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Abstract This paper proposes a foot-mounted Zero VelocityUpdate (ZVU) aided Inertial Measurement Unit (IMU) filteringalgorithm for pedestrian tracking in indoor environment. Thealgorithm outputs are the foot kinematic parameters, whichinclude foot orientation, position, velocity, acceleration, and gaitphase. The foot motion filtering algorithm incorporates methodsfor orientation estimation, gait detection, and positionestimation. A novel Complementary Filter (CF) is introduced tobetter pre-process the sensor data from a foot-mounted IMUcontaining tri-axial angular rate sensors, accelerometers, andmagnetometers and to estimate the foot orientation withoutresorting to GPS data. A gait detection is accomplished using a

simple states detector that transitions between states based onacceleration measurements. Once foot orientation is computed,position estimates are obtained by using integratingacceleration and velocity data, which has been corrected at stepstance phase for drift using an implemented ZVU algorithm,leading to a position accuracy improvement. We illustrate ourfindings experimentally by using of a commercial IMU duringregular human walking trial in a typical public building.Experiment results show that the positioning approach achievesapproximately a position accuracy less than 1 m and improvesthe performance regarding a previous work of literature.

I. INTRODUCTION edestrian navigation is useful for finding and guidingemergency first responders, blind persons, security

personal and for a wide range of augmented realityapplications [1-3]. Numerous applications requiring a self-contained personal navigation system working in indoor andoutdoor environments, does not need any infrastructuresupport, and is not susceptible to interference [4], [5].Position tracking of human movement commonly requires anunrestricted line-of-sight to an installed infrastructureconsisting of one or more transmitters and/or receivers. Suchsystems require extensive setup and calibration of thetracking volume, which may be of limited size and maysuffer from occlusion. Examples of this type of tracking aregenerally based on radio frequency, such as GPS that is ableto receive satellite signals in most indoor environments [6],[7], or may use optical-based systems, such as videotracking. An infrastructure-independent solution for thisproblem is a pedestrian dead reckoning system based on

H. Fourati is with the Department of Automatic Control, GIPSA-Lab,UMR 5216, NeCS Team, Grenoble University, France.e-mail: [email protected]

N. Manamanni is with the Automatic Control group, CReSTIC-URCA,Reims Champagne Ardenne University, France.e-mail: [email protected]

shoe-mounted Inertial Measurements Units (IMUs).Applications using commercially available IMUs containingtriads of orthogonally mounted accelerometers, angular ratesensors, and magnetometers have been successfullydemonstrated [7-9]. Many researches have focused on usinginertial sensors combined with magnetic ones to estimate thepedestrians location relative to a known starting position.

Throughout the research, one of the main approaches toposition tracking is an adaptation of the well-knownstrapdown navigation algorithm, which incorporates doubleintegration of the measured acceleration to estimate distanceand/or position. The growth in position uncertainty thatarises from the integration of the acceleration error ismitigated by a technique that is commonly referred to asZero Velocity Updating (ZVU). Most types of humanmovement, such as walking and running, have repeatedrecognizable periods during which the velocity andacceleration of the foot are zero. These brief periods occurbefore entering the swing phase of the gait cycle each timethe foot contacts the ground during the stance phase, asshown in Fig. 1. The use of a foot-mounted IMU providessensor data for recognition of these periods. This provides ameans to determine the velocity drift error and to facilitateits correction in preparation for subsequent integration toderive position. Since this correction is applied at the end ofevery walking step, it provides a type of immediaterecalibration of the sensor.

Fig. 1. Key phases in a stride. During 1 T , all velocity components of pointA in the sole of the boot are zero [10]

Shoe-mounted navigation systems have been investigatedbefore. Some previous works have exploited the ZVUtechnique. As a matter of fact, one of the first systems basedon the above solution can be attributed to Foxlin [9]. Besidesthe ZVU, Foxlins system uses a tri-axial magnetometersensor to compute a yaw measurement that is used as aninput measurement to an Extended Kalman Filter (EKF). Thestep detector is based on thresholding the average value ofthe gyro and the accelerometer output signals during a period

Position Estimation Approach by Complementary Filter-aided IMUfor Indoor Environment

H. Fourati, and N. Manamanni, Member, IEEE

P

hal-00797042,version1-5Mar2013

Author manuscript, published in "12th biannual European Control Conference (ECC 2013), Zurich : Switzerland (2013)"
http://hal.archives-ouvertes.fr/http://hal.archives-ouvertes.fr/hal-00797042

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of time. Experimental results showed a 0.3% errorperformance of the walked distance. In another work byOjeda and Borenstein [10], 2% error of walked distance wasreported. A combined GPS and shoe-mounted navigationsystem is proposed by Godha et al. in [11]. The systemimplements a standard 15-state error model and exploits GPSmeasurements to bound drift errors in outdoor scenarios. The

step detection is carried out through the analysis of themagnitude of the accelerometer signals and its movingacceleration variance over a number of samples. Accordingto the authors, the system performed quite well in indoor(with no GPS) and outdoor tests. Another pedestriannavigation system was proposed by Suh et al. in [12]. Thesystem consists of a 15-state error model where attitude isrepresented by means of quaternion. A very sophisticatedstep detector based on force sensors, attached to the shoessole, and hidden Markov model filtering is used to determinewhen to apply zero velocity measurements to the EKF. Thesystem performance was tested with short paths of 14 meters

long maximum. Therefore, no conclusions can be madeabout the advantage of using such a sophisticated stepdetector. Moreover, the need for additional sensors to detecta step may be a serious drawback. In a recent work by Bebeket al. [7], a position error of less than 1% was reported. Thiswork incorporated an additional calibration based on thetotal drift accumulated during an initial walk. Thisinformation was used to correct subsequent walks to producedesirable results. Since these works were based on the ZVU,it was necessary to identify the time instants of swing phaseand stance phase with a high degree of accuracy. Someresearchers have developed specific electronic circuits to aid

in the detection of the foot stance phase. For example, in [5],a shoe-mounted radar was developed to detect the instancesof the foot zero velocity.

In this paper, we propose a foot-mounted CF-aided IMUapproach for pedestrian tracking in indoor environmentswithout resorting to GPS data. The primary contributions ofthis paper are the following:

1) The use of robust CF instead of the known EKF.Indeed, in attitude estimation, EKF presents somedrawbacks such as the difficulty to guarantee the globalconvergence of the filter due to the linear approximationof the nonlinear process model [9]. In this paper, the

overall CF design is greatly simplified to accurately pre-process the sensors data from an IMU (accelerometer,magnetometer and gyroscope) and to estimate orientationin complementary way during both static and dynamicmotion. Previous works in pedestrian navigation, forexample [2], [4], [8-10], estimate the quaternion ofattitude only by integrating the well-known quaternionkinematic differential equation. However, this solutionwould be prone to drifting over time due to the build-up ofbias and drift errors in gyroscope.2) CF approach without the intermediate step of gyro biasestimation and correction. Previous attitude estimation

approaches added this step, which increases the computingtime [13], [14].3) A reliable gait detection method requiring only inputfrom foot-mounted accelerometer sensors without addinga threshold on gyroscope measurements as it was used inprevious literature works [10].4) Real-world experimental results, which indicate that the

aforementioned methods are accurate.5) A practical comparison with a previous famous workdeveloped in [10].The remainder of this paper presents previous foot motion

filtering algorithms and their drawbacks. Section II describesthe proposed foot motion filtering algorithm and includes aseparate section for each of the major components.Discussion and results pertaining to real-world experimentsare presented in Section III with a comparison to previouswork. The final section summarizes the conclusion that canbe drawn from this paper.

II. FOOT MOTION ALGORITHM OVERVIEW This section presents the motion filtering algorithm based

on the use of a foot-mounted IMU. A block diagram of theapproach is shown in Fig. 2.

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n nq f q

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C F9 9D42C F9 9D42 3F493F49C 39D4243CDC 39D4243CD

843 243CD843 243CD

G1h

f nq

d

A

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1 p

v

1+ G

n nq f q

f

f

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d

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Fig. 2. Block diagram of the foot motion tracking algorithm that producesthe foot orientation quaternion, foot position, foot velocity, and gait phase.

The upper, middle, and lower portions of the diagramcorrespond to the three main components of the algorithm.The upper portion of the diagram depicts the quaternion-based CF for estimating foot orientation represented by aquaternion n q from the acceleration measurement f , the

local magnetic field measurement h , and the angular rate

measurement G . The middle portion of the diagram depictsthe position and velocity estimation filter. The outputs arethe foot velocity estimate v and the foot position estimate p . The lower portion of the diagram shows the gait phase

detection algorithm. At any given moment, the gait phase(gait is the pattern of movement of the limbs of humansduring locomotion over a solid substrate), denoted by adetector d , will have one of two values, which correspondto the swing phase (encompasses the entire time the foot is inthe air for limb advancement) or the stance phase(encompasses the entire period during which the foot is on


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the ground) of the normal walking cycle. Each of the maincomponents of the filter algorithm is described in detail inthe following sub-sections.

A. Quaternion based CF for orientation estimation

The upper portion of Fig. 2 shows a CF for estimatingorientation of a foot to which an IMU is attached. This part

represents one of the technical contributions of the paper.The input to this filter is nine components: three componentsof the accelerometer measurement f , three components of

the local magnetic field measurement h , and threecomponents of the angular rate measurement G . The output

of the filter is the estimated foot orientation represented by aquaternion n q . All measurements provided by the IMU are

performed in the body-fixed frame ( ), , B B B B X Y Z withrespect to the Earth-fixed frame ( ), , N N N N X Y Z , which istangent to the Earths surface (Local Tangent Plane, LTP).The

N X -axis points true North. The

N Z -axis points

towards the interior of the Earth, perpendicular to thereference ellipsoid. The N Y -axis completes the right-handed

coordinate system, pointing East.As stated above, the objective of this section is to design a

CF for tracking of foot orientation. To do so, it is necessaryto establish a process model representing motion dynamicsof the foot segment. For simplicity, we adopted the well-known quaternion kinematic differential equation [15], [16]:

12 G

q q = 1 (1)

where the product between q and g is quaternion

multiplication. 02 3= 4 5T T

vect q q q is the theoretical unit

quaternion that denotes the mathematical representation ofrigid body attitude between two frames 1) body-fixed frame

B and 2) Earth-fixed frame N . 1 2 3= 2 34 5T

vect q q q q

represents the vector part of q . More details about

quaternion can be found in [17]. 0T T

G g 2 3= 4 5 is a pure

vector quaternion with the scalar part equal to zero and the

vector part

T

g gx gy gz 2 3=

4 5 corresponding to thetheoretical components of the angular rate, expressed in B .

g is measured by a 3-axis gyroscope and can be often

corrupted with noises and bias [18].Equation (1) describes the time rate of attitude variation as aresult of rigid body angular rates measured by the gyroscope.Applying the quaternion multiplication in (1), we obtain:

,

3 3 ,0 ,

12

T n vect

n gn n vect

qq

I q q

2 36 7=

2 36 7+ 4 54 51 (2)

where nq is the real quaternion, ,2 3

4 5n vect q represents the

skew-symmetric matrix [16], [19]:

,1 ,3 ,2

, ,2 ,3 ,1

,3 ,2 ,1

0

0

0

2 3 2 36 7 6 72 3 = = 6 7 6 74 56 7 6 74 5 4 5

n n n

n vect n n n

n n n

q q q

q q q q

q q q

(3)

and 3 3 I is the identity matrix of dimension 3.

The process model ( )2 composed of (2) and the linearmeasurement model y can be written such as:

( ),

3 3 , 0 ,

12:

T n vect

n gn n vect

T

x y z x y z

qq

I q q

y f f f h h h

8 2 39 = 6 79 2 3+6 7 4 5A 4 59

2 3=9 4 5B

1

(4)

where the output 6 y is built by stacking the

accelerometer and magnetometer measurements. The relationbetween the outputs y and the state of the system nq will be

mentioned later in equations (7) and (8).The algorithm designed for orientation estimation is a type offilter that blends two sources of data in a complementarymanner. In this case, the filter blends the static low-frequency information provided by accelerometers andmagnetometers, and the dynamic high-frequency informationprovided by the angular rate sensors. The aim of the CF is toensure a compromise between the accuracy provided byshort-term integration of the gyroscope data and the long-term measurements precision obtained by the accelerometerand the magnetometer [13]. To compensate for the drifts onthe estimated quaternion that are observed during theintegration of the differential equation in (4), a correctionterm T is introduced in this equation based on a quaternionproduct . We propose the following CF:

,

3 3 , 0 ,

1

2

T n vect

n gn n vect

qq 1 T

I q q

C D2 3E F6 7= E F2 36 7+ 4 54 5

1 (5)

where nq denotes the estimated quaternion. The correction

term T is calculated from a fusion approach ofaccelerometer and magnetometer data. To calculate thecorrection term T , we consider the modeling error

( ) ( ) n2 q y y= . The estimated output is given by y :

T

x y z x y z y f f f h h h2 3= 4 5 (6)

Measurements of the estimated accelerations x f , y f and z f

can be calculated assuming that there are no accelerationexcept gravity such as:

0T

x y z n q n f f f f q G q2 3= = 4 5 (7)


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where [ ]0 0 0 9.8 T qG = is a pure vector quaternionwith the scalar part equal to zero and the vector part

[ ]0 0 9.81 T G = corresponding to the theoretical

components of the gravity. nq is the complementary

quaternion of nq , i.e. ,0 ,1 ,2 ,3 T

n n n n nq q q q q 2 3= 4 5 .

Measurements of the estimated Earths magnetic field xh ,

yh and zh can be calculated such as:

0T

x y z n q nh h h h q m q2 3= = 4 5 (8)

where [ ]0 0 T q x zm m m= is a pure vector quaternionwith the scalar part equal to zero and the vector part

[ ]0 T x zm m m= corresponding to the theoreticalcomponents of the Earths magnetic field. Currently, the

parameters of the theoretical model of the geomagnetic fieldm closest to reality can be deduced from [20]. In our case,we considered that the magnetic disturbances are low andtheir impact is negligible on the attitude estimation.The minimization of the modeling error ( )n2 q is performedfrom a regression method that minimizes the scalar squarederror criterion function ( )n3 q related to ( )n2 q :

( ) ( ) ( ) T n n n3 q 2 q 2 q= (9)

The Levenberg Marquardt Algorithm is used to minimize thenon-linear function

( )

n3 q . The unique solution to this

problem can be written in the following form:

( ) ( ) n n4 q K 2 q= (10)

where1

3 3T T K k X X 5 I X

2 3= +4 5 is the gain of the filter.

6 3 X

is the Jacobian matrix defined by:

0 0

2 2 0 0

0 0

T z y z y

T

z x z x

y x y x

f f h h

X f h f f h h

f f h h

2 36 72 32 3 2 3= = 6 74 5 4 54 56 7 4 5

(11)

The positive constant 5 is chosen to ensure the non-singularity of the minimization problem. The positiveconstant k combines low bandwidth accelerometer andmagnetometer readings with high bandwidth gyroscopemeasurements. ( )n4 q represents a part of the correctionterm T .To achieve the quaternion product in (5), the term T mustbe of dimension 4 as:

( )

1 6

3 1

11 00 n

T 2 qK

2 3 2 3= 6 7 6 7

6 7 4 54 5 (12)

The scalar part of quaternion error is fixed to 1 to force theerror quaternion to represent small angles of rotation.Finally, the complementary filter can be written as follows:

( ),

3 3 ,0 ,

1 0 0 0 0 0 0 101

02 0

T n vect

n gnn n vect

qq 1

2 qK I q q

2 36 7C D2 3 2 3E F 6 76 7= 6 7E F 6 72 36 7+ 4 54 54 5 6 74 5

1

(13)

B. Position and Velocity Estimation with ZVU

The middle portion of Fig. 2 shows the position andvelocity estimation approach. The input to this filter is themeasured acceleration vector f in the body coordinates and

the estimated quaternion representing the orientation of thebody ( )n q t generated by the complementary orientationfilter, and the output is the estimated position ( ) p t andvelocity ( )v t relative to a fixed earth coordinate frame.

( )n q t serves to transform the body coordinate accelerationinto the earth coordinate system using the quaternionoperator [17]:

( ) ( )*n n a q t f q t = (14)

The acceleration vectors f and a are treated as pure vector

quaternions, with the scalar part being equal to zero whenperforming quaternion multiplication [17]. After obtaining

the acceleration vector 0T T

ea a2 3= 4 5 in the earth coordinate

system, gravitational acceleration G is subtracted fromT

ex ey ezea a a a2 3= 4 5 to derive the motion-induced

acceleration [16]:

( ) ( )e A t a t G= (15)

The result of (15) is integrated to obtain the 3-D velocityvector in the earth coordinate system:

( ) ( )2

1

.T

T

v t A t dt = 1 (16)

where [ ]1 2,T T denotes the sampling period. Theoretically,the velocity vector resulting from (16) can be immediatelyintegrated once again to obtain position. However, due to thepresence of measurement noise and drift in the measuredacceleration vector f and the estimation errors in the

estimated quaternion ( )n q t , an immediate integration of


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( )v t results in unbounded error growth in positionestimation in a relatively short time. An approach to reduceerror growth in the position estimation is to apply a velocitycorrection method called the ZVU.This method is early introduced in [10]. The concept of theZVU is based on the observation that human foot motionsare cyclic, and when a foot is in the stance phase or incontact with the ground, its velocity is theoretically to bezero. Due to bias error in acceleration measurements, theestimated foot velocity obtained from (16) may not be zerowhile the foot is in the stance phase. In this paper, wepropose to correct the velocity bias error by resetting thevelocity to zero at these moments. This corrected velocity isintegrated again to obtain the estimated position ( ) p t suchas:

( ) ( )2

1

.T

T

p t v t dt = 1 (17)

It is noted that all sensor measurements and position/velocityvectors are 3-D in this paper.

C. Gait phase detection algorithm

The use of the ZVU for correcting foot velocity needs toaccurately detect the stance and swing phases of foot motion.The use of accelerometer data was examined for thispurpose. The foot acceleration seemed to provide a meansfor the detection of the transitions between the stance phaseand swing phase.The gait phase detection algorithm is essentially a state

detector with two states Stance ( 0d = ) and Swing ( 1d = ).The operation of the state detector must be synchronizedwith the users foot motion. That is, when the users foot wasin the stance phase, the state detector must be equal to 0.Conversely, when the users foot is in the swing phase, thestate detector should be equal to 1. When walking, the gaitcycle begins just after the foot strikes the ground, usuallywith heels first, causing a large peak acceleration followedby an oscillation, see Fig. 3.

The foot remains stationary for approximately 0.5 s.During the stance phase the accelerometer should onlymeasure the earth gravitational acceleration and the velocity

is zero. In practice, this is not trivial, because theaccelerometers suffer from drift, so they never show exactlygravity. To detect a walking event based on an accelerometersignal, we proceed as follows:We start by taking the squared Euclidean norm of the

acceleration 22i 6 f = :

2 2 2 22i x y z

6 f f f f = = + + (18)

where x f , y f , z f are the acceleration output of the IMU inthree different axes. Eq. (18) can be altered to include

several stationary properties of the system. We calculateafter the variance of the squared norm from a sliding windowusing the following equation [8]:

( ) ( )( )2

2

1

11

i j

e i i ji j e

Var j 6 6 ee

=

= +

= (19)

where i 6 is the squared norm of the measured acceleration f and ( )i j 6 e is the mean of i 6 over e samples. Properly

applied, the variance of the squared norm can be useful fordetecting gait events where the signal changes suddenly,such as a heel strike and the stance phase initiation. If thevariance of a manipulated signal is to be used for gait eventdetection, the sample size e must be chosen appropriately sothat the variance test is adequately sensitive to slow signalchanges and adequately responsive to fast ones. It was foundthat a threshold of five to ten was suitable for a gait event.This parameter was adjusted by trial-and-error until a

satisfactory result was achieved.

Fig. 3. The norm squared of a walking foot. The black arrow shows thestance, respective stride phases duration

The variance should be limited during the stance phasebelow an experimental threshold L :

( )2eVar j L< (20)

The detector d , with two states Stance ( 1d = ) and Swing ( 0d = ), which is introduced in this work uses therequirement reported in (20). If this requirement is satisfied,

the detector 1d = which mean that we belong to the stancephase, else we are in the Swing phase and 0d = . Thethreshold L was adjusted by trial-and-error until asatisfactory result was achieved. It was found that a samplesize of fifteen to twenty was suitable to better identify thestance and swing phases.

III. INDOOR EXPERIMENTS AND RESULTS

A. Foot-mounted IMU

To examine the effectiveness of the motion filteringalgorithm based on the use of a foot-mounted IMU, several


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experiments have been performed for different walkingscenarios.We used the MTi IMU module developed by XsensTechnologies [21] to collect data. The module is mounted ona foot as shown in Fig. 4. The module samples sensor datafor a tri-axial accelerometer, a tri-axial gyroscope and a tri-axial magnetometer at 100 Hz and transfers the raw data to a

laptop over USB, which in turn timestamps and logs it. Thecollected data are processed offline using MATLAB. Thesoftware consists of the quaternion based CF, the positionand velocity estimation with ZVU and the gait phasedetection algorithm.

Fig. 4. Foot-mounted MTi Experiments were preformed at an indoor location to

collect walk data for different users. The set of experimentswere performed in the corridors of CReSTIC laboratory atReims Champagne Ardenne University. Data was collectedfor 3 volunteers at this location. In order to establish theground truth trajectory, the subjects were made to walk on amanually surveyed path marked on the corridor laboratory.In the experiment the path starts and ends at the sameposition. The path includes rectangle shaped walking (lengthis 80 m) and had several straight stretches followed by sharpright-angle turns in clockwise and anti-clockwise directionsto test the accuracy of our motion filtering algorithm (seeFig. 5).

Fig. 5. Indoor walking path during a 80 m trajectory length

In this paper, we choose to represent the results obtainedfrom one volunteer. The same experiment was repeated fourtimes to appropriately choose the sample size e and thethreshold L . These parameters were adjusted by trial-and-error until a satisfactory result was achieved so that thevariance test is adequately sensitive to slow signal changes

and adequately responsive to fast ones. It was found that asample size 8e = and the threshold 16 L = are suitable for agait event. Fig. 6 depicts the squared norm of the measuredacceleration i 6 , the mean ( )i jmo 6 e= of i 6 over e

samples, the variance ( )2eVar j of the squared norm and thestates detector d . As we can see, the stance and swing

phases are clearly identified.

0 10 20 30 40 50 60 70 80 900

1000

2000

3000

X (

m / s

2 ) 2

0 10 20 30 40 50 60 70 80 900

500

1000

m o ( m / s

2 ) 2

0 10 20 30 40 50 60 70 80 900

2

4

6x 105

V (

m / s

2 ) 4

0 10 20 30 40 50 60 70 80 90-0.5

00.5

11.5

Time (s)

d

Fig. 6. The squared norm of the measured acceleration i 6 , the average

( )i jmo 6 e= , the variance ( )2

eVar j and the states detector d

Fig. 7 shows the three-axis foot velocity v prior toapplying the ZVU. The presence of drift is evident in allthree components of velocity. Moreover, the drift in thevelocity appears to be linear, which confirms the assumptionthat the acceleration bias is constant over the short period ofa swing phase. Fig. 7 shows also the same velocity v afterapplying the ZVU. It is seen that the corrected foot velocityduring the stance phase is now zero.

0 10 20 30 40 50 60 70 80 90-10

0

10

20

v x

( m / s )

0 10 20 30 40 50 60 70 80 90-5

0

5

10

15

v y

( m / s )

0 10 20 30 40 50 60 70 80 90-10

-5

0

5

Time (s)

v z

( m / s )

With correction stepWithout correction step



Fig. 7. Three-axis foot velocity v prior and after applying the ZVU

Fig. 8 shows the 3D view reconstruction result of therectangle shaped walking by using the proposed motionfiltering algorithm which follows the designed trajectorywith high consistence. The difference between the startingand ending point is smaller than 0.3 m. Then, the position


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estimation error is less than 0.37 % of the total distancetraveled.

-10

-5

0

5

10

-20

-15

-10

-5

0

5-5

0

5

X (m)Y (m)

Z (

m )

Fig. 8. Walking experiment: The reconstruction of the rectangle trajectory

B. Comparison with previous work

In Fig. 9, we compare our reconstruction result of thewalking trajectory with the one obtained from previous workdeveloped by Ojeda and Borenstein [10].

Fig. 9. Walking experiment: The reconstruction of the rectangle trajectoryusing method developed by Ojeda and Borenstein [10]

In [10], the authors used only gyroscope measurements toestimate the quaternion of attitude by integrating the well-known quaternion kinematic differential equation. However,this solution would be prone to drifting over time due to thebuild-up of bias and drift errors. In contrary, the approachherein proposed takes advantage of the precision near to zero( 1 2 ), given by the rate gyros integration in the short term( 1 sec ) and the reliable long term accuracy provided byaccelerometer and magnetometer measurements. Theresulting structure of the proposed CF blends two frequencyregions and is based on the complementary filtering theory:1) the accelerometer and magnetometer data are

characterized by a low frequency region, where the attitudeis usually more accurate, 2) the gyroscope data is located inthe high frequency region, where the integration of theangular velocity yields better attitude estimates.

It is obvious that the reconstruction result using themethod in [10] is deviated from the designed trajectoryfurther. Our proposed approach improves the performance

greatly.

IV. CONCLUSION This paper presents an algorithm for estimating human

foot position during normal walking based on estimates offoot orientation, velocity, acceleration, and gait phase usinginertial/magnetic sensor measurements. The measurementsare provided by an IMU attached to a foot. Orientationestimation is accomplished by a quaternion-based CF toblend the high frequency information provided by angularrate sensors and the low-frequency information provided byaccelerometers and magnetometers. For this purpose, a foot

gait phase detection algorithm based on the use ofaccelerometer measurements was presented. With footorientation readily available as a result of the quaternion-based CF, foot acceleration in the body coordinate frame isconveniently converted into the earth coordinate frame usingthe foot orientation quaternion. Foot velocity is obtained bynumerically integrating corrected foot accelerationmeasurements obtained during the swing phase. Due tosensor noise, accelerometer measurements tend to drift. Thedrift is corrected using the ZVU technique. Experimentswere conducted to evaluate the algorithm. The experimentalresults suggest that the achievable position accuracy of thealgorithm is about 0.37 % of the total walked distance.

REFERENCES [1] K. Sagawa, Y. Satoh, and H. Inooka, Non-restricted measurement of

walking distance, IEEE International Conference Systems, Man,Cybernetics. , Nashville, TN, pp. 18471852, October. 2000.

[2] C. Fischer P. T. Sukumar, and M. Hazas, Tutorial: implementationof a pedestrian tracker using foot-mounted inertial sensors, IEEEPervasive Computing , DOI: 10.1109/MPRV.2012.16, January 2012.

[3] J. Rantakokko, J. Rydell, P. Stromback, P. Handel, J. Callmer, D.Tornqvist, F. Gustafsson, M. Jobs, M. Gruden, M, Accurate andreliable soldier and first responder indoor positioning: multisensorsystems and cooperative localization, IEEE WirelessCommunications , vol. 18, no.2, pp. 10-18, April 2011.

[4] C. Fischer and H. Gellersen, Location and Navigation Support forEmergency Responders: A Survey, IEEE Pervasive Computing , vol.9, no. 1, pp. 38-47, January-March 2010.

[5] C. Zhou, J. Downey, D. Stancil, and T. Mukherjee, A Low-PowerShoe-Embedded Radar for Aiding Pedestrian Inertial Navigation,

IEEE Transactions on Microwave Theory and Techniques , vol. 58,no. 10, pp. 2521-2528, October 2010.

[6] D. Skournetou and E. Lohan, Pulse shaping investigation for theapplicability of future gnss signals in indoor environments,

International Conference on Indoor Positioning and Indoor Navigation (IPIN) , pp. 1-7, September 2010.

[7] O. Bebek, M. A. Suster, S. Rajgopal, M. J. Fu, X. Huang, M. C.Cavusoglu, D. J. Young, M. Mehregany, A. J. van den Bogert, and C.H. Mastrangelo, Personal navigation via high-resolutiongaitcorrected inertial measurement units, IEEE Transactions on

Instrumentation and Measurement , vol. 59, no. 11, pp. 30183027,November 2010.


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[8] I. Skog, P. Handel, J. O. Nilsson, and J. Rantakokko, Zero-velocitydetection-An algorithm evaluation, IEEE Transactions on

Biomedical Engineering , vol. 57, no. 11, pp. 2657-2666, November2010.

[9] E. Foxlin. Pedestrian tracking with shoe-mounted inertial sensors. IEEE Computer Graphics and Applications , vol. 25, no.6, pp. 38-46,November-December 2005.

[10] L. Ojeda, and J. Borenstein, Non-GPS Navigation for SecurityPersonnel and First Responders, Journal of Navigation , vol. 60, no.

3, pp. 391-407, September 2007.[11] S. Godha and G. Lachapelle, Foot mounted inertial system forpedestrian navigation, Measurement Science and Technology , vol.19, no. 7, July 2008.

[12] Y. Soo Suh and S. Park, Pedestrian inertial navigation with gaitphase detection assisted zero velocity updating, 4 th InternationalConference on Autonomous Robots and Agents (ICARA) , Wellington,pp. 336-341, February 2009.

[13] R. Mahony, T. Hamel, and J. M. Pflimlin, Nonlinear complementaryfilters on the special orthogonal group , IEEE Transactions on

Automatic Control , Vol. 53, no. 5, pp. 1203-1218, 2008.[14] R. Cunha, C. Silvestre and J. Hespanha, Output-feedback control for

stabilization on SE(3), Systems & Control Letters , vol. 57, pp. 10131022, 2008.

[15] H. Fourati, N. Manamanni, L. Afilal, and Y. Handrich, NonlinearFiltering Approach for the Attitude and Dynamic Body Acceleration

Estimation Based on Inertial and Magnetic Sensors: Bio-loggingApplication, IEEE Sensors Journal , vol. 11, no. 1, January 2011.

[16] M. D. Shuster, A survey of attitude representations, Journal of the Astronautical Science , vol. 41, no. 4, pp. 493-517, October-December1993.

[17] J. B. Kuipers, Quaternion and Rotation Sequences , Princeton, NJ:Princeton University Press, 1999.

[18] R.G. Brown and P.Y.C Hwang, Introduction to Random Signal and Applied Kalman Filtering , 3 rd Ed. New York: John Wiley, 1997.

[19] H. Fourati, N. Manamanni, L. Afilal, and Y. Handrich, Aquaternion-based Complementary Sliding Mode Observer for attitudeestimation: application in free-ranging animal motions, 49 th IEEEConference on Decision and Control (CDC) , Atlanta, USA, 2010, pp.5056-5061.

[20] Astrosurf, (2012, February). http://www.astrosurf.com.[21] Xsens Motion Technologies, (2012, February). Available:

http://www.xsens.com.


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