substitute the center m _j and variance σ _j ² of the Gaussian function corresponding to each group of chromosomes obtained in 3.3, and the connection weight W _j from the hidden layer to the output layer into the RBF neural network, and N RBF neural networks can be obtained network.

2）使用步骤2中获得的学习样本，根据1）中得到的N个RBF神经网络，可以得到不同的实时均值法的计算步长Y_step，分别采用实时均值法对样本数据进行处理，可以得到N组抑制随机漂移误差后的角速度数据

J=1,2,...,N。2) Using the learning samples obtained in step 2, according to the N RBF neural networks obtained in 1), the calculation step size Y _step of different real-time mean method can be obtained, and the real-time mean method is used to process the sample data respectively, and it can be obtained N sets of angular velocity data after suppressing random drift errors

J=1,2,...,N.

3）计算适应度3) Calculate fitness

第J个染色体适应度函数：The fitness function of the Jth chromosome:

${f f}_{J J} = = \frac{11}{E E. [[(({w w}_{J J}^{RT RT} - - {w w}_{J J}^{ZT ZT})) * * {(({w w}_{J J}^{RT RT} - - {w w}_{J J}^{ZT ZT}))}^{T T}]]},, J J = = 1,2 1,2,, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, N N - - - - - - ((44))$

式中，

为转台输出的角速度，

为采用实时均值法后的MEMS陀螺仪角速度数据。In the formula,

is the output angular velocity of the turntable,

It is the MEMS gyroscope angular velocity data after adopting the real-time averaging method.

3.5：判断是否达到终止条件。若满足，则将最优染色体对应的数据构成最优RBF神经网络；若不满足，则执行种群演化（选择、重组、变异）操作，返回步骤3.3。3.5中，终止条件（由两个条件构成，到达以下任一条件即结束循环）：3.5: Determine whether the termination condition is met. If it is satisfied, the data corresponding to the optimal chromosome will be used to form the optimal RBF neural network; if it is not satisfied, the population evolution (selection, recombination, mutation) operation will be performed, and return to step 3.3. In 3.5, the termination condition (consisting of two conditions , the loop ends when one of the following conditions is reached):

(1).种群演化的次数达到预先设定的循环次数NumCycle（一般50≤NumCy≤cl1e）；(1). The number of population evolution reaches the preset number of cycles NumCycle (generally 50≤NumCy≤cl1e);

(2).适应度满足：(2). The fitness meets:

${f f}_{J J} > > \frac{11}{α α * * E E. [[(({w w}_{J J}^{o o} - - {w w}_{J J}^{ZT ZT})) * * {(({w w}_{J J}^{o o} - - {w w}_{J J}^{ZT ZT}))}^{T T}]]},, J J = = 1,2 1,2,, \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot,, N N - - - - - - ((55))$

式中，

为转台输出的角速度，

为陀螺仪原始输出的角速度，α是一个比例调节系数（一般取0.01≤α＜1），E[·]函数是求期望。In the formula,

is the output angular velocity of the turntable,

is the angular velocity of the original output of the gyroscope, α is a proportional adjustment coefficient (generally 0.01≤α<1), and the E[·] function is to find the expectation.

3.5中，演化操作包括以下步骤：In 3.5, the evolution operation includes the following steps:

1）选择1) select

采用最优个体保留原则和轮盘赌选择法进行个体选择。首先保留父代种群中适应度前3的个体，直接复制作为子代；然后再利用轮盘赌法对剩余个体进行选择，直到产生N个个体；The optimal individual retention principle and the roulette wheel selection method were used for individual selection. First keep the top 3 individuals with the fitness in the parent population, and directly copy them as offspring; then use the roulette method to select the remaining individuals until N individuals are produced;

2）交叉2) cross

根据设定的交叉概率P_c（P_c由专家经验确定，一般取值范围0.4≤P_c≤0.8）确定染色体是否要交叉，交叉算子采用两点交叉法。According to the set crossover probability P _c (P _c is determined by expert experience, the general value range is 0.4 ≤ P _c ≤ 0.8) to determine whether the chromosomes are to be crossed, and the crossover operator uses the two-point crossover method.

设两条交叉的染色体分别为：Let the two crossed chromosomes be:

${PG PG}_{11} = = [[{A A}_{11}^{{P P}_{11}},, {A A}_{22}^{{P P}_{11}},, \cdot \cdot \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{9090}^{{P P}_{11}}]] - - - - - - ((66))$

${PG PG}_{22} = = [[{A A}_{11}^{{P P}_{22}},, {A A}_{22}^{{P P}_{22}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{9090}^{{P P}_{22}}]] - - - - - - ((77))$

式中，

分别代表对应染色体上第i个、j个基因（二进制表示）。In the formula,

Respectively represent the i-th and j-th genes on the corresponding chromosome (binary representation).

随机产生两个正整数r₁,r₂(0＜r₁,r₂≤90)，将处于r₁～r₂之间（包括r₁,r₂，下面以r₁＜r₂为例）的染色体段作为互换对象，这样可以得到两个新的子代：Randomly generate two positive integers r ₁ , r ₂ (0<r ₁ , r ₂ ≤90), which will be between r ₁ and r ₂ (including r ₁ , r ₂ , take r ₁ <r ₂ as an example below) The chromosome segment of is used as an exchange object, so that two new offspring can be obtained:

${CG CG}_{11} = = [[{A A}_{11}^{{P P}_{11}},, {A A}_{22}^{{P P}_{11}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{{r r}_{11} - - 11}^{{P P}_{11}},, {A A}_{{r r}_{11}}^{{P P}_{22}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{{r r}_{22}}^{{P P}_{22}},, {A A}_{{r r}_{22} + + 11}^{{P P}_{11}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{9090}^{{P P}_{11}}]] - - - - - - ((88))$

${CG CG}_{22} = = [[{A A}_{11}^{{P P}_{22}},, {A A}_{22}^{{P P}_{22}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{{r r}_{11} - - 11}^{{P P}_{22}},, {A A}_{{r r}_{11}}^{{P P}_{11}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{{r r}_{22}}^{{P P}_{11}},, {A A}_{{r r}_{22} + + 11}^{{P P}_{22}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{9090}^{{P P}_{22}}]] - - - - - - ((99))$

3）变异3) Variation

根据设定的变异概率P_m（P_m由专家经验确定，一般取值范围0.001≤P_m≤0.2）确定染色体是否要变异，变异算子采用基本变异算子。即在染色体上随机挑选一个或多个基因座进行变动（本发明采用二进制编码，变动就是基因值取反，即0→1或1→0）。According to the set mutation probability P _m (P _m is determined by expert experience, the general value range is 0.001≤P _m ≤0.2) to determine whether the chromosome should be mutated, and the mutation operator adopts the basic mutation operator. That is, one or more loci are randomly selected on the chromosome to be changed (the present invention adopts binary code, and the change is the inversion of the gene value, that is, 0→1 or 1→0).

步骤4:MEMS陀螺仪随机漂移误差的抑制Step 4: Suppression of MEMS Gyroscope Random Drift Errors

实时采集MEMS陀螺仪的输出角速度变化量，输入到步骤3训练好的RBF神经网络，就可以实时获得不同情况下的实时均值的计算步长。然后根据计算步长，采用实时均值法处理MEMS陀螺的原始输出数据，就可以得到随机漂移误差抑制后的角速度数据。Collect the output angular velocity variation of the MEMS gyroscope in real time and input it to the RBF neural network trained in step 3 to obtain the calculation step size of the real-time mean value in different situations in real time. Then, according to the calculation step, the raw output data of the MEMS gyroscope is processed by the real-time average method, and the angular velocity data after the random drift error is suppressed can be obtained.

实施例：Example:

步骤1:建立RBF神经网络初始模型Step 1: Establish the initial model of RBF neural network

设置RBF神经网络为单输入单输出，输入量为x＝[Δw]（Δw为前后两个采样时刻的MEMS陀螺仪角速度变化量），输出量为y＝[Y_step]（Y_step为实时均值法的计算步长），径向基向量h＝[h₁ h₂…h_j…h₅]^T，其中h_j为高斯基函数（设n＝5，即5个隐含层单元），即：Set the RBF neural network to single input and single output, the input is x=[Δw] (Δw is the angular velocity change of the MEMS gyroscope at the two sampling moments before and after), and the output is y=[Y _step ] (Y _step is the real-time average Calculation step size of the method), the radial basis vector h=[h ₁ h ₂ …h _j …h ₅ ] ^T , where h _j is the Gaussian basis function (set n=5, that is, 5 hidden layer units), that is :

${h h}_{j j} = = exp exp ((- - \frac{{| | | | x x - - {m m}_{j j} | | | |}^{22}}{22 {σ σ}_{j j}^{22}})),, j j = = 1,2 1,2 \cdot \cdot \cdot \cdot \cdot &Center Dot;,, 55 - - - - - - ((11))$

W＝[w₁,w₂,…,w₅]^T (2)W＝[w ₁ ,w ₂ ,…,w ₅ ] ^T (2)

则RBF神经网络的输出为：Then the output of the RBF neural network is:

y＝[Y_step]＝W^Th (3)y=[Y _step ]=W ^T h (3)

得到1-5-1的RBF神经网络初始模型，其中高斯基函数的中心m_j、方差σ_j ²和权向量W的初始值由步骤3.3中对初始种群解码后数据确定。Obtain the initial model of the 1-5-1 RBF neural network, where the initial values of the center m _j of the Gaussian function, the variance σ _j ² and the weight vector W are determined by the decoded data of the initial population in step 3.3.

步骤2:获取学习样本Step 2: Get Learning Samples

本实施例采用ADIS16375惯性系统（内置一个三轴陀螺仪和一个三轴加速度计），将MEMS陀螺仪通过夹具固定在单轴速率转台上，采集单轴的角速度，然后在

（

是MEMS陀螺仪可以量测的最大角加速度，本实施例取）范围内按等间隔

分别给转台输入50个角加速度，在给转台输入每一个角加速度的同时采集MEMS陀螺仪输出的角速度和转台输出的角速度。在完成所有的不同角加速度下的MEMS陀螺仪输出和转台输出的数据采集后，可以得到50组训练样本。This embodiment adopts the ADIS16375 inertial system (built-in a three-axis gyroscope and a three-axis accelerometer), fixes the MEMS gyroscope on the single-axis rate turntable through the fixture, collects the single-axis angular velocity, and then

(

is the maximum angular acceleration that the MEMS gyroscope can measure, and this embodiment takes ) range at equal intervals

Input 50 angular accelerations to the turntable respectively, and collect the angular velocity output by the MEMS gyroscope and the angular velocity output by the turntable while inputting each angular acceleration to the turntable. After completing the data collection of MEMS gyroscope output and turntable output under all different angular accelerations, 50 sets of training samples can be obtained.

单元1：5个高斯基函数的中心m_j，j＝1,2…,5；Unit 1: Center m _j of 5 Gaussian base functions, j=1,2...,5;

单元2：5个高斯基函数的方差σ_j ²，j＝1,2…,5；Unit 2: Variance σ _j ² of 5 Gaussian base functions, j=1,2...,5;

单元3：5个隐含层到输出层的连接权值W_j，j＝1,2…,5；Unit 3: Connection weight W _j from the 5 hidden layers to the output layer, j=1,2...,5;

中心m_j、方差σ_j ²、连接权值W_j都采用6位二进制数表示，所以一个染色体的总长度为90。Center m _j , variance σ _j ² , and connection weight W _j are all represented by 6-bit binary numbers, so the total length of a chromosome is 90.

3.2：种群的初始化，生成初始的30个染色体。3.2: Initialization of the population, generating an initial 30 chromosomes.

1）将3.3中解码获得的各组染色体对应的高斯基函数的中心m_j和方差σ_j ²，以及隐含层到输出层的连接权值W_j代入RBF神经网络，可以得到30个RBF神经网络。1) Substitute the center m _j and variance σ _j ² of the Gaussian function corresponding to each group of chromosomes obtained in 3.3, and the connection weight W _j from the hidden layer to the output layer into the RBF neural network, and 30 RBF neural networks can be obtained network.

2）使用步骤2中获得的学习样本，根据1）中得到的30个RBF神经网络，可以得到不同的实时均值法的计算步长Y_step，分别采用实时均值法对样本数据进行处理，可以得到n组抑制随机漂移误差后的角速度数据

j=1,2,...,30。2) Using the learning samples obtained in step 2, according to the 30 RBF neural networks obtained in 1), different calculation step lengths Y _step of the real-time mean value method can be obtained, and the real-time mean value method is used to process the sample data respectively, and it can be obtained n groups of angular velocity data after suppressing random drift errors

j=1,2,...,30.

3）计算适应度3) Calculate fitness

第j个染色体适应度函数：The jth chromosome fitness function:

${f f}_{j j} = = \frac{11}{E E. [[(({w w}_{j j}^{RT RT} - - {w w}_{j j}^{ZT ZT})) * * {(({w w}_{j j}^{RT RT} - - {w w}_{j j}^{ZT ZT}))}^{T T}]]},, j j = = 1,2 1,2,, \cdot \cdot \cdot &Center Dot; \cdot &Center Dot;,, 3030 - - - - - - ((44))$

式中，

为转台输出的角速度，

为采用实时均值法后的MEMS陀螺仪角速度数据。In the formula,

is the output angular velocity of the turntable,

(1).种群演化的次数达到预先设定的循环次数NumCycle（本该实施例选择NumCycle＝50）；(1). The number of population evolution reaches the preset number of cycles NumCycle (in this embodiment, NumCycle=50 is selected);

(2).适应度满足：(2). The fitness meets:

${f f}_{j j} > > \frac{11}{α α * * E E. [[(({w w}_{j j}^{o o} - - {w w}_{j j}^{ZT ZT})) * * {(({w w}_{j j}^{o o} - - {w w}_{j j}^{ZT ZT}))}^{T T}]]},, j j = = 1,2 1,2,, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, n no - - - - - - ((55))$

式中，

为转台输出的角速度，

为陀螺仪原始输出的角速度，α是一个比例调节系数（本实施例取α＝0.1），E[·]函数是求期望。In the formula,

is the output angular velocity of the turntable,

is the angular velocity originally output by the gyroscope, α is a proportional adjustment coefficient (in this embodiment, α=0.1), and the E[·] function is to find the expectation.

1）选择1) select

采用最优个体保留原则和轮盘赌选择法进行个体选择。首先保留父代种群中适应度前3的个体，直接复制作为子代；然后再利用轮盘赌法对剩余个体进行选择，直到产生30个个体；The optimal individual retention principle and the roulette wheel selection method were used for individual selection. First keep the top 3 individuals with the fitness in the parent population, and directly copy them as offspring; then use the roulette method to select the remaining individuals until 30 individuals are produced;

2）交叉2) cross

根据设定的交叉概率P_c（本实施例选取P_c＝0.5）确定染色体是否要交叉，交叉算子采用两点交叉法。According to the set crossover probability P _c (P _c =0.5 is selected in this embodiment), it is determined whether the chromosomes are to be crossed over, and the crossover operator adopts the two-point crossover method.

设两条交叉的染色体分别为：Let the two crossed chromosomes be:

${PG PG}_{11} = = [[{A A}_{11}^{{P P}_{11}},, {A A}_{22}^{{P P}_{11}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{9090}^{{P P}_{11}}]] - - - - - - ((66))$

式中，

${CG CG}_{11} = = [[{A A}_{11}^{{P P}_{11}},, {A A}_{22}^{{P P}_{11}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{{r r}_{11} - - 11}^{{P P}_{11}},, {A A}_{{r r}_{11}}^{{P P}_{22}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{{r r}_{22}}^{{P P}_{22}},, {A A}_{{r r}_{22} + + 11}^{{P P}_{11}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{9090}^{{P P}_{11}}]] - - - - - - ((88))$

${CG CG}_{22} = = [[{A A}_{11}^{{P P}_{22}},, {A A}_{22}^{{P P}_{22}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{{r r}_{11} - - 11}^{{P P}_{22}},, {A A}_{{r r}_{11}}^{{P P}_{11}},, \cdot &Center Dot; \cdot \cdot \cdot \cdot,, {A A}_{{r r}_{22}}^{{P P}_{11}},, {A A}_{{r r}_{22} + + 11}^{{P P}_{22}},, \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, {A A}_{9090}^{{P P}_{22}}]] - - - - - - ((99))$

3）变异3) Variation

根据设定的变异概率P_m（本实施例选取P_m＝0.05）确定染色体是否要变异，变异算子采用基本变异算子。即在染色体上随机挑选一个或多个基因座进行变动（本发明采用二进制编码，变动就是基因值取反，即0→1或1→0）。According to the set mutation probability P _m (P _m =0.05 is selected in this embodiment), it is determined whether the chromosome should be mutated, and the mutation operator adopts the basic mutation operator. That is, one or more loci are randomly selected on the chromosome to be changed (the present invention adopts binary code, and the change is the inversion of the gene value, that is, 0→1 or 1→0).

步骤4：MEMS陀螺仪随机漂移误差的抑制Step 4: Suppression of MEMS Gyroscope Random Drift Errors

4.1实时采集MEMS陀螺仪输出的角速度。4.1 Collect the angular velocity output by the MEMS gyroscope in real time.

4.2将MEMS陀螺仪角速度的变化量作为输入，代入到步骤3训练得到的最优RBF神经网络，可以实时得到实时均值法的计算步长L。4.2 The angular velocity change of the MEMS gyroscope is used as an input, which is substituted into the optimal RBF neural network trained in step 3, and the calculation step size L of the real-time mean method can be obtained in real time.

4.3根据4.2确定的计算步长L，采用实时均值法处理MEMS陀螺仪的输出的角速度数据，可以得到抑制随机漂移误差后的角速度数据。4.3 According to the calculation step size L determined in 4.2, the angular velocity data output by the MEMS gyroscope is processed by the real-time average method, and the angular velocity data after suppressing the random drift error can be obtained.

如图3所示，是MEMS陀螺仪原始输出数据和采用本发明的方法抑制随机漂移后的数据对比图，可以明显看到采用本发明的方法很好的抑制了随机漂移误差，可以达到预期的效果。As shown in Figure 3, it is the original output data of the MEMS gyroscope and the data comparison chart after adopting the method of the present invention to suppress the random drift. It can be clearly seen that the random drift error is well suppressed by the method of the present invention, and the desired effect can be achieved. Effect.

本发明根据MEMS陀螺仪的不同工作状态，利用RBF神经网络合理调整实时均值法的计算步长，可以有效抑制MEMS陀螺仪的随机漂移误差。该发明计算量小，可以在便捷的在工程上。According to different working states of the MEMS gyroscope, the invention uses the RBF neural network to reasonably adjust the calculation step size of the real-time mean value method, and can effectively suppress the random drift error of the MEMS gyroscope. The invention has a small amount of calculation and can be used conveniently in engineering.

本发明说明书中未作详细描述的内容属于本领域专业技术人员公知的现有技术。The contents not described in detail in the description of the present invention belong to the prior art known to those skilled in the art.

Claims

1. a processing method of MEMS gyroscope random drift error, it is characterized in that comprising the steps:

Step 1: Set the RBF neural network as single input and single output, the input value is x=[Δw], Δw is the angular velocity variation of the MEMS gyroscope, the output value is y=[Y _step ], and Y _step is the calculation step of the real-time mean value method Long, radial basis vector h=[h ₁ h ₂ …h _j …h _n ] ^T , where h _j is the Gaussian base function, n is the number of hidden layer units,

{h h}_{j j} = = exp exp ((- - \frac{{| | | | x x - - {m m}_{j j} | | | |}^{22}}{22 {σ σ}_{j j}^{22}})),, j j = = 1,2 1,2 \cdot &Center Dot; \cdot \cdot \cdot &Center Dot; n no

In the formula, x is the input quantity of the RBF neural network, m _j and σ _j ² are the center and variance of the Gaussian function of the jth hidden layer unit of the RBF neural network, respectively;

The weight vector W of RBF neural network=[w ₁ ,w ₂ ,…,w _n ] ^T ,

Then the output of the RBF neural network y=[Y _step ]=W ^T h; the initial model of the RBF neural network of 1-n-1 is obtained, in which the center m _j of the Gaussian function, the variance σ _j ² and the initial value of the weight vector W Determined by the decoded data of the initial population in step 3;

Step 2: Fix the MEMS gyroscope on the single-axis rate turntable, and then

Within the range, input k angular accelerations to the single-axis rate turntable at equal intervals, and collect the angular velocity output by the MEMS gyroscope and the angular velocity output by the turntable while inputting each angular acceleration to the single-axis rate turntable to obtain k groups of training samples;

is the maximum angular acceleration that the MEMS gyroscope can measure, and the equal interval

k is the number of groups of collected data, 20≤k≤50;

Step 3: Use the training samples obtained in step 2 to train the initial model of the RBF neural network obtained in step 1, and use the genetic algorithm to modify the center, variance, and connection weights from the hidden layer to the output layer of the Gaussian function of the RBF neural network Carry out optimization, and finally obtain the optimal RBF neural network, which specifically includes the following steps:

3.1: Chromosomes are encoded in binary, and the binary encoding of each chromosome includes the center m _j of n Gaussian functions, the variance σ _j ² of n Gaussian functions, and the connection weight W _j of n hidden layers to the output layer , j=1,2...n; center m _j , variance σ _j ² , and connection weight W _j are all represented by p-bit binary numbers, and the total length of a chromosome is 3*p*n, 4≤p≤8;

3.2: Initialization of the population, generating initial N chromosomes, 30≤N≤80;

3.3: Chromosome decoding, converting the three parts of each chromosome in binary code into decimal numbers;

3.4: Calculate the fitness of each chromosome, the specific steps are as follows:

1) Substitute the center m _j and variance σ _j ² of the Gaussian function corresponding to each group of chromosomes obtained by decoding, and the connection weight W _j from the hidden layer to the output layer into the RBF neural network to obtain N RBF neural networks;

3) Calculate the fitness function of the jth chromosome

f_{j} = \frac{1}{E. [(w_{j}^{RT} - w_{j}^{ZT}) * {(w_{j}^{RT} - w_{j}^{ZT})}^{T}]},

In the formula, is the angular velocity output by the turntable;

3.5: Judging whether any one of the two termination conditions is met, if yes, then form the optimal RBF neural network with the data corresponding to the optimal chromosome; if not, perform the population evolution operation and return to step 3.3; the termination Conditions include:

(1). The number of population evolution reaches the preset number of cycles NumCycle, 50≤NumCycle≤100;

(2). Fitness satisfaction

f_{j} > \frac{1}{α * E. [(w_{j}^{o} - w_{j}^{ZT}) * {(w_{j}^{o} - w_{j}^{ZT})}^{T}]},

In the formula,

Described evolution operation comprises the following steps:

1) Keep the top 3 individuals with fitness in the parent population and copy them directly as offspring; then use the roulette method to select the remaining individuals until N individuals are produced;

2) Determine whether the chromosomes are to be crossed according to the set crossover probability P _c , 0.4≤P _c ≤0.8, and the crossover operator adopts the two-point crossover method;

Let the two crossed chromosomes be

and

{PG}_{2} = [A_{1}^{P_{2}}, A_{2}^{P_{2}}, &Center Dot; &Center Dot; &Center Dot;, A_{90}^{P_{2}}],

In the formula,

and

Represent the genes on the corresponding chromosomes respectively;

Randomly generate two positive integers r ₁ and r ₂ less than or equal to 90, r ₁ < r ₂ , and take the chromosome segment greater than or equal to r ₁ and less than or equal to r ₂ as the exchange object, and obtain two new offspring:

{CG CG}_{11} = = [[{A A}_{11}^{{P P}_{11}},, {A A}_{22}^{{P P}_{11}},, \cdot &Center Dot; \cdot &Center Dot; \cdot \cdot,, {A A}_{{r r}_{11} - - 11}^{{P P}_{11}},, {A A}_{{r r}_{11}}^{{P P}_{22}},, \cdot \cdot \cdot &Center Dot; \cdot \cdot,, {A A}_{{r r}_{22}}^{{P P}_{22}},, {A A}_{{r r}_{22} + + 11}^{{P P}_{11}},, \cdot &Center Dot; \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{9090}^{{P P}_{11}}]]

{CG CG}_{22} = = [[{A A}_{11}^{{P P}_{22}},, {A A}_{22}^{{P P}_{22}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{{r r}_{11} - - 11}^{{P P}_{22}},, {A A}_{{r r}_{11}}^{{P P}_{11}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{{r r}_{22}}^{{P P}_{11}},, {A A}_{{r r}_{22} + + 11}^{{P P}_{22}},, \cdot \cdot \cdot \cdot \cdot \cdot,, {A A}_{9090}^{{P P}_{22}}]]

3) Determine whether the chromosome should be mutated according to the set mutation probability P _m , 0.001≤P _m ≤0.2, the mutation operator adopts the basic mutation operator, and randomly selects one or more loci on the chromosome to invert the gene value;

Step 4: Collect the output angular velocity variation of the MEMS gyroscope in real time, input it to the optimal RBF neural network in step 3, and obtain the calculation step size of the real-time mean value in different situations in real time; then according to the calculation step size, use the real-time mean value method to process The original output data of the MEMS gyroscope can be used to obtain the angular velocity data after the random drift error is suppressed.