pedestrianheadingestimationmethodsbasedonmultiplephone … · 2021. 8. 31. ·...

Research ArticlePedestrianHeadingEstimationMethodsBased onMultiple PhoneCarrying Modes

Ying Guo1 Hanshuo Liu 1 Jin Ye1 Shengli Wang2 and Chenxi Duan1

1College of Geodesy and Geomatics Shandong University of Science and Technology Qingdao 266590 China2Ocean Science and Engineering College Shandong University of Science and Technology Qingdao 266590 China

Correspondence should be addressed to Hanshuo Liu 704664122qqcom

Received 31 May 2021 Revised 16 August 2021 Accepted 22 August 2021 Published 31 August 2021

Academic Editor Juraj Machaj

Copyright copy 2021 Ying Guo et al is 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

e development of smartphone Micro-Electro-Mechanical Systems (MEMS) inertial sensors has provided opportunities toimprove indoor navigation and positioning for location-based services One area of indoor navigation research uses pedestriandead reckoning (PDR) technology in which the mobile phone must typically be held to the pedestrianrsquos chest In this paper weconsider navigation in three other mobile phone carrying modes ldquocallingrdquo ldquopocketrdquo and ldquoswingingrdquo For the calling mode inwhich the pedestrian holds the phone to their face the rotation matrix method is used to convert the phonersquos gyroscope data fromthe calling state to the holding state allowing calculation of the stable pedestrian forward direction For a phone carried in apedestrianrsquos trouser pocket a heading complementary equation is established based on principal component analysis and rotationapproach methods In this case the pedestrian heading is calculated by determining a subset of data that avoid 180deg directionalambiguity and improve the heading accuracy For the swinging mode a heading capture method is used to obtain the heading ofthe lowest point of the pedestrianrsquos arm swing as they hold the phone e direction of travel is then determined by successivelyadding the heading offsets each time the arm droops Experimental analysis shows that 95 of the heading errors of the abovethree methods are less than 581deg 1073deg and 922deg respectively ese results present better heading accuracy and reliability

1 Introduction

e prevalence of small- and high-precision sensors inmobile phones has been partly enabled by the rapid de-velopment of Micro-Electro-Mechanical Systems (MEMS)[1] ese sensors give smartphones capabilities that wouldnot otherwise be available [2] For example smartphonescan use internal sensors (inertial sensors radio frequencysignals etc) to improve indoor pedestrian navigation andpositioning for location-based services [3] Pedestrian deadreckoning (PDR) technology [4ndash6] which uses smartphoneinertial sensors has attracted the attention of researchersbecause of its strong anti-interference properties and abilityto quickly determine precise pedestrian positions [7ndash9]However the technology still faces some indoor positioningchallenges For example a change in the relative positionbetween a smartphone and a pedestrian will lead to a de-crease in positioning accuracy [10 11] and pedestrian

posture changes can also cause positioning errors [12 13]erefore to ensure reliable heading and positioning in-formation most mobile phone PDR technologies require themobile phone to be stabilised against a pedestrianrsquos chestimpacting the phonersquos portability [14]

e challenges affecting PDR heading accuracy andstability can be resolved by establishing suitable headingestimation methods for different mobile phone carryingmodes such as ldquocallingrdquo (in which the phone is held againstthe userrsquos face) ldquopocketrdquo and ldquoswingingrdquo By treating themotions of mobile phones carried in swinging hands ortrouser pockets as regular oscillation states Tian et al [15]calculated pedestrian headings according to the mean os-cillation values Lee and Huang [16] proposed a magne-tometer-based heading estimation method that allowedgood positioning accuracy in the calling swinging andpocket carrying modes By studying the body movements ofpedestrians walking with mobile phones in their trouser

HindawiMobile Information SystemsVolume 2021 Article ID 1193268 10 pageshttpsdoiorg10115520211193268

pockets Steinhoff and Schiele [17] proposed a rotationapproach (RA) based on quaternion and principal com-ponent analysis (PCA) Deng et al [18] used PCA to estimatethe headings of mobile phones carried in the trouser pocketand swinging states and they used a heading offset methodto estimate pedestrian headings in the calling state Wanget al [19] argued that the previously existing PCA methodscould not guarantee that the horizontal acceleration within astride would be completely horizontal which would affectthe estimation of pedestrian headings ey therefore pro-posed a PCA-based method with global accelerations (PCA-GA) and they demonstrated experimentally that theirmethod provided higher accuracy than existing PCAmethods e RA method was subsequently improved byZheng et al [20] and experimentally shown to be moreeffective in the pocket state

However the above-referenced methods face somechallenges In the calling state the selection of a fixedheading offset may be inaccurate and can incur furthererrors due to the instability of true heading offsets In thepocket and swing states the PCA-based methods used toestimate pedestrian headings have a 180deg directional am-biguity limitation the improved RA method avoids the 180degambiguity but calculations that use only gyroscope dataoffer limited accuracy And reliance on magnetometer datafor heading estimation can be affected by magnetic inter-ference in indoor environments

Based on these observations we consider pedestrianheading estimation methods for three phone carrying modes(calling pocket and swinging) e rotation matrix methodis used in the calling state not only considering the problemof nonhorizontal head rotations but also making im-provements to the accuracy and stability of the headingestimates e complementary PCA and RA methods areadopted for the pocket state avoiding the 180deg directionalambiguity and reducing the impacts of cumulative errorse heading capture method is used in the swinging statebecause of the methodrsquos calculation speed and accuracyese methods reduce the heading errors caused by attitudetransformations in the three states hence improving thereliability of heading estimation

2 Heading Estimation in Three CarryingModes

Commonly used mobile phone carrying modes includeholding calling pocket and swinging Due to its goodstability and the more mature heading estimation methodthe holding mode offers the most accurate and reliablepedestrian heading estimates erefore we focus on pe-destrian heading estimation methods for the other threemobile phone carrying modes

21 Calling Mode Heading Estimation Based on a RotationMatrix Method Some authors have treated the calling stateas a stable state assuming a fixed horizontal rotation angleΔβ [18] between the holding state and the calling stateUnder this assumption a pedestrianrsquos heading can be ob-tained by subtracting the angle from the heading angle of the

mobile phone attitude in the calling state e heading errorof this method is largely derived from uncertainty in thechoice of the angle Furthermore when calling a pedes-trianrsquos head will inevitably shake adding to the potential thatuse of a fixed angle will cause unnecessary errors To avoiderrors caused by uncertainty and variation of the relativeangle a rotation matrix method is used here Equation (1) asfollows is used to calculate the rotation matrix in the callingstate [21] and equation (2) is used to convert the gyroscopedata from the calling state to the holding state

Cnb

cosφ minussinφ 0

sinφ cosφ 0

0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1 0 0

0 cosψ sinψ

0 minussinψ cosψ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

cos θ 0 minussin θ

0 1 0

sin θ 0 cos θ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

gyrprime Cnbgyr (2)

gyr is a vector containing the gyroscopersquos three com-ponents of angular velocity and gyrprime is the gyroscope dataafter translation to the holding state As defined below φ istermed the adaptive heading offset and ψ and θ are the pitchand roll angles of the phone in the calling state respectively

φ Δβ + Δφ

ψ arcsinminusax

g1113888 1113889

θ arctanay

az

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Among them a is the phonersquos three-axis accelerometerdata Δβ is a fixed horizontal rotation angle calculated fromthe heading before and after the carrying mode change Δφis the relative heading change caused by the nonhorizontalrotation of the head in the state of making a call which isdetected by the changes in the pitch and roll angles and g isthe local acceleration due to gravity e corrected gyro-scope data are obtained through the rotation matrixmethod which effectively avoids the errors caused by thenonhorizontal shaking of the mobile phone in the callingstate

To calculate the quaternion and pedestrian heading weused the corrected gyroscope [22]

φcalling minusarctan

2 q1q2 minus q0q3( 1113857

q20 minus q

21 + q

22 minus q

23

1113888 1113889 (4)

To verify the reliability of the rotation matrix methodan experimental comparative analysis was conducted Asthe z-axis of the gyroscope undergoes the largest changeswhen turning in the holding state the z-axis data of thegyroscope were selected for comparison (Figure 1)

As shown in Figure 1 when a pedestrian followed asequence of instructions (ldquogo straightrdquo ldquoturn rightrdquo andldquoturn leftrdquo) the gyroscope z-axis data obtained by the ro-tation matrix method in the calling state were approximately

2 Mobile Information Systems

the same as the data obtained from the holding statehowever in the calling state the unprocessed data did notrespond significantly during the turns and hence did notcapture the pedestrianrsquos heading changes

22 Pocket Mode Heading Estimation Based on a RA-PCAMethod

221 Existing Heading Estimation Methods and AnalysisWhen a pedestrian walks with a mobile phone in theirtrouser pocket the phone not only moves with the pedes-trianrsquos legs but also may change its relative position withinthe pocket erefore the directly calculated mobile phoneattitude is difficult to accurately represent the pedestrianrsquosheading in this state Some authors have used PCA methodsbased on acceleration data for pedestrian heading estimation[18] others have calculated quaternions based on gyroscopedata and used RA methods to calculate the rotation axes forpedestrian heading estimation [20]

However the PCA approach is affected by 180deg ambi-guity between the forward and backward swings of themobile phone and by unstable horizontal accelerations eRA method generates errors due to the cumulative drift ofthe gyroscope and the method is limited by the rotationalinstability of the phonersquos orientation relative to the pedes-trianrsquos pocket erefore independent use of the acceler-ometer-based PCA method or the gyroscope-based RAmethod can produce limited results

To improve the accuracy of the pedestrian heading es-timation in the pocket state we propose an RA-PCA al-gorithm that leverages the complementary characteristics ofthe RA and PCA methods In this approach gravity ac-celerometer data are used to avoid the 180deg ambiguity andthe RA and PCA heading methods are combined to reduceoverall heading errors

222 Heading Estimation Based on RA-PCA As a mobilephone in a trouser pocket swings back and forth with apedestrianrsquos legs the accelerations obtained by the PCAmethod will swing back and forth to produce a 180degambiguity in the direction of travel e RA method canalso incur a 180deg change in forward direction if thephonersquos rotation axis changes To avoid the influence of180deg ambiguity on heading estimation it is necessary toselect a suitable subset of data for use in the headingcalculation

(1) Selection of Data for the Heading Calculation In theprocess of walking with each step one leg will be the centreof gravity and the other leg will move forward e 180degheading ambiguity can be resolved by estimating the pe-destrianrsquos heading using only the data where the leg carryingthe phone is moving forward (Figure 2)

e measured parameter shown in the figure is calcu-lated from the x and y axes of the gravity accelerometer(equation (5)) e subset of data for use in heading esti-mation are obtained between the peak and successive troughof the value

gxy

g2x + g

2y

1113969

(5)

(2) Pedestrian Heading Estimation From the selected subsetof accelerometer data PCA can be used to obtain theprincipal vectors and equation (6) can be applied to convertthe principal vectors from the mobile phone coordinatesystem to the navigation coordinate system

vni (1)

vni (2)

vni (3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ C

nb

vi(1)

vi(2)

vi(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (6)

By projecting vi(lowast) onto the horizontal plane theprincipal vector vn

i (1) vni (2)( 1113857 can be calculated for the

pedestrianrsquos direction of travel i is a sample point the PCAheading at the corresponding sample point can then beobtained

headingPCAi arctanvn

i (2)

vni (1)

1113888 1113889 (7)

e RA method determines the axis of rotationaccording to the change of the quaternion as a pedestrianwalks [22] Here the rotation axis in a data subset is cal-culated according to its quaternion transformation As therotation axis is perpendicular to the direction of movementof the phone the axis is projected onto the horizontal planeand the relative heading of the pedestrian is then calculatedaccording to the direction of the horizontal plane axisTaking one step as an example the number of samplingpoints in the data subset is t and the change of the qua-ternion is calculated by

50 100 150 200 250 300Sampling points

2

15

1

05

0

-05

-1

-15

-2

Ang

ular

velo

city

(rad

s)

gostraight

gostraight

turnright

turnle

holdingcallingcalling+rotation matrix method

Figure 1 Comparison of gyroscope z-axis data in holding mode incalling mode and in calling mode after correction using the ro-tation matrix method

Mobile Information Systems 3

qt1tm

(0)

qt1tm

(1)

qt1tm

(2)

qt1tm

(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

qt1(0)

qt1(1)

qt1(2)

qt1(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

otimes

qtm(0)

qtm(1)

qtm(2)

qtm(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)

t1 and tm are respectively represented as the firstsampling point and the m th sampling point in the datasubset q

t1tm

(lowast) is the quaternion change from t1 to tm andqt1(lowast) is the quaternion of the t1 sampling point

A quaternion can be understood as a process of rotationfrom one point to another along a certain axis [23] Simi-larly the rotation axis uq of this process can be roughlyestimated based on the quaternions before and after therotation Here u is the average value of the rotation axiswithin the subset of data selected for heading estimationis rotation axis is converted to the navigation coordinatesystem to obtain un then un is projected onto the horizontalplane and the rotation axis vector is normalised to obtainthe direction of the rotation axis in the navigation coordinatesystem

qt1tm

cos ϕ sinϕ middot uq1113960 1113961

uq q1

sinϕ

q2sinϕ

q3

sinϕ1113890 1113891

un C

nbu

headingRAi arctanun

i (2)

uni (1)

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

e above RA and PCA methods use the same datasubsets for each calculation φPCA

i and φRAi are the PCA and

RA relative heading respectively Using a complementarycoefficient K the trust degree of the PCA method isadaptively restricted such that the trust degree of the PCA

heading is reduced when the PCAmethod is unstable Use ofthis coefficient establishes the complementary RA-PCApedestrian heading φRAminusPCA

i in the pocket mode

φRAminusPCAi KφPCA

i +(1 minus K)φRAi (10)

e coefficient K is obtained by the following equation

K

1φprime

Δφgt 2

12 Δφle 2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(11)

When the phonersquos screen is facing towards the pedes-trianrsquos right (the phone is usually in the left leg pocket at thistime) K minusK and when the phonersquos screen is facing to-wards the pedestrianrsquos left (the phone is in the right legpocket) K K φprime is obtained by

φprime

φPCAi

11138681113868111386811138681113868

11138681113868111386811138681113868 minus φRAi

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

1113969

(12)

e RA method using the gyroscope is stable but it isaffected by cumulative error from the gyroscope readingswhereas the PCA method based on the accelerometer data isless stable but it can partially compensate for the cumulativeerror of the RAmethod A comparison of PCA RA and RA-PCA headings obtained using the abovemethods is shown inFigure 3 e PCA headings progressively deviated from thereference headings as the test progressed Although the RAheading was stable there were still some systematic errorsobserved e RA-PCA method leveraged complementaryinformation from the PCA method but it retained thestability of the RAmethod and improved the overall headingaccuracy

23 Swinging Mode Heading Estimation Based on a HeadingCaptureMethod e swinging mode is similar to the pocketmode so the pedestrian heading can be obtained using theRA-PCA method However compared to the pocket statethe swinging state has stronger regularity [24] so we canquickly capture more reliable pedestrian heading by use of iterefore a swinging mode heading capture method isestablished based on the regular swing of a pedestrianrsquos armis method captures the specific point where the arm passesby the pedestrianrsquos body each time the arm swings eheading angle of the mobile phone is obtained at this lowestpoint in the motion of the pedestrianrsquos hand e headingoffset is then removed from the captured heading angle ofthe mobile phone to obtain the walking direction of thepedestrian

In this method when the pitch angle in the attitude ofthe phone is close to 0deg it is considered that the arm is closeto the lowest point in its swing so the heading angle of themobile phone is captured each time the pitch angle crosses 0deg(Figure 4)

As the mobile phone is not necessarily facing the pe-destrianrsquos forward direction during the swing process it isnecessary to determine the offset angle Δβswing between the

10 20 30 40 50 60 70 80Sampling points

10

98

96

94

92

9

88

Acce

lera

tion

(ms

2 )

Figure 2 Selection of a data subset for use in heading directionestimation


heading angle of the mobile phone and the forward directionof the pedestrian when the arm is at its lowest point Afterswitching to the swing arm state the phonersquos headings at thetwo drooping points in the first swing cycle can be used tocalculate the heading offset

Δβswing 12

1113944

2

i1φswing

i minus φlast (13)

where φlast is the pedestrianrsquos heading before the swing andφswing

i is the mobile phonersquos heading captured by thismethodese headings are all calculated using equation (4)e pedestrianrsquos heading at each subsequent step is obtainedby subtracting the heading offset from the phonersquos headingat that swingrsquos lowest point

24 Pedestrian Heading Estimation Flowchart e mainprocedures for obtaining the direction of a pedestrianrsquostravel in the above three mobile phone carrying modes are asfollows mobile phone accelerometer data and gyroscopedata are extracted to determine the mobile phone carryingmode When the mobile phone is in a holding state thequaternion method is used to estimate the heading angle ofthe mobile phone which is used as the pedestrianrsquos heading

When the phone is in a calling state the rotation matrixmethod is used to calculate the pedestrianrsquos heading Whenthe phone is in a pocket state a subset of forward motiondata is extracted and the RA-PCA method is used to cal-culate the pedestrianrsquos heading When in a swinging modethe heading capture method is used to obtain the pedes-trianrsquos heading

A flowchart representing the carrying modes and theirrespective heading estimation methods is shown in Figure 5

3 Experiment

An OPPO R9s smartphone was used to experimentally testour pedestrian heading estimation methods and to collectdata at a sampling frequency of 50Hz Some parameters ofthis smartphonersquos inertial sensors are shown in Table 1

e walking route for our testing of the three carryingmodes was rectangular with a total length of approximately100 metres When pedestrians use a phone with their left orright hands (or carry a phone in their left or right trouserpockets) the posture and rotation processes of their phonesare different To verify the effectiveness of our methods inleft- and right-side use each set of tests included compar-ative experiments on both sides

31 Calling State Experiment For the calling state testingpedestrians first walked a certain distance with their mobilephones in a holding state then switched to a calling state towalk the next part of the route and finally returned to aholding state to reach the end destination As shown inFigure 6 this part of the experiment compared the actual(reference) walking route to the headings estimated usingthe heading offset method and this paperrsquos proposed rota-tion matrix method e comparative heading errors areplotted in Figure 7 and summarised in Table 2

Figures 6 and 7 and Table 2 demonstrate that the rotationmatrix method captured the pedestrian walking route moreaccurately In the calling state 95 of the heading errorsusing our method were within 524deg in the left-sided ex-periment and 581deg in the right-sided experiment 50 of theheading errors were within 278deg and 277deg respectivelyese results were more accurate than the heading offsetmethod estimates

32 Pocket State Experiment e pocket mode experimentsstarted with a pedestrian carrying the mobile phone in aholding state then putting the mobile phone in their left orright leg trouser pocket for the next section of the route (thephonersquos screen is facing towards the pedestrianrsquos right orleft) and then returning the phone to the holding state forthe final section is experiment used the RA PCA andRA-PCA methods to estimate pedestrian headings from thecollected data Figure 8 compares the actual walking route tothe results from each of the pocket mode heading estimationmethods e comparative heading errors are plotted inFigure 9 and summarised in Table 3

Figures 8 and 9 and Table 3 show that whether themobilephone was carried in a left or right leg trouser pocket the

0 500 1000 1500 2000 2500Sampling points

0

-50

-100

-150

-200

Hea

ding

(deg)

PCARA

RA-PCAreference heading

Figure 3 Comparison of pocket mode heading estimationmethods

150 200 250 300 350Sampling points

15

10

5

0

-5

-10

-15

-20

Ang

le (deg

)

reference

pitch angleyaw angle

Figure 4 Arm droop point capture method As a pedestrianrsquos armswings the heading angle is captured each time the phonersquos pitchangle crosses 0deg (red boxes)


RA-PCA method produced lower heading estimation errorsthan the PCA or RA methods alone 95 of the RA-PCAheading errors in the left and right pocket tests were within802deg and 699deg respectively and 50 of the heading errors

were within 359deg and 225deg respectively An earlier studyobtained a root mean square error of 417deg using the im-proved RA method [20] Our root mean square error wasapproximately 39deg using the RA method which is similar to

ACCampampGYR

Carrying modes

Holding Calling Pocket Swinging

Output pedestrian heading

Rotationmatrix method

Data range

RA-PCA

HeadingcaptureQuaternion

Figure 5 Flowchart of pedestrian heading estimation methods for multiple mobile phone carrying modes

Table 1 Specifications of the OPPO R9s smartphonersquos inertial sensors

ACC GYRFull scale plusmn2 g plusmn2000degsNonlinearity 05 FS 01 FSBias stability mdash 15deghNoise density 180 μg

Hz

radic0008degs

Hz

radic

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

-5

reference routeheading offsetrotation matrix

turn calling

turn holding

startpoint

(a)

Y (m

)

30

25

20

15

10

5

0

-5-20 -15 -10 -5 0 5

X (m)


turn calling

turn holding

startpoint

35

(b)

Figure 6 Reference and estimated paths of the walking route used in the calling mode experiments (a) Phone carried in the left hand(b) Phone carried in the right hand


that studyrsquos findings In our experiments the RA-PCAmethod achieved higher heading accuracy (289deg) than theRA method

33 Swinging State Experiment e swinging state experi-ment was similar to the previous experiments but tested theoriginal heading method and our heading capture methodFigure 10 compares the actual and estimated walking routes

from the swinging state experiment Figure 11 shows thecomparative heading errors and the overall errors aresummarised in Table 4

Figures 10 and 11 and Table 4 demonstrate that the rawheading method was unstable in the swinging modewhereas the heading calculated using the heading capturemethod was relatively stable In the left-handed experimentthe route from the original heading method deviated sig-nificantly from the reference route (Figure 10(a)) In the

0 2 4 6 8Heading error (deg)

100

80

60

40

20

0

Per (

)

Heading offsetRotation matrix

(a)

100

80

60

40

20

0

Per (

)

0 2 4 6 8 10 12Heading error (deg)


(b)

Figure 7 Comparison of pedestrian heading estimation errors of the callingmode experiments (a) Phone carried in the left hand (b) Phonecarried in the right hand

Table 2 Calling state heading error comparisons (in degrees)

Heading estimation methodPhone in the left hand Phone in the right hand

50 error 95 error 50 error 95 errorHeading offset 378 698 333 648Rotation matrix 278 524 277 581

-25 -20 -15 -10 -5 0 5X (m)

reference routePCARARA-PCA

Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket

turn holdingstartpoint

(a)

-20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(b)

Figure 8 Reference and estimated paths of the walking route used in the pocket mode experiments (a) Phone carried in the left pocket(b) Phone carried in the right pocket


right-handed experiment (Figure 10(b)) the raw headingmethodrsquos route deviation was less pronounced In rawheading a part of step frequency points is close to the armdrooping point and the average heading of the other part ofthe points is consistent with the forward direction 95 of

the heading errors from the heading capture method werewithin 670deg and 922deg for the left and right hands respec-tively and 50 of the heading errors were within 305deg and206deg respectively ese errors were much lower than thosefrom the raw heading method


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(a)


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(b)

Figure 9 Comparison of pedestrian heading estimation errors of the pocket mode experiments (a) Phone carried in the left pocket(b) Phone carried in the right pocket

Table 3 Pocket state heading error comparisons (in degrees)

Heading estimation methode left pocket e right pocket

50 error 95 error 50 error 95 errorPCA 1761 4269 967 3374RA 471 1303 584 1203RA-PCA 359 1073 225 699

-20 -15 -10 -5 0 5X (m)

reference routeraw heading routeheading capture

Y (m

)

30

25

20

15

10

5

0

-5

35

turn swinging

turn holding startpoint

(a)

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

35

turn swinging

turn holding


startpoint

(b)

Figure 10 Reference and estimated paths of the walking route used in the swinging mode experiments (a) Phone carried in the left hand(b) Phone carried in the right hand


4 Conclusion

In this paper based on the three carrying modes of smartphones calling pocket and swinging we study the methodsfor determining the direction of pedestrians in the abovemodes e results are as follows

(1) In the calling state a rotation matrix was establishedaccording to the change of the pedestrianrsquos postureand was used to adjust the phonersquos sensor data fromthe calling state to the accurate pedestrian headingIn experimental comparison with the traditionalheading offset method over a 100m rectangularwalking route the rotation matrix method reducedthe 95 heading error by approximately 25 whenthe phone was held in the left hand and 10 whenthe phone was held in the right hand

(2) In the pocket state a subset of the data was selectedwhere the phone would be moving forward steadilyduring walking Complementary advantages of thePCA and RA methods were leveraged to establish acombined RA-PCA heading equation In experi-mental results from a 100m rectangular route theRA-PCA method reduced the 95 pedestrianheading errors in the left and right leg pocket tests byapproximately 74 and 79 respectively relative tothose from the PCA method e correspondingimprovements when the RA-PCA method wascompared with the RA method were approximately18 and 42 respectively

(3) In the swinging state the drooping points of thepedestrianrsquos arm were captured during each armswing and the heading offset between the phone andthe direction of travel was captured in the first swingcycle of the pedestrianrsquos arm e forward directionof the pedestrian was determined by correcting theheading of the mobile phone using this headingoffset In experimental tests similar to those alreadydescribed the 95 heading errors using this methodwere greatly improved (by approximately 56ndash72)compared to those of the raw heading method

e methods presented in the paper achieved goodresults in three conventional carrying modes Howeverheading accuracy will be affected when more complicatedcarrying modes are considered

Data Availability

e inertial data of the smartphone used to support theresults of this study can be obtained from the correspondingauthor (e-mail 704664122qqcom)

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] X He R Jin and H Dai ldquoLeveraging spatial diversity forprivacy-aware location-based services in mobile networksrdquo

0 10 155 20 25 30Heading error (deg)

Raw headingHeading capture

100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)

Figure 11 Comparison of pedestrian heading estimation errors of the swinging mode experiments (a) Phone carried in the left hand(b) Phone carried in the right hand

Table 4 Swinging state heading error comparison (in degrees)

Heading estimation methode left hand e right hand

50 error 95 error 50 error 95 errorHeading capture 305 670 206 922Raw heading 551 2351 824 2082


IEEE Transactions on Information Forensics and Securityvol 13 no 6 pp 1524ndash1534 2018

[2] L Zhang J Liu J Lai and Z Xiong ldquoPerformance analysis ofadaptive neuro fuzzy inference system control for MEMSnavigation systemrdquo Mathematical Problems in Engineeringvol 2014 Article ID 961067 7 pages 2014

[3] E D Kaplan and C Hegarty Understanding GPS Principlesand Applications Artech House Norwood MA USA 2005

[4] W Elloumi A Latoui R Canals A Chetouani andS Treuillet ldquoIndoor pedestrian localization with a smart-phone a comparison of inertial and vision-based methodsrdquoIEEE Sensors Journal vol 16 no 13 pp 5376ndash5388 2016

[5] F Hu Z Zhu and J Zhang ldquoMobile panoramic vision forassisting the blind via indexing and localizationrdquo in Pro-ceedings of the Computer Vision-ECCV 2014 Workshopspp 600ndash614 Zurich Switzerland September 2015

[6] L-F Shi Y Wang G-x Liu S Chen Y-L Zhao andY-F Shi ldquoA fusion algorithm of indoor positioning based onPDR and RSS fingerprintrdquo IEEE Sensors Journal vol 18no 23 pp 9691ndash9698 2018

[7] Z Chen H Zou H Jiang Q Zhu Y Soh and L Xie ldquoFusionofWiFi smartphone sensors and landmarks using the kalmanfilter for indoor localizationrdquo Sensors vol 15 no 1pp 715ndash732 2015

[8] Q Zeng J Wang Q Meng X Zhang and S Zeng ldquoSeamlesspedestrian navigation methodology optimized for indooroutdoor detectionrdquo IEEE Sensors Journal vol 18 no 1pp 363ndash374 2018

[9] A Manos I Klein and T Hazan ldquoGravity-based methods forheading computation in pedestrian dead reckoningrdquo Sensorsvol 19 no 5 p 1170 2019

[10] J Zwiener A Lorenz and R Jager ldquoAlgorithm and systemdevelopment for seamless out-indoor navigation with low-cost GNSS and foot-mounted MEMS sensorrdquo in Proceedingsof the International Scientific Congress and Exhibition Inter-expo Geo-Siberia pp 83ndash97 Novosibirsk Russia April 2014

[11] J O Nilsson D Zachariah I Skog and P Handel ldquoCoop-erative localization by dual foot-mounted inertial sensors andinter-agent rangingrdquo EURASIP Journal on Advances in SignalProcessing vol 2013 17 pages 2013

[12] S Qiu Z Wang H Zhao K Qin Z Li and H Hu ldquoInertialmagnetic sensors based pedestrian dead reckoning by meansof multi-sensor fusionrdquo Information Fusion vol 39pp 108ndash119 2018

[13] L Zheng W Zhou W Tang X Zheng A Peng andH Zheng ldquoA 3D indoor positioning system based on low-costMEMS sensorsrdquo Simulation Modelling Practice and Aeoryvol 65 pp 45ndash56 2016

[14] L Xu Z Xiong J Liu Z Wang and Y Ding ldquoA novelpedestrian dead reckoning algorithm for multi-mode rec-ognition based on smartphonesrdquo Remote Sensing vol 11no 3 p 294 2019

[15] Q Tian Z Salcic K I-K Wang and Y Pan ldquoA multi-modedead reckoning system for pedestrian tracking using smart-phonesrdquo IEEE Sensors Journal vol 16 no 7 pp 2079ndash20932016

[16] J-S Lee and S-M Huang ldquoAn experimental heuristic ap-proach to multi-pose pedestrian dead reckoning withoutusing magnetometers for indoor localizationrdquo IEEE SensorsJournal vol 19 no 20 pp 9532ndash9542 2019

[17] U Steinhoff and B Schiele ldquoDead reckoning from the pocket-anexperimental studyrdquo inProceedings of the 2010 IEEE InternationalConference on Pervasive Computing and Communications (Per-Com) pp 162ndash170 Mannheim Germany March 2010

[18] 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

[19] B Wang X Liu B Yu R Jia and X Gan ldquoPedestrian deadreckoning based on motion mode recognition using asmartphonerdquo Sensors vol 18 no 6 2018

[20] L Zheng X Zhan X Zhang S Wang and W YuanldquoHeading estimation for multimode pedestrian dead reck-oningrdquo IEEE Sensors Journal vol 20 no 15 pp 8731ndash87392020

[21] Y Guo H Liu J Ye and F Yuan ldquoPedestrian headingcorrection method based on AHDE and mobile phone gy-roscoperdquo Journal of Chinese Inertial Technology vol 29 no 1pp 8ndash15 2021

[22] Y Guo X Ji Q Liu G Li and Y Xu ldquoHeading correctionalgorithm based on mobile phone gyroscoperdquo Journal ofChinese Inertial Technology vol 25 no 6 pp 719ndash724 2017

[23] T Akenine-Moller T Moller and E Haines Real-TimeRendering A K Peters Natick MA USA 2002

[24] J Ma Research of a Smartphone Based Indoor Pedestrian DeadReckoning System Shanghai Jiao Tong University ShanghaiChina 2014


pockets Steinhoff and Schiele [17] proposed a rotationapproach (RA) based on quaternion and principal com-ponent analysis (PCA) Deng et al [18] used PCA to estimatethe headings of mobile phones carried in the trouser pocketand swinging states and they used a heading offset methodto estimate pedestrian headings in the calling state Wanget al [19] argued that the previously existing PCA methodscould not guarantee that the horizontal acceleration within astride would be completely horizontal which would affectthe estimation of pedestrian headings ey therefore pro-posed a PCA-based method with global accelerations (PCA-GA) and they demonstrated experimentally that theirmethod provided higher accuracy than existing PCAmethods e RA method was subsequently improved byZheng et al [20] and experimentally shown to be moreeffective in the pocket state

However the above-referenced methods face somechallenges In the calling state the selection of a fixedheading offset may be inaccurate and can incur furthererrors due to the instability of true heading offsets In thepocket and swing states the PCA-based methods used toestimate pedestrian headings have a 180deg directional am-biguity limitation the improved RA method avoids the 180degambiguity but calculations that use only gyroscope dataoffer limited accuracy And reliance on magnetometer datafor heading estimation can be affected by magnetic inter-ference in indoor environments

Based on these observations we consider pedestrianheading estimation methods for three phone carrying modes(calling pocket and swinging) e rotation matrix methodis used in the calling state not only considering the problemof nonhorizontal head rotations but also making im-provements to the accuracy and stability of the headingestimates e complementary PCA and RA methods areadopted for the pocket state avoiding the 180deg directionalambiguity and reducing the impacts of cumulative errorse heading capture method is used in the swinging statebecause of the methodrsquos calculation speed and accuracyese methods reduce the heading errors caused by attitudetransformations in the three states hence improving thereliability of heading estimation

2 Heading Estimation in Three CarryingModes

Commonly used mobile phone carrying modes includeholding calling pocket and swinging Due to its goodstability and the more mature heading estimation methodthe holding mode offers the most accurate and reliablepedestrian heading estimates erefore we focus on pe-destrian heading estimation methods for the other threemobile phone carrying modes

21 Calling Mode Heading Estimation Based on a RotationMatrix Method Some authors have treated the calling stateas a stable state assuming a fixed horizontal rotation angleΔβ [18] between the holding state and the calling stateUnder this assumption a pedestrianrsquos heading can be ob-tained by subtracting the angle from the heading angle of the

mobile phone attitude in the calling state e heading errorof this method is largely derived from uncertainty in thechoice of the angle Furthermore when calling a pedes-trianrsquos head will inevitably shake adding to the potential thatuse of a fixed angle will cause unnecessary errors To avoiderrors caused by uncertainty and variation of the relativeangle a rotation matrix method is used here Equation (1) asfollows is used to calculate the rotation matrix in the callingstate [21] and equation (2) is used to convert the gyroscopedata from the calling state to the holding state

Cnb

cosφ minussinφ 0

sinφ cosφ 0

0 0 1

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

1 0 0

0 cosψ sinψ

0 minussinψ cosψ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

cos θ 0 minussin θ

0 1 0

sin θ 0 cos θ

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

gyrprime Cnbgyr (2)

gyr is a vector containing the gyroscopersquos three com-ponents of angular velocity and gyrprime is the gyroscope dataafter translation to the holding state As defined below φ istermed the adaptive heading offset and ψ and θ are the pitchand roll angles of the phone in the calling state respectively

φ Δβ + Δφ

ψ arcsinminusax

g1113888 1113889

θ arctanay

az

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

Among them a is the phonersquos three-axis accelerometerdata Δβ is a fixed horizontal rotation angle calculated fromthe heading before and after the carrying mode change Δφis the relative heading change caused by the nonhorizontalrotation of the head in the state of making a call which isdetected by the changes in the pitch and roll angles and g isthe local acceleration due to gravity e corrected gyro-scope data are obtained through the rotation matrixmethod which effectively avoids the errors caused by thenonhorizontal shaking of the mobile phone in the callingstate

To calculate the quaternion and pedestrian heading weused the corrected gyroscope [22]

φcalling minusarctan

2 q1q2 minus q0q3( 1113857

q20 minus q

21 + q

22 minus q

23

1113888 1113889 (4)

To verify the reliability of the rotation matrix methodan experimental comparative analysis was conducted Asthe z-axis of the gyroscope undergoes the largest changeswhen turning in the holding state the z-axis data of thegyroscope were selected for comparison (Figure 1)

As shown in Figure 1 when a pedestrian followed asequence of instructions (ldquogo straightrdquo ldquoturn rightrdquo andldquoturn leftrdquo) the gyroscope z-axis data obtained by the ro-tation matrix method in the calling state were approximately










gxy

g2x + g

2y

1113969

(5)


vni (1)

vni (2)

vni (3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ C

nb

vi(1)

vi(2)

vi(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (6)





i (2)

vni (1)

1113888 1113889 (7)


50 100 150 200 250 300Sampling points

2

15

1

05

0

-05

-1

-15

-2

Ang

ular

velo

city

(rad

s)

gostraight

gostraight

turnright

turnle




qt1tm

(0)

qt1tm

(1)

qt1tm

(2)

qt1tm

(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

qt1(0)

qt1(1)

qt1(2)

qt1(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

otimes

qtm(0)

qtm(1)

qtm(2)

qtm(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)


t1tm



qt1tm


uq q1

sinϕ

q2sinϕ

q3

sinϕ1113890 1113891

un C

nbu

headingRAi arctanun

i (2)

uni (1)

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)









K

1φprime

Δφgt 2

12 Δφle 2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(11)


φprime

φPCAi

11138681113868111386811138681113868

11138681113868111386811138681113868 minus φRAi

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

1113969

(12)





10 20 30 40 50 60 70 80Sampling points

10

98

96

94

92

9

88

Acce

lera

tion

(ms

2 )




Δβswing 12

1113944

2

i1φswing

i minus φlast (13)






3 Experiment







0 500 1000 1500 2000 2500Sampling points

0

-50

-100

-150

-200

Hea

ding

(deg)

PCARA




15

10

5

0

-5

-10

-15

-20

Ang

le (deg

)

reference






ACCampampGYR

Carrying modes




Data range

RA-PCA





Hz

radic0008degs

Hz

radic

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

-5


turn calling

turn holding

startpoint

(a)

Y (m

)

30

25

20

15

10

5

0

-5-20 -15 -10 -5 0 5

X (m)


turn calling

turn holding

startpoint

35

(b)








100

80

60

40

20

0

Per (

)


(a)

100

80

60

40

20

0

Per (

)



(b)





-25 -20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(a)

-20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(b)






PCARARA-PCA

100

80

60

40

20

0

Per (

)

(a)


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(b)





-20 -15 -10 -5 0 5X (m)


Y (m

)

30

25

20

15

10

5

0

-5

35

turn swinging


(a)

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

35

turn swinging

turn holding


startpoint

(b)



4 Conclusion






Data Availability




References




100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)







































gxy

g2x + g

2y

1113969

(5)


vni (1)

vni (2)

vni (3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ C

nb

vi(1)

vi(2)

vi(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (6)





i (2)

vni (1)

1113888 1113889 (7)


50 100 150 200 250 300Sampling points

2

15

1

05

0

-05

-1

-15

-2

Ang

ular

velo

city

(rad

s)

gostraight

gostraight

turnright

turnle




qt1tm

(0)

qt1tm

(1)

qt1tm

(2)

qt1tm

(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

qt1(0)

qt1(1)

qt1(2)

qt1(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

otimes

qtm(0)

qtm(1)

qtm(2)

qtm(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)


t1tm



qt1tm


uq q1

sinϕ

q2sinϕ

q3

sinϕ1113890 1113891

un C

nbu

headingRAi arctanun

i (2)

uni (1)

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)









K

1φprime

Δφgt 2

12 Δφle 2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(11)


φprime

φPCAi

11138681113868111386811138681113868

11138681113868111386811138681113868 minus φRAi

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

1113969

(12)





10 20 30 40 50 60 70 80Sampling points

10

98

96

94

92

9

88

Acce

lera

tion

(ms

2 )




Δβswing 12

1113944

2

i1φswing

i minus φlast (13)






3 Experiment







0 500 1000 1500 2000 2500Sampling points

0

-50

-100

-150

-200

Hea

ding

(deg)

PCARA




15

10

5

0

-5

-10

-15

-20

Ang

le (deg

)

reference






ACCampampGYR

Carrying modes




Data range

RA-PCA





Hz

radic0008degs

Hz

radic

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

-5


turn calling

turn holding

startpoint

(a)

Y (m

)

30

25

20

15

10

5

0

-5-20 -15 -10 -5 0 5

X (m)


turn calling

turn holding

startpoint

35

(b)








100

80

60

40

20

0

Per (

)


(a)

100

80

60

40

20

0

Per (

)



(b)





-25 -20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(a)

-20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(b)






PCARARA-PCA

100

80

60

40

20

0

Per (

)

(a)


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(b)





-20 -15 -10 -5 0 5X (m)


Y (m

)

30

25

20

15

10

5

0

-5

35

turn swinging


(a)

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

35

turn swinging

turn holding


startpoint

(b)



4 Conclusion






Data Availability




References




100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)































qt1tm

(0)

qt1tm

(1)

qt1tm

(2)

qt1tm

(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

qt1(0)

qt1(1)

qt1(2)

qt1(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

otimes

qtm(0)

qtm(1)

qtm(2)

qtm(3)

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)


t1tm



qt1tm


uq q1

sinϕ

q2sinϕ

q3

sinϕ1113890 1113891

un C

nbu

headingRAi arctanun

i (2)

uni (1)

1113888 1113889

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)









K

1φprime

Δφgt 2

12 Δφle 2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(11)


φprime

φPCAi

11138681113868111386811138681113868

11138681113868111386811138681113868 minus φRAi

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

11138681113868111386811138681113868

1113969

(12)





10 20 30 40 50 60 70 80Sampling points

10

98

96

94

92

9

88

Acce

lera

tion

(ms

2 )




Δβswing 12

1113944

2

i1φswing

i minus φlast (13)






3 Experiment







0 500 1000 1500 2000 2500Sampling points

0

-50

-100

-150

-200

Hea

ding

(deg)

PCARA




15

10

5

0

-5

-10

-15

-20

Ang

le (deg

)

reference






ACCampampGYR

Carrying modes




Data range

RA-PCA





Hz

radic0008degs

Hz

radic

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

-5


turn calling

turn holding

startpoint

(a)

Y (m

)

30

25

20

15

10

5

0

-5-20 -15 -10 -5 0 5

X (m)


turn calling

turn holding

startpoint

35

(b)








100

80

60

40

20

0

Per (

)


(a)

100

80

60

40

20

0

Per (

)



(b)





-25 -20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(a)

-20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(b)






PCARARA-PCA

100

80

60

40

20

0

Per (

)

(a)


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(b)





-20 -15 -10 -5 0 5X (m)


Y (m

)

30

25

20

15

10

5

0

-5

35

turn swinging


(a)

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

35

turn swinging

turn holding


startpoint

(b)



4 Conclusion






Data Availability




References




100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)
































Δβswing 12

1113944

2

i1φswing

i minus φlast (13)






3 Experiment







0 500 1000 1500 2000 2500Sampling points

0

-50

-100

-150

-200

Hea

ding

(deg)

PCARA




15

10

5

0

-5

-10

-15

-20

Ang

le (deg

)

reference






ACCampampGYR

Carrying modes




Data range

RA-PCA





Hz

radic0008degs

Hz

radic

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

-5


turn calling

turn holding

startpoint

(a)

Y (m

)

30

25

20

15

10

5

0

-5-20 -15 -10 -5 0 5

X (m)


turn calling

turn holding

startpoint

35

(b)








100

80

60

40

20

0

Per (

)


(a)

100

80

60

40

20

0

Per (

)



(b)





-25 -20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(a)

-20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(b)






PCARARA-PCA

100

80

60

40

20

0

Per (

)

(a)


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(b)





-20 -15 -10 -5 0 5X (m)


Y (m

)

30

25

20

15

10

5

0

-5

35

turn swinging


(a)

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

35

turn swinging

turn holding


startpoint

(b)



4 Conclusion






Data Availability




References




100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)

































ACCampampGYR

Carrying modes




Data range

RA-PCA





Hz

radic0008degs

Hz

radic

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

-5


turn calling

turn holding

startpoint

(a)

Y (m

)

30

25

20

15

10

5

0

-5-20 -15 -10 -5 0 5

X (m)


turn calling

turn holding

startpoint

35

(b)








100

80

60

40

20

0

Per (

)


(a)

100

80

60

40

20

0

Per (

)



(b)





-25 -20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(a)

-20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(b)






PCARARA-PCA

100

80

60

40

20

0

Per (

)

(a)


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(b)





-20 -15 -10 -5 0 5X (m)


Y (m

)

30

25

20

15

10

5

0

-5

35

turn swinging


(a)

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

35

turn swinging

turn holding


startpoint

(b)



4 Conclusion






Data Availability




References




100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)




































100

80

60

40

20

0

Per (

)


(a)

100

80

60

40

20

0

Per (

)



(b)





-25 -20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(a)

-20 -15 -10 -5 0 5X (m)


Y (m

)

30

35

25

20

15

10

5

0

-5

turn pocket


(b)






PCARARA-PCA

100

80

60

40

20

0

Per (

)

(a)


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(b)





-20 -15 -10 -5 0 5X (m)


Y (m

)

30

25

20

15

10

5

0

-5

35

turn swinging


(a)

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

35

turn swinging

turn holding


startpoint

(b)



4 Conclusion






Data Availability




References




100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)


































PCARARA-PCA

100

80

60

40

20

0

Per (

)

(a)


PCARARA-PCA

100

80

60

40

20

0

Per (

)

(b)





-20 -15 -10 -5 0 5X (m)


Y (m

)

30

25

20

15

10

5

0

-5

35

turn swinging


(a)

-20 -15 -10 -5 0 5X (m)

Y (m

)

30

25

20

15

10

5

0

35

turn swinging

turn holding


startpoint

(b)



4 Conclusion






Data Availability




References




100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)































4 Conclusion






Data Availability




References




100

80

60

40

20

0

Per (

)

(a)



100

80

60

40

20

0

Per (

)

(b)































pedestrianheadingestimationmethodsbasedonmultiplephone … · 2021. 8. 31. ·...

Documents