401
1 INTRODUCTION
The GPS system is a part of a satellite‐based
navigationsystem.ThefullyoperationalGPSincludes
24 or 28 active satellites approximately uniformly
dispersedaroundsixcircularorbitswithfourormore
satellites each. Theoretically, three or more GPS
satelliteswill always be visiblefrom most points
on
the earth’s surface, and four or more GPS satellites
can be used to determine an observer’s position
anywhereontheearth’ssurface24hoursperday.The
GPS receiver can offer positioning information with
output rate between 1 and 10 Hz. However, the
system performance depends largely on the
signal
environments. GPS uses the energy of the radio
wavesforobtainingthenavigationparametershence
it is prone to jamming. Also the signal may get
obstructed in urban areas due to tall buildings and
otherobstacles[1‐2].
In an INS system, the angular rate and specific
force measurements from
the Inertial Measurement
Unit (IMU) are processed to yield the position,
velocityandattitudesolution.General,inertialIMU,
which incorporates three‐axis accelerometers and
three‐axisgyroscopes,canbeusedaspositioningand
attitude monitoring devices. Such systems can
navigateautonomouslyandprovidemeasurementsat
ahigherdatarate(e.g.,
100Hz).However,thesystem
has to be initialized and calibrated carefully before
application.Moreover,thesensorerrorsaregrowing
unboundedlyovertime.Thepresenceofresidualbias
errors may deteriorate the long‐term positioning
accuracy[3‐4].
Data Integration from GPS and Inertial Navigation
Systems for Pedestrians in Urban Area
K.Bikonis&J.Demkowicz
GdanskUniversityofTechnology,Gdansk,Poland
ABSTRACT: The GPS system is widely used in navigation and the GPS receiver can offer long‐term stable
absolutepositioninginformation.Theoverallsystemperformancedependslargelyonthesignalenvironments.
ThepositionobtainedfromGPSisoftendegradedduetoobstructionandmultipath
effectcausedbybuildings,
cityinfrastructureandvegetation,whereas,thecurrentperformanceachievedbyinertialnavigation systems
(INS)isstillrelativelypoorduetothelargeinertialsensorerrors.ThecomplementaryfeaturesofGPSandINS
arethemainreasonswhyintegratedGPS/INSsystemsarebecomingincreasinglypopular.GPS/INSsystems
offer
ahighdatarate,highaccuracypositionandorientationthatcanworkinallenvironments,particularly
thosewheresatelliteavailabilityisrestricted.
In the paper integration algorithm of GPS and INS systems data for pedestrians in urban area is presented. For data
integration an Extended Kalman Filter (EKF) algorithm is proposed. Complementary characteristics of GPS and INS with
EKF can overcome the problem of huge INS drifts, GPS outages, dense multipath effect and other individual problems
associated with these sensors.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 7
Number 3
September 2013
DOI:10.12716/1001.07.03.12
402
Due to the complimentary characteristics of GPS
and INS, they are often integrated to obtain a
completeandcontinuousnavigationsolution[5‐7].
The inertial sensors used in IMU are made in
MEMS (Micro Electro‐Mechanical Systems)
technology. MEMS technology enables
miniaturization,massproduction and cost reduction
ofmanysensors.
Inparticular,MEMSinertialsensors
that include an acceleration sensor and an angular
velocitysensor(gyroscope,orsimply“gyro”)arethe
mostpopulardevices.AlmostallMEMSacceleration
sensorshaveaseismicmassandsupportspring made
ofsilicon.ThestructureofMEMSgyrosissomewhat
similar to that of
acceleration sensors – a mass
supportedbyaspringiscontinuouslyvibratedinthe
device, and the Coriolis force generated by the
appliedangularvelocityaffectsthemovementofthe
mass (vibrating gyroscope). The mass in a MEMS
deviceisverysmall,andtherefore,theinertialforces
acting on the mass,
especially the Coriolis force, are
also extremely small. Thus, the design of the circuit
thatmeasuresthemovementinmassduetotheforce
is important in addition to the design of the
mechanicalstructure.RecentlyMEMSinertialsensors
havebeenbuiltwithanintegratedcircuit,withsensor
structureon
asingledevicechip[4].
AtypicalstructureofaMEMSaccelerationsensor
is shown in Figure 1 [4], where a silicon mass is
supportedbysiliconspringsandthedisplacementof
the mass due to acceleration is measured by
capacitance change between the mass and fixed
electrodes. Since the mass
is very small and the
displacement is also small, the resolution of the
deviceisgenerallylimitedtoaround0.1mgHz
‐1/2
.
Figure1.StructureofMEMSaccelerationsensor(2‐axis)[4].
The basic structure of MEMS gyroscopes is similar to
acceleration sensors, i.e., a mass is supported by springs.
The main difference in operation is that the angular velocity
is obtained by measuring the Coriolis force on the vibrating
mass. Thus, the movement of the mass should have at least
two degrees of freedom. The device is shown in Figure 2
[4].
Figure2.ConceptualstructureofanMEMSgyroscope[4].
Inertial sensors have numerous applications. INS
is a self‐contained system that integrates three
acceleration and three angular velocity components
with respect to time and transforms them into the
navigation frame to deliver position, velocity, and
attitude components. The three orthogonal linear
accelerations are continuously measured through
three‐axis accelerometers while
three gyroscopes
monitor the three orthogonal angular rates in an
inertial frame of reference. In general, IMU, which
incorporatesthree‐axis accelerometers and three‐axis
gyroscopes, can be used as positioning and attitude
monitoring devices. However, INS cannot operate
appropriatelyasastand‐alonenavigationsystem.
The presence of residual
bias errors in both the
accelerometersandthegyroscopes,whichcanonlybe
modeledasstochastic processes,maydeterioratethe
long‐term positioning accuracy. Hence, the INS/GPS
data integration is the desirable solution to provide
navigation system that has better performance in
comparisonwitheitheraGPSoranINSstand
‐alone
system.
2 IMUDESCRIPTION
WeuseacommerciallyavailableIMU,modelMTi‐G
fromXsensTechnologies.Figure3showsthissensor.
Itssizeis58x58x22mm(WxLxH),anditweights50
grams.
The IMU has three orthogonally‐oriented
accelerometers, three gyroscopes, three
magnetometers and GPS reciver. The accelerometers
and
gyroscopes are MEMS solid state with
capacitative readout, providing linear acceleration
and rate of turn, respectively. Magnetometers use a
thin‐film magnetoresistive principle to measure the
earth magnetic field. The performance of each
individual MEMS sensor within the MTi IMU are
summarizedintable1andGPSreceiverintable2.
403
Figure3. MTi‐G Xsens IMU with annotated sensor
Cartesiancoordinates.
The MTi‐G sensor has a built‐in algorithm that
provides the absolute heading and attitude of the
unit,whichisexpressedastherotationmatrix
.It
can be used to directly transform the readings from
thesensor(S)totheglobal(G)Cartesiancoordinates
frames. The typical absolute orientation errors are
summarized in table 3. Performance is quite good
whenever the earth magnetic field is not disturbed,
forexamplebymetallicobjects,powerlines,personal
computers,oranydevicecontainingelectro‐magnetic
motors.
Table1.PerformanceofindividualsensorsinXsensIMU.
A G M
Axes 3 3 3
FullScaleFS ±50m/s
2
±300°/s ±750mGuass
Linearit
y
0.1%ofFS 0.2%ofFS 0.2%ofFS
Biasstabilit
y
0.02m/s
2
1°/s 0.1 mGuass
Bandwidth 30Hz 40Hz 10Hz
Maxu
p
daterate 512 512 512
A–accelerometers,G–gyroscopes,M–magnetometers
Table2.GPSreceiverparameters.
Receivertype 50channelsL1frequency,C/A
code
GPSu
p
daterate 4Hz
Start‐u
p
timecoldstart 29s
Trackin
g
sensitivit
y
‐160dBm
Timin
g
Accurac
y
50nsRMS
Table3. Performance of attitude and heading as provided
XsensfusionalgorithminmatrixR
GS
Staticaccurac
y
(
roll/
p
itch
)
<0.5°
Staticaccurac
y
(
headin
g)
* <1°
D
y
namicaccurac
y
2°RMS
An
g
ularresolution 0.005°
*inhomogeneousmagneticenvironment
3 NAVIGATIONALGORITHSUSINGDATA
FROMIMU
The conventional IMU navigation algorithm is to
integrate the gyroscopes and accelerometers data
(Figure4).However,thepositionvaluesobtainedby
this method are reliable for only a short period of
time.Thisisduetotheaccelerometer’sinherentdrift
erroraswellas
thegyroratedrifterror,whichmeans
that when double integration of the acceleration
measurements, the drift error is also accumulated
overtimeandincreasesdramaticallywithtime.Sothe
estimated position will be far away from the actual
position.
Rate-gyroscope
signals
Orientation
Project
accelerations
onto global
axes
Accelometer
signals
Correct for
gravity
Position
Initial
position
Initial
velocity
Figure4.ConventionalIMUnavigationalgorithm.
OtherIMUnavigationmethodpedestrian‐oriented
can be based on a step detection algorithm and use
orientationinformationdirectlyfromIMU.Thereare
several step detection algorithms that have been
proposedbyresearchesintheliterature[3,8].
The algorithm implemented for step detection
consist of the following four steps [8].
First step,
computethemagnitudeoftheaccelerationa
iforeach
sampleI,like
222
iii
ixyz
aaaa
. (1)
Second step, computes the local acceleration
variance,toremovegravity,like
2
2
1
21
i
iw
ajj
jiw
aa
w
, (2)
where
j
a is a local mean acceleration value, is
computedlike
1
21
iw
j
q
qiw
aa
w
, (3)
and w defines the size of the averaging window in
samples.Thirdstep,usestwothresholds.First(T
1)is
applied to detect the swing phase (B
1i), whereas the
second(T
2)appliedtodetectthestancephase(B2i)ina
singlestepwhilewalking.
11
1
0
i
a
i
TT
B
otherwise
. (4)
22
2
0
i
a
i
TT
B
otherwise
. (5)
Fourthstep,isdetectedinsampleiwhenaswing
phase ends and stance phase starts. Figure 5 shows
details of this step detection method. Step detection
also is possible using data from gyroscope and
magnetometer[3].
404
Figure5.ConventionalIMUnavigationalgorithm.
Alsoit is necessary to estimate the Stride Length
(SL) at every detected step in order to calculate the
total forward movement of a person while walking.
SL depends on the person, its leg length, and its
walking speed and the nature of the movements
duringwalking, andetc.Thealgorithm
proposedby
Weinberg [9] assumes that SL is proportional to the
bounce,orverticalmovement,ofthehumanhip.This
hipbounceisestimatedfromthelargestacceleration
differencesateachstep.Thealgorithmimplemented
forSLestimationconsistsofthefollowing threesteps
[8].Firststep,computethemagnitude
ofaccelerations
a
i,asineq.1.Secondstep,Low‐Passfilterthissignal
().Inparticularweuseafilteroforder6andcut‐off
frequencyat5Hz.Thirdstep,estimatetheSLusing
Weisbergexpression.
1
4
~~
max min
JJ
kk
aa
k
ji w ji w
SL K
(6)
where the maximum and minimum operations are
applied over the filtered accelerationsin a
window of size 2w+1 around the sample i
(k)
corresponding to the k stance detection. K is a
constant that has to be selected experimentally or
calibrated.Table4showsexamples resultsforK=1.In
theWeinbergmethodology,usingafixedKvalue,is
valid for accurately estimating SL even at different
walkingspeed.
Table4.ResultsforStrideLength(SL)estimationalgorithm.
Ste
p
1 Ste
p
2 Ste
p
3 Ste
p
4 Ste
p
5
SLforK=1 1.17m 1.26m 1.25m 1.29m 1.41m
Navigation method based on step detection
algorithm and use orientation information directly
from IMU is a good solution for estimating human
trajectories. However, the drift of position obtained
by this method is proportional to the travelled
distance,changes inwalkingspeed(Kisaconstant),
changesinwalkingdirection,data
qualityfromIMU
(accelerometers,gyroscopesandmagnetometers)and
etc.
4 ALGORITHMFORINSANDGPSDATA
INTEGRATION
The INS/GPS data integration algorithm is based on
Extended Kalman Filter (EKF) usage [10, 11]. EKF uses
Taylor series, where the idea of a linear approximation to
describe a function in the neighborhood of some point by a
linear function is applied. The algorithm works in a two-
step prediction/correction process. In the prediction step,
the Kalman filter produces estimates of the current state
variables. Because of the recursive nature of the algorithm,
it can be run in real time. The present input measurements
and the previously calculated state is used; no additional
past information is required [12]. The very idea is presented
in the Figure 6 where
ˆ
k
x
,
ˆ
k
x
are á priori and á
posteriori system state,
k
P
,
k
P are á priori and á
posteriori covariance matrix,
H is measurement
matrix,
k
K is Kalman gain,
R
,
Q
are process and
state variance of the system,
k
z is measurement matrix,
A is process model.
1
ˆ
k
x
1k
P
0,,
ˆˆ
11
kkk
uxfx
T
kkk
T
kkkk
WQWAPAP
11
1
T
kkk
T
kkk
T
kkk
VRVHPHHPK
0,
ˆˆˆ
kkkkk
xhzKxx
kkkk
PHKIP
Figure6.EKF sensor data integration algorithm diagram.
Predictioncanbedescribedasfollows(7)and(8)
in the Figure 6, where
, ,
f
xuw is nonlinear
function,whichusesapreviousfilterstateaswellas
controlimpactandtheprocessnoise.
k
A (or
J
A )is
aJacobian,
f
withrespectto
x
,
k
W (or
J
W )isa
Jacobian,
f
withrespectto w function.Where A
and
W arefollows:
[]
[, ] 1 1
[]
, 0
ˆ
,
i
J
ij k k
j
f
Axu
x
, (12)
[]
[, ] 1 1
[]
, 0
ˆ
,
i
J
ij k k
j
f
Wxu
x
. (13)
Andcorrectionisappliedasfollows(9),(10)and
(11)intheFigure6,where
k
H (or
J
H )isJacobian,
derivativeofthe function
h withrespect to
x
,
k
V
(or
J
V )isJacobianaswell,function
h
derivativeof
withrespectto
v and
, hxv isnonlinearfunction
representing state and measurement relation.
Jacobians
H
and V canbeexpressedasfollows:
405
[]
[, ]
[]
, 0
i
J
ij k
j
h
Hx
x
, (14)
[]
[, ]
[]
, 0
i
J
ij k
j
h
Vx
x
, (15)
where:
11
, ,0
kkk
xfxu
. (16)
AllJacobiansoughttoberecalculatedineverystep
iteration,whentheGPS/IMUmodelisgenerated.
Thestateestimatevectorconsistsof20elements
[
ˆ
]
x
yz xyz
T
xyzbxbybz
x
xyzv v v qb b b
g
(11)
initialized with:
[0 0 0, 0 0 0,1 0 0 0, 0.001 0.001 0.001,
0 0 0, 0.001 0.001 0.001 0
ˆ
,
T
x
(12)
where x y z is location [m], v
x
v
y
v
z
is velocity [m/s], q is
quaternion vector, b
x
b
y
b
z
is bias [G], φxφyφzisrotation
phase [rad],φ
bxφbyφbz is rotation biases, g is
gravitation.
The observation covariance matrix R is diagonal
matrix consisting of GPS position error (5 m) and
velocityerror(0.5m/s)indirectionx,y,z,whilethe
covariancenoisediagonalmatrixequals:
[0.5 0.5 0.5, 0.5 0.5 0.5,
0.00001 0.00001 0.00001 0.00001, 0.01 0.01 0.01,
0.001 0.001 0.001, 0.001 0.001 0.001, 0.01]
Q diagonal
(13)
5 RESULTS
The purpose of this study is to track the position of a
pedestrian walking outside. One foot of the pedestrian is
mounted with an IMU, which is used to measure the
acceleration and angular rate of the walking foot. The GPS
module is attached to a straight pole with the GPS antenna
on the top of it so that the GPS position signal can be
obtained more easily. The pedestrian localization is
achieved by integrating the inertial and GPS information.
Figure7showsIMUandGPSantennalocalizationon
thebody.
Figure7.IMUandGPSantennalocalizationonthebody.
The IMU/GPS based pedestrian localization
algorithmisfirstlyimplementedwhenapedestrianis
walking along a 20m×20m square. The result of the
IMU/GPSalgorithmusingEKFisshowninfigure8.
Figure8.Thepedestriantrajectoryrepresentedbydifferent
methodologiesfor20mx20msquare.
Another test was conducted in an environment
shown in figure 9 and the results of the IMU/GPS
algorithmusingEKFisshowninfigure10.
Figure9.Theenvironmenttestarea.
406
Figure10.Thepedestriantrajectoryrepresentedbydifferent
methodologiesforenvironment.
ItisobviousthatEKFcorrectedtrajectory ismore
accurate than the trajectory calculated by IMU and
GPS separately. Result for EKF is nearly GPS
trajectorywhenGPSerrorsarebetween1to5 meters.
6 CONCLUSIONS
Inthis paper, weproposedanEKFto integration of
GPSandINSsystems
dataforpedestrianslocationin
urbanenvironment. Obtained results show thatEKF
algorithm is more accurate and robust, than
algorithms using data from GPS and INS systems
separately. However, the situation of long‐term GPS
outage is not considered in this paper. Our future
work will focus on the improvement
of the
localizationaccuracyinlong‐termoperations.
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