Accelerometer North Finding System Based on the Wavelet Packet De-noising Algorithm and Filtering Circuit

Transcription

1 Sensors & Transducers 204 by IFSA Pubishing, S. L. Acceerometer North Finding System Based on the Waveet Packet De-noising Agorithm and Fitering Circuit LU Yonge, Pan Yingjun, REN Chunhua, 2 LIU Yu Key Lab for Optoeectronic Technoogy & System of MOE, Chongqing University, Chongqing , China 2 Optica Communication Technoogy Institute of Chongqing University of Posts and Teecommunications, Chongqing , China Te.: , fax: E-mai: uyonge08@63.com Received: 30 June 204 /Accepted: 28 Juy 204 /Pubished: 3 Juy 204 Abstract: This paper demonstrates a method and system for north finding with a ow-cost piezoeectricity acceerometer based on the Coriois acceeration principe. The proposed setup is based on the choice of an acceerometer with residua noise of 35 ng Hz -/2. The pane of the north finding system is aigned parae to the oca eve, which heps to eiminate the effect of pane error. The Coriois acceeration caused by the earth s rotation and the acceeration s instantaneous veocity is much weaker than the g-sensitivity acceeration. To get a high accuracy and a shorter time for north finding system, in this paper, the Fitering Circuit and the waveet packet de-nosing agorithm are used as the foowing. First, the hardware is designed as the aternating currents across by fitering circuit, so the DC wi be isoated and the weak AC signa wi be ampified. The DC is interfering signa generated by the earth's gravity. Then, we have used a waveet packet to fiter the signa which has been done through the fitering circuit. Finay, compare the north finding resuts measured by waveet packet fitering with those measured by a ow-pass fiter. Waveet fiter de-noise data shows that waveet packet fitering and waveet fiter measurement have high accuracy. Waveet Packet fitering has stronger abiity to remove burst noise and higher engineering environment adaptabiity than that of Waveet fitering. Experimenta resuts prove the effectiveness and project impementation of the acceerometer north finding method based on waveet packet de-noising agorithm. Copyright 204 IFSA Pubishing, S. L. Keywords: Acceerometer, North finding, Coriois acceeration, Waveet packet, De-noising.. Introduction North finding is a key factor in many ocation systems and is typicay obtained by using digita magnetic compasses []. There are many instruments capabe of achieving degree north finding accuracies. However, the magnetic compass north finding system can be easiy degraded by nearby ferrous materias or by eectromagnetic interference [2]. Gyroscope compass using the comprehensive effect of earth rotation anguar veocity [], [3]. The piece of the gyroscope north finding system is too high. The ceestia north finding system can t work on the ground we, and it does not work underground [4], [5]

2 In the 2 st century, traditiona natura resource is reativey scarce [6]. Before nascent energy appears, the smaer reserves of resource expoitation and traditiona resources secondary expoitation seem to be particuary important. One of the key technoogies for the resources secondary expoitation and smaer reserves resource expoitation is north finding technoogy, which need ow cost and high accuracies. With the continuous improvement of the accuracy of the acceerometer and maturity of digita signa processing technoogy [7], making the acceerometer north finding system which based on Coriois acceeration becomes a reaity. The pane of turntabe error, samping error et a. restrict the measurement accuracy of the north finding based on acceerometer. There are many improvements, such as choosing more performance acceerometer to measure the Coriois acceeration [8], improving the accuracy of the samping circuit, or increasing the speed of the turntabe. These improvements can improve the north finding measurement accuracy. However, this hardware improvement requires higher cost and onger time. In this paper, we discuss the most significant error sources that degrade the performance of acceerometer north finding system. This is done in order to maximize the performance of the acceerometer. Theoreticay, if the errors of acceerometer are compensated, it is possibe to measure very sma acceeration, and we can get a high eve of the system s measurement. First, the signa of the acceerometer wi be fitered through the fiter circuit. In this part, the direct current signa wi be removed from the signa, which is caused by the gravity. Then it is unused for the north finding. The AC signa wi be ampified by the OP07. Finay, the waveet packet wi further fiter the noise component of the AC signa. This method further effective combination of hardware and software to achieve ow cost, strong anti-interference north finding system. where a c is the acceeration of the partice in the rotating system, v is the veocity of the partice in the rotating system, and w e is the anguar veocity vector which has magnitude equa to the rotation rate ω and is directed aong the axis of rotation of the rotating reference frame, and the symbo represents the cross product operator. Just as showed the Fig.. When the acceerometer moves with the turntabe, the direction of the acceerometer s veocity is changing, so the ange between the direction of earth s rotation in the oca pane and the direction of the acceerometer s speed is changing with the acceerometer moving. As a resut, the Coriois acceeration is ony reevant to the ange. In other words, we can find the north by measuring the Coriois acceeration. In this way, acceerometer outputs the idea transfer curve shown in Fig.. The peak corresponds to the true north, so by seeking peak of the ine can we achieve the north finding purposes. ω e (a) 2. The Principe of Acceerometer North Finding System The acceerometer north finding system is based on the principe of the Coriois acceeration. The mathematica expression for the Coriois force appeared in an 835 paper written by French scientist Gaspard-Gustave Coriois [9]. At a given rate of rotation of the observer, the magnitude of the Coriois acceeration of the object is proportiona to the veocity of the object and aso to the sine of the ange between the direction of movement of the object and the axis of rotation. The vector formua for the magnitude and direction of the Coriois acceeration [0] is: a = 2v w, () c e (b) Fig.. Schematic for (a) an acceerometer movement (b) the acceerometer output. 245

3 3. Anaysis the Acceerometer Output Signa and Hardware Design Acceerometer s output signa contains four parts: a constant vaue output (acceerometer sensitive gravitationa fied); Coriois acceeration vaues; samping circuit measurement error; and acceerometer output error. Foowing formua: a= a + ε + ε + a, (2) g a c Sensitive acceerometer output a g is as a constant gravitationa fied; acceerometer output error ε a is white noise; samping circuit error ε is the same as the white noise error; a c is the Coriois acceeration which incudes north finding information. Coriois acceeration just as the foowing: input, but certain artifacts may affect the measurement response due to senor dynamic and eectronic noise []. The acceerometer s noise and the outside interference vibration wi affect the accuracy of north finding. Waveet transform (WT) is a signa processing too that can be considered as an extension of the traditiona Fourier transform with adjustabe window ocation and size [2]. Waveet packet transform (WPT) is an extension of WT that provides a compete eve-by-eve frequency-time decomposition [3], [4]. The basic concept of the WPT and its matrix representation are briefy presented here. The main characteristic of WPT is that it aso decomposes high frequency bands which are kept intact for waveet decomposition (WT) [6]. Therefore, the time frequency information in the high frequency bands can aso be anayzed in detais. a = 2v w = 2ω r w, (3) c e e where v is the inear veocity of the acceerometer, and ω is the acceerometer rotationa anguar veocity. r is the distance from the center of the turntabe to the acceerometer, and ω e is the anguar veocity of the Earth's rotation component in the horizonta direction. The output of the north finding systems just is as the foowing. The distance r between the acceerometer and the center of the turntabe is 0 cm, and the rotation speed of the turntabe is 8 R/S. The earth s rotation component in the horizonta direction in the north atitude is 6.3e-05 rad/s. In this way, the ampitude of the Coriois acceeration is 7.9e-05 G, and the frequency is 8 Hz. Using origina data for finding north is difficut because the Coriois acceeration is far ess than that of gravity acceerometer. In order to improve the measured signa quaity, the stand procedures, such as isoation and ampification, have been used. As mentioned above, the main purpose of the system is three-fod: first, to isoate the direct current, the vaue of which is much bigger than the aternating current vaue, the current signa wi change into the votage signa in the current samping circuit which is provided with a resistors R0, the direct votage wi be cut-off, whie aternating votage wi pass through the capacitance C. And second, to ampify the aternating votage was reaized by using two typica operationa (OP07) ampifiers, at ast, the votage to frequency converter was using AD652. The schematic circuit is just as the Fig The Principe of the Waveet Packet The acceerometer has been widey used in various appications, however, such anaog transducer-incorporated eectronic measurement system produces signa proportiona to the desired Fig. 2. The schematic circuit diagram for isoation and ampification. It aso can seect corresponding frequency band adaptivey according to the characteristics of the anayzed signa, matching with the signa spectrum [5], thereby increasing the time frequency resoution. Hence, WPT has a wider range of appications than the WT since it can achieve a very fine resoution in both high and ow frequency bands. The waveet transform can be impemented by means of a pair of ow-pass and high-pass waveet fiters. Define h(k) and g(k)=(-) k h(-k). These fiters, aso known as quadrature mirror fiters, are constructed from the seected waveet function ψ (t) and their corresponding scaing function ϕ (t) is just as foows [7]: ϕ( x) = hkϕ(2 t k), (4) ψ( x) = gkϕ(2 t k) To perform waveet packet transform of a signa at a certain eve, the function in the eq. (4) is expressed as: u2n( x) = 2 hkun(2 t k), (5) u2n+ ( x) = 2 gkun(2 t k) 246

4 where u 0 (t) = φ (t), and u (t) = ψ (t). The signa is decomposed as [8], [9]: d j,2n( k) = h 2kd j+, n( ), (6) d j,2n+ ( k) = g 2kd j+, n( ) where d j, n is defined as the waveet coefficients at the eve j, n is defined as sub-band, d j+,2n and d j+,2n+ are defined as the waveet coefficients at the eve j+, 2n and 2n+ and they are sub-bands, and the m is the number of the waveet coefficients. Reconstruction formua of the waveet packer transform is: origina date we. Compare with the waveet packet fitering resut, the data of waveet fitering has a better smooth, and the waveet fitering can show much more information. The two curves of the waveet fitering and waveet packet fitering are very simiar, which means there is a sma difference between the two kinds of the fitering. However, the waveet packet fitering can suppress the outside interference signa which is better than the waveet fitering. More detais are shown in the Fig. 5. The Fig. 5 is just part of the Fig. 4., d ( k) = h d () + g d () j+, n k 2 j,2n k 2 j,2n+ (7) 5. Experiment Resuts In this paper, we chose the piezoeectricity acceerometer as the acceeration sensor, the measure range of the acceerometer is 5 G, scae factor is 0 V/G and the residua noise is 35 ng Hz -/2. The acceerometer is fixed on the sma turntabe, and the turntabe is paced on the pane of the two axis turntabe, which can hep the pane of the sma turntabe parae with the horizonta pane. As shown in Fig. 3. As we know, the change of the temperature infuences the accuracy of acceeration measurement. We put the system in the aboratory, and the temperature is 20 for 2 hours. Fig. 4. The difference of different fitering resut. Fig. 5. The partia ampification of the fitering resut. Fig. 3. The north finding experimenta system. In the Fig. 4, is the origina data, the back coor curve is the resut of ow-pass fitering, the rad coor curve is the resut of the waveet fitering and the bue coor curve is the resut of the waveet packet fitering. We can see from the Fig. 4 that a of the three ways of fitering can suppress the noise of the The fitering effects of the three ways are just as the Tabe. The ow-pass fitering way can get ess SNR and PSNR, the SNR of ow-pass fitering is 77.3 % to the SNR of waveet fiter, and % to that of the waveet packet fitering, respectivey. The PSNR of the ow-pass fitering is % to PSNR of waveet fiter and % to that of waveet packet fitering, respectivey. However, the resut of the ow-pass fitering is with bigger RMSE and worse simiitude. Both of the waveet fitering and waveet packet fitering have ess RMSE and more simiitude. The SNR, PSNR, RMSE and simiitude of the both fitering ways are in the same eve. Combine with the Fig. 5, we can know that in the same condition, the waveet packet fitering can 247

5 eiminate burst noise better than the waveet packet. In other words, the north finding system with waveet packet fitering can depress the outside interference signa we. The ow-pass fitering way de-noise can get idea resut. However, the ow-pass fitering way can t remove the noise. The noise s frequency is cose to the frequency of the signa of the acceeration, as shown in the Fig. 5. Tabe. The resut of the different. Low-pass Waveet Waveet fiter fiter packet fiter SNR PSNR RMSE Simiarity % % % The error of north finding Summary In this paper, the waveet packet fitering de-noise way is used in the north finding system, the isoation and ampification circuit are designed, the foowing experiment and test have been done, and the date shows that the north finding system de-noise with ow-pass fiter way can reach ess SNR and RSNR eve. However, it can t find the true north perfecty. The SNR, PSNR, RMSR and simiitude of the both of waveet fiter and waveet packet fiter are in the same eve. However, the waveet packet fiter can remove burst noise we. In this way, the system can adopt the abnorma vibration in the environment compete and it has a better robust faut toerance. The experimenta resuts indicated that the acceerometer north finding based on the waveet packer fiter de-noise is rationaity, and the fitering way is effective. The above work gives a theoretica guidance for the acceerometer north finding system in the engineering. Acknowedgements This work was supported in part by the Nationa Natura Science Foundation of China under Grant and Grant 62749, in part by the Natura Science Foundation Project of CQ CSTC under Grant CSTC202jjB References []. L. I. Iozan, M. Kirkko-Jaakkoa, J. Coin, J. Takaa, C. Rusu, Using a MEMS gyroscope to measure the Earth's rotation for gyrocompassing appications, Measurement Science and Technoogy, Vo. 23, No. 2, 202, pp. -8. [2]. Li Ji, Zhang Qi, Chen Dixiang, Magnetic interferentia fied compensation in geomagnetic measurement, Transactions of the Institute of Measurement and Contro, Vo. 36, Issue 2, 204, pp [3]. Xie Mu-Jun, Li Li-Ting, Wang Zhi-Qian, Study and appication of variabe period samping in strap-down north seeking system, Energy Procedia, Vo. 6, Part C, 202, pp [4]. Lijun Zhang, Huabo Yang, Shifeng Zhang, Hong Cai, Shan Qian, Strapdown stear-inertia guidance system for aunch vehice, Aerospace Science and Technoogy, Vo. 33, 204, pp [5]. H. Zhang, W. Zheng, J. Wu, G. Tang, Investigation on singe-star stear-inertia guidance principe using equivaent formation compression theory, Science in China, Series E: Technoogica Sciences, Vo. 52, No. 0, 2009, pp [6]. N. Barbaios, P. Tzionas, A robust approach for muti-agent natura resource aocation based on stochastic optimization agorithms, Appied Soft Computing, Vo. 8, May 204, pp [7]. Caudia Comi, Aberto Corigiano, Ado Ghisi, Sarah Zerbini, A resonant micro acceerometer based on eectrostatic stiffness variation, Mechanica, Vo. 48, 203, pp [8]. Guofu Sun, Qitai Gu, Acceerometer based north finding system, in Proceedings of the IEEE Position Location and Navigation Symposium, San Diego, CA, 3-6 March 2000, pp [9]. Gaspard-Gustave de Coriois, Sur es équations du mouvement reatif des systèmes de corps, Journa de Écoe Poytechnique, cahier, XV, cahier XXIV, 835, pp [0]. David Hestenes, New foundations for cassica mechanics, Kuwer Academic Pubishers, The Netherands, 990, pp. 32. []. W.-C. Lin, C.-X. Dai, D.-L. Deng, K-S. Ou, Performance evauation of drift-free integration for navigation and veocity feedback appications, Journa of the Chinese Institute of Engineers, Vo. 35, Issue 6, 202, pp [2]. S. A. Neid, P. D. McFadden, M. S. Wiiams, A review of time-frequency methods for structura vibration anaysis, Engineering Structures, Vo. 25, Issue (6), 2003, pp [3]. Pave Boškoski, Đani Juričić, Faut detection of mechanica drives under variabe operating conditions based on waveet packet Rényi entropy signatures, Mechanica Systems and Signa Processing, Vo. 3, August 202, pp [4]. Kexin Xing, Peipei Yang, Jian Huang, Yongji Wang, Quanmin Zhu, A rea-time EMG pattern recognition method for virtua myoeectric hand contro, Neurocomputing, Vo. 36, 204, pp [5]. Tian He, Denghong Xiao, Qiang Pan, Anaysis on accuracy improvement of rotor-stator rubbing ocaization based on acoustic emission beamforming method, Utrasonics, Vo. 54, Issue, January 204, pp [6]. Pengfei Li, Yongying Jiang, Jiawei Xiang, Experimenta investigation for faut diagnosis based on a hybrid approach using waveet packet and support vector cassification, The Scientific Word Journa, Vo. 204, 204, Artice ID 45807, pp. -0. [7]. Ruqiang Yan, Robert X. Gao, Xuefeng Chen, Waveets for faut diagnosis of rotary machines: A review with appications, Signa Processing, Vo. 96, 204, pp. -5. [8]. R. R. Coifman, M. V. Wickerhauser, Entropy-based agorithms for best basis seection, IEEE 248

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