766 ieee sensors journal, vol. 17, no. 3, february 1, 2017...

766 IEEE SENSORS JOURNAL, VOL. 17, NO. 3, FEBRUARY 1, 2017

In-Motion Initial Alignment for Odometer-AidedStrapdown Inertial Navigation System

Based on Attitude EstimationLubin Chang, Member, IEEE, Hongyang He, and Fangjun Qin

Abstract— This paper investigates the in-motion initial align-ment for odometer-aided strapdown inertial navigation systemwith main focus on handling the severe disturbance inherent inthe odometer. An attitude estimation-based alignment method isproposed through ingeniously attitude matrix decomposition andvelocity rate equation reconstruction. The attitude estimation-based method can attenuate the disturbance in the odometer toa certain extent and can avoid some additional approximations.However, the severe disturbance in the odometer cannot behandled adequately by the attitude estimation structure. In thisrespect, a low-pass finite impulse response digital filter is usedto attenuate the disturbance in the odometer preliminarily.Experimental results are reported to validate the effectivenessof the proposed alignment methods and the superiority ofattitude estimation-based method over attitude determination-based method.

Index Terms— Attitude determination, attitude estimation, ini-tial alignment, odometer, strapdown inertial navigation system.

I. INTRODUCTION

AS A dead-reckoning navigation method, the strapdowninertial navigation system (SINS) can track the positionand orientation of the carrier relative to a known startingpoint with the measurements provided by the self-containedaccelerometers and gyroscopes [1]. The parameters of thestaring point are determined by the initial alignment. Sincethe initial position and velocity can be easily obtained fromother aiding sensors, the initial alignment is mainly referredto determining the initial attitude [2]. Since the in-motionalignment is an advantageous functionality for special applica-tion scenarios, much effort has been devoted to investigatingthe in-motion alignment. The in-motion alignment can not beaccomplished using only the outputs of the inertial sensorsand necessitates some external aiding information. The GlobalPositioning System (GPS) is widely used to prevent the long-term growth of the accumulated errors of the SINS [2]–[5].However, the GPS is prone to jamming and masking especiallyin urban areas. For land vehicles, odometer is a cost-effective

Manuscript received October 19, 2016; revised November 23, 2016;accepted November 23, 2016. Date of publication November 29, 2016; dateof current version January 6, 2017. This work was supported in part bythe National Natural Science Foundation of China under Grant 61304241,Grant 61374206, and Grant 41404002, and in part by the National Post-Doctoral Program for Innovative Talents under Grant BX 201600038. Theassociate editor coordinating the review of this paper and approving it forpublication was Dr. Amitava Chatterjee.

The authors are with the Department of Navigation Engineering, Naval Uni-versity of Engineering, Wuhan 430033, China (e-mail: [email protected];[email protected]).

Digital Object Identifier 10.1109/JSEN.2016.2633428

and conveniently-deployed sensor, which is proven to be apromising method to suppress the error drift of SINS [6]–[8].Moreover, both the odometer and SINS are self-contained,the integration of which is also expected to be immune todisturbance from/in surrounding environment.

Traditionally, the initial alignment is accomplished by twosuccessive stages, i.e. coarse alignment to obtain the roughlyknown attitude and fine alignment to refine the result bythe coarse alignment. When the roughly known attitude isobtained by the coarse alignment, the fine alignment canbe readily accomplished using the Kalman filtering basedmethods [5]. In this respect, the difficulty of initial alignmentlies in the coarse alignment stage. The traditional coarsealignment methods make use of the relationship betweenthe outputs of the inertial sensors and the earth rate andgravity directly, which are therefore, not suitable for in-motionalignment due to the vehicle maneuverability and externaldisturbance. Based on the decomposition of the body attitudeinto separate earth motion, inertial rate and constant initialattitude, a recursive alignment approach based on attitudedetermination has been developed in [9]–[20]. The attitudedetermination based alignment (ADBA) transforms the attitudealignment problem into a continuous attitude determinationproblem using finite vector observations. The ADBA has beenwidely approved as a promising substitute for the traditionalcoarse alignment due to its anti-disturbance and fastness. Mostof these ADBA methods are developed for GPS aided SINSand the extension to Doppler Velocity Log (DVL) aided SINSis reported in [17]–[19]. The odometer and DVL are both kindsof velocity encoders which provide velocity information in thevehicle coordinate system. Therefore, the methods developedin [17]–[19] can be readily used for odometer-aided SINSinitial alignment. Compared with GPS, the odometer/DVL cannot provide position and ground velocity information directlywhich is necessary for vector observations construction inADBA. Therefore, real-time position and ground velocityinformation during the odometer/DVL aided SINS alignmenthave to be approximated using their initial values, whichmay degrade the alignment performance to a certain extent.Another drawback of the ADBA for odometer aided SINSis its inability to handle the severe disturbance inherent inthe velocity output of the odometer. These aforementioneddrawbacks make the performance of ADBA for odometeraided SINS be compromised, e.g., slow convergence andvulnerability to divergence. For the first drawback, someresearchers have investigated the backtracking methodology

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CHANG et al.: IN-MOTION INITIAL ALIGNMENT FOR ODOMETER-AIDED SINS BASED ON ATTITUDE ESTIMATION 767

to obtain the position information [8], [17]. However, for thesecond drawback, to the authors’ best knowledge there isno method is reported in public to address such drawback.Actually, if the severe disturbance inherent in the odometercan not be handled appropriately, the ADBA can not beaccomplished and the following backtracking scheme thatnecessitates the roughly known results by ADBA, can alsonot be carried out.

The aforementioned facts represent the main motivation ofthis paper, which devotes itself to addressing the in-motionalignment for odometer aided SINS with main focus onhandling the severe disturbance inherent in the odometer. Theattitude estimation is widely approved as a promising substi-tute for attitude determination due to its capability of handlingthe noise in the model and estimating other parameters otherthan the attitude. In this respect, the attitude estimation basedmethod can be expected to attenuate the severe disturbance inthe odometer. Based on the aforementioned consideration, anattitude estimation based alignment (AEBA) method is pro-posed for odometer aided SINS. In AEBA, the process modelis derived by decomposing the attitude matrix and makinguse of the odometer outputs instead of the approximatingvalues. The measurement model is derived by constructingthe vector observations based on the special attitude matrixdecomposition and the specific equation in body frame. Theproposed AEBA can avoid some additional approximations inADBA and suppress the disturbance inherent in the odometerto a certain extent. However, the severe disturbance inherentin the odometer can not be attenuated adequately by theattitude estimation structure, as will be shown in the exper-imental study. In this respect, the low-pass finite impulseresponse (FIR) digital filter is used to attenuate the disturbancepreliminarily. The preprocessed odometer outputs are thenused in the ADBA to accomplish the alignment task.

The remaining of the paper is organized as follows.Section II is devoted to establishing the process and measure-ment model of the proposed AEBA method. Some discussionsand explanations of the proposed method have also beenpresented in this section. Experimental results using field testdata are reported in Section III. Finally, conclusions are drawnin Section IV.

II. ATTITUDE ESTIMATION-BASED ALIGNMENT

It is known that the attitude determination is virtually astatic method without taking the statistical properties of themeasurements into account. In contrast, the attitude estimationrefers to dynamic method where the dynamic model of vehiclemotion is used in a filtering algorithm. Meanwhile, the filteringstructure can also suppress the inherent disturbance in mea-surement to a certain extent. In this respect, the attitude esti-mation is generally superior over the attitude determination.This section is devoted to establishing the attitude estimationmodel for odometer aided SINS initial alignment.

A. Process Model

Denote n the local level navigation frame (East-North-Up,ENU), b the SINS body frame (Right-Forth-Up, RFU), i some

chosen inertial frames, and e the Earth frame. The essencefor SINS initial alignment is to determine the attitude Cnb (t)from body frame to navigation frame. According to the chainrule of the attitude matrix, the attitude matrix Cnb (t) can bedecomposed as

Cnb (t) = Cn(t)n(0)Cn(0)b(0)Cb(0)b(t) = Cn(t)b(0)Cb(0)b(t) (1)where b (0) and n (0) are the inertially non-rotating framesthat are aligned with the body and navigation frame at t0,respectively.

Denote the inertial reference frame b (0) as i . Accordingly

Ċib(t) = C ib(t)(ωbib×) wi th C ib(0) = I3×3 (2)

Ċin(t) = C in(t)(ωnin×) wi th C in(0) = Cb(0)n(0) (3)

ωbib denotes the body angular rate measured by gyroscopes inthe body frame. (·×) is the cross product matrix. The attitudechanges of C ib(t) can be calculated recursively by attitudeupdate algorithm with the accurate initial value and gyroscopeoutputs. In contrast, C in(t) can not be determined through suchmanner as the initial value is unknown and the correspondingangular rate is also unknown. For the filtering algorithm,the dynamic model can be initialized with some assumedvalue and the state can be modified using some correlatedmeasurement. This is just the intuitional motivation of theestablishment of attitude estimation model. That is, (3) can beused as the process model for AEBA. ωnin = ωnie+ωnen with ωniedenoting the earth rotation rate and ωnen the angular rate of thenavigation frame. Since the calculation of ωnen necessitates theknowledge of real-time ground velocity and position which,however, can not be obtained by odometer aided SINS, theangular rate ωnin has to be approximated as ω

nie in the ADBA,

which can introduce additional error. In the proposed AEBA,the angular rate ωnin is reconstructed using the body velocityprovided by the odometer to further improve the alignmentperformance. The angular rate of the navigation frame ωnen isexpressed as

ωnen = Fcvn (4)where

Fc =⎡⎣

0 −1/(RM + h) 01/(RN + h) 0 0

(tan L)/(RN + h) 0 0

⎤⎦

RM and RN are the main curvature radii of the prime meridianand the equator, respectively. h is altitude of the body. Duringthe AEBA, the latitude L is approximated using its initialknown values L0.

The relationship between vb and vn is given by

vn = Cnbvb = Cni C ibvb (5)Substituting (4) and (5) into (3) yields

Ċin(t) = C in(t)

{(ωnie + FcCni C ibvb

)×

}(6)

This is just the process model of the AEBA for odometeraided SINS initial alignment, among which C ib is calculatedrecursively using (2) and can be viewed as known value.


The attitude matrix C in(t) is just the state of the AEBA. In thenext sub-section, the corresponding measurement model willbe developed for the state C in(t).

B. Measurement Model

Given the linear/angular information by the accelerome-ters/gyroscopes, the vehicle’s ground velocity equation in thenavigation frame is given by

v̇n = Cnb f b −(2ωnie + ωnen

) × vn + gn (7)where f b represents the specific force in body frame and gn isthe gravity vector in navigation frame.

After some algebraic transformations, (7) can be trans-formed as

Cnb[v̇b +

(ωbie + ωbib

)× vn − f b

]= gn (8)

Substituting (1) into (8) yields

Cn(t)i Cib(t)

[v̇b +

(ωbie + ωbib

)× vb − f b

]= gn (9)

Multiplying C in(t) on both sides and ignoring the earthrotation rate ωbie yield

C ib(t)[v̇b + ωbib × vb − f b

]= C in(t) gn (10)

Integrating (10) on both sides over the time interval of interest∫ t

0C ib(t)

[v̇b + ωbib × vb − f b

]dτ =

∫ t0

C in(τ ) gndτ (11)

It should be noted that the time index inside the integratoris denoted by τ . According to the chain rule of the attitudematrix, C in(τ ) can be decomposed as

C in(τ ) = C in(t)Cn(t)n(τ ) (12)Substituting (12) into (11) yields∫ t

0C ib(t)

[v̇b + ωbib × vb − f b

]dτ = C in(t)

∫ t0

Cn(t)n(τ ) gndτ

(13)

It is known that τ is varying from 0 to t and therefore,C in(t) is a constant value for dτ , which is just the reason whyC ib(t) can be taken out the integrating operator in (13).

Further decomposing the attitude matrix Cn(t)n(τ ) yields

Cn(t)n(τ ) = Cn(t)n(0)Cn(0)n(τ ) (14)Substituting (14) into (13) and reorganizing the terms yield

the compact measurement model as

C in(t)βev = αev (15)in which

αev = Cb(0)b(t) vb − vb (0) −∫ t

0Cb(0)b(t) f

bdt (16a)

βev = Cn(t)n(0)∫ t

0Cn(0)n(τ ) g

ndτ (16b)

These values can all be calculated using the similar velocityintegration formula in [11]. The corresponding details are notpresented here for brevity.

The developed AEBA is a typical attitude estimation prob-lem and many fruitful filtering algorithms can be readilyused, as discussed in the survey paper [23]. In this paper,the unscented quaternion estimator (USQUE) is used as theworkhorse to carry out the task. The explicit details about theUSQUE can be referred in [24] and [25].

Eq. (6) and (15) formulate the continuous process andmeasurement model. In order to carry out the filtering processin the computer, the continuous model should be firstly writtenin the discrete-time form. (6) is actually an attitude updateequation and many fruitful update methods can be used readily,such as the single-sample and two-sample integration methods.In the developed method, the calculated attitude will also berevised in the filtering measurement update and therefore, thereis no need to use high rate integration method. In this respect,the used attitude update method in the proposed algorithm is asimple single-sample integration method, which is also knownas the Euler method. For the measurement model, the Eulermethod has also be used.

C. Discussions

Remark 1: Specifically, the odometer mounted on the vehi-cle’s wheels gives information on the traveled distance ofthe navigation system by measuring the number of full andfractional rotations of the vehicle’s wheels. Meanwhile, theinformation provided by the vehicle-mounted odometer isrepresented in the vehicle coordinate system (body frame).Moreover, motion of the wheeled vehicle on a surface isgoverned by two nonholonomic constraints. In this respect,the vehicle’s velocity expressed in the body frame is given by

vb = [ 0 �d/�t 0 ]T (17)where �d is the traveled distance during time period �t .Actually, (17) implies that the vehicle travels under idealconditions, i.e. there is no side slip along the direction of therear axle, no motion normal to the road surface and no wheelslips. In practical application, the assumed ideal conditionsmay be somewhat violated due to the presence of side slipand jounce. When the vehicle travels on an even keel, whichis always the case for the attitude alignment implementation,the aforementioned disturbance can be characterized by whitenoise.

To fully use the priori nonholonomic constraint, the spatialmisalignment of the SINS relative to the odometer should bewell calibrated. This is also a crucial stage for the accurateodometer aided SINS. Traditionally, the calibration stage isprior to the alignment stage [8] and many fruitful meth-ods have been developed to execute the calibration. Thispaper focuses on the attitude alignment method developmentand the calibration stage has been assumed to be achievedpreviously.

Remark 2: Although the filtering algorithm can suppressthe inherent disturbance in measurement to a certain extent,the original outputs of odometer can still not be used directlyin the proposed AEBA. The reasons are as follows: theability of the filtering algorithm to suppress the measurementdisturbance is due to taking the statistical properties of the


Fig. 1. Body velocity by different methods.

Fig. 2. Alignment procedure of the proposed AEBA method.

measurement into account. For the developed AEBA, the bodyvelocity vb appears both in the process and measurementmodel as shown in (6) and (16a). That is to say, the processnoise and measurement noise are correlated to each other,which can induce aggravating filtering degradation, especiallywhen the disturbance is severe. More seriously, the outputsof gyroscope and odometer are also correlated to each otherin the measurement model as shown in (16a), which canfurther degrade the filtering performance. It will be shownin the following experimental study that making use of theoriginal outputs of odometer in the AEBA can not reach asatisfied alignment performance. In this respect, it is desiredto preprocess the odometer output by some low-pass filter.In this paper, the FIR filter is used to attenuate the disturbanceinherent in the odometer preliminarily. In order to illustrate thedisturbance explicitly, the forward velocity by the odometerused in the experimental study is plotted in Fig. 1. In Fig. 1the reference velocity is provided by the integrated SINS/GPS,that is vbre f = CbnS I N S/G PSvnS I N S/G PS . It will be shown in theexperimental study that making use of the body velocity withsevere disturbance directly will much degrade the alignmentperformance (see Fig. 8, 11 and 14). Therefore, the bodyvelocity provided by the odometer should be preprocessedbefore it is used in the alignment procedure. It is shown inFig. 1 that the preprocessed velocity by FIR filter is nearlythe same with the reference data.

By far, the alignment procedure of the proposed AEBAmethod can be illustrated in Fig. 2.

Remark 3: The validity of introducing the body velocity vb

into the process model lies in the observable characteristicof the ground velocity vn in practical application. Accordingto [20], the attitude and velocity are both observable whenthe vehicle runs on a trajectory with line and curving pathsegments for the odometer aided SINS. This condition is verymoderate in practice and it is feasible to determine the atti-tude and velocity simultaneously in the alignment. When theground velocity vn is determined, the angular velocity ωnin willbe more accurate than it is approximated using ωnie directly.The process model of the proposed AEBA has made use of theobservable ground velocity vn information implicitly, whichcan further improve the alignment performance.

Remark 4: It should be noted that the FIR filter suffers fromtime-delayed characteristics of signals. The output of the FIRfilter at the current time t corresponds to the input at a formertime tM with a period of delay dT = t − tM . However, as oneof the superiority of the FIR filter over other low pass filtersis its ability to determine the time delay accurately. In ourused FIR filter, the time delay of the filter is 0.4s. In thisregard, simply applying FIR filter to odometer measurementscan lead to inaccurate estimation of the rotation matrix andtherefore, the time delay should be handled appropriately. Thetime delay caused by the FIR filter can be compensated inthe developed AEBA method as follows. The attitude matrixCnb (t) at current time t is given by

Cnb (t) = Cn(t)n(tM )Cn(tM )i C

ib(t) (18)

where Cn(tM )i can be derived using the developed AEBAmethod with the measurements of inertial sensors and odome-ter up to time tM . C ib(t) can be derived normally using the

corresponding angular rates up to the current time t . Cn(t)n(tM )can be derived as

Cn(t)n(tM ) =(

Cn(0)n(t)

)TCn(0)n(tM ) (19)

Remark 5: This paper and [16] both trace the thread ofimproving the alignment performance by transforming theSINS initial alignment problem into an attitude estimationproblem. However, the derived attitude estimation models arequite different with each other due to different aiding infor-mation and application field. In [16], the AEBA is developedfor the low-cost SINS aided with the GPS. The main effort ofthat work is devoted to estimating the gyroscope bias coupledwith the attitude and therefore, the gyroscope bias should bepart of the state vector. In this regard, attitude matrix Cnb (t)is decomposed as

Cnb (t) = Cn(t)n(0)Cn(0)b(0)Cb(0)b(t) = Cn(t)n(0)Cn(0)b(t) (20)and n (0) is selected as the inertial reference frame, which isdifferent with that in (1). With the attitude decomposition formin (20), the derived attitude estimation model is given by

Ċn(0)/ ib(t) = Cn(0)/ ib(t)

[(ω̃bib − εb

)×

](21)

where εb is the gyroscope bias.In this work, the AEBA is developed for the navigational

grade SINS aided with the odometer. The main effort of this


Fig. 3. Experiment platform and equipments.

TABLE I

SPECIFICATIONS OF THE GYROSCOPE AND ACCELEROMETER

work is devoted to attenuating the severe disturbance inherentin the odometer. In this respect, the velocity vector in thebody frame provided by the odometer should be incorporatedinto the measurement model or/and the process model, whichis just the main effort in Section II.A. In order to achievethis point, the attitude matrix Cnb (t) is decomposed as (1)and the reference frame is selected as b (0). Since differentattitude decomposition form and aided information are used,the following vector observations construction is also differentwith each other.

III. EXPERIMENTAL STUDY

In order to evaluate the performance of the proposed align-ment method, a car-mounted experiment was carried out. In theexperiment test, a navigation-grade ring laser SINS, a single-antenna GPS receiver and an odometer are equipped on thecar, as shown in Fig. 3. The SINS consists of three ring lasergyroscopes and three quartz accelerometers. The specificationsof the inertial sensors are listed in Tables I. The GPS providesvelocity with precision of about 0.1m

/s and position with

precision of about 10m. Its update rate is 1H z. The pulseequivalent of the used odometer is 0.08194m.

Specifically, the following four alignment methods werecarried out in the experiment:

ADBA1: ADBA without odometer outputs denoising.ADBA2: ADBA with odometer outputs denoising.AEBA1: AEBA without odometer outputs denoising.AEBA2: AEBA with odometer outputs denoising.The evaluation of ADBA1 and AEBA1 is used to demon-

strate the negative effect of the severe disturbance inherentin the odometer measurement. The evaluation of ADBA2 and

Fig. 4. Experiment sequence.

Fig. 5. Trajectory in the suburban area during the experiment.

AEBA2 is used to demonstrate the superiority of the AEBA2over the ADBA2 for odometer aided SINS. Actually, the supe-riority of the attitude estimation over the attitude determinationcan also be illustrated through the comparison of AEBA1 andADBA1, which will be shown in the following study.

The procedure of the experiment was designed as follows:firstly, make the car to be static for about 20 minutes and thestatic attitude alignment was performed to obtain the accurateinitial attitude for the following integrated navigation withmaneuverability. Meanwhile, the calibration for the odometeraided SINS has also been performed during this static stage.Since the initial conditions are very accurate, the attitudeoutputs of the integrated SINS/GPS can be used as the attitudereference for the alignment methods evaluation [12]. Theexperiment sequence is shown in Fig. 4.

The total trajectory during the experiment is shown inFig. 5. Since the in-motion alignment is an advantageous func-tionality for special application scenarios, three chosen 100stest segments data with different maneuvers were collectedto evaluate the aforementioned four methods. The odometeroutputs corresponding to the three data segments have alsobeen marked in Fig. 1. In each test, the initial conditions ofthe attitude quaternion were all set to be [1 0 0 0]T for thefour methods. For our proposed method, the initial covarianceof the attitude was set to be

([20°, 20°, 50°]T

)2, which is

used to account for the unknown and may be large initialmisalignment. The attitude alignment errors are summarized inTable II. The relative percent errors of the yaw angles estimatefor the four different alignment methods are summarized inTable III to highlight the robustness and reliability features ofthe proposed method.

Although the yaw angle estimates by ADBA1 and AEBA1have been presented in Table II, actually, they do not convergedue to the severe disturbance inherent in the odometer output.


TABLE II

ATTITUDE ALIGNMENT ERROR BY DIFFERENT METHODS USINGDIFFERENT DATA SEGMENTS (UNIT: DEG)

TABLE III

RELATIVE PERCENT ERROR FOR DIFFERENT ALIGNMENT METHODS(FOR YAW ANGLE ESTIMATE, ABSOLUTE VALUES)

However, compared with ADBA1, the alignment performanceof AEBA1 has been much improved, which proves thatthe developed AEBA method can suppress the disturbanceinherent in the odometer measurement to a certain extent.Unfortunately, the severe disturbance appears both in processand measurement model of AEBA and has much correlationswith disturbance inherent in the inertial sensors, which makethe suppression effect by only Kaman filtering be compro-mised. This fact indicates that it is necessary to preprocess theodometer output to denoise the inherent disturbance. When theFIR filter is integrated into the ADBA and AEBA methods,the resulting performance is much improved, as shown inTable II. The yaw angle estimates by ADBA2 and AEBA2 canboth reach a satisfied performance. Moreover, the AEBA2 canoutperform ADBA2 consistently for the yaw angle estimatefor all the three data segment. The superiority of AEBA2 overADBA2 lies in the developed attitude estimation model, inwhich the remnant disturbance in the odometer measurementcan be further suppressed and the angular rate of the navigationframe can be accounted for implicitly during the alignment.

In order to further illustrate the alignment performance ofthe four methods, the yaw angle estimate results by the fourmethods using the three data segment are also plotted inFig. 6-14. Fig. 6 plots the alignment results by ADBA2 andAEBA2 against the reference true value for the first data seg-ment and Fig. 7 plots the corresponding estimate error. Fig. 8plots the estimate error by ADBA1 and AEBA1 as comparisonfor the first data segment. Fig. 9 plots the alignment resultsby ADBA2 and AEBA2 against the reference true value forthe second data segment and Fig. 10 plots the corresponding

Fig. 6. Yaw angles estimate by ADBA2 and AEBA2 (first data segment).

Fig. 7. Yaw angles estimate error by ADBA2 and AEBA2 (first datasegment).

Fig. 8. Yaw angles estimate error by ADBA1 and AEBA1 (first datasegment).

estimate error. Fig. 11 plots the estimate error by ADBA1and AEBA1 as comparison for the second data segment.Fig. 12 plots the alignment results by ADBA2 and AEBA2against the reference true value for the third data segment andFig. 13 plots the corresponding estimate error. Fig. 14 plotsthe estimate error by ADBA1 and AEBA1 as comparison for


Fig. 9. Yaw angles estimate by ADBA2 and AEBA2 (second data segment).

Fig. 10. Yaw angles estimate error by ADBA2 and AEBA2 (second segment).

Fig. 11. Yaw angles estimate error by ADBA1 and AEBA1 (second segment).

the third data segment. For more illustrative, the alignmentresults by ADBA1 and AEBA1 are not plotted together withthat by ADBA2 and AEBA2 against the reference values dueto that they are much far away from the reference values.It is shown that the yaw angle estimate error by ADBA2 andAEBA2 reduces to about 5 degree in 25 seconds and about2 degree in 30 seconds for all the three data segments, which

Fig. 12. Yaw angles estimate by ADBA2 and AEBA2 (third segment).

Fig. 13. Yaw angles estimate error by ADBA2 and AEBA2 (third segment).

Fig. 14. Yaw angles estimate error by ADBA1 and AEBA1 (third segment).

indicates that the two methods have a very fast alignmentspeed. The superiority of AEBA1 over ADBA1 has also beenillustrated clearly. However, the improvement by AEBA1 isstill compromised due to the severe disturbance inherent inthe odometer measurement, as shown in Fig. 8, 11 and 14.


IV. CONCLUSION

A good attitude initialization is very important for thedead reckoning based odometer aided SINS. The newly-derived attitude determination based alignment method hasbeen proven to be an effective method for GPS aided SINSinitial alignment. However, when it is extended to the odome-ter aided SINS alignment, the corresponding performance iscompromised and voluntary to divergence due to the severedisturbance inherent in the odometer. This paper proposesan attitude estimation based alignment method to improvethe alignment performance of attitude determination basedalignment through ingeniously attitude matrix decompositionand velocity rate equation reconstruction. Since the severedisturbance can not be handled adequately by the attitudeestimation structure, the finite impulse response digital filteris used to preprocess the odometer outputs to denoise thedisturbance. Field test data is used to evaluate the proposedalignment methods. The results show that, with the disturbanceinherent in the odometer being well handled, the SINS canbe well aligned with a fast speed. The superiority of attitudeestimation based alignment over attitude determination basedalignment has also been well demonstrated.

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Lubin Chang (M’13) received the B.Sc. andPh.D. degrees in navigation from the Departmentof Navigation, Naval University of Engineering,Wuhan, China, in 2009 and 2014, respectively.

He is currently a Lecturer with the Naval Uni-versity of Engineering. He has published over 20scientific papers in international journals. His currentresearch interests include inertial navigation sys-tems, inertial-based integrated navigation systems,and state estimation theory. He was awarded afellowship from the Alexander von Humboldt Foun-

dation, Germany, in 2016. He was the recipient of the 2015 Excellent DoctoralDissertation of Hubei Provinces, the 2016 National Post doctoral Program forInnovative Talents, and the 2014 IET Premium Best Paper Award in science,measurement, and technology.

Hongyang He received the B.Sc. degree in mechan-ical design and automation from the School ofMarine Science and Technology, Northwestern Poly-technical University, Xi’an, China, in 2011, and theM.Sc. degree in navigation engineering from theNaval University of Engineering, Wuhan, China,in 2013.

He is currently a Doctor with the Department ofNavigation, Naval University of Engineering, wherehe involves in inertial navigation systems, and in-motion initial alignment algorithms.

Fangjun Qin received the B.Sc., M.Sc., andPh.D. degrees in navigation from the Depart-ment of Navigation, Naval University of Engi-neering, Wuhan, China, in 2002, 2005, and 2009,respectively.

He is currently an Associate Professor withthe Department of Navigation Engineering, NavalUniversity of Engineering. His scientific interestsinclude inertial navigation and INS/GPS integratednavigation technology.

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