Research on Fusion Algorithm Based on Butterworth Filter and Kalmar Filter

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1 nd International Conference on Artificial Intelligence and Engineering Applications (AIEA 2017) ISBN: Research on Fusion Algorithm Based on Butterworth Filter and Kalmar Filter ZONGYUAN LIU, WEIDONG SONG, HANZHOU WU and LEI ZHANG ABSRAC When the geomagnetic field strength is measured by the geomagnetic measurement unit, the measurement signal is distorted due to a variety of noise disturbances. In this paper, a geomagnetic measurement method based on Kalmar filter fusion is proposed, and the simulation model is built. he simulation results show that this filtering scheme can effectively filter high frequency noise and random noise, and realize the real signal reduction. KEYWORDS Geomagnetic measurement, simulation model, Kalmar filter, noise. INRODUCION As a low-cost transformation strategy, trajectory correction technology has won unprecedented opportunities for development, and will gradually become the preferred option for conventional weapons upgrades. rajectory correction is generally divided into two methods. One-dimensional correction refers to the range of the arrows to adjust, two-dimensional correction refers to the range and side to adjust [1]. he geomagnetic posture component is intended to provide accurate real-time posture for the artillery, providing prerequisites for the actuation of the guidance assembly during ballistic correction. Generally, the constant geomagnetic field is used to solve the attitude angle. However, due to the complicated noise signal in the measurement process, the measurement signal must be subjected to noise reduction. Common processing tools are: IIR filter, FIR filter, phase-loced loop, Kalmar filter, error compensation. As a single filter tool has limitations, this article will fuse the most commonly used and the most effective method, and ultimately achieve the intended purpose of dealing with complex noise. Zongyuan Liu, Mechanical Engineering College, Shijiazhuang , China; @163.com Weidong Song, Hanzhou Wu, Lei Zhang, Mechanical Engineering College, Shijiazhuang , China 551

2 GEOMAGNEIC FIELD MODEL ESABLISHED Geomagnetic field assumptions Geomagnetic field is the natural formation of the Earth's global magnetic field. Its strength is very small, generally (1 = 109 = 1Wb / m2 = 104Gs) [2], he geomagnetic field vector is related to the local latitude and longitude, and because the change rate of the geomagnetic field is very slow, the constant part (generated by the earth) accounts for more than 95%, and the geomagnetic field vector of the same location can be regarded as constant. he range of artillery is about m (earth radius of m), for the circumference of the Earth, less than 1% [3]. he shell can be considered where the magnetic field environment is constant. Geomagnetic field modeling Geomagnetic size can be measured by the magnetic field strength. he geography of the Arctic and magnetic South Pole has a certain angular deviation, the direction of geomagnetism and north of an angle of magnetic angle D, geomagnetic field is not horizontal. In the northern hemisphere to the ground, Set the magnetic dip angle I to the angle with the horizontal plane, F is the total magnetic vector, H is the geomagnetic horizontal projection, establish the geomagnetic field model. FN F cos Icos D FE F cos Isin D FD F sin I (1) F N, F E FD were geomagnetic northward, eastward, and ground components, respectively. Figure 1. Geomagnetic elements map. 552

3 Rolling angle model Out of the muzzle speed: 2V d 2V d g 0 0 (2) he initial number of revolutions: n 0 60V0 ( 60) / 2 (3) d he turn s angle out of muzzle: 0 n 0 2 dt (4) 0 Air damping attenuation: e xz vt (5) VgIs the muzzle velocity, η d is the entanglement, xz and is the pole damping coefficient GEOMAGNEIC MEASUREMEN PRINCIPLE AND ERROR ANALYSIS Geomagnetic field measurement generally use magnetic, the sensor wors by changing the magnetic flux through the sensor. When the shells are fired in the atmosphere, the geomagnetic field size is constant, the projectile roll will mae the sensor through the magnetic field changes. he local magnetic field is perpendicular to the sensor when the voltage is minimal, the geomagnetic field and the sensor parallel to the maximum voltage [4]. As shown in Figure 2, the magnetic sensor is mounted on the Y, Z axis and rotates with the shaft. B r Is the constant geomagnetic field, B by Bbz is the projection of the geomagnetic field on the rotating axis. Figure 2. Magnetic sensor wor diagram. 553

BUERWORH AND KALMAN FUSION FILER Due to the complex measurement of noise, it is almost impossible to extract the geomagnetic signal completely, and the real signal can only be estimated or predicted

4 BUERWORH AND KALMAN FUSION FILER Due to the complex measurement of noise, it is almost impossible to extract the geomagnetic signal completely, and the real signal can only be estimated or predicted from the observed signal and the system model. First, the Butterworth filter is used to filter the high frequency signal. Butterworth filter design In the specific environment, there are complex interference noises, a single use of Kalmar filter may cause the measurement signal is not accurate. In order to improve the accuracy of the measurement, the use of Butterworth filter signal pre-processing can be carried out before the Kalmar filter, Butterworth filter amplitude square function: 1 (6) 2 H a ( j ) 2N 1 ( / c ) Order calculation: A 10 A N 10 2lg( lg S / / ) P /10 p s (7) Ω p Is the pass band cutoff frequency, Ωs is the stop band cutoff frequency, Ap is the maximum attenuation of the pass band, and As is the minimum attenuation of the stop band. According to the simulation output Figure 3, you can get the filter to eliminate high frequency noise. But because of its slow transition of the transition zone, resulting in the signal is still part of the noise cannot be handled. he calculated variance of the noise is 0.74, and the variance after the Butterworth filter is 0.44, about 41.36% of the noise is processed. Figure 3. Preliminary results of the Butterworth filter. 554

5 aylor formula he classical Kalmar filter model is usually a linear system under white noise conditions, and the optimal estimation is made for the target, and the tracing characteristics are better. However, not all systems have linear properties. For nonlinear systems, one approach is approximated as a linear system, and the other approach is to get an approximation model for the second-order aylor's expansion to approach true value [5]. aylor expansion: f '' ( n) ' f ( x0) 2 f ( x0) x) f ( x0) f ( x0)( x x0) ( x x0) ( x x ) n Rn ( x) 2! n! ( 0 (8) Equation of state and measurement equation he dynamic equation representation of the discrete state space model: X( ) X( 1) W ( 1) Z( ) HX ( ) V ( ) (9) Where: is the discrete imex () is the state of the system at time ; is the state transition matrix s () is the observed signal of the system; W (-1) is the system input noise; V () is the observed noise of the system. he above equation is the general form of the state equation and the measurement equation. Reliable Kalmar filter algorithm requires a precise function model [7].Because the output of the magneto resistive sensor is a triangular function to change the voltage value, its characteristics determine its model is non-linear. If directly tae the classic form of Kalmar will produce a large system bias. First of all, start aylor of the system.hen establish the voltage of the mathematical model. Kalmar filtering process: State step prediction: / 1, 1 1 X X (10) Status Update: K X ( I K H ) X K Z (11) / 1 Filter gain matrix: 1 P / 1H ( H P / 1H R ) 1 K P H R (12) One step prediction covariance matrix: P / 1 / 1P 1 / 1 / 1Q 1 / 1 (13) 555

he signal of the Butterworth filter is further processed, not only eliminating the phase shift, but also controlling the signal noise

6 Covariance Matrix Update: P (14) ( I K H ) P / 1 SIMULAION MODELING AND ANALYSIS OF RESULS After simulation, it can be seen that the unfiltered signal basically covered by noise. he signal of the Butterworth filter is further processed, not only eliminating the phase shift, but also controlling the signal noise within a reasonable range. After Kalmar filter processing, the error mean is reduced from 1.11 to Figure 4. Simulation of real value, measurement values, and filter values. Figure 5. Kalmar filter before and after the error. 556

7 CONCLUSION In view of the geomagnetic measurement process, there are a variety of noise sources interfere with data distortion caused by the problem. In this paper, the establishment of an accurate system model to simulate the real signal. hrough the good low-pass through the Butterworth, filter out the high-frequency signal. And then use the Kalmar strong true value approximation ability to signal the estimation, and ultimately get more accurate signal. his method can mae full use of the advantages of the two filters, which improve the accuracy of the data measurement. he error mean is reduced by about 83.63%. REFERENCES 1. Yulin Yao. System and Filter Design of High - speed Projectile Rolling Angle Magnetic Measurement [D]. Master s degree thesis. Nanjing University of Science and echnology, China p Yunjian Ma. Design of Projectile Angular Velocity Measurement Device Based on Geomagnetic Sensor [J]. Journal of North University of China (Natural Science Edition) p Pan Qu. Real-time settlement of projectile roll angle based on geomagnetic measurement [D]. Master's degree thesis, p Yi-jin Guo. Study on Rotating Stable Rolling Angle Measurement Based on Magneto resistive Sensor [J]. Journal of Beijing Institute of echnology p Xiaoping Huang. Yan Wang. Kalmar filter principle and application [M]. Beijing: Electronic Industry Press, P Shunlan Liu. Jie Wu. Digital signal processing [M]. Xi'an: University of Electronic Science and echnology Press, P Hao ong. Geomagnetic posture and its application in precision guided ammunition [D]. Healthy University, Harbin Institute of echnology, p

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