Robust Heading Estimation for Indoor Pedestrian Navigation...

Research ArticleRobust Heading Estimation for Indoor Pedestrian NavigationUsing Unconstrained Smartphones

Zhian Deng 1 Xin Liu 2 Zhiyu Qu 1 Changbo Hou1 and Weijian Si1

1College of Information and Communication Engineering Harbin Engineering University Harbin 150001 China2School of Information and Communication Engineering Dalian University of Technology Dalian 116024 China

Correspondence should be addressed to Xin Liu liuxinstar1984dluteducn

Received 12 February 2018 Accepted 5 June 2018 Published 3 July 2018

Academic Editor Kunjie Xu

Copyright copy 2018 Zhian Deng 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

Heading estimation using inertial sensors built-in smartphones has been considered as a central problem for indoor pedestriannavigation For practical daily lives it is necessary for heading estimation to allow an unconstrained use of smartphones whichmeans the varying device carrying positions and orientations As a result three special human body motion states namelyrandomhandmovements carrying position transitions and user turns are introduced However most existing heading estimationapproaches neglect the three motion states which may render large estimation errors We propose a robust heading estimationsystem adapting to the unconstrained use of smartphones A novel detection and classification method is developed to detect thethree motion states timely and discriminate them accurately For normal working the user heading is estimated by a PCA-basedapproach If a user turn occurs it is estimated by adding horizontal heading change to previous user heading directly If one ofthe other two motion states occurs it is obtained by averaging estimation results of the adjacent normal walking steps Finally anoutlier filtering algorithm is developed to smooth the estimation results Experimental results show that our approach is capable ofhandling the unconstrained situation of smartphones and outperforms previous approaches in terms of accuracy and applicability

1 Introduction

For Global Navigation Satellite Systems- (GNSS-) deniedenvironments various indoor pedestrian navigation solu-tions [1ndash5] such as wireless local area positioning systemsultrawideband and radio frequency identification have beenproposed The usage of these infrastructure based solutionsis limited to the space where special equipment or infrastruc-tures are available Pedestrian dead reckoning (PDR) [6ndash8]using inertial sensors built-in a smartphone may overcomethis limitation since the inertial sensors are continuouslyavailable PDR achieves location estimation by combiningstep detection and step length estimation with user head-ing estimation Once each user step is detected the userposition is updated by adding the current estimated relativedisplacement to the user position estimated at previousstep Recently since smartphones are ubiquitous and carriedalmost everywhere we go it is more and more practicable todeploy PDR approach in our daily lives

User heading estimation is a central problem for PDRMost existing heading estimation solutions deploy traditionalattitude estimation based approaches [9 10] The user head-ing is estimated by adding a fixed user heading offset to theestimated device forward heading This approach performswell if the device is constrained to a fixed carrying positionand device orientation However for the smartphone in thetrouser pocket or swinging in hand the heading offset ischanging all the time and hard to be estimated Traditionalattitude estimation based approaches may render a largeheading estimation error due to the biased estimation of theheading offset

To address the heading estimation problem with devicesplaced in the trouser pocket or swinging in hand theuDirect approach [11] the PCA-based approach includingconventional PCA approach [12] and our previous proposedRMPCA approach [13] combining rotation matrix (RM) andPCA have been proposed The uDirect approach extractslocal walking direction directly at a specific region where the

HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 5607036 11 pageshttpsdoiorg10115520185607036

2 Wireless Communications and Mobile Computing

forward acceleration dominates the acceleration in the hori-zontal plane In contrast PCA-based approach ismore robustto the body locomotion dynamics since all acceleration sam-ples are exploited to extract the most variation of horizontalacceleration signals which is assumed to be parallel withwalking direction Recently to remove the restrictions ondevice carrying positions we proposed a heading estimationapproach independent of carrying position The carryingposition is recognized by a position classifier upon the dis-tinguishable acceleration patterns while assuming relativelystable device orientations under the same carrying positions

To enable a really unconstrained use of smartphones forheading estimation not only device carrying positions butalso the varying device orientations should be consideredThus several critical problems still need to be solved toenhance the reliability and applicability of heading estima-tion

Firstly the current heading estimation solutions aresensitive and nonrobust to random hand movements ForPCA-based approach the fundamental assumption is seri-ously corrupted by random hand movements which makethe maximum variance of the acceleration signals in thehorizontal plane deviate from the walking direction

Secondly three motion states namely hand movementscarrying positions transitions and user turns and theirimpacts on heading estimations have been paid little atten-tions Missed detection and confusion among the threemotion states may render a large heading estimation error

To solve the above problems we propose a robust headingestimation system using unconstrained smartphones Themain idea is that we select the related optimal headingestimation strategy based on the detection and discrimina-tion of three special motion states namely random handmovements carrying position transitions and user turns Anovel detection and classification method is developed todetect the three motion states timely and discriminate themaccurately If user turn occurs the user heading is estimatedby computing heading change in the horizontal plane directlyIf the other two motion states occur the user heading isassumed to be smooth and obtained by averaging estimationresults of the normal neighbor walking steps

The proposed estimation system deploys our previousRMPCA approach for heading estimation during normalwalking Finally the estimation results are further smoothedby filtering outliers caused by handmovements undetected orhand movements misclassified as user turns For simplicityin this work we only consider the two main pedestrianactivities namely walking and standing and assume thatthey have been already accurately recognized according totheir different acceleration patterns [14 15]

Experiments show that our heading estimation systemoutperforms existing approaches in terms of accuracy reli-ability and applicability under the unconstrained situationsIn summary our work makes the following contributions

(i) We propose a robust heading estimation system inde-pendent of carrying positions anddevice orientations

(ii) We point out that a large heading estimation errormay be introduced by PCA-based approach if the

following three motion states cannot be detected anddiscriminated random hand movements carryingposition transitions and user turn

(iii) We propose a novel detection and classificationmethod to detect and discriminate the above threemotion states

(iv) We develop an outlier filtering algorithm to removethe outliers of user heading estimation results

(v) We report the evaluation of the proposed detectionand classification technique based on extensive sam-ples collected from four participants and comparethe accuracy performance of our heading estimationapproach to existing approaches

In the rest of this paper we will firstly introduce anoverview of the proposed robust heading estimation systemusing unconstrained smartphones in Section 2 Section 3describes the detection and classification methods againstthe three special motion states in detail Section 4 describesthe robust user heading estimation approaches adapting thespecial motion states caused by unconstrained use of smart-phones The evaluations of experimental results are reportedin Section 5 Conclusions are presented in the last section

2 System Overview

Figure 1 shows an overview of the proposed robust user head-ing estimation system using unconstrained smartphonesTheproposed system selects user heading estimation schemebased on continuous motion states detection and classifi-cation results The basic idea of the motion state detectionand discrimination method is to exploit their distinguish-able acceleration and device attitude changing patterns Theattitude changing patterns include the accumulated pitchand roll angles the horizontal device heading change angleswhich can be derived from a continuous device attitudetracking model For practical smartphone uses we assumethat position transition and user turn cannot occur simul-taneously Similar assumption is given to hand movementand user turn motion states The assumptions are reasonablefor the following two reasons First the probability of bothmotion states happening is rather low when the probabilityof eachmotion state is low Second requiring device carryingposition transitions or significant hand movements whena user turn occurs is unnatural and also complicated forpedestrians

For heading estimation scheme selection during nor-mal walking without any special motion state detected wedeploy our previous RMPCA approach since the funda-mental assumption of PCA-based approach still holds Ifrandom hand movements or carrying position transitionsare detected the user heading is assumed to be smoothand calculated by averaging heading estimation results ofthe neighboring normal walking steps If user turns aredetected the user heading is obtained by adding horizontalheading change to previous user heading Besides to avoidintroducing estimation errors caused by undetected handmovements the estimation results are further smoothed byan outlier filtering algorithm

Wireless Communications and Mobile Computing 3

In order to describe the heading estimation problemwe define two coordinate systems namely global coordinatesystem (GCS) and device coordinate system (DCS) GCS isdefined by three axes119883119866 119884119866 and119885119866 of the Earth coordinatesystem which point east north and in the opposite directionof the gravity vector User heading estimation problem canbe considered as seeking walking direction expressions atGCS All raw inertial signals including acceleration andangular velocity samples are initially measured at DCS DCSis defined by axes 119883119863 119884119863 and 119885119863 The axis 119883119863 pointsrightward and119884119863 points forward while both axes are parallelwith the device screen The axis 119885119863 points outside of thescreen and is the cross-product of119883119863 and 119884119863

In this work we only investigate the most commonfour device carrying positions [17ndash20] namely held in hand(hand-held) against ear during phone call (phone-call)placed in trouser pocket (in-pocket) and swinging in hand(swinging-hand) For pedestrian activities we only considertwo situations namely normal walking and standing whichmay be easily recognized by their different accelerationpatterns [14 15] For simplicity we assume that the twoactivities are already accurately recognized

3 Detection and Classification ofthe Three Special Motion States

Three special motion states namely hand movements car-rying position transitions and user turns may render thefundamental assumption of PCA-based approaches seriouslycorruptedTherefore we develop detection and classificationmethod of the three motion states as seen in Figure 2 Wecollect acceleration signals from an accelerometer and obtainthe device attitude data from a continuous device attitudetracking model which will be presented in Section 41Then the collected data are divided into small segmentsfor subsequent detection and discrimination by a slidingwindow We select a window twice the size of user walkingstep period with 50 overlap between consecutive windowswhich is appropriate for detecting and discriminating themotion states accurately and timely

As shown in Figure 2 four parameters namely accu-mulated absolute acceleration change ΔAcc device head-ing change ΔYaw accumulated absolute pitch angle changeΔPitch and accumulated absolute roll angle changeΔRoll arecalculated as follows

ΔAcc = 119873Aminus1sum119894=1

(1003816100381610038161003816119860119888119888119909 (119894 + 1) minus 119860119888119888119909 (119894)1003816100381610038161003816+ 10038161003816100381610038161003816119860119888119888119910 (119894 + 1) minus 119860119888119888119910 (119894)10038161003816100381610038161003816+ 1003816100381610038161003816119860119888119888119911 (119894 + 1) minus 119860119888119888119911 (119894)1003816100381610038161003816)

(1)

ΔPitch = 119873Pminus1sum119894=1

(|119875119894119905119888ℎ (119894 + 1) minus 119875119894119905119888ℎ (119894)|) (2)

ΔRoll = 119873Rminus1sum119894=1

(|119877119900119897119897 (119894 + 1) minus 119877119900119897119897 (119894)|) (3)

ΔYaw = 119884119886119908 (119864119899119889119879119894119898119890) minus 119884119886119908 (119878119905119886119903119905119879119894119898119890) (4)

where 119860119888119888119909(119894) 119860119888119888119910(119894) 119860119888119888119911(119894) are the 119894th measured threedimensional acceleration signals at DCS 119875119894119905119888ℎ(119894) and 119877119900119897119897(119894)are the 119894th pitch and roll angle values of smartphone atGCS as seen in (13) in Section 41 and 119884119886119908(119878119905119886119903119905119879119894119898119890) and119884119886119908(119864119899119889119879119894119898119890) are the yaw values of smartphone at GCS atthe start time and end time of a slidingwindow as seen in (13)

After obtaining the four parameters we start to deploythem to detect and discriminate the three special motionstates by comparing the parameters with related thresholdvalues Firstly we detect and recognize the position transitionmotion by exploiting the significant acceleration changepatterns Figure 3 shows a classical example of accelerationsignals when position transitions occur during a pair ofdevice carrying positions Clearly all kinds of position tran-sitions consist of substantial acceleration change over threedimensions Moreover the acceleration changes are signifi-cantly larger than those of normal walking user turn motionstates and most hand movements with a relatively smallmagnitude This may be contributed to two reasons Firstposition transitions involve significant relative displacementand subsequently introduce extra acceleration Second thesubcomponents of the gravity vector added on the three axesare changing all the time due to the changing device attitudeTherefore we set a threshold value for the accumulatedabsolute acceleration change ΔAcc denoted as Th(ΔAcc)When the accumulated absolute acceleration change exceedsthe threshold value a position transition is assumed to occurTo avoid false detection we deploy the Random Forest basedcarrying position classifier proposed in [16] to confirm if thecarrying position is changed The carrying position classifierselects statistics of mean variance maximum andminimumover windowed acceleration samples as input features Fordetailed information about the carrying position classifierplease see [16] If a position transition does not occur andthe carrying position is not in-pocket hand movement witha large magnitude is detected

Secondly after excluding the position transition motionstate we detect and discriminate the remaining two motionstates We observe that the user turns only render deviceheading change in the horizontal plane while most handmovements may introduce significant roll and pitch anglechanges Therefore we set threshold values for the accumu-lated absolute pitch angle change ΔPitch and accumulatedabsolute roll angle change ΔRoll denoted as Th(ΔPitch)andTh(ΔRoll) respectively When the accumulated absolutepitch angle or roll angle change exceeds the related thresholdvalues respectively and the carrying position is not in-pocket a hand movement is assumed to occur

Finally if both carrying position transitions and handmovements are excluded we may infer that a user turnoccurs when the device heading change ΔYaw exceeds apredefined threshold value Th(ΔYaw) Otherwise no specialmotion state is detected The heading estimation is achievedby RMPCA approach Generally the choice of an appropri-ate threshold value is different for various device carryingpositions For in-pocket and swinging-hand positions thethreshold values are usually significantly larger than those


Special motion state detected

Yes

Position transition

Hand movement User turn

Yes YesYes

Averaging user headings of neighbor normal walking steps

Adding horizontal heading change to

previous user heading

No

RMPCA approach for normal walking

Ultimate user heading

Accelerometer Gyroscope Magnetometer

Device attitude tracking

Smartphone Sensing

Motion state detection and discrimination

Outlier filtering

Figure 1 Architecture of the proposed robust heading estimation system

of hand-held and phone-call positions due to a strongerintensity of the body locomotion

It should be noted that two false situations may happenthough their probabilities are rather low One is that a handmovement may be missed when it only introduces extraacceleration in the horizontal plane and have little impactson the pitch angles and yaw angles Another false situationis that a hand movement may be misclassified as a user turnwhen it only renders device heading change in the horizontalplane and have little impacts on the pitch angles and yawangles Fortunately large heading estimation errors caused bythe two false situations may be avoided by an outlier filteringalgorithm which will be given in Section 43

4 User Heading Estimation

The proposed user heading estimation approach consistsof three strategies an average of heading estimations ofthe neighboring normal walking steps adding horizontalheading change to user heading of previous step andRMPCAapproach Upon the detected and discrimination results ofthree special motion states the most suitable strategy isselected for heading estimation as seen in Figure 1 Thefirst strategy is selected when hand movements or carryingposition transitions are detected while the second strategyis employed when user turns occur During normal walking

RMPCA approach is used as the last strategy Besides toavoid heading estimation errors caused by undetected handmovements the estimation results of RMPCA are furthersmoothed by an outlier filtering algorithm

Two basic assumptions are used for heading estimationFirst the initial heading offset between user heading anddevice forward heading is zero since users need to holddevice in hand and gaze at it when they start the localizationapplication Second the initial user heading and relateddevice attitude are assumed to be known a priori [21 22]which can be obtained by Global Position System (GPS)tracking when the user enters a building landmarks orWiFilocalization

For both RMPCA approach and three special motionstates detection continuous device attitude information isrequired Therefore we firstly present the device attitudetracking model based on quaternions in Section 41 Thenwe describe the heading estimation strategies in detail inSection 42 An outlier filtering algorithm is developed inSection 43

41 Attitude Tracking Model An Extended Kalman Filter(EKF) is employed to fuse the inertial sensors and magne-tometer for device attitude tracking We deploy the quater-nion [23 24] to describe device attitude tracking modelsince it can avoid the singularity problems The relationship


ΔAcc gt Th(ΔAcc)

Carrying position changed

Device heading change ΔYaw

Accumulatedabsolute roll angle

change ΔRoll

Accumulated absolute acceleration

change ΔAccAccumulated

absolute pitch angle change ΔPitch

Calculation of four parameters

Carrying position Classification

Yes

No

NoRecognized position

transition motion

ΔRoll gtTh(ΔRoll)ΔPitch gtTh(ΔPitch)

Yes

No

ΔYaw gtTh(ΔYaw)

Not Carried in Pocket

Recognized hand movements

Yes

Yes

YesRecognized user

turn motion No

No special motionstate detected

Acceleration signals Device attitude tracking

Figure 2 Flowchart of the proposed three motion states detection and classification method

between GCS and real-time device attitude is constructed bythe quaternion vector and related rotation matrix The rota-tion matrix may transform any inertial signals represented atGCS into DCS as follows

h119863119862119878 (119905) = (R119863119862119878119866119862119878 (q (119905)))119879 h119866119862119878 (119905) (5)

where R119863119862119878119866119862119878 (q(119905)) is the rotation matrix of DCS correspond-ing to GCS at time 119905 and h119866119862119878(119905) and h119863119862119878(119905) are the same3 times 1 vectors represented at GCS and DCS respectively Wemay establish the one to one mapping relationship betweenrotation matrix and a quaternion vector

R119863119862119878119866119862119878 (q)

= [[[[

11990220 + 11990221 minus 11990222 minus 11990223 2 (11990211199022 minus 11990201199023) 2 (11990211199023 + 11990201199022)2 (11990211199022 + 11990201199023) 11990220 minus 11990221 + 11990222 minus 11990223 2 (11990221199023 minus 11990201199021)2 (11990211199023 minus 11990201199022) 2 (11990201199021 + 11990221199023) 11990220 minus 11990221 minus 11990222 + 11990223

]]]]

(6)

where q = [1199020 1199021 1199022 1199023 ]119879 is the normalized quaternionvectorwith the scalar part 1199020 and the vector part [1199021 1199022 1199023]119879and the parameter 119905 is omitted for simplicity

For device attitude estimation we firstly construct thestate equation of EKF Based on the kinematic law of rigid

body [24] the discrete-time state model of quaternions isgiven by

q119896+1 = exp (05 times Ω (w119896119879s)) q119896

= (I cos (05 times Δ120579119896) + Ω (w119896119879s) sin (05 times Δ120579119896)Δ120579119896 ) q119896(7)

where q119896 and q119896+1 are the quaternion vectors at time instants119896119879s and (119896 + 1)119879s 119879s is the time interval of state modelw119896 = [119908119909119896 119908119910

119896119908119911119896]119879 is the raw angular velocity vector

measured at DCS I is an 3 times 3 identity matrix Δ120579119896 =119879119904radic(119908119909

119896)2 + (119908119910

119896)2 + (119908119911

119896)2 andΩ(w119896119879s) is given by

Ω(w119896119879119904) = 119879119904[[[[[[[

0 minus119908119909119896 minus119908119910119896

minus119908119911119896119908119909119896 0 119908119911119896 minus119908119910119896119908119910

119896minus119908119911119896 0 119908119909119896119908119911119896 119908119910119896

minus119908119909119896 0

]]]]]]] (8)

In order to construct the state equation of EKF we deploy afirst order linearized approximation of the state model

q119896+1 = 119865119896q119896 + w119902119896 (9)


From hand-held to phone-calland back to hand-held

minus10minus5

05

10152025

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(a)

From hand-held to swinging-handand back to hand-held

5 10 15 20 25 300Time [s]

minus10

0

10

20

30

Acce

lera

tion

[mＭ

2]

x-axisy-axisz-axis

(b)

minus20

minus10

0

10

20

From hand-held to in-pocketand back to hand-held

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(c)

From swinging-hand to in-pocketand back to swinging-hand

minus20

minus10

0

10

20

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(d)

minus10

0

10

20

30

From phone-call to swinging-handand back to phone-call

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(e)

minus20

minus10

0

10

20

From phone-call to in-pocketand back to phone-call

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(f)

Figure 3 A typical example of acceleration signals when position transitions occur during a pair of device carrying positions (a) hand-held and phone-call (b) hand-held and swinging-hand (c) hand-held and in-pocket (d) swinging-hand and in-pocket (e) phone-call andswinging-hand (f) phone-call and in-pocket

where the linearized transition matrix 119865119896 = exp(05 timesΩ(w119896119879s)) andw119902119896= Ξ119896w119892119910119903119900119896 = minus1198791199042 [[e119896times] + 1199021198960I

minuse119879119896]w119892119910119903119900119896

(10)

where 1199021198960 and e119896 = [1199021198961 1199021198962 1199021198963]119879 are the scalar and vectorparts of the quaternion vector q119896 w119892119910119903119900

119896is the white Gaussian

noise of gyroscope outputs and [e119896times] is a standard vectorcross-product operator The real-time quaternion vector isdetermined once the initial value of quaternion vector isknown Based on the two basic assumptions of our headingestimation approach the related initial quaternion can beeasily calculated by initial user heading and device attitudethat are already known

Then we construct themeasurementmodel of EKF basedon the observed acceleration and magnetic field samplesmeasured at DCS

z119896+1 = [ a119896+1m119896+1

] = 120601 (q119896+1) + k119896+1

= [[(R119863119862119878119866119862119878 (q119896+1))119879 0

0 (R119863119862119878119866119862119878 (q119896+1))119879]][g

h]

+ [k119886119896+1k119898119896+1

]

(11)

where a119896+1 and g are the observed acceleration sample at DCSand related gravity vector sample at GCS m119896+1 and h are theobserved magnetic field sample at DCS and related magnetic


field sample at GCS and k119886119896+1 and k119898119896+1 are the white Gaussian

measurement noise of the acceleration and magnetic fieldvalues The covariance matrices of the acceleration andmagnetic field values are set according to [25] respectively

In order to construct the measurement equation of EKFwe linearize the nonlinear function 120601(sdot) in (11) by computingthe related Jacobian matrix

119867119896+1 = 120597120597q119896+1120601 (q119896+1)10038161003816100381610038161003816100381610038161003816q119896+1=qminus119896+1 (12)

where qminus119896+1 = 119865119896q119896 is a priori state estimate of the unavailabletrue state q119896+1 and q119896 is the EKF estimation result of the stateavailable at the previous time instant

According to the state equation (9) measurement equa-tion (11) and related parameters the EKF model for estimat-ing the real-time quaternion vector is constructed Detailedprocedures for executing the EKF model may be foundin [26] Therefore the real-time device attitude tracking isachieved We may calculate the real-time device yaw pitchand roll values at GCS as follows

119910119886119908 = arctan( 2 (11990201199023 minus 11990211199022)(11990220 minus 11990221 + 11990222 minus 11990223))119901119894119905119888ℎ = arcsin (2 (11990221199023 + 11990201199021))119903119900119897119897 = arctan( 2 (11990201199022 minus 11990211199023)(11990220 minus 11990221 minus 11990222 + 11990223))

(13)

42 Heading Estimation Strategy Selection During normalwalking we deploy RMPCA approach for heading estima-tion User heading is estimated step by step The walkingsteps are detected by a classic peak detection algorithm [27ndash29] which recognizes the peak acceleration caused by theunique heel strike during eachwalking stepWe firstly projectall acceleration within a walking step measured at DCS intoGCS

ACC119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))ACC119863119862119878 (119905) (14)

where ACC119866119862119878(119905) = [119860119862119862119909119866119862119878(119905) 119860119862119862119910119866119862119878(119905) 119860119862119862119911119866119862119878(119905)]119879is the acceleration sample represented at GCS at time 119905ACC119863119862119878(119905) is the related acceleration sample measured atDCS and R119863119862119878119866119862119878 (q(119905)) is the related rotation matrix betweenGCS and DCS All acceleration samples at GCS in thehorizontal plane can be given as

HACC119866119862119878 (119894) = [119860119862119862119909119866119862119878 (119894) 119860119862119862119910119866119862119878 (119894)]119879 119894 = 1 119873119860119888119888 (15)

where119873119860119888119888 is the number of acceleration samples within thewalking step and HACC119866119862119878(119894) is the ith acceleration samplein the horizontal planeThen we deploy PCA and extract thefirst eigenvector of the119873119860119888119888 acceleration samples in the hori-zontal plane as the ultimate global walking direction vectorWD119866119862119878 = [119882119863119909119866119862119878 119882119863119910119866119862119878]119879 The ambiguity problem ofPCA [30] can be solved by exploiting the phase relationship

between the user walking direction and the vertical acceler-ation [13] The ultimate user heading estimation 120595119906119904119890119903 can begiven as follows

120595119906119904119890119903 = arctan(119882119863119910119866119862119878119882119863119909119866119862119878) minus 1205872 (16)

For more details about RMPCA we refer readers to ourprevious work [13]

When three special motion states are detected extraacceleration may be introduced into the acceleration in thehorizontal plane Therefore the principal component of theacceleration in the horizontal plane may deviate from theuser walking direction For example when a handmovementoccurs the first eigenvector of PCAdeviates from thewalkingdirection and moves towards the hand movement directionSimilar observations may be seen when position transitionsor user turns occur Therefore when hand movements orposition transitions occur instead of deploying RMPCAapproach we obtain the user heading by averaging userheading estimation of the neighbor 119870 normal walking steps

120595119906119904119890119903 (119894) = sum1198702119896=1 [120595119906119904119890119903 (119894 minus 119896) + 120595119906119904119890119903 (119894 + 119896)]119870 (17)

where 120595119906119904119890119903(119894) is the user heading of the 119894th walking stepUsually without user turn the user heading is smooth andsetting 119870 equal to four may obtain a reasonable headingestimation result

When user turn occurs we calculate the user headingof current walking step by adding user heading change touser heading of previous walking step The horizontal deviceheading change is computed by the yaw angle change at GCS

120575120579 = 119873119892119910119903119900sum119896=1

119908119885119866119862119878 (119896) 119879119892119910119903119900 (18)

where 120575120579 is the horizontal device heading change within onewalking step 119908119885119866119862119878(119896) is the kth angular velocity componentrotating around 119885119866 at GCS 119873119892119910119903119900 is the total number ofangular velocity samples within the step 119879119892119910119903119900 is the relatedsampling intervalThe angular velocity sample at GCS can beobtained by angular velocity samplemeasured atDCS and therelated rotation matrix as follows

w119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))w119863119862119878 (119905) (19)

where w119866119862119878(119905) is the angular velocity sample vector withrespect to GCS at time tw119863119862119878(119905) is the related sample at DCSand R119863119862119878119866119862119878 (q(119905)) is the related rotation matrix

43 Outlier Filtering for Heading Estimation Results This sec-tion describes a postprocessing outlier filtering algorithm toremove the outliers caused by undetected hand movementsThis fault situation can be divided into two classes The firstclass is that a handmovement motion state is undetected andrecognized as a normal walking stateThe second class is thata hand movement state is misclassified as a user turn Duringnormal walking without significant user turns the heading


Outlier

10 20 30 400Steps

minus30

minus20

minus10

0

10

Yaw

angl

e at G

CS (d

egre

e)

Figure 4 Illustration of an outlier among user heading estimationsof RMPCA approach

estimation results of RMPCA are smooth and do not changesignificantly compared with neighbor steps If a user turnoccurs the user heading of current walking step may varysignificantly from that of the previous step being close tothat of the next step without the user turn In contrast if anundetected hand movement occurs the heading estimationresult may vary significantly from the heading estimationresults of both the previous step and the next step as shown inFigure 4Therefore from the above observations we developan outlier filtering algorithm to detect the fault situation bycomparing the difference values of heading estimation resultsbetween adjacent walking steps If one heading estimationresult is significantly larger (smaller) than previous walkingstep and smaller (larger) than the next walking step andthe two difference values exceed related threshold values anoutlier is detected and removed Then we correct the userheading by averaging the estimation results of the adjacentnormal walking steps

5 Evaluation

51 Experimental Setup We performed the user headingestimation experiments in indoor test environments asseen in Figure 5 In order to test the heading estimationperformance of both straight and nonstraight walking pathsthe test environment consisted of two symmetric parabolasone straight line and a half circle whose total length was769m Four subjects participated in the experiments witha smartphone Before each experimental run each subjectinitially held the phone in hand for few seconds to start thedeveloped user heading estimation application We also didall necessary calibrations to make the measurement outputsof all inertial sensors built in the smartphone as precise aspossible As in many other works [31 32] we assume that theinitial user heading was known To label the ground truthwe also applied a camera to record the entire walking path ofeach subjectThe user heading estimations were obtained andcompared with the true values for each walking step

In order to study the classification accuracy performanceof the proposed detection and discrimination algorithm eachsubject walked along the path with one hundred walking

108 m

108 m

162 m

216 m

39 m

Path one

Path twoPath three

Path four

Figure 5 Walking path of test environment consists of one straightline two symmetric parabolas and a half circle and is divided intofour subpaths by different colors Figure 5 is reproduced fromDengZA et al (2016) in [16] [under the Creative Commons AttributionLicensepublic domain]

steps including seventy steps for normal walking and theremaining steps for one of the three specialmotion states withan equal quantity Each subject repeated the procedure tentimes

In order to study the effects of three special motion stateson heading estimation accuracy individually we comparethe heading estimation errors between RMPCA and theproposed robust heading estimation approach when eachspecial motion state occurs individually For hand move-ments various kinds of hand locomotion with differentmagnitudes were performed during walking steps For car-rying position transitions we performed all twelve kindsof position transitions between four classic device carryingpositions For user turns we performed user turns varyingfrom 20 degrees to 180 degrees Each special motion state wascarried out one thousand times We assume that each specialmotion state is surrounded by normal walking steps duringpractical pedestrian walking

52 Classification Accuracy Results Table 1 shows the clas-sification results of the proposed three motion states detec-tion and discrimination algorithm The results show thatthe proposed detection and discrimination algorithm canclassify all three special motion states with high accuracyAn averaged classification accuracy of 976 is obtained forthe three special motion states For handmovements thoughthe probability is rather low some hand movements mayinvolve small pitch and roll angle changes while the yawangle changes exceed the threshold Therefore this kind ofhand movements may be misclassified as the user turnsFortunately these fault situations may not finally affect theuser heading estimation performance since the negativeeffects may be eliminated by the following outlier filteringalgorithm of the proposed user heading estimation approachFor carrying position transitions the accumulated absoluteacceleration changes are always large enough to distinguishthem from the other motion states The confusion betweenposition transitions and the other motion states can beneglected


Table 1 Confusion table of the proposed motion states detection and discrimination algorithm

Hand movement Position transition User turn Normal walkingHand movement 0952 0 0018 003Position transition 0007 0988 0005 0User turn 0 0011 0989 0Normal walking 0005 0 0 0995

Hand movement User turn Position transition

ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)

Figure 6 Mean absolute heading estimation errors of the proposedapproach and RMPCA when each special motion state occursindividually

53 Heading Estimation Results Figures 6 and 7 show themean and standard deviation of absolute estimation errors ofRMPCA approach and the proposed approach The headingestimation errors were calculated over the walking stepswhen the special motion states occurred Compared withRMPCA approach the proposed approach reduces the meanabsolute estimation error by 431 percent (109 degrees) 480percent (154 degrees) and 674 percent (382 degrees) forhand movement user turn and position transition motionstates respectively Compared with RMPCA approach theproposed approach reduces the standard deviation of abso-lute estimation error by 358 percent (24 degrees) 407percent (33 degrees) and 463 percent (44 degrees) for handmovement user turn and position transition motion statesrespectively Significant absolute heading estimation errorreduction can be achieved by the proposed robust headingestimation approach Among three special motion states theerror reduction of the position transition motion state is thelargest since the extra acceleration signals introduced bya position transition motion are always significantly largerthan those of the other two motion states For the proposedrobust heading estimation approach when three specialmotion states are detected and accurately discriminated anappropriate heading estimation scheme is selected ratherthan using RMPCA

Furthermore we study the overall heading estimationaccuracy of the proposed robust heading estimation approach

Hand movement User turn Position transition0

2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA

Figure 7 Standard deviation of absolute heading estimation errorsof the proposed approach and RMPCA when each special motionstate occurs individually

with all three special motion states involved The subjectwalked along the whole walking path which is divided intofour subpaths by different colors as seen in Figure 5 Thedevice carrying position was transited into another positionof the reminaing oneswith equal probability once the subpathchangedThe whole walking path required about 128 walkingsteps for each subject Each subject consciously did randomhand movements for fifteen times over the whole walkingpath They repeated the procedure for twenty times Weperformed user heading estimations over each walking stepand then a total number of more than ten thousand samplescan be used We also carried out and compared the proposedapproach without outlier filtering RMPCA approach [13]and uDirect approach [11]

Figure 8 shows the cumulative error distribution ofthe compared heading estimation approaches As seen inFigure 8 the 75th percentile absolute error of the pro-posed approach is 138 degrees while those of the proposedapproach without outlier filtering RMPCA and uDirect are142 262 and 344 degrees respectively The 90th percentileabsolute error of the proposed approach is 249 degreeswhile those of the proposed approach without outlier filter-ing RMPCA and uDirect are 281 427 and 549 degreesrespectively As seen in Figure 9 comparedwith the proposedapproach without outlier filtering RMPCA approach anduDirect approach the proposed approach reduces the meanabsolute estimation error by 139 percent (15 degrees) 469


ProposedProposed (Without outlier filtering)RMPCAuDirect

01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion

10 20 30 40 50 60 70 80 900Absolute heading estimation error (degrees)

Figure 8 Comparisons of absolute heading estimation error dis-tributions with all three special motion states involved in theexperiments

Standard deviation Mean

ProposedProposed (Without outlier filtering )RMPCAuDirect

0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)

Figure 9 Comparisons of mean and standard deviation of absoluteheading estimation errors with all three special motion statesinvolved in the experiments

percent (82 degrees) and 594 percent (136 degrees) respec-tively For standard deviation of absolute estimation error theproposed approach reduces it by 136 percent (06 degrees)345 percent (20 degrees) and 387 percent (24 degrees)respectively

The proposed approach achieves more significant head-ing estimation accuracy improvement than the comparedapproachesThis is because when three special motion statesoccur the proposed approach may detect and discriminatethemaccurately and timely and then select the related suitableheading estimation strategy The traditional RMPCA and

uDirect approaches may render large heading estimationerrors since extra acceleration caused by irregular bodylocomotion may violate the fundamental assumptions of tra-ditional approaches However these large heading estimationerrors may be always avoided by the proposed approach Ifone of the three special motion states is detected relatedoptimal heading estimation strategy will be carried out Forhand movements and position transitions the user headingestimations are obtained by averaging heading estimationresults of the neighboring normal walking steps For userturns the user headings are estimated by adding the yawangle change to the user heading of the previous step Besidesthe outlier filtering algorithm may also improve the headingestimation accuracy slightly since the outliers of headingestimations can be removed

6 Conclusions

This paper proposes a robust user heading estimationapproach adapting three special motion states namely randhand movements position transitions and user turns Whenthese three motion states occur the traditional approachesexploiting acceleration patterns may render large headingestimation errors Therefore we firstly develop the motionstate detection and discrimination algorithm to determinethe special motion state Then the most suitable strategy isselected for user heading estimation Finally an outlier filter-ing algorithm is developed to smooth the user heading esti-mation results Experimental results show that the proposedrobust heading estimation approach may improve the userheading estimation accuracy significantly Compared withRMPCA and uDirect approaches the proposed approachreduces the mean absolute user heading estimation error by469 percent (82 degrees) and 594 percent (136 degrees)respectively

Data Availability

The authors confirmed that the data supporting the findingsof this study were available within the article

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This research is supported by National Natural Science Foun-dation of China (Grants Nos 61301132 61300188 61671168and 61301131) and the Fundamental Research Funds forthe Central Universities (Grants Nos HEUCFJ180801 andHEUCF180801)

References

[1] M Zhou Y Tang Z Tian L Xie and W Nie ldquoRobust neigh-borhood graphing for semi-supervised indoor localization withlight-loaded location fingerprintingrdquo IEEE Internet of ThingsJournal 2017


[2] Y Sun W Meng C Li N Zhao K Zhao and N ZhangldquoHuman localization using multi-source heterogeneous data inindoor environmentsrdquo IEEE Access vol 5 pp 812ndash822 2017

[3] D Zou W Meng S Han K He and Z Zhang ldquoToward ubiq-uitous LBS Multi-radio localization and seamless positioningrdquoIEEEWireless CommunicationsMagazine vol 23 no 6 pp 107ndash113 2016

[4] M Jia X Gu Q Guo W Xiang and N Zhang ldquoBroadbandhybrid satellite-terrestrial communication systems based oncognitive radio toward 5Grdquo IEEE Wireless CommunicationsMagazine vol 23 no 6 pp 96ndash106 2016

[5] M Zhou Y Tang Z Tian and X Geng ldquoSemi-supervisedlearning for indoor hybrid fingerprint database calibration withlow effortrdquo IEEE Access vol 5 no 1 pp 4388ndash4400 2017

[6] M Zhou Y Tang W Nie L Xie and X Yang ldquoGrassMAgraph-based semi-supervised manifold alignment for indoorWLAN localizationrdquo IEEE Sensors Journal vol 17 no 21 pp7086ndash7095 2017

[7] P Zhang Q Zhao Y Li X Niu Y Zhuang and J Liu ldquoCollab-orative WiFi fingerprinting using sensor-based navigation onsmartphonesrdquo Sensors vol 15 no 7 pp 17534ndash17557 2015

[8] Z Xiao H Wen A Markham and N Trigoni ldquoRobust indoorpositioning with lifelong learningrdquo IEEE Journal on SelectedAreas in Communications vol 33 no 11 pp 2287ndash2301 2015

[9] H Lee J Lee J Cho and N Chang ldquoEstimation of headingangle difference between user and smartphone utilizing gravi-tational acceleration extractionrdquo IEEE Sensors Journal vol 16no 10 pp 3746ndash3755 2016

[10] Z-A Deng Y Hu J Yu and Z Na ldquoExtended Kalman filter forreal time indoor localization by fusing WiFi and smartphoneinertial sensorsrdquoMicromachines vol 6 no 4 pp 523ndash543 2015

[11] S AHoseinitabatabaei AGluhak R Tafazolli andWHeadleyldquoDesign realization and evaluation of uDirect-An approachfor pervasive observation of user facing direction on mobilephonesrdquo IEEE Transactions on Mobile Computing vol 13 no9 pp 1981ndash1994 2014

[12] U Steinhoff and B Schiele ldquoDead reckoning from the pocket -An experimental studyrdquo in Proceedings of the 8th IEEE Interna-tional Conference on Pervasive Computing and Communications(PerCom rsquo10) vol 60 pp 162ndash170 April 2010

[13] Z-A Deng G Wang Y Hu and D Wu ldquoHeading estimationfor indoor pedestrian navigation using a smartphone in thepocketrdquo Sensors vol 15 no 9 pp 21518ndash21536 2015

[14] S Saeedi and N El-Sheimy ldquoActivity recognition using fusionof low-cost sensors on a smartphone for mobile navigationapplicationrdquoMicromachines vol 6 no 8 pp 1100ndash1134 2015

[15] T OOshin S Poslad and Z Zhang ldquoEnergy-efficient real-timehuman mobility state classification using smartphonesrdquo IEEETransactions on Computers vol 64 no 6 pp 1680ndash1693 2015

[16] Z-A Deng G Wang Y Hu and Y Cui ldquoCarrying positionindependent user heading estimation for indoor pedestriannavigation with smartphonesrdquo Sensors vol 16 no 5 2016

[17] Y Li J Georgy X Niu Q Li and N El-Sheimy ldquoAutonomouscalibration ofMEMS gyros in consumer portable devicesrdquo IEEESensors Journal vol 15 no 7 pp 4062ndash4072 2015

[18] J Qian L Pei J Ma R Ying and P Liu ldquoVector graph assistedpedestrian dead reckoning using an unconstrained smart-phonerdquo Sensors vol 15 no 3 pp 5032ndash5057 2015

[19] M Kourogi and T Kurata ldquoA method of pedestrian deadreckoning for smartphones using frequency domain analysison patterns of acceleration and angular velocityrdquo in Proceedings

of the IEEEION Position Location and Navigation Symposium(PLANS rsquo14) vol 19 pp 164ndash168 IEEE May 2014

[20] F Ichikawa J Chipchase and R Grignani ldquoWherersquos the phoneA study of mobile phone location in public spacesrdquo in Proceed-ings of the 2nd International Conference on Mobile TechnologyApplications and Systems pp 1ndash8 IEEE November 2005

[21] F Li C Zhao G Ding J Gong C Liu and F Zhao ldquoA Reliableand accurate indoor localization method using phone inertialsensorsrdquo in Proceedings of the 14th International Conference onUbiquitous Computing pp 421ndash430 ACM September 2012

[22] Y Kim Y Chon and H Cha Smartphone-Based Collaborativeand Autonomous Radio Fingerprinting IEEE Press 2012

[23] A M Sabatini ldquoQuaternion-based extended kalman filter fordetermining orientation by inertial and magnetic sensingrdquoIEEE Transactions on Bio-Medical Engineering vol 53 no 72006

[24] J C K Chou ldquoQuaternion kinematic and dynamic differentialequationsrdquo IEEE Transactions on Robotics and Automation vol8 no 1 pp 53ndash64 1992

[25] Z Tian X FangM Zhou andL Li ldquoSmartphone-based indoorintegrated WiFiMEMS positioning algorithm in a multi-floorenvironmentrdquoMicromachines vol 6 no 3 pp 347ndash363 2015

[26] Y Bar-Shalom X Li and T Kirubarajan Estimation withApplications to Tracking and Navigation John Wiley amp SonsNew York NY USA 2001

[27] A Brajdic and R Harle ldquoWalk detection and step counting onunconstrained smartphonesrdquo in Proceedings of the ACM Inter-national Joint Conference on Pervasive and Ubiquitous Comput-ing (UbiComp rsquo13) pp 225ndash234 September 2013

[28] S He and S G Chan ldquoWi-Fi fingerprint-based indoor position-ing recent advances and comparisonsrdquo IEEE CommunicationsSurveys amp Tutorials vol 18 no 1 pp 466ndash490 2016

[29] Z Yang C Wu Z Zhou X Zhang X Wang and Y LiuldquoMobility increases localizability a survey on wireless indoorlocalization using inertial sensorsrdquo ACM Computing Surveysvol 47 no 3 article 54 pp 1ndash34 2015

[30] K Kunze P Lukowicz K Partridge and B Begole ldquoWhichway am I facing inferring horizontal device orientation froman accelerometer signalrdquo in Proceedings of the InternationalSymposium on Wearable Computers (ISWC rsquo09) pp 149-150IEEE Computer Society September 2009

[31] N Mohssen R Momtaz H Aly and M Youssef ldquoHumainea ubiquitous smartphone-based user heading estimation formobile computing systemsrdquo GeoInformatica vol 21 no 3 pp519ndash548 2017

[32] P Nguyen T Akiyama H Ohashi G Nakahara K Yamasakiand S Hikaru ldquoUser-friendly heading estimation for arbitrarysmartphone orientationsrdquo in Proceedings of the InternationalConference on Indoor Positioning and Indoor Navigation (IPINrsquo16) pp 1ndash7 IEEE October 2016

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom


forward acceleration dominates the acceleration in the hori-zontal plane In contrast PCA-based approach ismore robustto the body locomotion dynamics since all acceleration sam-ples are exploited to extract the most variation of horizontalacceleration signals which is assumed to be parallel withwalking direction Recently to remove the restrictions ondevice carrying positions we proposed a heading estimationapproach independent of carrying position The carryingposition is recognized by a position classifier upon the dis-tinguishable acceleration patterns while assuming relativelystable device orientations under the same carrying positions

To enable a really unconstrained use of smartphones forheading estimation not only device carrying positions butalso the varying device orientations should be consideredThus several critical problems still need to be solved toenhance the reliability and applicability of heading estima-tion

Firstly the current heading estimation solutions aresensitive and nonrobust to random hand movements ForPCA-based approach the fundamental assumption is seri-ously corrupted by random hand movements which makethe maximum variance of the acceleration signals in thehorizontal plane deviate from the walking direction

Secondly three motion states namely hand movementscarrying positions transitions and user turns and theirimpacts on heading estimations have been paid little atten-tions Missed detection and confusion among the threemotion states may render a large heading estimation error

To solve the above problems we propose a robust headingestimation system using unconstrained smartphones Themain idea is that we select the related optimal headingestimation strategy based on the detection and discrimina-tion of three special motion states namely random handmovements carrying position transitions and user turns Anovel detection and classification method is developed todetect the three motion states timely and discriminate themaccurately If user turn occurs the user heading is estimatedby computing heading change in the horizontal plane directlyIf the other two motion states occur the user heading isassumed to be smooth and obtained by averaging estimationresults of the normal neighbor walking steps

The proposed estimation system deploys our previousRMPCA approach for heading estimation during normalwalking Finally the estimation results are further smoothedby filtering outliers caused by handmovements undetected orhand movements misclassified as user turns For simplicityin this work we only consider the two main pedestrianactivities namely walking and standing and assume thatthey have been already accurately recognized according totheir different acceleration patterns [14 15]

Experiments show that our heading estimation systemoutperforms existing approaches in terms of accuracy reli-ability and applicability under the unconstrained situationsIn summary our work makes the following contributions

(i) We propose a robust heading estimation system inde-pendent of carrying positions anddevice orientations

(ii) We point out that a large heading estimation errormay be introduced by PCA-based approach if the

following three motion states cannot be detected anddiscriminated random hand movements carryingposition transitions and user turn

(iii) We propose a novel detection and classificationmethod to detect and discriminate the above threemotion states

(iv) We develop an outlier filtering algorithm to removethe outliers of user heading estimation results

(v) We report the evaluation of the proposed detectionand classification technique based on extensive sam-ples collected from four participants and comparethe accuracy performance of our heading estimationapproach to existing approaches

In the rest of this paper we will firstly introduce anoverview of the proposed robust heading estimation systemusing unconstrained smartphones in Section 2 Section 3describes the detection and classification methods againstthe three special motion states in detail Section 4 describesthe robust user heading estimation approaches adapting thespecial motion states caused by unconstrained use of smart-phones The evaluations of experimental results are reportedin Section 5 Conclusions are presented in the last section

2 System Overview

Figure 1 shows an overview of the proposed robust user head-ing estimation system using unconstrained smartphonesTheproposed system selects user heading estimation schemebased on continuous motion states detection and classifi-cation results The basic idea of the motion state detectionand discrimination method is to exploit their distinguish-able acceleration and device attitude changing patterns Theattitude changing patterns include the accumulated pitchand roll angles the horizontal device heading change angleswhich can be derived from a continuous device attitudetracking model For practical smartphone uses we assumethat position transition and user turn cannot occur simul-taneously Similar assumption is given to hand movementand user turn motion states The assumptions are reasonablefor the following two reasons First the probability of bothmotion states happening is rather low when the probabilityof eachmotion state is low Second requiring device carryingposition transitions or significant hand movements whena user turn occurs is unnatural and also complicated forpedestrians

For heading estimation scheme selection during nor-mal walking without any special motion state detected wedeploy our previous RMPCA approach since the funda-mental assumption of PCA-based approach still holds Ifrandom hand movements or carrying position transitionsare detected the user heading is assumed to be smoothand calculated by averaging heading estimation results ofthe neighboring normal walking steps If user turns aredetected the user heading is obtained by adding horizontalheading change to previous user heading Besides to avoidintroducing estimation errors caused by undetected handmovements the estimation results are further smoothed byan outlier filtering algorithm









(1)


(|119875119894119905119888ℎ (119894 + 1) minus 119875119894119905119888ℎ (119894)|) (2)


(|119877119900119897119897 (119894 + 1) minus 119877119900119897119897 (119894)|) (3)

ΔYaw = 119884119886119908 (119864119899119889119879119894119898119890) minus 119884119886119908 (119878119905119886119903119905119879119894119898119890) (4)







Yes

Position transition


Yes YesYes




No





Smartphone Sensing


Outlier filtering











ΔAcc gt Th(ΔAcc)




change ΔRoll






Yes

No


transition motion


Yes

No

ΔYaw gtTh(ΔYaw)



Yes

Yes

YesRecognized user

turn motion No





h119863119862119878 (119905) = (R119863119862119878119866119862119878 (q (119905)))119879 h119866119862119878 (119905) (5)


R119863119862119878119866119862119878 (q)

= [[[[


]]]]

(6)




q119896+1 = exp (05 times Ω (w119896119879s)) q119896





119896)2 + (119908119910

119896)2 + (119908119911


Ω(w119896119879119904) = 119879119904[[[[[[[

0 minus119908119909119896 minus119908119910119896

minus119908119911119896119908119909119896 0 119908119911119896 minus119908119910119896119908119910

119896minus119908119911119896 0 119908119909119896119908119911119896 119908119910119896

minus119908119909119896 0

]]]]]]] (8)


q119896+1 = 119865119896q119896 + w119902119896 (9)



minus10minus5

05

10152025

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(a)


5 10 15 20 25 300Time [s]

minus10

0

10

20

30

Acce

lera

tion

[mＭ

2]

x-axisy-axisz-axis

(b)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(c)


minus20

minus10

0

10

20

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(d)

minus10

0

10

20

30


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(e)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(f)



minuse119879119896]w119892119910119903119900119896

(10)





z119896+1 = [ a119896+1m119896+1

] = 120601 (q119896+1) + k119896+1

= [[(R119863119862119878119866119862119878 (q119896+1))119879 0

0 (R119863119862119878119866119862119878 (q119896+1))119879]][g

h]

+ [k119886119896+1k119898119896+1

]

(11)






119867119896+1 = 120597120597q119896+1120601 (q119896+1)10038161003816100381610038161003816100381610038161003816q119896+1=qminus119896+1 (12)




(13)


ACC119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))ACC119863119862119878 (119905) (14)


HACC119866119862119878 (119894) = [119860119862119862119909119866119862119878 (119894) 119860119862119862119910119866119862119878 (119894)]119879 119894 = 1 119873119860119888119888 (15)



120595119906119904119890119903 = arctan(119882119863119910119866119862119878119882119863119909119866119862119878) minus 1205872 (16)



120595119906119904119890119903 (119894) = sum1198702119896=1 [120595119906119904119890119903 (119894 minus 119896) + 120595119906119904119890119903 (119894 + 119896)]119870 (17)



120575120579 = 119873119892119910119903119900sum119896=1

119908119885119866119862119878 (119896) 119879119892119910119903119900 (18)


w119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))w119863119862119878 (119905) (19)




Outlier

10 20 30 400Steps

minus30

minus20

minus10

0

10

Yaw

angl

e at G

CS (d

egre

e)



5 Evaluation



108 m

108 m

162 m

216 m

39 m

Path one

Path twoPath three

Path four









ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)





2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA






01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










(1)


(|119875119894119905119888ℎ (119894 + 1) minus 119875119894119905119888ℎ (119894)|) (2)


(|119877119900119897119897 (119894 + 1) minus 119877119900119897119897 (119894)|) (3)

ΔYaw = 119884119886119908 (119864119899119889119879119894119898119890) minus 119884119886119908 (119878119905119886119903119905119879119894119898119890) (4)







Yes

Position transition


Yes YesYes




No





Smartphone Sensing


Outlier filtering











ΔAcc gt Th(ΔAcc)




change ΔRoll






Yes

No


transition motion


Yes

No

ΔYaw gtTh(ΔYaw)



Yes

Yes

YesRecognized user

turn motion No





h119863119862119878 (119905) = (R119863119862119878119866119862119878 (q (119905)))119879 h119866119862119878 (119905) (5)


R119863119862119878119866119862119878 (q)

= [[[[


]]]]

(6)




q119896+1 = exp (05 times Ω (w119896119879s)) q119896





119896)2 + (119908119910

119896)2 + (119908119911


Ω(w119896119879119904) = 119879119904[[[[[[[

0 minus119908119909119896 minus119908119910119896

minus119908119911119896119908119909119896 0 119908119911119896 minus119908119910119896119908119910

119896minus119908119911119896 0 119908119909119896119908119911119896 119908119910119896

minus119908119909119896 0

]]]]]]] (8)


q119896+1 = 119865119896q119896 + w119902119896 (9)



minus10minus5

05

10152025

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(a)


5 10 15 20 25 300Time [s]

minus10

0

10

20

30

Acce

lera

tion

[mＭ

2]

x-axisy-axisz-axis

(b)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(c)


minus20

minus10

0

10

20

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(d)

minus10

0

10

20

30


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(e)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(f)



minuse119879119896]w119892119910119903119900119896

(10)





z119896+1 = [ a119896+1m119896+1

] = 120601 (q119896+1) + k119896+1

= [[(R119863119862119878119866119862119878 (q119896+1))119879 0

0 (R119863119862119878119866119862119878 (q119896+1))119879]][g

h]

+ [k119886119896+1k119898119896+1

]

(11)






119867119896+1 = 120597120597q119896+1120601 (q119896+1)10038161003816100381610038161003816100381610038161003816q119896+1=qminus119896+1 (12)




(13)


ACC119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))ACC119863119862119878 (119905) (14)


HACC119866119862119878 (119894) = [119860119862119862119909119866119862119878 (119894) 119860119862119862119910119866119862119878 (119894)]119879 119894 = 1 119873119860119888119888 (15)



120595119906119904119890119903 = arctan(119882119863119910119866119862119878119882119863119909119866119862119878) minus 1205872 (16)



120595119906119904119890119903 (119894) = sum1198702119896=1 [120595119906119904119890119903 (119894 minus 119896) + 120595119906119904119890119903 (119894 + 119896)]119870 (17)



120575120579 = 119873119892119910119903119900sum119896=1

119908119885119866119862119878 (119896) 119879119892119910119903119900 (18)


w119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))w119863119862119878 (119905) (19)




Outlier

10 20 30 400Steps

minus30

minus20

minus10

0

10

Yaw

angl

e at G

CS (d

egre

e)



5 Evaluation



108 m

108 m

162 m

216 m

39 m

Path one

Path twoPath three

Path four









ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)





2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA






01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Yes

Position transition


Yes YesYes




No





Smartphone Sensing


Outlier filtering











ΔAcc gt Th(ΔAcc)




change ΔRoll






Yes

No


transition motion


Yes

No

ΔYaw gtTh(ΔYaw)



Yes

Yes

YesRecognized user

turn motion No





h119863119862119878 (119905) = (R119863119862119878119866119862119878 (q (119905)))119879 h119866119862119878 (119905) (5)


R119863119862119878119866119862119878 (q)

= [[[[


]]]]

(6)




q119896+1 = exp (05 times Ω (w119896119879s)) q119896





119896)2 + (119908119910

119896)2 + (119908119911


Ω(w119896119879119904) = 119879119904[[[[[[[

0 minus119908119909119896 minus119908119910119896

minus119908119911119896119908119909119896 0 119908119911119896 minus119908119910119896119908119910

119896minus119908119911119896 0 119908119909119896119908119911119896 119908119910119896

minus119908119909119896 0

]]]]]]] (8)


q119896+1 = 119865119896q119896 + w119902119896 (9)



minus10minus5

05

10152025

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(a)


5 10 15 20 25 300Time [s]

minus10

0

10

20

30

Acce

lera

tion

[mＭ

2]

x-axisy-axisz-axis

(b)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(c)


minus20

minus10

0

10

20

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(d)

minus10

0

10

20

30


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(e)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(f)



minuse119879119896]w119892119910119903119900119896

(10)





z119896+1 = [ a119896+1m119896+1

] = 120601 (q119896+1) + k119896+1

= [[(R119863119862119878119866119862119878 (q119896+1))119879 0

0 (R119863119862119878119866119862119878 (q119896+1))119879]][g

h]

+ [k119886119896+1k119898119896+1

]

(11)






119867119896+1 = 120597120597q119896+1120601 (q119896+1)10038161003816100381610038161003816100381610038161003816q119896+1=qminus119896+1 (12)




(13)


ACC119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))ACC119863119862119878 (119905) (14)


HACC119866119862119878 (119894) = [119860119862119862119909119866119862119878 (119894) 119860119862119862119910119866119862119878 (119894)]119879 119894 = 1 119873119860119888119888 (15)



120595119906119904119890119903 = arctan(119882119863119910119866119862119878119882119863119909119866119862119878) minus 1205872 (16)



120595119906119904119890119903 (119894) = sum1198702119896=1 [120595119906119904119890119903 (119894 minus 119896) + 120595119906119904119890119903 (119894 + 119896)]119870 (17)



120575120579 = 119873119892119910119903119900sum119896=1

119908119885119866119862119878 (119896) 119879119892119910119903119900 (18)


w119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))w119863119862119878 (119905) (19)




Outlier

10 20 30 400Steps

minus30

minus20

minus10

0

10

Yaw

angl

e at G

CS (d

egre

e)



5 Evaluation



108 m

108 m

162 m

216 m

39 m

Path one

Path twoPath three

Path four









ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)





2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA






01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



ΔAcc gt Th(ΔAcc)




change ΔRoll






Yes

No


transition motion


Yes

No

ΔYaw gtTh(ΔYaw)



Yes

Yes

YesRecognized user

turn motion No





h119863119862119878 (119905) = (R119863119862119878119866119862119878 (q (119905)))119879 h119866119862119878 (119905) (5)


R119863119862119878119866119862119878 (q)

= [[[[


]]]]

(6)




q119896+1 = exp (05 times Ω (w119896119879s)) q119896





119896)2 + (119908119910

119896)2 + (119908119911


Ω(w119896119879119904) = 119879119904[[[[[[[

0 minus119908119909119896 minus119908119910119896

minus119908119911119896119908119909119896 0 119908119911119896 minus119908119910119896119908119910

119896minus119908119911119896 0 119908119909119896119908119911119896 119908119910119896

minus119908119909119896 0

]]]]]]] (8)


q119896+1 = 119865119896q119896 + w119902119896 (9)



minus10minus5

05

10152025

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(a)


5 10 15 20 25 300Time [s]

minus10

0

10

20

30

Acce

lera

tion

[mＭ

2]

x-axisy-axisz-axis

(b)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(c)


minus20

minus10

0

10

20

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(d)

minus10

0

10

20

30


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(e)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(f)



minuse119879119896]w119892119910119903119900119896

(10)





z119896+1 = [ a119896+1m119896+1

] = 120601 (q119896+1) + k119896+1

= [[(R119863119862119878119866119862119878 (q119896+1))119879 0

0 (R119863119862119878119866119862119878 (q119896+1))119879]][g

h]

+ [k119886119896+1k119898119896+1

]

(11)






119867119896+1 = 120597120597q119896+1120601 (q119896+1)10038161003816100381610038161003816100381610038161003816q119896+1=qminus119896+1 (12)




(13)


ACC119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))ACC119863119862119878 (119905) (14)


HACC119866119862119878 (119894) = [119860119862119862119909119866119862119878 (119894) 119860119862119862119910119866119862119878 (119894)]119879 119894 = 1 119873119860119888119888 (15)



120595119906119904119890119903 = arctan(119882119863119910119866119862119878119882119863119909119866119862119878) minus 1205872 (16)



120595119906119904119890119903 (119894) = sum1198702119896=1 [120595119906119904119890119903 (119894 minus 119896) + 120595119906119904119890119903 (119894 + 119896)]119870 (17)



120575120579 = 119873119892119910119903119900sum119896=1

119908119885119866119862119878 (119896) 119879119892119910119903119900 (18)


w119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))w119863119862119878 (119905) (19)




Outlier

10 20 30 400Steps

minus30

minus20

minus10

0

10

Yaw

angl

e at G

CS (d

egre

e)



5 Evaluation



108 m

108 m

162 m

216 m

39 m

Path one

Path twoPath three

Path four









ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)





2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA






01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




minus10minus5

05

10152025

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(a)


5 10 15 20 25 300Time [s]

minus10

0

10

20

30

Acce

lera

tion

[mＭ

2]

x-axisy-axisz-axis

(b)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(c)


minus20

minus10

0

10

20

Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(d)

minus10

0

10

20

30


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(e)

minus20

minus10

0

10

20


Acce

lera

tion

[mＭ

2]

5 10 15 20 25 300Time [s]

x-axisy-axisz-axis

(f)



minuse119879119896]w119892119910119903119900119896

(10)





z119896+1 = [ a119896+1m119896+1

] = 120601 (q119896+1) + k119896+1

= [[(R119863119862119878119866119862119878 (q119896+1))119879 0

0 (R119863119862119878119866119862119878 (q119896+1))119879]][g

h]

+ [k119886119896+1k119898119896+1

]

(11)






119867119896+1 = 120597120597q119896+1120601 (q119896+1)10038161003816100381610038161003816100381610038161003816q119896+1=qminus119896+1 (12)




(13)


ACC119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))ACC119863119862119878 (119905) (14)


HACC119866119862119878 (119894) = [119860119862119862119909119866119862119878 (119894) 119860119862119862119910119866119862119878 (119894)]119879 119894 = 1 119873119860119888119888 (15)



120595119906119904119890119903 = arctan(119882119863119910119866119862119878119882119863119909119866119862119878) minus 1205872 (16)



120595119906119904119890119903 (119894) = sum1198702119896=1 [120595119906119904119890119903 (119894 minus 119896) + 120595119906119904119890119903 (119894 + 119896)]119870 (17)



120575120579 = 119873119892119910119903119900sum119896=1

119908119885119866119862119878 (119896) 119879119892119910119903119900 (18)


w119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))w119863119862119878 (119905) (19)




Outlier

10 20 30 400Steps

minus30

minus20

minus10

0

10

Yaw

angl

e at G

CS (d

egre

e)



5 Evaluation



108 m

108 m

162 m

216 m

39 m

Path one

Path twoPath three

Path four









ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)





2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA






01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






119867119896+1 = 120597120597q119896+1120601 (q119896+1)10038161003816100381610038161003816100381610038161003816q119896+1=qminus119896+1 (12)




(13)


ACC119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))ACC119863119862119878 (119905) (14)


HACC119866119862119878 (119894) = [119860119862119862119909119866119862119878 (119894) 119860119862119862119910119866119862119878 (119894)]119879 119894 = 1 119873119860119888119888 (15)



120595119906119904119890119903 = arctan(119882119863119910119866119862119878119882119863119909119866119862119878) minus 1205872 (16)



120595119906119904119890119903 (119894) = sum1198702119896=1 [120595119906119904119890119903 (119894 minus 119896) + 120595119906119904119890119903 (119894 + 119896)]119870 (17)



120575120579 = 119873119892119910119903119900sum119896=1

119908119885119866119862119878 (119896) 119879119892119910119903119900 (18)


w119866119862119878 (119905) = R119863119862119878119866119862119878 (q (119905))w119863119862119878 (119905) (19)




Outlier

10 20 30 400Steps

minus30

minus20

minus10

0

10

Yaw

angl

e at G

CS (d

egre

e)



5 Evaluation



108 m

108 m

162 m

216 m

39 m

Path one

Path twoPath three

Path four









ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)





2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA






01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Outlier

10 20 30 400Steps

minus30

minus20

minus10

0

10

Yaw

angl

e at G

CS (d

egre

e)



5 Evaluation



108 m

108 m

162 m

216 m

39 m

Path one

Path twoPath three

Path four









ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)





2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA






01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






ProposedRMPCA

0

10

20

30

40

50

60

Mea

n ab

solu

te es

timat

ion

erro

r (de

gree

s)





2

4

6

8

10

Stan

dard

dev

iatio

n of

erro

r (de

gree

s)

ProposedRMPCA






01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




01

02

03

04

05

06

07

08

09

1

Cum

ulat

ive E

rror

dist

ribut

ion





0

5

10

15

20

25

Abso

lute

estim

atio

n er

ror (

degr

ees)





6 Conclusions


Data Availability




Acknowledgments


References





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Robust Heading Estimation for Indoor Pedestrian Navigation...

Documents

Transcript of Robust Heading Estimation for Indoor Pedestrian Navigation...