0 Introduction

The aircraft attitude is an important part of aircraft navigation and attitude control system[1,2]. The precision of aircraft attitude directly affects the carrier attitude control precision and positioning accuracy. Attitude description parameters include mainly cosine matrix, Euler angle and attitude quaternion. The attitude quaternion[3-5] is widely used in flight control system based on its small computation, non-singularity and full pose. But the quaternion belongs to the rotation vector, and its four variables are not independent. It is constrained by the normalized parameters. In the combination of quaternion and nonlinear filtering algorithm, the method based on quaternion to extend Kaman filter algorithm[6,7] is commonly used. However, nonlinearity of the system is strong, and the attitude estimation is often inaccurate. For the actual strong non-linear and non-Gaussian problem, this simple method by using the mean and variance is not enough to represent the true state distribution. The method of particle filter (PF) algorithm[8,9] completely overcomes the problem of system nonlinearity and Gaussian hypothesis[10-12], and it becomes the most suitable filtering method for nonlinear system at present.

In this paper, an aircraft attitude estimation of MEMS sensor based on modified particle filter is proposed, which avoids the shortcomings of Newton method. Taking the STM32F103 as the control core, the attitude information module is composed of the MEMS sensor, the three-axis gyroscope and three-axis accelerometer. The latter two are used to collect the aircraft attitude information in real time, and the attitude estimation processing system is designed. The acquired attitude information data is sent to the STM32 microprocessor to preprocesses via the wireless transceiver module. The data fusion and attitude estimation are completed in the microprocessor.

1 Conjugate gradient method correction

The postures of accelerometer and magnetometer are better than the horizontal and magnetic north poles, which can show good performance under static state and non-magnetic interference mode. The magnetic field interference will bring a serious deviation. Only a sensor can not estimate the precise attitude information data. The corresponding components of magnetometer on the three axes of carrier coordinate system are mx, my and mz. The corresponding components on the three axes of the coordinate system are ax, ay and az.

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“政银企户保”小额贷款应规范贴息流程，对于重复贴息的贷款应事先明确贴息顺序。由于贴息资金有限，其他部门补贴应先于县担保中心补贴拨付。县担保中心应以其他部门补贴手续的书面通知为准，根据实际情况，合理调整贴息金额。扶贫办与担保中心应共同制定贴息资金分配方案，并与财政部门协商，单独开设贴息账户，便于贴息资金的核算统计。此外，对于利息补贴核算不准、发放失误现象，应采取责任到人的制度，提升相关人员业务素质。

1) The error function can be defined as

In Fig.1, f(q)=E(q)TE(q) is the error objective equation. When the objective function f(q) reaches the minimum value, the difference between the attitude angle and the true value of the quaternion is the smallest.

2017年7月6日，正在工作的成锐突然收到公司通知，让他到公司后勤处上班，并且自即日起从事保洁员工作。

新媒体环境有效缓解了学生的心理压力，这能够有效释放学生的心理压力，但由于新媒体平台本身就是一个虚拟性的平台，当中必然会存在众多的虚假信息。学生长期处在这样没有情感交流的环境下，其一旦回归到现实社会中，必然会引发众多新的心理问题，那么，在进行高校学生心理健康教育时，必须要积极推行线上线下相结合的模式。高校必须要密切关注学生的心理变化，对群体性心理问题和个别性的心理问题进行区分，通过针对性地分析，再利用主题班会、谈话等方式有效解决相关的问题[5]。可以说，当代学生的心理健康问题，绝对不是一朝一夕之间形成的，部分是属于突发事件的应激反应，那么，这就需要建立一个常态化的预警机制，以此进行有效的预防。

(1)

Quaternion optimization problem can be converted into error function f(q)=E(q)TE(q). It is used to calculate the minimum value of the problem.

The error function E(k) is established by using the conjugate gradient method to solve the quaternion update step size γn and the gradient direction dn. The measured attitude angle data is modeled by the particle, and the particle weight is updated by the observed value to obtain the estimation and variance of optimized state. The weight fusion is made to determine the optimal weighting factor based on the conjugate gradient method and the modified particle filter.

5.犊牛地方流行性肺炎。在鼻腔、咽、喉可见急性、卡他性炎症。腔窦内有渗出物和血液。扁桃体肿胀、充血。支气管黏膜肿胀、出血，支气管腔常充满纤维蛋白、粘液和血液的混合物。在肺切面上，可见肺炎区与健肺交界处水肿。肺小叶与纤维蛋白粘连。胸膜上有许多出血点。纤维素性心包炎。慢性感染时，肺小叶纤维化。

Qmin,(n+1)=Qmin,n+γndn,

(2)

gn-1=fn-1, gn=fn, d1=-g,

修昔底德认为，雅典和斯巴达均应对伯罗奔尼撒战争承担不可推卸的责任。战争不可避免有两个条件：一是雅典势力不断发展，几乎达到与斯巴达势均力敌的程度；二是雅典的快速崛起引发了斯巴达心理层面上的恐慌［1］63。通过分析21世纪的中美关系，我们可以发现中美关系的现状并不完全符合修昔底德提出的这两大前提条件。

(3)

The success of further refinement will open new doors for developing new functional abundant and non-toxic materials in thermoelectric devices at low cost.

(4)

where γn is the optimal step size, and dn is a gradient and represents the iterative direction of the system.

3) According to the conjugate gradient method, f(q)=E(q)TE(q) can be calculated by

f=JT(q)E(q),

(5)

where JT(q) is the Jacobin matrix of E(q).

学生已经具备了整数的四则运算、小数的意义和性质，乘法运算律的相关知识内容与方法.在这种情况下，应注意调动学生头脑中的已有认知经验，利用旧知识建构并重组新知识.如乘法运算律与小数乘法的意义及小数乘法计算法则之间的关系，通过已经学过的知识习得对新知识的理解.

The attitude correction process shown in Fig.1 is designed by adopting the conjugate gradient method and MEMS sensor.

2 Modified particle filter fusion

2.1 Modified particle filter optimization

Particle scarcity is the main drawback of particle filtration. Doucet proved the inevitability of particle scarcity phenomenon in the particle filter algorithm. Therefore, the particle is assumed to initialize the state variable x0～p(x0), and the modified particle filter is defined as follows.

Table 1 shows the physical quantities output by the MEMS sensor.

2) The PF algorithm is used to update the particles， and its general form can be expressed as

(10)

3) The corresponding weights of particles are calculated.

4) The re-sample particles and weights are calculated, and they are expressed as

(12)

In the experiment, the 8-dimensional trajectories of particles are analyzed to determine the optimal position of the particle motion in Fig.2. And the average fitness of particle swarm iteration can reach 96%-99%, and the attitude parameters optimized by particle swarm optimization are more credible.

The data fusion result is where βi is the weighting factor for the i sensor. The total mean square error is written as

2.2 Weighted fusion

2) The conjugate gradient method is used to optimize the aircraft attitude. According to Eq.(2), vector posture quaternion can be updated as

2、定时约谈，让学生保持倾诉的习惯，随时掌握思想动态。学生突然变得有自闭倾向，主要原因是心理矛盾冲突，有话说不出口，不知道向谁说，利用电话、短信、QQ等线上交流方式，时刻掌握事情发展动态及学生心理。

(13)

where δ2 is the variance of the i sensor. According to the mean square error criterion, the weighting factor can be written as

(14)

where δi has the minimum value, and its general form can be expressed as

(15)

The sensor weights are determined only by their variances. As long as the various sensor weights meet Eq.(15), the total mean square error is the minimum as

The system samples at 100 Hz and stores 500 points of data. Because the magnetometer did not be used, so the pitch angle and roll angle were static test, horizontal sliding and dynamic testing. After the processor completes the posture calculation, the data is sent to the host computer through the 2.4 GHz wireless data transmission module.

(16)

3 Hardware implementation

The three-axis magnetometer (TAM) and the gyro are used as attitude sensors. Sampling period of the TAM is 10 s. The 10-order international geomagnetic reference field (IGRF) model is used to approximate the magnetic field distribution, and the measured noise of magnetometer is assumed to be zero. The attitude calculation module takes STM32F103 as the control core. And MEMS sensor, three-axis gyroscope and three-axis accelerometer are used as the posture information collection module to calculate the attitude information data as shown in Fig.3. They communicate with STM32 via I2C protocol with data bus and clock bus. The acquired attitude information data is sent to the STM32 microprocessor via the wireless transceiver module. The microprocessor preprocesses the current gesture information. The data fusion and attitude estimation are completed in the microprocessor.

笔者以湖北医药学院2016级临本学生为实验对象，在授课过程中，选取三周共12个学时的的时间内对近1 000名学生实施问卷星“微测试”试用，在课前声明“微测试”不和平时成绩挂钩，完全自愿的情况下，试卷有效回收率达到60%以上，说明此种教学方式得到了学生的广泛认可。

天然气中的n-C5、i-C5、C6、C7、C8、C9、C10等重组分对MDEA溶液吸收能力的影响见图1和表1。

4 Experimental data analysis

4.1 MEMS performance parameters and performance specifications

6-axis MEMS can effectively reduce the measurement noise and improve the measurement accuracy by using advanced digital filtering technology. In the module, the attitude calculator is integrated with the proposed particle filter algorithm, which can output the current attitude of the module accurately in the dynamic environment. The attitude measurement accuracy is 0.01°, and the stability is extremely high. The performance is even better than some professional inclinometers. The MEMS sensor does not contain the magnetic field meter. There is no observation of the magnetic field on the yaw angle, so the yaw angle is calculated by the pure integral. It can only achieve a short time of the rotation angle measurement. And X, Y axis angles can be filtered through the gravity field correction. It will be no drift phenomenon.

1) Initialization phase： k=0. The initial test probability distribution p(x0) carries out the samples of N particles：

The six-axis module uses a high-precision gyro accelerometer MPU6050, and the processor is used to read MPU6050 measurement data. This module allows the user to avoid developing MPU6050 complex I2C protocol. Sensor parameters are as follows: acceleration: 6.1e-5g; angular velocity: 7.6e-3 (°)/s; acceleration: 0.01g; angular velocity: 0.05 (°)/s; stance measurement stability: 0.01 °.

急性肾小球肾炎的发病是因为溶血性链球菌感染所致,患者的肾脏有抗原抗体复合物沉积,导致了病理损害,有弥漫性肾小球炎性病变,该疾病临床发病快速,有血尿和蛋白尿等症状,大部分的患者预后情况理想,在进行几个月治疗后,能够痊愈。

4.2 Accuracy comparison of attitude angle measurement data

In order to test the effectiveness of fusion strategy, the quaternion method, the conjugate gradient method and the proposed method are used to estimate the attitude angle data. According to Tables 2-4, the attitude is measured by the quaternion method, and the error of attitude angle data is relatively large.

After the estimation by the conjugate gradient method, the measurement error is reduced. But with the increase of measurement time, the error of measurement increases. The measurement error is kept near 2° after the weighted fusion algorithm is adopted. The convergence of measured value is good, which means that the weighted fusion method can reduce small gyro drift error. The measured value is relatively stable, and the attitude estimation data can maintain good convergence performance.

4.3 Relative error comparison of attitude estimation method

In order to test the validity of the attitude angle of proposed method, Figs.4 and 5 show the comparisons of three attitude angle measurement errors by using the proposed method. When the attitude change is large, the three kinds of attitude angle measurement errors reach 3° in Fig.4. The pitch angle vibration trend is relatively violent.

Meanwhile, the roll angle and heading angle vibration trends are relatively slow, and the maximum measurement error is about 3.5°. Three kinds of attitude angle measurements will tend to be stable after a certain time.

When the attitude change is small in Fig.5, the measurement error is up to 0.4°. The heading angle vibration trends are relatively intense, and the pitch angle and roll angle vibration trends are relatively slow. The maximum measurement error is about 0.3°. It shows the proposed particle filter weighted fusion method can reduce the measurement error. The aircraft has good static performance and dynamic performance.

The quaternion method, the conjugate gradient method and method in Ref.[4] are used to track the attitude of the vehicle for 120 s, as shown in Fig.6, respectively.

The measured error is smaller than other methods by particle filter weighted fusion method. It indicates that the aircraft attitude estimation could remain relatively stable, and weighted fusion reduces the attitude angle estimation error.

4.4 Step tracking comparison

In order to detect tracking characteristics of the aircraft of proposed method, the feedback control system with the optimized method is added to the UAV model by using the Matlab software test environment in Fig.7.

The step size of the simulation is set to 0.001 s, and the 4 order (Runge Kutta) is used to track the step. The yaw angle, pitch angle and roll angle are subjected to step tracking with amplitude of 30° in Figs.8-11.

It can be seen that the proposed method can better track the position and attitude of the aircraft from the step tracking curves of Figs.8-11. In the cases of external interference and uncertainties of UAV own parameters, the proposed method is more robust.

5 Conclusion

The weighted density of particle is obtained by combining the modified particle filter and the conjugate gradient method. The conjugate gradient method is weighted with the particle filter. The attitude analysis system based on STM32 is designed as the core, which can make the attitude of aircraft have good static and dynamic characteristics. The attitude angle based on modified particle filter weighted fusion is stable and accurate. Moreover, it has better robustness and stability.

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