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©2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Note: This is a revised version of the paper. For the final published paper, please refer to http://ieeexplore.ieee.org/document/8533740

Comparing Heading Estimates from Multiple Wearable Inertial and Magnetic Sensors Mounted

on Lower Limbs

Chandra Tjhai and Kyle O’KeefePosition, Location, And Navigation (PLAN) Group

Department of Geomatics Engineering, Schulich School of EngineeringUniversity of Calgary

Alberta, CanadaEmail: [email protected] and [email protected]

Abstract—This paper presents heading estimations from mul-tiple low-cost wearable sensors distributed on the lower limbsegments. A low-cost commercial motion capture suit from Enfluxis used to record accelerometer, gyroscope and magnetometermeasurements. Roll and pitch angles from each sensor areestimated to level each magnetometer. The sensor orientationsare computed using a Kalman filter. The step length is computedusing the sensor mounted on the pelvis while the stride lengthis computed using the foot-mounted sensors. The results showthat the pelvis is the best location to track pedestrian headingwhile other sensors have poor performance due to difficulty inestimating the roll and pitch angles.

I. INTRODUCTION

Recent Micro-Electro Mechanical System (MEMS) technol-ogy advancement has enabled the mass production of inertialand magnetic sensors. These MEMS devices are small in sizeand very low cost. Given these advantages, MEMS sensorshave allowed researchers to analyse human gait using inertialsensors for clinical study, athlete performance monitoring andmotion capture. There are commercially available inertial-based motion capture systems in the market such as Xsens[1] or Shimmer [2]. The development of pedestrian navigationsystems is also affected by this advancement of MEMS tech-nology both in terms of managing MEMS sensor limitationsand also to address the presence of multiple sensors.

Inertial sensors have become the most common sensorsused in the applications of indoor positioning. The mostbasic inertial-based method is to implement a dead-reckoningalgorithm. In the case of pedestrian applications, this methodconsists of step detection and step-size estimation followedby heading determination. However, this simple algorithmdepends on accurate initial position, step-size and headingestimations. Another method is based on the strapdown inertialnavigation and its accuracy deteriorates over time becauseof sensor error accumulation. Other aiding systems, such aswireless localization or magnetometers, have been used toimprove positioning accuracy by providing external estimatesof position and heading.

Early work in pedestrian navigation was implemented usingfoot-mounted inertial sensor by Foxlin [3]. The computational

method was based on the integration of inertial navigationsystem (INS) and zero velocity updates (ZUPT). Similar workswere also reported by Jimenez et al. [4] and Zampella et al.[5]. Other inertial-based pedestrian navigation systems involveputting sensor in the pocket [6], [7], on the waist [8], [9] orusing it with a handheld device [10]–[12]. Kwakkel [13] andLee [14] have reported the use of multiple wearable sensors forpedestrian navigation. Most of the works reported have utilizedhigh-end MEMS sensors which can cost thousands of dollars.However, there exist extremely low-cost inertial sensors thatare widely available in the market.

This paper focuses on the feasibility of using multiplevery low-cost sensors for pedestrian navigation. The purposeof this research is to investigate the performance of multi-wearable low-cost sensors and gait kinematics integration forpedestrian tracking. The objective of this paper is to evaluatethe heading estimation computed from different wearablesensors mounted on lower limb segments. The experimentaldata used in this paper were obtained using a commercialmotion capture clothing product. In addition, two off-the-self sensors are used to capture the motion of the two feet.This paper is organized as follows: The next two sectionsprovide a brief explanation of walking gait and the algorithmused in pedestrian navigation. The fourth section explainsthe experiment conducted for evaluating the algorithm and isfollowed by results and discussion.

II. HUMAN WALKING GAIT

Human walking motion is guided by the rotational motionsof the lower limbs. The legs experience two alternating phasesknown as stance and swing. The foot is temporarily static onthe ground during the stance phase and it experiences fourevents during each gait cycle: heel-strike, foot-flat, heel-off,and toe-off. In the swing phase, one of the leg swings forwardand this motion creates a step/stride length that represents bodydisplacement. The step length refers to the distance betweenthe two feet while a stride length is defined as the distancetravelled by one of the feet between two successive stancephases.

978-1-5386-5635-8/18/$31.00 c© 2018 IEEE

https://ieeexplore.ieee.org/document/8533740

2018 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 24-27 September 2018, Nantes, France

Fig. 1. Kinematics model of lower limbs, adopted from [15]

In gait kinematics, the walking motion is usually describedin three orthogonal planes as shown in Fig. 1. The frontalplane divides the body into front and back, the sagittal planesplits between the left and right sides while transverse planedistinguishes the upper and lower body segments. The humanwalking motion is mainly captured on the sagittal plane and theheading can be tracked on the transverse plane. Meanwhile, thefrontal plane captures a small rolling motion (rotation aboutforward axis) during walking.

The step detection algorithm implemented in this paper isbased on the foot’s angular rate measurements captured on thesagittal plane. Four foot gait cycle events can be detected usingthe slope of the angular rate signals. The most important eventis the foot-flat event in which a zero-velocity constraint can beimplemented. Every heel-strike event detected corresponds toa step or stride and this event has very distinct accelerometerand gyroscope signals.

III. PEDESTRIAN NAVIGATION ALGORITHM

The dead-reckoning algorithm used in the paper is basedon a step-heading system. This algorithm consists of threeprocesses: step detection, step-size estimation and headingdetermination.

A. Step Detection

Step detection is the first data processing in a pedestriandead-reckoning method. This work uses the foot’s gyroscopesignals to detect the step event. Other sensors (such as the

accelerometer and magnetometer) can also be used [16]. Theadvantage of using the gyroscope signals is that it allowsdetection of all four foot gait cycle events. The cycle starts withfoot-flat where the bottom surface of the foot is completely onthe ground. When the subject begins to walk, the foot rotatesforward and the cycle changes from heel-off to toe-off eventsbefore entering full swing. Then, the foot’s heel hits the ground(heel-strike) and it continues to rotate downward until the nextfoot-flat. The details the of step detection algorithm can befound in reference [17].

B. Step-Size Estimation

The second process in pedestrian navigation is to estimatestep-size. Two mathematical models are used in this work,one model is for step length estimation based on pelvisacceleration and the other model is based on foot’s accelerationfor estimating stride length.

Weinberg [18] developed a mathematical model for steplength estimation that is based on the vertical displacement ofthe hip. Using the pelvis’ acceleration signal, the step lengthestimator can be written as follows:

Step Length = k 4√amax − amin (1)

where amax, amin, and k represent the maximum and mini-mum acceleration values, and a scale factor, respectively.

Kim et al. [19] developed a mathematical model for stridelength estimation using the mean acceleration value of the footover one stride. This model is written as follows:

Stride Length = k3

√∑Ni=1 |ai|N

(2)

where ai represents the acceleration values during one strideand k is a scale factor for tuning.

C. Sensor Orientation Estimation

This work uses a 7-segment stick figure to model the humanlower limb segments: pelvis, thighs, shanks, and feet. Eachsegment is mounted with a low-cost inertial/magnetic sensor.Each sensor module provides three sets of triad measurements:specific force (f bib), angular rates (ωbib) and magnetic fieldstrengths (mb

e).

f bib =[fx fy fz

]Tωbib =

[ωx ωy ωz

]Tmbe =

[mx my mz

]TAn extended Kalman filter is used to estimate attitude angles

of each sensor package. The state vector consists of attitudeangles, angular rates and gyroscope bias.

x =[Φnb ωbib bbω

]T(3)

where Φnb represents three attitude angles: roll (φ), pitch (θ),and yaw (ψ), while ωbib and bbω are the angular rate and its biasvectors, respectively. In the case of low-cost inertial sensors,


the gyroscope is usually not able to detect the Earth angularrate (ωbie) and the transport rate (ωben) for pedestrian motion.Thus, the attitude angle derivatives are assumed to be equalto the angular rate measurements. The state-space model is alinear constant velocity model and it is written asΦnb

ωbibbbω

k+1

≈

I3 ∆t I3 03×3

03×3 I3 03×3

03×3 03×3 I3

Φnb

ωbibbbω

k

+

0

wω

wb

k(4)

where wω and wb represent the uncertainties of angular rateand gyroscope bias predictions. These errors are modelled withcertain power spectral densities, Sg and Sbd, respectively.

Qk =

13Sg∆t

3 I312Sg∆t

2 I3 03×3

12Sg∆t

2 I3 Sg∆t I3 03×3

03×3 03×3 Sbd∆t I3

(5)

The accelerometer is used to estimate roll and pitch angles.The gyroscope is used to update the angular rate vector andthe magnetometer is used to observe the yaw angle. Themeasurement update equations are:

φ = arctan

(−fy−fz

)+ vφ (6)

θ = arctan

fx√f2y + f2

z

+ vθ (7)

ψ = arctan

(−my cosφ+mz sinφ

mx cos θ +my sinφ sin θ +mz cosφ sin θ

)+ vψ (8)

ωbib = ωbib + bbω + vω (9)

where v is the measurement uncertainty that can be variedbased on the detected foot gait phases. The goal of thisorientation filtering is to estimate the pedestrian’s heading (i.e.the pedestrian’s yaw angle). The roll and pitch angles are usedto correct the tilted magnetometer measurements as shown inEq. (8).

D. Pedestrian Navigation Filter

In order to evaluate the overall navigation solution, a simpleextended Kalman filter is used. The state vector contains threebasic navigation parameters: the North-East coordinates (N ,E) and the heading angle (ψ). The filter is propagated usingthe following equations

Nk+1 = Nk + (s ∆t) cosψk

Ek+1 = Ek + (s ∆t) sinψk (10)ψk+1 = ψk

where s represents a constant walking speed and ∆t is the timeduration between two successive stance phases. The position

and heading errors are modelled as random walk processeswith process noise Qk and it can be written as follows

Qk =

∫ ∆t

0

Fk,k+1

Sp 0 0

0 Sp 0

0 0 Sψ

FTk,k+1 dτ (11)

where Fk,k+1 is the state-space model of Eq. (10) while Spand Sψ represent the power spectral densities of position andheading errors, respectively.

The step-size estimation results from Eq. (1) and (2) alongwith the yaw angle estimates from the orientation filters areused in the measurement update. The step-size measurementequation is defined as

d =√

(Nk −Nk−1)2 + (Ek − Ek−1)2 + vd (12)

where the coordinates (Nk, Ek) are the parameters of interestthat represent the current location. The coordinates (Nk−1,Ek−1) are location information from the previous step update.

IV. EXPERIMENTS

An experiments with multiple inertial/magnetic sensors wasconducted in order to analyse the performance of the sensorfusion algorithms described in the previous section. Thisexperiments utilized multiple wearable sensors and a GNSSreceiver.

A. Motion Capture Pants

Fig. 2. Enflux sensors taken out from pants: The circular device containsBLE and pelvis sensor. The rectangular devices (about the size of a 25-centCanadian dollar, 24 mm diameter) are distributed on thighs and shanks.

A commercially available motion capture clothing productfrom Enflux [20] was used to measure the motions of thepelvis, thighs and shanks of a test subject. The productconsisted of a pair of pants that included five sensor modules.These sensors are shown in Fig. 2. This device utilizesBluetooth low energy (BLE) for communication and sendsall sensor data to a computer that must be carried by or nearthe subject. Each module provides three set of measurements:specific force, angular rates and magnetic intensities. Fourmodules were located on the outer side of the legs while onemodule was located at the back side of pelvis.


B. Foot-mounted Sensors

Fig. 3. Foot-mounted sensors with a micro-controller and a micro-SD cardstorage

Since the Enflux pants do not capture foot motion, two off-the-shelf inertial/magnetic sensors (MPU-9250) from TDK-Invensense [21] were mounted on the feet. A micro-controllerwas used to read sensor measurements with inter-integratedcircuit (I2C) buses. Then, the data were written on a micro-SD card. This foot module is shown in Fig. 3.

C. Experiment Setup

Fig. 4. Sensor units distributed on lower limbs and a GNSS receiver is carriedinside a hip bag

An outdoor walking experiment was conducted in a parkinglot area at the University of Calgary. The locations of sensorsmounted on lower limbs are shown in Fig. 4. A GNSS receiverwas used and carried inside a hip bag. A NovAtel antenna (notshown in the figure) was attached to a pole and carried by handby the test subject. The reference trajectory was generatedby GNSS kinematic positioning for comparison. The Enfluxraw data were logged using a Microsoft Windows 10 laptopwith the provided Enflux C API [22]. This C library containsproprietary BLE 4.0 communication protocol functions thatallow for real-time data logging. The foot raw data werelogged into a micro-SD card using a micro-controller.

V. RESULTS AND DISCUSSION

A. Preliminary Study

Fig. 5. Estimated roll angles of thighs during treadmill walk

Fig. 6. Estimated roll and pitch angles of pelvis during treadmill walk

A treadmill walk was previously performed to study the per-formance of off-the-shelf sensors in estimating the orientationsof lower limb segments [23], [24]. The results showed that theoff-the-self wearable sensors were able to estimate reasonablygood pitch angles of the thighs and shanks. However, it is notthe case in estimating the roll angles as shown in Fig. 5. Whena person performs normal walking, the rotational motions infrontal plane are typically small. Low-cost inertial sensorsseem to have difficulties in estimating these weak signals. Asimilar trend can also be seen in the roll and pitch anglesof the pelvis during normal walking as shown in Fig. 6. Instatic mode, accerolmeter observations can be used to level theplatform, however because the pelvis, thighs and shanks are incontinuous motion, it is difficult to separate the gravity signalfrom the limb segment acceleration. The rotational motions


of the pelvis in all three planes are usually small and thevalues only vary within 10 degrees. This preliminary study hasshown that it is difficult to estimate small angles using only thegyroscope observations such that magnetometer levelling willonly remove the effect of the pitch angle for thighs and shanks,and we must assume the effect of the roll angle is negligible.In the case of the pelvis sensor, there will be no magnetometerlevelling computation as both the pitch and roll angles are toodifficult to detect using gyroscope measurements.

B. Step Detection and Step-Size Estimation

The step detection algorithm is applied to the foot-mountedsensors and this method allows the detection of foot gait cycleevents. Unfortuately the commercial sensor unit mounted onpelvis does not provide sufficient data rate in order to obtaingood acceleration signals. The Enflux system is only able toprovide a 10 Hz sampling frequency with its BLE module.

Fig. 7. Step and stride lengths

The step length is computed using the acceleration signalsfrom the pelvis according to Eq. (1). As shown in Fig. 7, thestep length can be estimated using the maximum and minimumvalues of pelvis accelerations between the period when thefoot is in heel-strike and in toe-off. In this period, the legrotates about the ankle while the foot is static on the ground.In the case of stride length estimation using Eq. (2), the meanfoot acceleration value from the swinging leg is needed. Theparameter k in Eq. (1) and (2) can be tuned according to thetotal distance travelled from the reference position.

C. Heading Estimation

The estimated heading angles from each sensor module areplotted in Fig. 8 along with the reference heading generated bythe GNSS positioning solution. The results show that pelvisis a good location to put sensor for heading determination.The other units can be used to estimate the walking directionbut care must be taken to compensate the offset of sensoralignment with the forward axis of human body. This offsetdepends both on how the sensor is mounted and on the walkinggait of each person. A histogram of heading errors are plottedon Fig. 9 and it is clear that there are offsets between the

Fig. 8. Comparison between estimated and reference heading angles

Fig. 9. Histogram of estimated heading errors

estimated heading from the left and right segments. The largevariations in the values are due to poor estimation of roll andpitch angles at each segment.

D. Positioning Results

After estimating the step-size and heading, the positioningresults can be computed. In this work, the simple PDR filterdescribed in Section III-D is used. The heading informationfrom both legs can be combined using a simple weightedaverage method. The weighting scale is tuned based on theoverall heading error of one side. The weighted averageheading can be computed as follows

ψ = W ψL + (1−W ) ψR (13)

where W represents the weight, ψL and ψR are referring to theestimated heading from the left and right segments. Some ofthe estimated headings have large errors and this can cause the


simple filter to diverge. The filter is propagated at a constantspeed of 1.32 m/s.

Fig. 10. Position solution computed using step length and average headingfrom combined thighs, shanks, and pelvis with thighs

Fig. 11. Position solution computed using step-size and average heading frompelvis

Positioning solutions are plotted on Figs. 10 and 11. Theresults show that the combined heading from thighs is betterthan the weighted average heading of the shanks. The lowersegments of the legs usually experience higher rotationalmotions and hence it more difficult to estimate accurate sensororientations. The results can be improved when the pelvisheading is used as shown by the green line trajectory. Fig.11 shows that the positioning solution computed using pelvisheading is significantly better than other sensors. There arestill some errors between the reference and estimated endingpoints. This is because the step-size solutions do match withthe actual values and it is also coupled with the small erroraccumulation from the pelvis heading.

VI. SUMMARY AND FUTURE WORK

A commercial motion capture clothing system and off-the-self inertial/magnetic sensors were used in pedestrian dead-reckoning computation. It is difficult to estimate sensor ori-entations accurately on the frontal plane due to the low-costsensor performance. The pelvis is the best location to be usedin tracking the pedestrian walking direction because there areless rolling and pitching motions. Step-size estimation usingmathematical models may not accurately match with the realvalues.

To improve the filter performance, a higher data rate inertial-based motion capture system should be used in order toobserve the kinematics of the lower limbs. High data ratesensors will allow evaluation of step-size estimation using thepitch angles of thighs and shanks. More complex PDR sensorfusion algorithms could then be used to fuse all informationextracted from the wearable sensors.

VII. ACKNOWLEDGMENT

The authors would like to thank Mr. Bruce Wright forproviding us with the Enflux motion capture clothing.

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