Research ArticleA Gyro Signal Characteristics Analysis Method Based onEmpirical Mode Decomposition

Qinghua Zeng12 Shanshan Gu12 Jianye Liu12 Sheng Liu3 and Weina Chen12

1 Jiangsu Key Laboratory of Internet of Things and Control Technologies Nanjing University of Aeronautics and Astronautics29 Jiangjun Road Nanjing 211106 China2Navigation Research Center College of Automation Engineering Nanjing University of Aeronautics and Astronautics29 Jiangjun Road Nanjing 211106 China3AVIC Luoyang Electro-Optical Equipment Research Institute Luoyang 471009 China

Correspondence should be addressed to Qinghua Zeng zengqhnuaaeducn

Received 9 March 2016 Revised 14 June 2016 Accepted 22 June 2016

Academic Editor Andrea Cusano

Copyright copy 2016 Qinghua Zeng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

It is difficult to analyze the nonstationary gyro signal in detail for the Allan variance (AV) analysis method A novel approachin the time-frequency domain for gyro signal characteristics analysis is proposed based on the empirical mode decompositionand Allan variance (EMDAV) The output signal of gyro is decomposed by empirical mode decomposition (EMD) first and thenthe decomposed signal is analyzed by AV algorithm Consequently the gyro noise characteristics are demonstrated in the time-frequency domain with a three-dimensional (3D) manner Practical data of fiber optic gyro (FOG) and MEMS gyro are processedby the AV method and the EMDAV algorithm separately The results indicate that the details of gyro signal characteristics indifferent frequency bands can be described with the help of EMDAV and the analysis dimensions are extended compared with thecommon AVThe proposed EMDAV as a complementary tool of the AV which provides a theoretical reference for the gyro signalpreprocessing is a general approach for the analysis and evaluation of gyro performance

1 Introduction

As a key device for angular velocity detection gyro plays animportant role in inertial navigation system However theerrors caused by the influence of gyro working environmentwill be accumulated with working time and the navigationaccuracy will be deteriorated [1] Consequently it is impor-tant to analyze the characteristic of gyro signal which ishelpful to identify the performance of the gyros

The traditional Allan variance (AV) algorithm whichcan reflect the characteristics of signal is widely used toevaluate the performance of gyro [2 3] However it can onlyachieve the signal characteristics analysis in the time domainActually due to the complexity of practical gyro signal itis difficult to obtain the signal species and distributionscomprehensively in time domain So it is essential to analyzethe gyro signal in the time-frequency domain

Wavelet transform and empirical mode decomposition(EMD) are commonly adopted to implement the signal time-frequency analysis Nonetheless the problems of frequencyoverlapping threshold instability and decomposition andreconstruction algorithm errors existing in the wavelet trans-form bring some limitations for the gyro signal processing[4] While being an adaptive local time-frequency analysismethod [5] EMD does not possess the above disadvantagesThe signal can be decomposed by its characteristic to a finitenumber of empirical mode functions by EMD which iscommonly applied in signal denoising [6] trend extraction[7] and so on

In this paper a gyro signal characteristic analysisapproach based on the empirical mode decomposition andAllan variance (EMDAV) is proposed which employs AV toanalyze the decomposed gyro signal of EMD Compared withthe sole time domain characteristic of gyro signal obtained by

Hindawi Publishing CorporationJournal of SensorsVolume 2016 Article ID 3613878 7 pageshttpdxdoiorg10115520163613878

2 Journal of Sensors

traditional AV the proposed method enriches the real gyroperformance evaluation approaches supplies more detailedgyro signal characteristics information in the joint time-frequency domain and provides the theoretical basis for thedenoising threshold determination in signal preprocessing

2 Allan Variance Analysis

As a common analysis tool in the time domain AV is widelyapplied to identify the gyro errors characteristics Assumingthat there is a gyro signal sample sequence of 119909(119905) with thelength of119873 and the sampling frequency of119891 its discrete-timeAV can be expressed as [8]

1205902

AVAR (120591) =1

2⟨(119909119905119896+120591

(120591) minus 119909119905119896

(120591))2

⟩ (1)

where the operator ⟨sdot⟩ denotes ensemble averaging 119909119905119896

(120591) isthe averaged measure of FOG signal at time 119905

119896 and 120591 = 119873119891

is observation intervalIt is assumed that the various error sources are statistically

independent then the AV can be described as the sumof squares of quantization noise angle random walk biasinstability rate random walk and rate ramp [9 10]

1205902

(120591) = 1205902

QN (120591) + 1205902

ARW (120591) + 1205902

BI (120591) + 1205902

RRW (120591)

+ 1205902

RR (120591)

=31198762

1205912+

1198732

120591+

21198612

120587ln 2 +

1198702120591

3+

11987721205912

2

(2)

where 120590ARW 120590RRW 120590BI 120590QN and 120590RR are the variances of theabove five kinds of errors separately and 119876 119873 119861 119870 and 119877

are the corresponding AV coefficients

3 EMDAV Analysis

The traditional AV analysis method which presents the gyronoise characteristics in the only timedomain cannot reflect itsdistributions among different frequency bands However thenoise characteristics vary with the frequency To reveal moredetails of the gyro noise characteristic the EMDAV methodis proposed in this paper

As a method utilized to analyze the nonlinear and non-stationary signal EMD decomposes the signal on the basisof time scale characteristics There is no need to set the basicfunctions in advance for EMDwhich can decompose any typeof signal Thus EMD has obvious advantages in processingnonlinear and nonstationary signal

The EMDAV algorithm proposed in the paper is basedon the EMD and AV After decomposing the gyro signal withEMD the AV can be obtained with the help of intrinsic modefunction (IMF) Lastly the AV logarithmic curve over timeand frequency can be depicted The detailed algorithm flowchart is shown in Figure 1

The steps of the EMDAV based on gyro signal character-istics analysis method can be summarized as follows

(1) Find all the local maxima and minima of the originalsignal 119909(119905)

Begin

Find the local maxima andminima of signal

Fit an upper envelope and alow envelope

Compute the mean of thetwo envelopes

Obtain IMF

Stopping criterion

End

No

Yes

Calculate the Allanvariance corresponding to the

IMF components

Depict the Allan variancelogarithmic curve

lt one constant

Figure 1 Flow chart of AV algorithm based on EMD

(2) Fit the estimated points of the first step using naturalcubic spline to form an upper envelope of 119890max(119905) and a lowerenvelope of 119890min(119905)

(3) Compute the mean of the two envelopes

119898119894(119905) =

119890max (119905) + 119890min (119905)

2 (3)

where 119894 = 1 2 119899 119899 is the number of decomposition levels(4) Refine the estimate ℎ

119894(119905) of the IMF by subtracting the

mean solved in the previous step from the current signal

ℎ119894(119905) = 119909

119894(119905) minus 119898

119894(119905) (4)

where

119909119894(119905) =

119909 (119905) 119894 = 1

119909 (119905) minus

119894minus1

sum119895=1

ℎ119895(119905) 119894 ge 2

(5)

(5) Proceed from step (1) again unless a stopping criterionhas been fulfilled The stopping criterion is [11]

SD =

119879

sum119905=0

[

1003816100381610038161003816ℎ119894minus1 (119905) minus ℎ119894(119905)

10038161003816100381610038162

ℎ2119894minus1

(119905)] (6)

Journal of Sensors 3

(a)

MEMS gyro

(b)

Figure 2 FOG and MEMS gyros (a) FOG on turntable and (b) MEMS gyro

where SD is a screening threshold The iteration stops whenSD is smaller than a constant The constant value can be setbetween 02 and 03 [12]

Eventually the IMF components of ℎ1(119905) ℎ2(119905) ℎ

119899(119905)

and the remainder of 119903119899(119905) can be obtainedThen the original

signal can be expressed as

119909 (119905) =

119899

sum119894=1

ℎ119894(119905) + 119903

119899(119905) (7)

(6) Calculate the AV coefficients corresponding to the IMFcomponents and analyze the signal characteristics in differentfrequency bands

From the above EMDAV procedures we can see that theIMF of ℎ

119894(119905) indicates the different frequency components

With the increase of decomposition level the frequency ofdecomposed signal decreases gradually Namely the first IMFrepresents the highest frequency component of the originalsignal The frequencies of subsequent IMFs reduce almost inthe form of the negative power of 2 [13] until the frequencyof the remainder is very small Consequently each IMFcorresponds to the signal component of different frequency

Compared with the traditional AV analysis method thecharacteristics and distributions of gyro signal in differentfrequency bands can be depicted in detail with EMDAValgorithm One more piece of dimensional information canbe shown in three-dimensional (3D) logarithmic graph ofEMDAV compared to that in 2D curve of traditional AV

4 Experiment Results and Analysis

To verify the algorithm proposed in this paper AV andEMDAV are compared to analyze the FOG and MEMS gyrosignals Practical fiber optical gyro (FOG) and microelectro-mechanical system (MEMS) gyro static signals are acquiredwith the sampling frequency of 100Hz and the samplingduration of 600 s The scene of experiment is shown inFigure 2

As we all know traditional AV coefficients come fromoriginal gyro signal and we can compare them with EMDAV

coefficients at the same time Figure 3 shows the originalsignals and parts of IMF components decomposed by EMDIt can be seen that the characteristics of FOG and MEMSgyro signals are similar the first level of decomposed signalbelongs to high frequency part and the frequency decreaseswith the increasing of decomposition level

Theoriginal signals and IMF components decomposed byEMD are analyzed with AV and corresponding coefficients(AV coefficients and EMDAV coefficients) are plotted in alogarithmic graph as shown in Figure 4 FromFigure 4we canfind that the 16 curves in the first group from top to bottomare the AV logarithm curves of MEMS gyro original signal(the 0 level traditional AV) and IMFs (1ndash15 levels EMDAV)respectively Because of the poor accuracy of MEMS gyrothe biggest AV value reaches 105 The 16 profiles in thesecond group are the respective AV logarithm curves of FOGgyro original signal (the 0 level traditional AV) and IMFs(EMDAV) where the biggest AV value reaches 1 Taking theAV values at correlation time of 001 s for comparison themaximum is from the original signal for both gyros by whichthe first level of decomposed signals followed The AV valuesdecrease until the decomposition level increases to the lastone whose value corresponds to the minimum

In addition it can be seen from Table 1 and Figure 4that the signal distributions of FOG and MEMS gyro aresimilar that is to say with the increase of decomposition levelthe proportion of angle random walk is reduced while theproportion of rate randomwalk is increasedAlso it is obviousthat angle random walk is dominant in the high frequencysignal while rate randomwalk accounts for a large proportionin the low frequency signal In consequence gyro signal canbe denoised specifically with the demand of the navigationsystem

Figure 5 shows the relationship between AV and EMDAVcoefficients where the zero level means the AV coefficient oforiginal gyro signals As mentioned before the frequency ofeach IMF is decreased in the form of negative power of 2gradually which indicates the fact that the higher the EMDdecomposition levels the smaller the signal frequency It also

4 Journal of Sensors

0 100 200 300 400 500 600123

Orig

in

t (s)

times10minus3

0 100 200 300 400 500 600minus2

02

IMF

7

t (s)

times10minus4

0 100 200 300 400 500 600minus5

05

IMF

4IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)

t (s)

times10minus4

0 100 200 300 400 500 600minus5

05

IMF

1

t (s)

times10minus4

0 100 200 300 400 500 600minus1

01

IMF

12

t (s)

times10minus5

0 100 200 300 400 500 600minus5

05

IMF

10

t (s)

times10minus5

0 100 200 300 400 500 600minus2

02

IMF

15

t (s)

times10minus6

(a)

t (s)0 100 200 300 400 500 600

minus2minus1

0

Orig

in

t (s)0 100 200 300 400 500 600

minus050

05

IMF

1

t (s)0 100 200 300 400 500 600

minus010

01

IMF

4

t (s)0 100 200 300 400 500 600

minus010

01

IMF

7

t (s)0 100 200 300 400 500 600

minus0020

002IM

F 10

t (s)0 100 200 300 400 500 600

minus0020

002

IMF

12

t (s)0 100 200 300 400 500 600

minus505

IMF

15

times10minus3

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

(b)

Figure 3 IMFs from EMD of gyro signals (a) EMD of FOG signal and (b) EMD of MEMS gyro signal

Table 1 AV coefficients of gyro signals on some frequencies

Signal AV coefficients119873 (∘h12) 119861 (∘h) 119870 (∘h32) 119877 (∘h2) 119876 (120583rad)

FOG

AV (original signal) 140119890 minus 3 571119890 minus 1 1221198901 4431198901 355119890 minus 2

EMDAV (signalsdecomposed byEMD)

Level 1 160119890 minus 3 464119890 minus 1 9841198900 3561198901 376119890 minus 2

Level 4 415119890 minus 4 175119890 minus 1 3951198900 1441198901 740119890 minus 3

Level 7 133119890 minus 4 666119890 minus 2 1201198900 4251198900 190119890 minus 3

Level 10 219119890 minus 5 102119890 minus 2 320119890 minus 1 1241198900 317119890 minus 4

Level 15 432119890 minus 7 210119890 minus 4 236119890 minus 2 772119890 minus 2 615119890 minus 6

MEMS gyro

AV (original signal) 591119890 minus 1 3101198901 6201198902 2241198903 1391198900

EMDAV (signalsdecomposed byEMD)

Level 1 137119890 minus 1 1411198901 2101198902 7151198902 8781198900

Level 4 101119890 minus 1 9851198901 2161198903 7851198903 2371198900

Level 7 993119890 minus 2 4921198901 8501198902 2991198903 1401198900

Level 10 159119890 minus 2 7361198900 2541198902 9811198902 230119890 minus 1

Level 15 130119890 minus 3 612119890 minus 1 6541198901 1801198902 181119890 minus 2

Journal of Sensors 5

Table 2 Performance contrasts between AV and EMDAV

AV EMDAVSignal Stationary signal Stationary and nonstationary signalResult presentation (fingerprint) 2D 3DDomain of signal analysis Time domain Time-frequency domainAbility of signal identification at different frequencies No YesNumbers of obtained parameters can be referenced Less MoreReference for signal denoising No Yes

Correlation time (s)

AVEMDAV 1EMDAV 2EMDAV 3EMDAV 4EMDAV 5EMDAV 6EMDAV 7

EMDAV 8EMDAV 9EMDAV 10EMDAV 11EMDAV 12EMDAV 13EMDAV 14EMDAV 15

MEMS gyro

FOG

1010

105

100

10minus5

10minus10

10minus15

Alla

n va

rianc

e (de

g2h

2)

10minus2 10minus1 100 101 102 103

Figure 4 Logarithmic diagram of AV and EMDAV

shows that the EMDAVcoefficients trend to decreasewith thedecrease of signal frequency

From the comparison of Figures 5(a) and 5(b) thecoefficients of MEMS gyro are much larger than that of FOGnamely the accuracy of MEMS gyro is worse than FOG Asfor FOG (in Figure 5(a)) the EMDAV coefficients in the 5thlevel are larger which means that the angle random walknoise bias instability noise rate random walk noise and rateramp noise are more dominant The EMDAV coefficients ofthe 8th level and higher level are very small and the EMDdenoising method will be effective when the decompositionlevels are larger than 7 As forMEMS gyro (in Figure 5(b)) theEMDAV coefficients are dominant in the 2nd level and arelargest for 4 parameters and reference decomposition levelof 9 will be applicable for EMD denoising method Thereforethe algorithm proposed in this paper can provide guidancefor gyro denoising

The relationships among AV values of IMFs correlationtime and EMD decomposition levels are shown in the AV

and EMDAV 3D logarithmic graph of Figure 6 where thetop curves are AV values of MEME gyro while the bottomare of FOG Traditional AV logarithmic diagram is the 2Dcurve on the 0 level and EMDAV logarithmic diagram is the3D view on 1ndash15 levels It can be found that though the AVvalues of MEMS gyro are larger than that of FOG the signalmagnitudes of the both gyros tend to reducewith the decreaseof frequency The 3D figures of both FOG and MEMS gyrosignals show the special characteristics of the FOG andMEMS gyro performance The AV values decrease with theincrease of EMD levels and correlation time The ridgeswhich also can be seen from Figure 4 are the collections ofthe points with a zero slope in logarithmic diagram of everyIMF signal Obviously the ridge of FOG signal is consistentwith that of MEMS gyro signal

The contrasts between AV and EMDAV are listed inTable 2 As can be seen from the table EMDAV can ana-lyze the both stationary and nonstationary signals with theanalysis results showing the 3D relationship (served as the3D fingerprint of a gyro) among AV time and frequency Inaddition various kinds of noises can be identified to providemore details about the signal characteristics of gyro EMDAVcan obtain more referable parameters than AV and provide areference for signal denoising

5 Conclusion

An AV analysis algorithm based on EMD for gyro error isproposed in this paper The AV value is calculated by thesignal decomposed based on the characteristic time scale andthe signal characteristics of gyro error in different frequencybands are revealed Theoretical analysis and experiments ofpractical FOG and MEMS gyro data indicate the following

(1) Compared with the characteristic of gyro error inthe sole time domain given by the traditional AVthe EMDAV algorithm can describe the distributionson different kinds of gyro signals in time-frequencydomain

(2) The EMDAV algorithm extends the dimensions ofgyro signal characteristics analysis and hence obtainsmore parameters than traditional AV

(3) The EMDAV algorithm is able to determine thedecomposition level for gyro signal denoising andprovide a theoretical guidance to the gyro signaldenoising and other preprocessing algorithms

6 Journal of Sensors

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times10minus3

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

1020

EMD decomposition level

0 2 4 6 8 10 12 14 160

2040

EMD decomposition level

R(d

egh

2)

0 2 4 6 8 10 12 14 160

002004

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)

(a)

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

0 2 4 6 8 10 12 14 160

100200

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

20004000

EMD decomposition level

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times104

0 2 4 6 8 10 12 14 1605

10

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)R

(deg

h2)

(b)

Figure 5 Relationship between AV coefficients (level 0) and EMDAV coefficients (a) FOG and (b) MEMS gyro

100

10minus5

10minus10

15

10

5

0 10minus2100

102

Alla

n va

rianc

e (de

g2h

2) MEMS gyro

FOG

t (s)

EMD decomposition level

(a)

Alla

n va

rianc

e (de

g2h

2)

MEMS gyro

FOG

t (s)

100

10minus10

102

100

10minus215

10

5

0

EMD decomposition level

(b)

Figure 6 AV and EMDAV 3D logarithmic graph (a) front view and (b) back view

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been mainly funded by the FundamentalResearch Funds for the Central Universities (NS2015037) andpartly funded by the National Natural Science Foundation

of China (Grants nos 61533008 and 61374115 to Jianye Liu)and Jiangsu Key Laboratory of Internet ofThings andControlTechnologies

References

[1] J Lai P Lv J Liu and B Jiang ldquoNoncommutativity erroranalysis of strapdown inertial navigation system under thevibration in UAVsrdquo International Journal of Advanced RoboticSystems vol 9 article 134 2012

Journal of Sensors 7

[2] R Peesapati S L Sabat K P Karthik J Nayak and NGiribabu ldquoEfficient hybrid Kalman filter for denoising fiberoptic gyroscope signalrdquo Optik vol 124 no 20 pp 4549ndash45562013

[3] V V Chikovani ldquoPerformance parameters comparison of ringlaser coriolis vibratory and fiber-optic gyros based on Allanvariance analysisrdquo in Proceedings of the IEEE 2nd InternationalConference on Actual Problems of Unmanned Air VehiclesDevelopments (APUAVD rsquo13) pp 153ndash156 IEEE Kiev UkraineOctober 2013

[4] C-S Qu T-Z Lu and Y Tan ldquoA modified empirical modedecomposition method with applications to signal de-noisingrdquoActa Automatica Sinica vol 36 no 1 pp 67ndash73 2010

[5] Y Gan L Sui G Xiao and Y Duan ldquoEMD de-noising theoryconsidering static and dynamic conditions and its applicationsin INSrdquo LectureNotes in Electrical Engineering vol 245 pp 507ndash515 2013

[6] Y Zhang SWang andD Xia ldquoEMD-based denoisingmethodsin the MEMS gyroscope de-driftrdquo in Proceedings of the 5thIEEE International Conference on NanoMicro Engineered andMolecular Systems (NEMS rsquo10) pp 591ndash594 Xiamen ChinaJanuary 2010

[7] H Tian R Yuan C Zhang J Jin N Song and S LinldquoNonlinear empirical mode predictive drift extraction on fiberoptical gyroscoperdquo Optik vol 122 no 5 pp 415ndash421 2011

[8] S Jain S Nandy G Chakraborty C S Kumar R Ray andS N Shome ldquoError modeling of various sensors for roboticsapplication using allan variance techniquerdquo in Proceedings ofthe IEEE International Conference on Signal Processing Com-munications and Computing (ICSPCC rsquo11) pp 1ndash4 IEEE XirsquoanChina September 2011

[9] N Zhang and X Li ldquoResearch on theoretical improvement ofdynamic Allan variance and its applicationrdquo Acta Optica Sinicavol 31 no 11 pp 70ndash75 2011

[10] J C Li F Q Gao G L Wang W Gao W Zhu and M WangldquoAnalysis of dynamic Allan variance for fiber optic gyro undervibration and variable temperature conditionsrdquo Chinese Journalof Lasers vol 40 no 9 pp 1ndash7 2013

[11] S Dang W Tian and F Qian ldquoEMD- and LWT-based stochas-tic noise eliminatingmethod for fiber optic gyrordquoMeasurementvol 44 no 10 pp 2190ndash2193 2011

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciences vol 454 no 1971 pp 903ndash995 1998

[13] Y Gan and L F Sui ldquoDe-noising method for gyro signal basedon EMDrdquo Acta Geodaetica et Cartographica Sinica vol 40 no6 pp 745ndash750 2011

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2 Journal of Sensors

traditional AV the proposed method enriches the real gyroperformance evaluation approaches supplies more detailedgyro signal characteristics information in the joint time-frequency domain and provides the theoretical basis for thedenoising threshold determination in signal preprocessing

2 Allan Variance Analysis

As a common analysis tool in the time domain AV is widelyapplied to identify the gyro errors characteristics Assumingthat there is a gyro signal sample sequence of 119909(119905) with thelength of119873 and the sampling frequency of119891 its discrete-timeAV can be expressed as [8]

1205902

AVAR (120591) =1

2⟨(119909119905119896+120591

(120591) minus 119909119905119896

(120591))2

⟩ (1)

where the operator ⟨sdot⟩ denotes ensemble averaging 119909119905119896

(120591) isthe averaged measure of FOG signal at time 119905

119896 and 120591 = 119873119891

is observation intervalIt is assumed that the various error sources are statistically

independent then the AV can be described as the sumof squares of quantization noise angle random walk biasinstability rate random walk and rate ramp [9 10]

1205902

(120591) = 1205902

QN (120591) + 1205902

ARW (120591) + 1205902

BI (120591) + 1205902

RRW (120591)

+ 1205902

RR (120591)

=31198762

1205912+

1198732

120591+

21198612

120587ln 2 +

1198702120591

3+

11987721205912

2

(2)

where 120590ARW 120590RRW 120590BI 120590QN and 120590RR are the variances of theabove five kinds of errors separately and 119876 119873 119861 119870 and 119877

are the corresponding AV coefficients

3 EMDAV Analysis

The traditional AV analysis method which presents the gyronoise characteristics in the only timedomain cannot reflect itsdistributions among different frequency bands However thenoise characteristics vary with the frequency To reveal moredetails of the gyro noise characteristic the EMDAV methodis proposed in this paper

As a method utilized to analyze the nonlinear and non-stationary signal EMD decomposes the signal on the basisof time scale characteristics There is no need to set the basicfunctions in advance for EMDwhich can decompose any typeof signal Thus EMD has obvious advantages in processingnonlinear and nonstationary signal

The EMDAV algorithm proposed in the paper is basedon the EMD and AV After decomposing the gyro signal withEMD the AV can be obtained with the help of intrinsic modefunction (IMF) Lastly the AV logarithmic curve over timeand frequency can be depicted The detailed algorithm flowchart is shown in Figure 1

The steps of the EMDAV based on gyro signal character-istics analysis method can be summarized as follows

(1) Find all the local maxima and minima of the originalsignal 119909(119905)

Begin

Find the local maxima andminima of signal

Fit an upper envelope and alow envelope

Compute the mean of thetwo envelopes

Obtain IMF

Stopping criterion

End

No

Yes

Calculate the Allanvariance corresponding to the

IMF components

Depict the Allan variancelogarithmic curve

lt one constant

Figure 1 Flow chart of AV algorithm based on EMD

(2) Fit the estimated points of the first step using naturalcubic spline to form an upper envelope of 119890max(119905) and a lowerenvelope of 119890min(119905)

(3) Compute the mean of the two envelopes

119898119894(119905) =

119890max (119905) + 119890min (119905)

2 (3)

where 119894 = 1 2 119899 119899 is the number of decomposition levels(4) Refine the estimate ℎ

119894(119905) of the IMF by subtracting the

mean solved in the previous step from the current signal

ℎ119894(119905) = 119909

119894(119905) minus 119898

119894(119905) (4)

where

119909119894(119905) =

119909 (119905) 119894 = 1

119909 (119905) minus

119894minus1

sum119895=1

ℎ119895(119905) 119894 ge 2

(5)

(5) Proceed from step (1) again unless a stopping criterionhas been fulfilled The stopping criterion is [11]

SD =

119879

sum119905=0

[

1003816100381610038161003816ℎ119894minus1 (119905) minus ℎ119894(119905)

10038161003816100381610038162

ℎ2119894minus1

(119905)] (6)

Journal of Sensors 3

(a)

MEMS gyro

(b)

Figure 2 FOG and MEMS gyros (a) FOG on turntable and (b) MEMS gyro

where SD is a screening threshold The iteration stops whenSD is smaller than a constant The constant value can be setbetween 02 and 03 [12]

Eventually the IMF components of ℎ1(119905) ℎ2(119905) ℎ

119899(119905)

and the remainder of 119903119899(119905) can be obtainedThen the original

signal can be expressed as

119909 (119905) =

119899

sum119894=1

ℎ119894(119905) + 119903

119899(119905) (7)

(6) Calculate the AV coefficients corresponding to the IMFcomponents and analyze the signal characteristics in differentfrequency bands

From the above EMDAV procedures we can see that theIMF of ℎ

119894(119905) indicates the different frequency components

With the increase of decomposition level the frequency ofdecomposed signal decreases gradually Namely the first IMFrepresents the highest frequency component of the originalsignal The frequencies of subsequent IMFs reduce almost inthe form of the negative power of 2 [13] until the frequencyof the remainder is very small Consequently each IMFcorresponds to the signal component of different frequency

Compared with the traditional AV analysis method thecharacteristics and distributions of gyro signal in differentfrequency bands can be depicted in detail with EMDAValgorithm One more piece of dimensional information canbe shown in three-dimensional (3D) logarithmic graph ofEMDAV compared to that in 2D curve of traditional AV

4 Experiment Results and Analysis

To verify the algorithm proposed in this paper AV andEMDAV are compared to analyze the FOG and MEMS gyrosignals Practical fiber optical gyro (FOG) and microelectro-mechanical system (MEMS) gyro static signals are acquiredwith the sampling frequency of 100Hz and the samplingduration of 600 s The scene of experiment is shown inFigure 2

As we all know traditional AV coefficients come fromoriginal gyro signal and we can compare them with EMDAV

coefficients at the same time Figure 3 shows the originalsignals and parts of IMF components decomposed by EMDIt can be seen that the characteristics of FOG and MEMSgyro signals are similar the first level of decomposed signalbelongs to high frequency part and the frequency decreaseswith the increasing of decomposition level

Theoriginal signals and IMF components decomposed byEMD are analyzed with AV and corresponding coefficients(AV coefficients and EMDAV coefficients) are plotted in alogarithmic graph as shown in Figure 4 FromFigure 4we canfind that the 16 curves in the first group from top to bottomare the AV logarithm curves of MEMS gyro original signal(the 0 level traditional AV) and IMFs (1ndash15 levels EMDAV)respectively Because of the poor accuracy of MEMS gyrothe biggest AV value reaches 105 The 16 profiles in thesecond group are the respective AV logarithm curves of FOGgyro original signal (the 0 level traditional AV) and IMFs(EMDAV) where the biggest AV value reaches 1 Taking theAV values at correlation time of 001 s for comparison themaximum is from the original signal for both gyros by whichthe first level of decomposed signals followed The AV valuesdecrease until the decomposition level increases to the lastone whose value corresponds to the minimum

In addition it can be seen from Table 1 and Figure 4that the signal distributions of FOG and MEMS gyro aresimilar that is to say with the increase of decomposition levelthe proportion of angle random walk is reduced while theproportion of rate randomwalk is increasedAlso it is obviousthat angle random walk is dominant in the high frequencysignal while rate randomwalk accounts for a large proportionin the low frequency signal In consequence gyro signal canbe denoised specifically with the demand of the navigationsystem

Figure 5 shows the relationship between AV and EMDAVcoefficients where the zero level means the AV coefficient oforiginal gyro signals As mentioned before the frequency ofeach IMF is decreased in the form of negative power of 2gradually which indicates the fact that the higher the EMDdecomposition levels the smaller the signal frequency It also

4 Journal of Sensors

0 100 200 300 400 500 600123

Orig

in

t (s)

times10minus3

0 100 200 300 400 500 600minus2

02

IMF

7

t (s)

times10minus4

0 100 200 300 400 500 600minus5

05

IMF

4IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)

t (s)

times10minus4

0 100 200 300 400 500 600minus5

05

IMF

1

t (s)

times10minus4

0 100 200 300 400 500 600minus1

01

IMF

12

t (s)

times10minus5

0 100 200 300 400 500 600minus5

05

IMF

10

t (s)

times10minus5

0 100 200 300 400 500 600minus2

02

IMF

15

t (s)

times10minus6

(a)

t (s)0 100 200 300 400 500 600

minus2minus1

0

Orig

in

t (s)0 100 200 300 400 500 600

minus050

05

IMF

1

t (s)0 100 200 300 400 500 600

minus010

01

IMF

4

t (s)0 100 200 300 400 500 600

minus010

01

IMF

7

t (s)0 100 200 300 400 500 600

minus0020

002IM

F 10

t (s)0 100 200 300 400 500 600

minus0020

002

IMF

12

t (s)0 100 200 300 400 500 600

minus505

IMF

15

times10minus3

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

(b)

Figure 3 IMFs from EMD of gyro signals (a) EMD of FOG signal and (b) EMD of MEMS gyro signal

Table 1 AV coefficients of gyro signals on some frequencies

Signal AV coefficients119873 (∘h12) 119861 (∘h) 119870 (∘h32) 119877 (∘h2) 119876 (120583rad)

FOG

AV (original signal) 140119890 minus 3 571119890 minus 1 1221198901 4431198901 355119890 minus 2

EMDAV (signalsdecomposed byEMD)

Level 1 160119890 minus 3 464119890 minus 1 9841198900 3561198901 376119890 minus 2

Level 4 415119890 minus 4 175119890 minus 1 3951198900 1441198901 740119890 minus 3

Level 7 133119890 minus 4 666119890 minus 2 1201198900 4251198900 190119890 minus 3

Level 10 219119890 minus 5 102119890 minus 2 320119890 minus 1 1241198900 317119890 minus 4

Level 15 432119890 minus 7 210119890 minus 4 236119890 minus 2 772119890 minus 2 615119890 minus 6

MEMS gyro

AV (original signal) 591119890 minus 1 3101198901 6201198902 2241198903 1391198900

EMDAV (signalsdecomposed byEMD)

Level 1 137119890 minus 1 1411198901 2101198902 7151198902 8781198900

Level 4 101119890 minus 1 9851198901 2161198903 7851198903 2371198900

Level 7 993119890 minus 2 4921198901 8501198902 2991198903 1401198900

Level 10 159119890 minus 2 7361198900 2541198902 9811198902 230119890 minus 1

Level 15 130119890 minus 3 612119890 minus 1 6541198901 1801198902 181119890 minus 2

Journal of Sensors 5

Table 2 Performance contrasts between AV and EMDAV

AV EMDAVSignal Stationary signal Stationary and nonstationary signalResult presentation (fingerprint) 2D 3DDomain of signal analysis Time domain Time-frequency domainAbility of signal identification at different frequencies No YesNumbers of obtained parameters can be referenced Less MoreReference for signal denoising No Yes

Correlation time (s)

AVEMDAV 1EMDAV 2EMDAV 3EMDAV 4EMDAV 5EMDAV 6EMDAV 7

EMDAV 8EMDAV 9EMDAV 10EMDAV 11EMDAV 12EMDAV 13EMDAV 14EMDAV 15

MEMS gyro

FOG

1010

105

100

10minus5

10minus10

10minus15

Alla

n va

rianc

e (de

g2h

2)

10minus2 10minus1 100 101 102 103

Figure 4 Logarithmic diagram of AV and EMDAV

shows that the EMDAVcoefficients trend to decreasewith thedecrease of signal frequency

From the comparison of Figures 5(a) and 5(b) thecoefficients of MEMS gyro are much larger than that of FOGnamely the accuracy of MEMS gyro is worse than FOG Asfor FOG (in Figure 5(a)) the EMDAV coefficients in the 5thlevel are larger which means that the angle random walknoise bias instability noise rate random walk noise and rateramp noise are more dominant The EMDAV coefficients ofthe 8th level and higher level are very small and the EMDdenoising method will be effective when the decompositionlevels are larger than 7 As forMEMS gyro (in Figure 5(b)) theEMDAV coefficients are dominant in the 2nd level and arelargest for 4 parameters and reference decomposition levelof 9 will be applicable for EMD denoising method Thereforethe algorithm proposed in this paper can provide guidancefor gyro denoising

The relationships among AV values of IMFs correlationtime and EMD decomposition levels are shown in the AV

and EMDAV 3D logarithmic graph of Figure 6 where thetop curves are AV values of MEME gyro while the bottomare of FOG Traditional AV logarithmic diagram is the 2Dcurve on the 0 level and EMDAV logarithmic diagram is the3D view on 1ndash15 levels It can be found that though the AVvalues of MEMS gyro are larger than that of FOG the signalmagnitudes of the both gyros tend to reducewith the decreaseof frequency The 3D figures of both FOG and MEMS gyrosignals show the special characteristics of the FOG andMEMS gyro performance The AV values decrease with theincrease of EMD levels and correlation time The ridgeswhich also can be seen from Figure 4 are the collections ofthe points with a zero slope in logarithmic diagram of everyIMF signal Obviously the ridge of FOG signal is consistentwith that of MEMS gyro signal

The contrasts between AV and EMDAV are listed inTable 2 As can be seen from the table EMDAV can ana-lyze the both stationary and nonstationary signals with theanalysis results showing the 3D relationship (served as the3D fingerprint of a gyro) among AV time and frequency Inaddition various kinds of noises can be identified to providemore details about the signal characteristics of gyro EMDAVcan obtain more referable parameters than AV and provide areference for signal denoising

5 Conclusion

An AV analysis algorithm based on EMD for gyro error isproposed in this paper The AV value is calculated by thesignal decomposed based on the characteristic time scale andthe signal characteristics of gyro error in different frequencybands are revealed Theoretical analysis and experiments ofpractical FOG and MEMS gyro data indicate the following

(1) Compared with the characteristic of gyro error inthe sole time domain given by the traditional AVthe EMDAV algorithm can describe the distributionson different kinds of gyro signals in time-frequencydomain

(2) The EMDAV algorithm extends the dimensions ofgyro signal characteristics analysis and hence obtainsmore parameters than traditional AV

(3) The EMDAV algorithm is able to determine thedecomposition level for gyro signal denoising andprovide a theoretical guidance to the gyro signaldenoising and other preprocessing algorithms

6 Journal of Sensors

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times10minus3

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

1020

EMD decomposition level

0 2 4 6 8 10 12 14 160

2040

EMD decomposition level

R(d

egh

2)

0 2 4 6 8 10 12 14 160

002004

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)

(a)

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

0 2 4 6 8 10 12 14 160

100200

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

20004000

EMD decomposition level

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times104

0 2 4 6 8 10 12 14 1605

10

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)R

(deg

h2)

(b)

Figure 5 Relationship between AV coefficients (level 0) and EMDAV coefficients (a) FOG and (b) MEMS gyro

100

10minus5

10minus10

15

10

5

0 10minus2100

102

Alla

n va

rianc

e (de

g2h

2) MEMS gyro

FOG

t (s)

EMD decomposition level

(a)

Alla

n va

rianc

e (de

g2h

2)

MEMS gyro

FOG

t (s)

100

10minus10

102

100

10minus215

10

5

0

EMD decomposition level

(b)

Figure 6 AV and EMDAV 3D logarithmic graph (a) front view and (b) back view

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been mainly funded by the FundamentalResearch Funds for the Central Universities (NS2015037) andpartly funded by the National Natural Science Foundation

of China (Grants nos 61533008 and 61374115 to Jianye Liu)and Jiangsu Key Laboratory of Internet ofThings andControlTechnologies

References

[1] J Lai P Lv J Liu and B Jiang ldquoNoncommutativity erroranalysis of strapdown inertial navigation system under thevibration in UAVsrdquo International Journal of Advanced RoboticSystems vol 9 article 134 2012

Journal of Sensors 7

[2] R Peesapati S L Sabat K P Karthik J Nayak and NGiribabu ldquoEfficient hybrid Kalman filter for denoising fiberoptic gyroscope signalrdquo Optik vol 124 no 20 pp 4549ndash45562013

[3] V V Chikovani ldquoPerformance parameters comparison of ringlaser coriolis vibratory and fiber-optic gyros based on Allanvariance analysisrdquo in Proceedings of the IEEE 2nd InternationalConference on Actual Problems of Unmanned Air VehiclesDevelopments (APUAVD rsquo13) pp 153ndash156 IEEE Kiev UkraineOctober 2013

[4] C-S Qu T-Z Lu and Y Tan ldquoA modified empirical modedecomposition method with applications to signal de-noisingrdquoActa Automatica Sinica vol 36 no 1 pp 67ndash73 2010

[5] Y Gan L Sui G Xiao and Y Duan ldquoEMD de-noising theoryconsidering static and dynamic conditions and its applicationsin INSrdquo LectureNotes in Electrical Engineering vol 245 pp 507ndash515 2013

[6] Y Zhang SWang andD Xia ldquoEMD-based denoisingmethodsin the MEMS gyroscope de-driftrdquo in Proceedings of the 5thIEEE International Conference on NanoMicro Engineered andMolecular Systems (NEMS rsquo10) pp 591ndash594 Xiamen ChinaJanuary 2010

[7] H Tian R Yuan C Zhang J Jin N Song and S LinldquoNonlinear empirical mode predictive drift extraction on fiberoptical gyroscoperdquo Optik vol 122 no 5 pp 415ndash421 2011

[8] S Jain S Nandy G Chakraborty C S Kumar R Ray andS N Shome ldquoError modeling of various sensors for roboticsapplication using allan variance techniquerdquo in Proceedings ofthe IEEE International Conference on Signal Processing Com-munications and Computing (ICSPCC rsquo11) pp 1ndash4 IEEE XirsquoanChina September 2011

[9] N Zhang and X Li ldquoResearch on theoretical improvement ofdynamic Allan variance and its applicationrdquo Acta Optica Sinicavol 31 no 11 pp 70ndash75 2011

[10] J C Li F Q Gao G L Wang W Gao W Zhu and M WangldquoAnalysis of dynamic Allan variance for fiber optic gyro undervibration and variable temperature conditionsrdquo Chinese Journalof Lasers vol 40 no 9 pp 1ndash7 2013

[11] S Dang W Tian and F Qian ldquoEMD- and LWT-based stochas-tic noise eliminatingmethod for fiber optic gyrordquoMeasurementvol 44 no 10 pp 2190ndash2193 2011

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciences vol 454 no 1971 pp 903ndash995 1998

[13] Y Gan and L F Sui ldquoDe-noising method for gyro signal basedon EMDrdquo Acta Geodaetica et Cartographica Sinica vol 40 no6 pp 745ndash750 2011

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Submit your manuscripts athttpwwwhindawicom

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

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DistributedSensor Networks

International Journal of

Journal of Sensors 3

(a)

MEMS gyro

(b)

Figure 2 FOG and MEMS gyros (a) FOG on turntable and (b) MEMS gyro

where SD is a screening threshold The iteration stops whenSD is smaller than a constant The constant value can be setbetween 02 and 03 [12]

Eventually the IMF components of ℎ1(119905) ℎ2(119905) ℎ

119899(119905)

and the remainder of 119903119899(119905) can be obtainedThen the original

signal can be expressed as

119909 (119905) =

119899

sum119894=1

ℎ119894(119905) + 119903

119899(119905) (7)

(6) Calculate the AV coefficients corresponding to the IMFcomponents and analyze the signal characteristics in differentfrequency bands

From the above EMDAV procedures we can see that theIMF of ℎ

119894(119905) indicates the different frequency components

With the increase of decomposition level the frequency ofdecomposed signal decreases gradually Namely the first IMFrepresents the highest frequency component of the originalsignal The frequencies of subsequent IMFs reduce almost inthe form of the negative power of 2 [13] until the frequencyof the remainder is very small Consequently each IMFcorresponds to the signal component of different frequency

Compared with the traditional AV analysis method thecharacteristics and distributions of gyro signal in differentfrequency bands can be depicted in detail with EMDAValgorithm One more piece of dimensional information canbe shown in three-dimensional (3D) logarithmic graph ofEMDAV compared to that in 2D curve of traditional AV

4 Experiment Results and Analysis

To verify the algorithm proposed in this paper AV andEMDAV are compared to analyze the FOG and MEMS gyrosignals Practical fiber optical gyro (FOG) and microelectro-mechanical system (MEMS) gyro static signals are acquiredwith the sampling frequency of 100Hz and the samplingduration of 600 s The scene of experiment is shown inFigure 2

As we all know traditional AV coefficients come fromoriginal gyro signal and we can compare them with EMDAV

coefficients at the same time Figure 3 shows the originalsignals and parts of IMF components decomposed by EMDIt can be seen that the characteristics of FOG and MEMSgyro signals are similar the first level of decomposed signalbelongs to high frequency part and the frequency decreaseswith the increasing of decomposition level

Theoriginal signals and IMF components decomposed byEMD are analyzed with AV and corresponding coefficients(AV coefficients and EMDAV coefficients) are plotted in alogarithmic graph as shown in Figure 4 FromFigure 4we canfind that the 16 curves in the first group from top to bottomare the AV logarithm curves of MEMS gyro original signal(the 0 level traditional AV) and IMFs (1ndash15 levels EMDAV)respectively Because of the poor accuracy of MEMS gyrothe biggest AV value reaches 105 The 16 profiles in thesecond group are the respective AV logarithm curves of FOGgyro original signal (the 0 level traditional AV) and IMFs(EMDAV) where the biggest AV value reaches 1 Taking theAV values at correlation time of 001 s for comparison themaximum is from the original signal for both gyros by whichthe first level of decomposed signals followed The AV valuesdecrease until the decomposition level increases to the lastone whose value corresponds to the minimum

In addition it can be seen from Table 1 and Figure 4that the signal distributions of FOG and MEMS gyro aresimilar that is to say with the increase of decomposition levelthe proportion of angle random walk is reduced while theproportion of rate randomwalk is increasedAlso it is obviousthat angle random walk is dominant in the high frequencysignal while rate randomwalk accounts for a large proportionin the low frequency signal In consequence gyro signal canbe denoised specifically with the demand of the navigationsystem

Figure 5 shows the relationship between AV and EMDAVcoefficients where the zero level means the AV coefficient oforiginal gyro signals As mentioned before the frequency ofeach IMF is decreased in the form of negative power of 2gradually which indicates the fact that the higher the EMDdecomposition levels the smaller the signal frequency It also

4 Journal of Sensors

0 100 200 300 400 500 600123

Orig

in

t (s)

times10minus3

0 100 200 300 400 500 600minus2

02

IMF

7

t (s)

times10minus4

0 100 200 300 400 500 600minus5

05

IMF

4IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)

t (s)

times10minus4

0 100 200 300 400 500 600minus5

05

IMF

1

t (s)

times10minus4

0 100 200 300 400 500 600minus1

01

IMF

12

t (s)

times10minus5

0 100 200 300 400 500 600minus5

05

IMF

10

t (s)

times10minus5

0 100 200 300 400 500 600minus2

02

IMF

15

t (s)

times10minus6

(a)

t (s)0 100 200 300 400 500 600

minus2minus1

0

Orig

in

t (s)0 100 200 300 400 500 600

minus050

05

IMF

1

t (s)0 100 200 300 400 500 600

minus010

01

IMF

4

t (s)0 100 200 300 400 500 600

minus010

01

IMF

7

t (s)0 100 200 300 400 500 600

minus0020

002IM

F 10

t (s)0 100 200 300 400 500 600

minus0020

002

IMF

12

t (s)0 100 200 300 400 500 600

minus505

IMF

15

times10minus3

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

(b)

Figure 3 IMFs from EMD of gyro signals (a) EMD of FOG signal and (b) EMD of MEMS gyro signal

Table 1 AV coefficients of gyro signals on some frequencies

Signal AV coefficients119873 (∘h12) 119861 (∘h) 119870 (∘h32) 119877 (∘h2) 119876 (120583rad)

FOG

AV (original signal) 140119890 minus 3 571119890 minus 1 1221198901 4431198901 355119890 minus 2

EMDAV (signalsdecomposed byEMD)

Level 1 160119890 minus 3 464119890 minus 1 9841198900 3561198901 376119890 minus 2

Level 4 415119890 minus 4 175119890 minus 1 3951198900 1441198901 740119890 minus 3

Level 7 133119890 minus 4 666119890 minus 2 1201198900 4251198900 190119890 minus 3

Level 10 219119890 minus 5 102119890 minus 2 320119890 minus 1 1241198900 317119890 minus 4

Level 15 432119890 minus 7 210119890 minus 4 236119890 minus 2 772119890 minus 2 615119890 minus 6

MEMS gyro

AV (original signal) 591119890 minus 1 3101198901 6201198902 2241198903 1391198900

EMDAV (signalsdecomposed byEMD)

Level 1 137119890 minus 1 1411198901 2101198902 7151198902 8781198900

Level 4 101119890 minus 1 9851198901 2161198903 7851198903 2371198900

Level 7 993119890 minus 2 4921198901 8501198902 2991198903 1401198900

Level 10 159119890 minus 2 7361198900 2541198902 9811198902 230119890 minus 1

Level 15 130119890 minus 3 612119890 minus 1 6541198901 1801198902 181119890 minus 2

Journal of Sensors 5

Table 2 Performance contrasts between AV and EMDAV

AV EMDAVSignal Stationary signal Stationary and nonstationary signalResult presentation (fingerprint) 2D 3DDomain of signal analysis Time domain Time-frequency domainAbility of signal identification at different frequencies No YesNumbers of obtained parameters can be referenced Less MoreReference for signal denoising No Yes

Correlation time (s)

AVEMDAV 1EMDAV 2EMDAV 3EMDAV 4EMDAV 5EMDAV 6EMDAV 7

EMDAV 8EMDAV 9EMDAV 10EMDAV 11EMDAV 12EMDAV 13EMDAV 14EMDAV 15

MEMS gyro

FOG

1010

105

100

10minus5

10minus10

10minus15

Alla

n va

rianc

e (de

g2h

2)

10minus2 10minus1 100 101 102 103

Figure 4 Logarithmic diagram of AV and EMDAV

shows that the EMDAVcoefficients trend to decreasewith thedecrease of signal frequency

From the comparison of Figures 5(a) and 5(b) thecoefficients of MEMS gyro are much larger than that of FOGnamely the accuracy of MEMS gyro is worse than FOG Asfor FOG (in Figure 5(a)) the EMDAV coefficients in the 5thlevel are larger which means that the angle random walknoise bias instability noise rate random walk noise and rateramp noise are more dominant The EMDAV coefficients ofthe 8th level and higher level are very small and the EMDdenoising method will be effective when the decompositionlevels are larger than 7 As forMEMS gyro (in Figure 5(b)) theEMDAV coefficients are dominant in the 2nd level and arelargest for 4 parameters and reference decomposition levelof 9 will be applicable for EMD denoising method Thereforethe algorithm proposed in this paper can provide guidancefor gyro denoising

The relationships among AV values of IMFs correlationtime and EMD decomposition levels are shown in the AV

and EMDAV 3D logarithmic graph of Figure 6 where thetop curves are AV values of MEME gyro while the bottomare of FOG Traditional AV logarithmic diagram is the 2Dcurve on the 0 level and EMDAV logarithmic diagram is the3D view on 1ndash15 levels It can be found that though the AVvalues of MEMS gyro are larger than that of FOG the signalmagnitudes of the both gyros tend to reducewith the decreaseof frequency The 3D figures of both FOG and MEMS gyrosignals show the special characteristics of the FOG andMEMS gyro performance The AV values decrease with theincrease of EMD levels and correlation time The ridgeswhich also can be seen from Figure 4 are the collections ofthe points with a zero slope in logarithmic diagram of everyIMF signal Obviously the ridge of FOG signal is consistentwith that of MEMS gyro signal

The contrasts between AV and EMDAV are listed inTable 2 As can be seen from the table EMDAV can ana-lyze the both stationary and nonstationary signals with theanalysis results showing the 3D relationship (served as the3D fingerprint of a gyro) among AV time and frequency Inaddition various kinds of noises can be identified to providemore details about the signal characteristics of gyro EMDAVcan obtain more referable parameters than AV and provide areference for signal denoising

5 Conclusion

An AV analysis algorithm based on EMD for gyro error isproposed in this paper The AV value is calculated by thesignal decomposed based on the characteristic time scale andthe signal characteristics of gyro error in different frequencybands are revealed Theoretical analysis and experiments ofpractical FOG and MEMS gyro data indicate the following

(1) Compared with the characteristic of gyro error inthe sole time domain given by the traditional AVthe EMDAV algorithm can describe the distributionson different kinds of gyro signals in time-frequencydomain

(2) The EMDAV algorithm extends the dimensions ofgyro signal characteristics analysis and hence obtainsmore parameters than traditional AV

(3) The EMDAV algorithm is able to determine thedecomposition level for gyro signal denoising andprovide a theoretical guidance to the gyro signaldenoising and other preprocessing algorithms

6 Journal of Sensors

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times10minus3

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

1020

EMD decomposition level

0 2 4 6 8 10 12 14 160

2040

EMD decomposition level

R(d

egh

2)

0 2 4 6 8 10 12 14 160

002004

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)

(a)

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

0 2 4 6 8 10 12 14 160

100200

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

20004000

EMD decomposition level

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times104

0 2 4 6 8 10 12 14 1605

10

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)R

(deg

h2)

(b)

Figure 5 Relationship between AV coefficients (level 0) and EMDAV coefficients (a) FOG and (b) MEMS gyro

100

10minus5

10minus10

15

10

5

0 10minus2100

102

Alla

n va

rianc

e (de

g2h

2) MEMS gyro

FOG

t (s)

EMD decomposition level

(a)

Alla

n va

rianc

e (de

g2h

2)

MEMS gyro

FOG

t (s)

100

10minus10

102

100

10minus215

10

5

0

EMD decomposition level

(b)

Figure 6 AV and EMDAV 3D logarithmic graph (a) front view and (b) back view

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been mainly funded by the FundamentalResearch Funds for the Central Universities (NS2015037) andpartly funded by the National Natural Science Foundation

of China (Grants nos 61533008 and 61374115 to Jianye Liu)and Jiangsu Key Laboratory of Internet ofThings andControlTechnologies

References

[1] J Lai P Lv J Liu and B Jiang ldquoNoncommutativity erroranalysis of strapdown inertial navigation system under thevibration in UAVsrdquo International Journal of Advanced RoboticSystems vol 9 article 134 2012

Journal of Sensors 7

[2] R Peesapati S L Sabat K P Karthik J Nayak and NGiribabu ldquoEfficient hybrid Kalman filter for denoising fiberoptic gyroscope signalrdquo Optik vol 124 no 20 pp 4549ndash45562013

[3] V V Chikovani ldquoPerformance parameters comparison of ringlaser coriolis vibratory and fiber-optic gyros based on Allanvariance analysisrdquo in Proceedings of the IEEE 2nd InternationalConference on Actual Problems of Unmanned Air VehiclesDevelopments (APUAVD rsquo13) pp 153ndash156 IEEE Kiev UkraineOctober 2013

[4] C-S Qu T-Z Lu and Y Tan ldquoA modified empirical modedecomposition method with applications to signal de-noisingrdquoActa Automatica Sinica vol 36 no 1 pp 67ndash73 2010

[5] Y Gan L Sui G Xiao and Y Duan ldquoEMD de-noising theoryconsidering static and dynamic conditions and its applicationsin INSrdquo LectureNotes in Electrical Engineering vol 245 pp 507ndash515 2013

[6] Y Zhang SWang andD Xia ldquoEMD-based denoisingmethodsin the MEMS gyroscope de-driftrdquo in Proceedings of the 5thIEEE International Conference on NanoMicro Engineered andMolecular Systems (NEMS rsquo10) pp 591ndash594 Xiamen ChinaJanuary 2010

[7] H Tian R Yuan C Zhang J Jin N Song and S LinldquoNonlinear empirical mode predictive drift extraction on fiberoptical gyroscoperdquo Optik vol 122 no 5 pp 415ndash421 2011

[8] S Jain S Nandy G Chakraborty C S Kumar R Ray andS N Shome ldquoError modeling of various sensors for roboticsapplication using allan variance techniquerdquo in Proceedings ofthe IEEE International Conference on Signal Processing Com-munications and Computing (ICSPCC rsquo11) pp 1ndash4 IEEE XirsquoanChina September 2011

[9] N Zhang and X Li ldquoResearch on theoretical improvement ofdynamic Allan variance and its applicationrdquo Acta Optica Sinicavol 31 no 11 pp 70ndash75 2011

[10] J C Li F Q Gao G L Wang W Gao W Zhu and M WangldquoAnalysis of dynamic Allan variance for fiber optic gyro undervibration and variable temperature conditionsrdquo Chinese Journalof Lasers vol 40 no 9 pp 1ndash7 2013

[11] S Dang W Tian and F Qian ldquoEMD- and LWT-based stochas-tic noise eliminatingmethod for fiber optic gyrordquoMeasurementvol 44 no 10 pp 2190ndash2193 2011

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciences vol 454 no 1971 pp 903ndash995 1998

[13] Y Gan and L F Sui ldquoDe-noising method for gyro signal basedon EMDrdquo Acta Geodaetica et Cartographica Sinica vol 40 no6 pp 745ndash750 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Journal of Sensors

0 100 200 300 400 500 600123

Orig

in

t (s)

times10minus3

0 100 200 300 400 500 600minus2

02

IMF

7

t (s)

times10minus4

0 100 200 300 400 500 600minus5

05

IMF

4IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)IM

F (d

egs

)

t (s)

times10minus4

0 100 200 300 400 500 600minus5

05

IMF

1

t (s)

times10minus4

0 100 200 300 400 500 600minus1

01

IMF

12

t (s)

times10minus5

0 100 200 300 400 500 600minus5

05

IMF

10

t (s)

times10minus5

0 100 200 300 400 500 600minus2

02

IMF

15

t (s)

times10minus6

(a)

t (s)0 100 200 300 400 500 600

minus2minus1

0

Orig

in

t (s)0 100 200 300 400 500 600

minus050

05

IMF

1

t (s)0 100 200 300 400 500 600

minus010

01

IMF

4

t (s)0 100 200 300 400 500 600

minus010

01

IMF

7

t (s)0 100 200 300 400 500 600

minus0020

002IM

F 10

t (s)0 100 200 300 400 500 600

minus0020

002

IMF

12

t (s)0 100 200 300 400 500 600

minus505

IMF

15

times10minus3

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

IMF

(deg

s)

(b)

Figure 3 IMFs from EMD of gyro signals (a) EMD of FOG signal and (b) EMD of MEMS gyro signal

Table 1 AV coefficients of gyro signals on some frequencies

Signal AV coefficients119873 (∘h12) 119861 (∘h) 119870 (∘h32) 119877 (∘h2) 119876 (120583rad)

FOG

AV (original signal) 140119890 minus 3 571119890 minus 1 1221198901 4431198901 355119890 minus 2

EMDAV (signalsdecomposed byEMD)

Level 1 160119890 minus 3 464119890 minus 1 9841198900 3561198901 376119890 minus 2

Level 4 415119890 minus 4 175119890 minus 1 3951198900 1441198901 740119890 minus 3

Level 7 133119890 minus 4 666119890 minus 2 1201198900 4251198900 190119890 minus 3

Level 10 219119890 minus 5 102119890 minus 2 320119890 minus 1 1241198900 317119890 minus 4

Level 15 432119890 minus 7 210119890 minus 4 236119890 minus 2 772119890 minus 2 615119890 minus 6

MEMS gyro

AV (original signal) 591119890 minus 1 3101198901 6201198902 2241198903 1391198900

EMDAV (signalsdecomposed byEMD)

Level 1 137119890 minus 1 1411198901 2101198902 7151198902 8781198900

Level 4 101119890 minus 1 9851198901 2161198903 7851198903 2371198900

Level 7 993119890 minus 2 4921198901 8501198902 2991198903 1401198900

Level 10 159119890 minus 2 7361198900 2541198902 9811198902 230119890 minus 1

Level 15 130119890 minus 3 612119890 minus 1 6541198901 1801198902 181119890 minus 2

Journal of Sensors 5

Table 2 Performance contrasts between AV and EMDAV

AV EMDAVSignal Stationary signal Stationary and nonstationary signalResult presentation (fingerprint) 2D 3DDomain of signal analysis Time domain Time-frequency domainAbility of signal identification at different frequencies No YesNumbers of obtained parameters can be referenced Less MoreReference for signal denoising No Yes

Correlation time (s)

AVEMDAV 1EMDAV 2EMDAV 3EMDAV 4EMDAV 5EMDAV 6EMDAV 7

EMDAV 8EMDAV 9EMDAV 10EMDAV 11EMDAV 12EMDAV 13EMDAV 14EMDAV 15

MEMS gyro

FOG

1010

105

100

10minus5

10minus10

10minus15

Alla

n va

rianc

e (de

g2h

2)

10minus2 10minus1 100 101 102 103

Figure 4 Logarithmic diagram of AV and EMDAV

shows that the EMDAVcoefficients trend to decreasewith thedecrease of signal frequency

From the comparison of Figures 5(a) and 5(b) thecoefficients of MEMS gyro are much larger than that of FOGnamely the accuracy of MEMS gyro is worse than FOG Asfor FOG (in Figure 5(a)) the EMDAV coefficients in the 5thlevel are larger which means that the angle random walknoise bias instability noise rate random walk noise and rateramp noise are more dominant The EMDAV coefficients ofthe 8th level and higher level are very small and the EMDdenoising method will be effective when the decompositionlevels are larger than 7 As forMEMS gyro (in Figure 5(b)) theEMDAV coefficients are dominant in the 2nd level and arelargest for 4 parameters and reference decomposition levelof 9 will be applicable for EMD denoising method Thereforethe algorithm proposed in this paper can provide guidancefor gyro denoising

The relationships among AV values of IMFs correlationtime and EMD decomposition levels are shown in the AV

and EMDAV 3D logarithmic graph of Figure 6 where thetop curves are AV values of MEME gyro while the bottomare of FOG Traditional AV logarithmic diagram is the 2Dcurve on the 0 level and EMDAV logarithmic diagram is the3D view on 1ndash15 levels It can be found that though the AVvalues of MEMS gyro are larger than that of FOG the signalmagnitudes of the both gyros tend to reducewith the decreaseof frequency The 3D figures of both FOG and MEMS gyrosignals show the special characteristics of the FOG andMEMS gyro performance The AV values decrease with theincrease of EMD levels and correlation time The ridgeswhich also can be seen from Figure 4 are the collections ofthe points with a zero slope in logarithmic diagram of everyIMF signal Obviously the ridge of FOG signal is consistentwith that of MEMS gyro signal

The contrasts between AV and EMDAV are listed inTable 2 As can be seen from the table EMDAV can ana-lyze the both stationary and nonstationary signals with theanalysis results showing the 3D relationship (served as the3D fingerprint of a gyro) among AV time and frequency Inaddition various kinds of noises can be identified to providemore details about the signal characteristics of gyro EMDAVcan obtain more referable parameters than AV and provide areference for signal denoising

5 Conclusion

An AV analysis algorithm based on EMD for gyro error isproposed in this paper The AV value is calculated by thesignal decomposed based on the characteristic time scale andthe signal characteristics of gyro error in different frequencybands are revealed Theoretical analysis and experiments ofpractical FOG and MEMS gyro data indicate the following

(1) Compared with the characteristic of gyro error inthe sole time domain given by the traditional AVthe EMDAV algorithm can describe the distributionson different kinds of gyro signals in time-frequencydomain

(2) The EMDAV algorithm extends the dimensions ofgyro signal characteristics analysis and hence obtainsmore parameters than traditional AV

(3) The EMDAV algorithm is able to determine thedecomposition level for gyro signal denoising andprovide a theoretical guidance to the gyro signaldenoising and other preprocessing algorithms

6 Journal of Sensors

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times10minus3

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

1020

EMD decomposition level

0 2 4 6 8 10 12 14 160

2040

EMD decomposition level

R(d

egh

2)

0 2 4 6 8 10 12 14 160

002004

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)

(a)

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

0 2 4 6 8 10 12 14 160

100200

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

20004000

EMD decomposition level

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times104

0 2 4 6 8 10 12 14 1605

10

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)R

(deg

h2)

(b)

Figure 5 Relationship between AV coefficients (level 0) and EMDAV coefficients (a) FOG and (b) MEMS gyro

100

10minus5

10minus10

15

10

5

0 10minus2100

102

Alla

n va

rianc

e (de

g2h

2) MEMS gyro

FOG

t (s)

EMD decomposition level

(a)

Alla

n va

rianc

e (de

g2h

2)

MEMS gyro

FOG

t (s)

100

10minus10

102

100

10minus215

10

5

0

EMD decomposition level

(b)

Figure 6 AV and EMDAV 3D logarithmic graph (a) front view and (b) back view

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been mainly funded by the FundamentalResearch Funds for the Central Universities (NS2015037) andpartly funded by the National Natural Science Foundation

of China (Grants nos 61533008 and 61374115 to Jianye Liu)and Jiangsu Key Laboratory of Internet ofThings andControlTechnologies

References

[1] J Lai P Lv J Liu and B Jiang ldquoNoncommutativity erroranalysis of strapdown inertial navigation system under thevibration in UAVsrdquo International Journal of Advanced RoboticSystems vol 9 article 134 2012

Journal of Sensors 7

[2] R Peesapati S L Sabat K P Karthik J Nayak and NGiribabu ldquoEfficient hybrid Kalman filter for denoising fiberoptic gyroscope signalrdquo Optik vol 124 no 20 pp 4549ndash45562013

[3] V V Chikovani ldquoPerformance parameters comparison of ringlaser coriolis vibratory and fiber-optic gyros based on Allanvariance analysisrdquo in Proceedings of the IEEE 2nd InternationalConference on Actual Problems of Unmanned Air VehiclesDevelopments (APUAVD rsquo13) pp 153ndash156 IEEE Kiev UkraineOctober 2013

[4] C-S Qu T-Z Lu and Y Tan ldquoA modified empirical modedecomposition method with applications to signal de-noisingrdquoActa Automatica Sinica vol 36 no 1 pp 67ndash73 2010

[5] Y Gan L Sui G Xiao and Y Duan ldquoEMD de-noising theoryconsidering static and dynamic conditions and its applicationsin INSrdquo LectureNotes in Electrical Engineering vol 245 pp 507ndash515 2013

[6] Y Zhang SWang andD Xia ldquoEMD-based denoisingmethodsin the MEMS gyroscope de-driftrdquo in Proceedings of the 5thIEEE International Conference on NanoMicro Engineered andMolecular Systems (NEMS rsquo10) pp 591ndash594 Xiamen ChinaJanuary 2010

[7] H Tian R Yuan C Zhang J Jin N Song and S LinldquoNonlinear empirical mode predictive drift extraction on fiberoptical gyroscoperdquo Optik vol 122 no 5 pp 415ndash421 2011

[8] S Jain S Nandy G Chakraborty C S Kumar R Ray andS N Shome ldquoError modeling of various sensors for roboticsapplication using allan variance techniquerdquo in Proceedings ofthe IEEE International Conference on Signal Processing Com-munications and Computing (ICSPCC rsquo11) pp 1ndash4 IEEE XirsquoanChina September 2011

[9] N Zhang and X Li ldquoResearch on theoretical improvement ofdynamic Allan variance and its applicationrdquo Acta Optica Sinicavol 31 no 11 pp 70ndash75 2011

[10] J C Li F Q Gao G L Wang W Gao W Zhu and M WangldquoAnalysis of dynamic Allan variance for fiber optic gyro undervibration and variable temperature conditionsrdquo Chinese Journalof Lasers vol 40 no 9 pp 1ndash7 2013

[11] S Dang W Tian and F Qian ldquoEMD- and LWT-based stochas-tic noise eliminatingmethod for fiber optic gyrordquoMeasurementvol 44 no 10 pp 2190ndash2193 2011

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciences vol 454 no 1971 pp 903ndash995 1998

[13] Y Gan and L F Sui ldquoDe-noising method for gyro signal basedon EMDrdquo Acta Geodaetica et Cartographica Sinica vol 40 no6 pp 745ndash750 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 5

Table 2 Performance contrasts between AV and EMDAV

AV EMDAVSignal Stationary signal Stationary and nonstationary signalResult presentation (fingerprint) 2D 3DDomain of signal analysis Time domain Time-frequency domainAbility of signal identification at different frequencies No YesNumbers of obtained parameters can be referenced Less MoreReference for signal denoising No Yes

Correlation time (s)

AVEMDAV 1EMDAV 2EMDAV 3EMDAV 4EMDAV 5EMDAV 6EMDAV 7

EMDAV 8EMDAV 9EMDAV 10EMDAV 11EMDAV 12EMDAV 13EMDAV 14EMDAV 15

MEMS gyro

FOG

1010

105

100

10minus5

10minus10

10minus15

Alla

n va

rianc

e (de

g2h

2)

10minus2 10minus1 100 101 102 103

Figure 4 Logarithmic diagram of AV and EMDAV

shows that the EMDAVcoefficients trend to decreasewith thedecrease of signal frequency

From the comparison of Figures 5(a) and 5(b) thecoefficients of MEMS gyro are much larger than that of FOGnamely the accuracy of MEMS gyro is worse than FOG Asfor FOG (in Figure 5(a)) the EMDAV coefficients in the 5thlevel are larger which means that the angle random walknoise bias instability noise rate random walk noise and rateramp noise are more dominant The EMDAV coefficients ofthe 8th level and higher level are very small and the EMDdenoising method will be effective when the decompositionlevels are larger than 7 As forMEMS gyro (in Figure 5(b)) theEMDAV coefficients are dominant in the 2nd level and arelargest for 4 parameters and reference decomposition levelof 9 will be applicable for EMD denoising method Thereforethe algorithm proposed in this paper can provide guidancefor gyro denoising

The relationships among AV values of IMFs correlationtime and EMD decomposition levels are shown in the AV

and EMDAV 3D logarithmic graph of Figure 6 where thetop curves are AV values of MEME gyro while the bottomare of FOG Traditional AV logarithmic diagram is the 2Dcurve on the 0 level and EMDAV logarithmic diagram is the3D view on 1ndash15 levels It can be found that though the AVvalues of MEMS gyro are larger than that of FOG the signalmagnitudes of the both gyros tend to reducewith the decreaseof frequency The 3D figures of both FOG and MEMS gyrosignals show the special characteristics of the FOG andMEMS gyro performance The AV values decrease with theincrease of EMD levels and correlation time The ridgeswhich also can be seen from Figure 4 are the collections ofthe points with a zero slope in logarithmic diagram of everyIMF signal Obviously the ridge of FOG signal is consistentwith that of MEMS gyro signal

The contrasts between AV and EMDAV are listed inTable 2 As can be seen from the table EMDAV can ana-lyze the both stationary and nonstationary signals with theanalysis results showing the 3D relationship (served as the3D fingerprint of a gyro) among AV time and frequency Inaddition various kinds of noises can be identified to providemore details about the signal characteristics of gyro EMDAVcan obtain more referable parameters than AV and provide areference for signal denoising

5 Conclusion

An AV analysis algorithm based on EMD for gyro error isproposed in this paper The AV value is calculated by thesignal decomposed based on the characteristic time scale andthe signal characteristics of gyro error in different frequencybands are revealed Theoretical analysis and experiments ofpractical FOG and MEMS gyro data indicate the following

(1) Compared with the characteristic of gyro error inthe sole time domain given by the traditional AVthe EMDAV algorithm can describe the distributionson different kinds of gyro signals in time-frequencydomain

(2) The EMDAV algorithm extends the dimensions ofgyro signal characteristics analysis and hence obtainsmore parameters than traditional AV

(3) The EMDAV algorithm is able to determine thedecomposition level for gyro signal denoising andprovide a theoretical guidance to the gyro signaldenoising and other preprocessing algorithms

6 Journal of Sensors

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times10minus3

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

1020

EMD decomposition level

0 2 4 6 8 10 12 14 160

2040

EMD decomposition level

R(d

egh

2)

0 2 4 6 8 10 12 14 160

002004

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)

(a)

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

0 2 4 6 8 10 12 14 160

100200

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

20004000

EMD decomposition level

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times104

0 2 4 6 8 10 12 14 1605

10

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)R

(deg

h2)

(b)

Figure 5 Relationship between AV coefficients (level 0) and EMDAV coefficients (a) FOG and (b) MEMS gyro

100

10minus5

10minus10

15

10

5

0 10minus2100

102

Alla

n va

rianc

e (de

g2h

2) MEMS gyro

FOG

t (s)

EMD decomposition level

(a)

Alla

n va

rianc

e (de

g2h

2)

MEMS gyro

FOG

t (s)

100

10minus10

102

100

10minus215

10

5

0

EMD decomposition level

(b)

Figure 6 AV and EMDAV 3D logarithmic graph (a) front view and (b) back view

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been mainly funded by the FundamentalResearch Funds for the Central Universities (NS2015037) andpartly funded by the National Natural Science Foundation

of China (Grants nos 61533008 and 61374115 to Jianye Liu)and Jiangsu Key Laboratory of Internet ofThings andControlTechnologies

References

[1] J Lai P Lv J Liu and B Jiang ldquoNoncommutativity erroranalysis of strapdown inertial navigation system under thevibration in UAVsrdquo International Journal of Advanced RoboticSystems vol 9 article 134 2012

Journal of Sensors 7

[2] R Peesapati S L Sabat K P Karthik J Nayak and NGiribabu ldquoEfficient hybrid Kalman filter for denoising fiberoptic gyroscope signalrdquo Optik vol 124 no 20 pp 4549ndash45562013

[3] V V Chikovani ldquoPerformance parameters comparison of ringlaser coriolis vibratory and fiber-optic gyros based on Allanvariance analysisrdquo in Proceedings of the IEEE 2nd InternationalConference on Actual Problems of Unmanned Air VehiclesDevelopments (APUAVD rsquo13) pp 153ndash156 IEEE Kiev UkraineOctober 2013

[4] C-S Qu T-Z Lu and Y Tan ldquoA modified empirical modedecomposition method with applications to signal de-noisingrdquoActa Automatica Sinica vol 36 no 1 pp 67ndash73 2010

[5] Y Gan L Sui G Xiao and Y Duan ldquoEMD de-noising theoryconsidering static and dynamic conditions and its applicationsin INSrdquo LectureNotes in Electrical Engineering vol 245 pp 507ndash515 2013

[6] Y Zhang SWang andD Xia ldquoEMD-based denoisingmethodsin the MEMS gyroscope de-driftrdquo in Proceedings of the 5thIEEE International Conference on NanoMicro Engineered andMolecular Systems (NEMS rsquo10) pp 591ndash594 Xiamen ChinaJanuary 2010

[7] H Tian R Yuan C Zhang J Jin N Song and S LinldquoNonlinear empirical mode predictive drift extraction on fiberoptical gyroscoperdquo Optik vol 122 no 5 pp 415ndash421 2011

[8] S Jain S Nandy G Chakraborty C S Kumar R Ray andS N Shome ldquoError modeling of various sensors for roboticsapplication using allan variance techniquerdquo in Proceedings ofthe IEEE International Conference on Signal Processing Com-munications and Computing (ICSPCC rsquo11) pp 1ndash4 IEEE XirsquoanChina September 2011

[9] N Zhang and X Li ldquoResearch on theoretical improvement ofdynamic Allan variance and its applicationrdquo Acta Optica Sinicavol 31 no 11 pp 70ndash75 2011

[10] J C Li F Q Gao G L Wang W Gao W Zhu and M WangldquoAnalysis of dynamic Allan variance for fiber optic gyro undervibration and variable temperature conditionsrdquo Chinese Journalof Lasers vol 40 no 9 pp 1ndash7 2013

[11] S Dang W Tian and F Qian ldquoEMD- and LWT-based stochas-tic noise eliminatingmethod for fiber optic gyrordquoMeasurementvol 44 no 10 pp 2190ndash2193 2011

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciences vol 454 no 1971 pp 903ndash995 1998

[13] Y Gan and L F Sui ldquoDe-noising method for gyro signal basedon EMDrdquo Acta Geodaetica et Cartographica Sinica vol 40 no6 pp 745ndash750 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Journal of Sensors

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times10minus3

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

1020

EMD decomposition level

0 2 4 6 8 10 12 14 160

2040

EMD decomposition level

R(d

egh

2)

0 2 4 6 8 10 12 14 160

002004

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)

(a)

0 2 4 6 8 10 12 14 160

051

EMD decomposition level

0 2 4 6 8 10 12 14 160

100200

EMD decomposition level

B(d

egh

)

0 2 4 6 8 10 12 14 160

20004000

EMD decomposition level

0 2 4 6 8 10 12 14 16012

EMD decomposition level

times104

0 2 4 6 8 10 12 14 1605

10

EMD decomposition level

Q(120583

rad)

N(d

egh

12)

K(d

egh

32

)R

(deg

h2)

(b)

Figure 5 Relationship between AV coefficients (level 0) and EMDAV coefficients (a) FOG and (b) MEMS gyro

100

10minus5

10minus10

15

10

5

0 10minus2100

102

Alla

n va

rianc

e (de

g2h

2) MEMS gyro

FOG

t (s)

EMD decomposition level

(a)

Alla

n va

rianc

e (de

g2h

2)

MEMS gyro

FOG

t (s)

100

10minus10

102

100

10minus215

10

5

0

EMD decomposition level

(b)

Figure 6 AV and EMDAV 3D logarithmic graph (a) front view and (b) back view

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research has been mainly funded by the FundamentalResearch Funds for the Central Universities (NS2015037) andpartly funded by the National Natural Science Foundation

of China (Grants nos 61533008 and 61374115 to Jianye Liu)and Jiangsu Key Laboratory of Internet ofThings andControlTechnologies

References

[1] J Lai P Lv J Liu and B Jiang ldquoNoncommutativity erroranalysis of strapdown inertial navigation system under thevibration in UAVsrdquo International Journal of Advanced RoboticSystems vol 9 article 134 2012

Journal of Sensors 7

[2] R Peesapati S L Sabat K P Karthik J Nayak and NGiribabu ldquoEfficient hybrid Kalman filter for denoising fiberoptic gyroscope signalrdquo Optik vol 124 no 20 pp 4549ndash45562013

[3] V V Chikovani ldquoPerformance parameters comparison of ringlaser coriolis vibratory and fiber-optic gyros based on Allanvariance analysisrdquo in Proceedings of the IEEE 2nd InternationalConference on Actual Problems of Unmanned Air VehiclesDevelopments (APUAVD rsquo13) pp 153ndash156 IEEE Kiev UkraineOctober 2013

[4] C-S Qu T-Z Lu and Y Tan ldquoA modified empirical modedecomposition method with applications to signal de-noisingrdquoActa Automatica Sinica vol 36 no 1 pp 67ndash73 2010

[5] Y Gan L Sui G Xiao and Y Duan ldquoEMD de-noising theoryconsidering static and dynamic conditions and its applicationsin INSrdquo LectureNotes in Electrical Engineering vol 245 pp 507ndash515 2013

[6] Y Zhang SWang andD Xia ldquoEMD-based denoisingmethodsin the MEMS gyroscope de-driftrdquo in Proceedings of the 5thIEEE International Conference on NanoMicro Engineered andMolecular Systems (NEMS rsquo10) pp 591ndash594 Xiamen ChinaJanuary 2010

[7] H Tian R Yuan C Zhang J Jin N Song and S LinldquoNonlinear empirical mode predictive drift extraction on fiberoptical gyroscoperdquo Optik vol 122 no 5 pp 415ndash421 2011

[8] S Jain S Nandy G Chakraborty C S Kumar R Ray andS N Shome ldquoError modeling of various sensors for roboticsapplication using allan variance techniquerdquo in Proceedings ofthe IEEE International Conference on Signal Processing Com-munications and Computing (ICSPCC rsquo11) pp 1ndash4 IEEE XirsquoanChina September 2011

[9] N Zhang and X Li ldquoResearch on theoretical improvement ofdynamic Allan variance and its applicationrdquo Acta Optica Sinicavol 31 no 11 pp 70ndash75 2011

[10] J C Li F Q Gao G L Wang W Gao W Zhu and M WangldquoAnalysis of dynamic Allan variance for fiber optic gyro undervibration and variable temperature conditionsrdquo Chinese Journalof Lasers vol 40 no 9 pp 1ndash7 2013

[11] S Dang W Tian and F Qian ldquoEMD- and LWT-based stochas-tic noise eliminatingmethod for fiber optic gyrordquoMeasurementvol 44 no 10 pp 2190ndash2193 2011

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciences vol 454 no 1971 pp 903ndash995 1998

[13] Y Gan and L F Sui ldquoDe-noising method for gyro signal basedon EMDrdquo Acta Geodaetica et Cartographica Sinica vol 40 no6 pp 745ndash750 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Sensors 7

[2] R Peesapati S L Sabat K P Karthik J Nayak and NGiribabu ldquoEfficient hybrid Kalman filter for denoising fiberoptic gyroscope signalrdquo Optik vol 124 no 20 pp 4549ndash45562013

[3] V V Chikovani ldquoPerformance parameters comparison of ringlaser coriolis vibratory and fiber-optic gyros based on Allanvariance analysisrdquo in Proceedings of the IEEE 2nd InternationalConference on Actual Problems of Unmanned Air VehiclesDevelopments (APUAVD rsquo13) pp 153ndash156 IEEE Kiev UkraineOctober 2013

[4] C-S Qu T-Z Lu and Y Tan ldquoA modified empirical modedecomposition method with applications to signal de-noisingrdquoActa Automatica Sinica vol 36 no 1 pp 67ndash73 2010

[5] Y Gan L Sui G Xiao and Y Duan ldquoEMD de-noising theoryconsidering static and dynamic conditions and its applicationsin INSrdquo LectureNotes in Electrical Engineering vol 245 pp 507ndash515 2013

[6] Y Zhang SWang andD Xia ldquoEMD-based denoisingmethodsin the MEMS gyroscope de-driftrdquo in Proceedings of the 5thIEEE International Conference on NanoMicro Engineered andMolecular Systems (NEMS rsquo10) pp 591ndash594 Xiamen ChinaJanuary 2010

[7] H Tian R Yuan C Zhang J Jin N Song and S LinldquoNonlinear empirical mode predictive drift extraction on fiberoptical gyroscoperdquo Optik vol 122 no 5 pp 415ndash421 2011

[8] S Jain S Nandy G Chakraborty C S Kumar R Ray andS N Shome ldquoError modeling of various sensors for roboticsapplication using allan variance techniquerdquo in Proceedings ofthe IEEE International Conference on Signal Processing Com-munications and Computing (ICSPCC rsquo11) pp 1ndash4 IEEE XirsquoanChina September 2011

[9] N Zhang and X Li ldquoResearch on theoretical improvement ofdynamic Allan variance and its applicationrdquo Acta Optica Sinicavol 31 no 11 pp 70ndash75 2011

[10] J C Li F Q Gao G L Wang W Gao W Zhu and M WangldquoAnalysis of dynamic Allan variance for fiber optic gyro undervibration and variable temperature conditionsrdquo Chinese Journalof Lasers vol 40 no 9 pp 1ndash7 2013

[11] S Dang W Tian and F Qian ldquoEMD- and LWT-based stochas-tic noise eliminatingmethod for fiber optic gyrordquoMeasurementvol 44 no 10 pp 2190ndash2193 2011

[12] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciences vol 454 no 1971 pp 903ndash995 1998

[13] Y Gan and L F Sui ldquoDe-noising method for gyro signal basedon EMDrdquo Acta Geodaetica et Cartographica Sinica vol 40 no6 pp 745ndash750 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of