IMU/GPS based pedestrian localization · localization, Global Positioning System(GPS) is considered as the main tool. However, since GPS signals can be blocked and inﬂuenced by

IMU/GPS Based Pedestrian LocalizationLing Chen and Huosheng Hu

School of Computer Science and Electronic EngineeringUniversity of Essex, Colchester CO4 3SQ, United Kingdom

E-mail: {lcheno, hhu}@essex.ac.uk

Abstract—The low cost Inertial Measurement Unit(IMU) canbe used to provide accurate position information of a pedestrianwhen it is combined with Global Positioning System(GPS).This paper investigates how the integration of IMU anf GPScan be effectively used in pedestrian localization. The positioncalculation is achieved in sequence by three different strategies,namely basic double integration of IMU data, Zero-velocityUpdate (ZUPT) and Extended Kalman Filter(EKF) based fusionof IMU and GPS data. Experiments that are conducted in twofields show that EKF based localization outperform the doubleintegration and ZUPT methods in terms of both positioningaccuracy and robustness.

Keywords-IMU;GPS;Localization;ZUPT;EKF

I. INTRODUCTION

It is highly demanded that a navigation system is able tokeep tracking the location of a person, such as in search andrescue operations, as well as training exercises, location-awarecomputing and augmented reality [1]. To realize the pedestrianlocalization, Global Positioning System(GPS) is considered asthe main tool. However, since GPS signals can be blockedand influenced by high buildings, human bodies, mountains,a GPS normally has errors between 1 to 10 meters, which isunacceptable for some applications.

An Inertial Navigation System(INS) could be deployed tolocate a pedestrian based on accelerometers, gyroscopes andmagnetometers. The unit integrating these sensors together iscalled Inertial Measurement Unit(IMU). As opposed to GPS,IMU will not be affected by the environment where the pedes-trian is located. Integral calculations of accelerations fromaccelerometers and angular rates from gyroscopes produce theposition, velocity as well as the orientation information of thepedestrian. However, the mean-squared navigation errors of anIMU increase with time quadratically or cubically without aboundary.

As for the pedestrian localization, some methods are basedon step counters and the estimation of step length [2], [3],multiplying the counters by a step length yields the distancethat the pedestrian has walked. Other methods apply dou-ble integration of the accelerations when the pedestrian iswalking [4], [5]. Jimenez et. al [6]and Isaac Skog et. al [7]combine Zero-Velocity Update(ZUPT) with Extended KalmanFilter(EKF) which is used to correct the IMU errors. However,high accuracy of positioning is only achieved in a shortdistance since IMU errors can not be eliminated completely.In this paper, instead of using IMU alone, we integrate ZUPTstrategy of IMU with GPS by designing an EKF algorithm to

(a) Foot Mounted IMU

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(b) GPS Receiver

Fig. 1. Placement of IMU and GPS receiver module. (a) Foot-Mounted IMU;(b) GPS Module

optimally estimate the position and attitude of a person whilewalking.

The rest of the paper is organized as follows. Section IIbriefly presents the system configuration. Section III intro-duces the basic position calculation equation using XsensMti IMU. Then error correction by stop detection(ZUPT) isdiscussed in Section IV to improve the position calculationaccuracy. In section V, an EKF algorithm is applied to theIMU/GPS based pedestrian localization, where GPS signalsare fused with IMU to provide more accurate trajectoryinformation than ZUPT. Section VI presents some experi-mental results to validate the proposed IMU/GPS localizationalgorithm. Finally, a brief conclusion and future work arepresented in Section VII.

II. SYSTEM CONFIGURATION

The purpose of this study is to track the position of apedestrian walking outside. One foot of the pedestrian ismounted with an IMU (MTi from Xsens), which is usedto measure the acceleration and angular rate of the walkingfoot(see Figure 1a). The GPS module (from Phidgets) isattached to a straight pole with the GPS antenna on the topof it so that the GPS position signal can be obtained moreeasily. The pedestrian localization is achieved by integratingthe inertial and GPS information.

As shown in Figure 2, there are two coordinate systemsinvolved in the pedestrian tracking: 1) Inertial sensor bodyframe (B); 2) The global reference frame (W ) whose X-Yplane is parallel with the earth surface with X axis pointing tothe East, Y axis pointing to the North and Z axis pointing to

2012 4th Computer Science and Electronic Engineering Conference (CEEC) University of Essex, UK

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Fig. 2. Body frame B, global frame W and their coordinate transformationR

W

B

the Up direction according to the right-hand rule. RWB is the

rotation transformation between the inertial sensor frame Band global frame W . Obviously, the position of a pedestrianshould be based on the global frame W . In order to yieldpedestrian position by integrating accelerations and angularrate in W , the accelerations and angular rates measured in thebody frame B need to be projected onto the global frame Wusing rotation transformation RW

B .

III. BASIC POSITION CALCULATION

The basic position calculation principle is based on theStrapdown IMU navigation algorithm [8]. The first step ofthe conventional IMU navigation algorithm is to integratethe angular rate information with respect to time to yieldorientation. However, with Xsens Mti IMU, the accurateorientation information can be directly obtained thanks to thebuilt-in micro processor running a kalman filter to fuse multi-sensor data from accelerometer, gyros and magnetometer. Thisis one of the advantages of using the Mti IMU. We will directlyuse the orientation data from the inertial sensor and use unitquaternion Q = (qw, q1, q2, q3) to represent RW

B . Quaternionrepresentation does not have a Gimbal lock problem andfacilitates transformation and calculation in a simple form.

Using state space representation, the system’s state vectorcan be given as follows:

Xk = (Pk Vk Ok)T

= (xk yk zk xk yk zk φk θk ψk )T

(1)

where Pk = (xk, yk, zk)T is the position of the pedestrian in

frame W , Vk = (xk, yk, zk)T is the velocity of the foot of the

pedestrian, Ok = (φk, θk, ψk) is the orientation-Euler Angleof the IMU.

As analyzed above, the useful acceleration data is the footaccelerations in reference frame W , which are represented asaWk . It is calculated from the inertial measurements using

aWk = Qk ∗ aBk ∗Q

′

k −G (2)

where * is the quaternion multiplication. G = (0, 0, g)T

represents the earth gravity. Qk = (qw,k, q1,k, q2,k, q3,k) isa quaternion representation of the rotation transformationbetween the inertial sensor frame B and the global referenceframe W . The acceleration measured by the inertial sensoraBk includes the acceleration caused by a specific force andgravity. After transforming the acceleration into frame W andsubtracting the gravity, the aWk represents the accelerationcaused by the specific force only imposed on the target.

There is a transformation formula between quaternion andEuler Angle, which is represented as follows:

Xk(7 : 9) = Ok =

⎛⎝ φk

θkψk

⎞⎠

= Q2Euler(Q)

=

⎛⎝ atan2(2(qwq1 + q2q3), 1− 2(q21 + q22))

arcsin(2(qwq2 − q3q1))atan2(2(qwq3 + q1q2), 1− 2(q22 + q23))

⎞⎠(3)

where Qk = (qw, q1, q2, q3), Q2Euler(Q) represents thefunction of Q to convert quaternion value to Euler angle.

The rest elements of Xk can be written as Xk(1 : 6),which then can be obtained after double integration of theacceleration, the discrete form of which is

Xk(1 : 6) =

(Pk

Vk

)=

(I I ∗ TS0 I

)Xk−1(1 : 6)

+

(T 2S/2 ∗ ITS ∗ I

)aWk−1

(4)

where Ts is the sensor sampling time interval, I is a 3×3identity matrix, aWk−1 is calculated with equation (2). Byiteratively implementing equation (4) with the initial state, theposition and velocity of the pedestrian can be calculated real-timely.

However, the position values obtained by this method arereliable for only a short period of time. This is due to theaccelerometer’s inherent drift error as well as the gyro ratedrift error, which means that when double integration of theacceleration measurements, the drift error is also accumulatedover time and increases dramatically with time. So the es-timated position will be far away from the actual position.This can be seen from the experiment described as follows:The IMU data is collected when the pedestrian, whose rightfoot is mounted with the IMU, is walking around a squareof 30m×30m (see Figure 3 ). The collected IMU data isthen substituted into equation (2) and (4) without consideringany error compensation methods, the calculated trajectory ofthe pedestrian can be seen in Figure 4. It is clear from thefigure that the calculated trajectory is tremendously away from


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Fig. 3. The square of 30m×30m where pedestrian walks and IMU data iscollected

the true one, which is quite unacceptable. Therefore, effortsshould be taken to correct the accumulated error, which willbe discussed in the following part of this paper.

IV. ERROR CORRECTION BY STOP DETECTION

It is noted that when a person walks, their feet alternatelyundergo a stationary stance phase and a moving stride phase.During the stationary stance phase, the velocity of the feetshould be zeros. As long as the stationary stance phase isdetected, setting the velocity of the feet of this phase as zerosis likely to correct some drift errors, and thus the accuracy ofpedestrian localization should be improved compared with thebasic position calculation algorithm described in the previoussection. This method of correcting the position error is knownas zero-velocity updates (ZUPTs).

There are several stop detection algorithms that have beenapplied by researchers in the literature. For instance, Felizet al. [9] consider current state as stop phase only when thetotal angular velocity value is lower than a given threshold,otherwise, the state is considered as moving stride phase. Thismethod is not robust because it can not eliminate the smallfluctuations, although the fluctuation can be eliminated byfiltering, the filtering has the disadvantage of phrase lag whichaffects the real-time performance of the system. Jimenez et al.[6] implemented a multi-condition stance detection algorithmusing both sources of information (accelerometers and gyro-scopes) and an order low pass filter. This algorithm makes thedetection process robust so that it is able to adapt to both slowand quick walk. Therefore, we will adopt this algorithm todetect stop phase, the detail of which is described as follows:

1) Condition 1:

C1 =

{1 thrhdamin

< ‖ak‖ < thrhdamax

0 otherwise(5)

−3000 −2000 −1000 0 1000 2000

−500

0

500

1000

1500

x(East m)

y(N

orth

m)

True Trajectory

MTi Trajectory

0 50 100

0

20

40

Fig. 4. The true trajectory and the calculated pedestrian trajectory.

where ‖ak‖ = [abk(1)2 + abk(2)

2 + abk(3)2]0.5, thrhdamin

and thrhdamaxare the minimum and maximum threshold

respectively.2) Condition 2:

C2 =

{1 σ2

ab

k

> thrhdσa

0 otherwise(6)

where

σ2ab

k

=1

2s+ 1

k+s∑j=k−s

(abk − abk

2) (7)

is the local variance of the accelerations, abk is the localmean acceleration value, s is the size of the averagingwindow and thrhdσa

is the threshold.3) Condition 3:

C3 =

{1 ‖ωk‖ < thrhdωmax

0 otherwise(8)

where ‖ωk‖ = [ωbk(1)

2 + ωbk(2)

2 + ωbk(3)

2]0.5 is themagnitude of the gyroscope, thrhdωmax

is the threshold.These three conditions are combined together with logical

“AND” which means they must be satisfied simultaneously,a median filter is used to get rid of the abnormal states. Thecombined logical values “1” and “0” represents the stationarystance phase and the moving stride phase respectively. Figure5 shows the result of the stop detection.

Taking the stop detection into account, the equation (4) ismodified as follows:

Xk(1 : 6) =

(Pk

Vk

)=

(I I ∗ TS0 I ∗ Cstop

)Xk−1(1 : 6)

+

(T 2S/2 ∗ ITS ∗ I

)aWk−1

(9)

where Cstop is the logical value of the stop detection andCstop = C1 & C2 & C3.



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Fig. 5. The results of stop detection.

Multiplying Cstop resets the velocity of the foot as zeroswhen the stop is detected, which reduces the accumulatedvelocity error and thus further reduces the position error.Figure 6 shows the true trajectory and the pedestrian trajectorywith stop detection, it can be seen clearly that the pedestriantrajectory is slightly away from the true trajectory, which ismuch more acceptable than the situation when stop detectionis not considered. However, it can also be concluded that theerror correction by stop detection still needs to be improvedsince the pedestrian trajectory is away from the true trajectoryin terms of both orientation and distance. This phenomenoncan also be explained by the fact that drift errors from bothaccelerometers and gyroscopes are accumulated over time,which can not be eliminated only by stop detection.

V. ERROR CORRECTION BY GPS

The major disadvantage of IMU navigation is that the drifterror will accumulate over time causing the errors to beunbounded. In contrast, GPS errors are relatively noisy fromsecond to second, but exhibit no long-term drift [10]. There-fore, GPS is typically used for aiding IMU navigation makingthe GPS-aided IMU navigation superior to either of themalone. Hence, GPS is also used in this study for correcting theerror of foot-mounted IMU localization. An Extended KalmanFilter (EKF) algorithm is designed to implement the errorcorrection with GPS signal, which is presented as follows.

As described above, the system state vector at time k isequation (1). Considering the logical value of stop detection,the system transition model is:

Xk =

⎛⎝ Pk

Vk

Ok

⎞⎠ =

⎛⎝ I I ∗ Ts 0

0 I ∗ Cstop 0

0 0 0

⎞⎠

︸︷︷︸A

Xk−1

+

⎛⎝ T 2

s /2 ∗ ITs ∗ I0

⎞⎠

︸︷︷︸B

awk +

⎛⎝ 0

0

Q2Euler(Qk)

⎞⎠+wk

(10)

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Fig. 6. The true trajectory and the IMU calculated trajectory using stopdetection.

where A is the 9×9 state transition matrix, B is the controlmatrix, w is the process noise with covariance matrix Nk =E(wkw

Tk ).

The measurement model is

zk = HXk + nk (11)

where zk is the predicted measurement, Hk is the measure-ment matrix, and nk is the measurement noise with covariancematrix Rk = E(nkn

Tk ).

The signals from GPS are longitude, latitude, altitude,heading and velocity, only longitude, latitude and heading areused as the actual measurement in this study, as altitude andvelocity is too unreliable to use. The longitude and latitudemust be converted to coordinate in the global frame beforethey are fed into the EKF algorithm. The conversion formulapresented by Dupree in [11] is

xgps = cos(φ)

√1

( sin(φ)a

)2 + ( cos(φ)c

)2[(lon1− lon0) ∗

π

180]

ygps =

√1

( sin(φ)a

)2 + ( cos(φ)c

)2[(lat1− lat0) ∗

π

180]

(12)

where φ = π2 −

lat0+lat12 ∗ π

180 , (lon0, lat0) is the geographiccoordinates of the original point, (lon1, lat1) is the geographiccoordinates of the specific point, a = 6378136.6 meters, theequatorial radius of the earth, and c = 6356751.9 meters , thepolar radius of the earth. The actual measurement is therefore:

mk = (xgps, ygps, ψgps)T (13)

According to mk, the measurement matrix must be:

H =

⎛⎝ 1 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1

⎞⎠ (14)



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Fig. 7. The IMU/GPS based pedestrian localization algorithm.

Then the Kalman update equation

Xk = Xk +Kk ∗ (mk −HXk) (15)

where Kk is the Kalman gain, mk is the actual measurementwhich are GPS signals, Xk is the predicted system statedescribed as equation (10).

The Kalman gain is calculated with the usual formula:

Kk = ΣkHT (HΣkH

T +Rk)−1 (16)

where Σk is the state estimation covariance matrix, calculatedwith the classical form:

Σk = AΣk−1AT +Nk. (17)

The covariance matrix Σk at time k is then calculated withthe Kalman gain in the Joseph form equation Σk = (I9×9 −KkH)Σk(I9×9 −KkH)T +Rk.

From equation (2), we can see that any error of quaternionwill cause the drift error of acceleration in global frame.However, it should be noted that although the heading partof the error correction term Kk(ψk − ψgps) can be usedto correct the heading error of the pedestrian position, thecorrection value has not been embodied on the control inputterm-quaternion. In order to make the heading error correctiontake effect on the quaternion, the quaternion can be modifiedas:

Qk = ΔQk−1 ∗Qk (18)

where ΔQk−1 can be calculated with following formula:

Q = (w x y z)T = Euler2Q(φ, θ, ψ) (19)

Then ΔQk−1 = Euler2Q(0, 0,Kk ∗(mk−HXk)(9)), whereKk∗(mk−HXk)(9) is the heading part of the error correction

term, Euler2Q() is the function converting Euler angle toquaternion.

GPS signals are not always available because they can beblocked by high buildings, canyons or forests among others.When GPS is in outage, the predicted system state Xk willnot be updated by EKF, instead it is directly used for nextiteration of state calculation.

Figure 7 shows the diagram of the IMU/GPS based pedes-trian localization algorithm.

VI. EXPERIMENTS

The IMU/GPS based pedestrian localization algorithm isfirstly implemented when a pedestrian is walking along a30×30 square which is shown in Figure 3. The result ofthe implementation is shown in Figure 8 which presents thepedestrian trajectory represented by different methodologies.It can be seen that the IMU/GPS based localization algorithmusing EKF outperforms the ZUPT algorithm alone in tworespects: First, the EKF corrected trajectory is closer to thetrue trajectory than stop detection corrected trajectory to thetrue trajectory, in other words, the former is more accurate thanthe latter; Second, even though there is GPS outage duringthe walking, EKF corrected trajectory is only affected slightlythanks to the advantage of data fusion algorithm.

In order to further validate the accuracy of the IMU/GPSbased pedestrian localization algorithm, another test was con-ducted in an environment shown in Figure 9, and the corre-sponding trajectory represented by different methodologies ispresented in Figure 10. It is obvious that EKF corrected tra-jectory is more accurate than the trajectory calculated by stopdetection based algorithm. There are two spots of GPS outage,where EKF corrected trajectory keeps the same accuracy withplaces where GPS signals are available. Therefore, the result



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Fig. 8. The pedestrian trajectory represented by different methodologies,(0,0) is the starting point. The environment for this test is a 30×30 square.

Fig. 9. A larger testing environment compared to the 30×30 square

shows the superiority of the IMU/GPS integrated pedestrianlocalization algorithm over the ZUPT algorithm alone.

VII. CONCLUSION

This study presents a new IMU/GPS based pedestrian lo-calization algorithm, in the order of basic position calculationprinciple, error correction by stop detection (ZUPT) and errorcorrection by GPS data and EKF algorithm. By analyzingtheoretically and practical experiment, it is known that ZUPTbased position calculation method works better than basicposition calculation principle in terms of accuracy since theaccumulated integration error can be compensated by settingthe velocity as zero when the stance phase of the foot isdetected. However, even adopting ZUPT can not completelyeliminate the accumulated integration error, thus EKF basedIMU/GPS fusion algorithm is applied. The tests for two

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Fig. 10. The pedestrian trajectory represented by different methodologies,(0,0) is the starting point.The environment for this test is the one shown inFigure 9

different environments show that the error correction by GPSdata and EKF algorithm is accurate and robust. However, thesituation of long-term GPS outage is not considered in thispaper. Our future work will focus on the improvement of thelocalization accuracy in long-term operations.

REFERENCES

[1] S. Wan and E. Foxlin, “Improved pedestrian navigation based on drift-reduced mems imu chip,” in Proceedings of the 2010 InternationalTechnical Meeting of The Institute of Navigation, 2001, pp. 220–229.

[2] S. Cho and C. Park, “Mems based pedestrian navigation system,”Journal of Navigation, vol. 59, no. 01, pp. 135–153, 2006.

[3] P. Schneider, S. Crouter, O. Lukajic, and D. Bassett Jr, “Accuracy andreliability of 10 pedometers for measuring steps over a 400-m walk,”Medicine & Science in Sports & Exercise, vol. 35, no. 10, p. 1779, 2003.

[4] L. Ojeda and J. Borenstein, “Non-gps navigation for emergency respon-ders,” in 2006 International Joint Topical Meeting: Sharing Solutions forEmergencies and Hazardous Environments. Citeseer, 2006, pp. 12–15.

[5] X. Yun, E. Bachmann, H. Moore, and J. Calusdian, “Self-containedposition tracking of human movement using small inertial/magneticsensor modules,” in 2007 IEEE International Conference on Roboticsand Automation. IEEE, 2007, pp. 2526–2533.

[6] A. Jimenez, F. Seco, J. Prieto, and J. Guevara, “Indoor pedestriannavigation using an ins/ekf framework for yaw drift reduction and afoot-mounted imu,” in 2010 7th Workshop on Positioning Navigationand Communication (WPNC). IEEE, 2010, pp. 135–143.

[7] I. Skog, J. Nilsson, and P. Handel, “Evaluation of zero-velocity detectorsfor foot-mounted inertial navigation systems,” in 2010 InternationalConference onIndoor Positioning and Indoor Navigation (IPIN). IEEE,2010, pp. 1–6.

[8] O. Woodman, “An introduction to inertial navigation,” University ofCambridge, Computer Laboratory, Tech. Rep. UCAMCL-TR-696, 2007.

[9] R. Feliz, E. Zalama, and J. Gomez, “Pedestrian tracking using inertialsensors,” Journal of Physical Agents, vol. 3, no. 1, pp. 35–42, 2009.

[10] G. Schmidt and R. Phillips, “Ins/gps integration architectures,” NATO-OTAN, 2011.

[11] P. Dupree, “Autonomization of a mobile hexapedal robot using a gps,”SUN, 2009.



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IMU/GPS based pedestrian localization · localization, Global Positioning System(GPS) is considered as the main tool. However, since GPS signals can be blocked and inﬂuenced by