Direct georeferencing of a multi-sensor platform formobile mapping applications and damage detection
N. Diefenbach, A. Eichhorn
Institute of Geodesy, Group of Geodetic Measuring Systems and Sensor Technology,
Technical University of Darmstadt, Franziska-Braun-Str.7, 64287 Darmstadt, Germany

Abstract. Condition monitoring of highways is
an important prerequisite for timely transportation of wares. Only through early detection andrehabilitation of damaged spots of the pavement
it is possible to avoid wide-ranging limitations oftraffic and accompanying costly delays.
This paper presents a cost-effective realizationof a vehicle-mounted multi-sensor-system for direct geo-referencing through fusion of sensor datafrom both an inertial measurement unit (IMU)
and multiple receivers for the Global Navigation
Satellite Systems (GNSS), based on an Unscented
Kalman Filter (UKF).
To reduce the costs of such a system a lowcost IMU based on micro-mechanical systems(MEMS) was used. A new approach is the integration of a GNSS array consisting of four symmetrically placed antennas to determine the orientation. This leads to an increased position
accuracy for the multi-sensor-system as well as
an increased orientation accuracy, because all orientation angles of the platform can be introduced
as additional measurements in the estimation process. Furthermore, the sensor fusion is carriedout with an UKF, so that in contrast to the classic approach with an Extended Kalman Filter(EKF) the momentums of the non-linear systemequations are included up to the third order.
At first the realized system is evaluated throughprocessing in an EKF and an UKF architecture
based on simulated measurements. Afterwards areal experiment confirms the advantage of orientation aided sensor fusion through a GNSS arrayas well as the improved logging of complex trajectories through the UKF.
Keywords. Monitoring, multi-sensor-system,
Unscented Kalman Filter, road damages

1 Introduction
In the context of globalization and increasing
intra-European traffic additional burdens for theGerman road network become obvious. As a result, adequate monitoring of the road network,
consisting of a timely localisation of damages aswell as documentation of the successful rehabilitation measures, is needed.
To guarantee an appropriate quality management the Federal Highway Research Institute(BASt) carries out an annual inspection of the ca.
53.000 km of Federal Highways and examines therespective road substance. To accomplish thisin the given timeframe and budget appropriate
measurements methods have to be chosen.
The current used technique originates from thefield of Mobile Mapping. By equipping a measuring vehicle with special scanners that register
the ground lengthwise and crossways to the direction of motion and can be up to 4 meters long,the kinematic detection of the street is accomplished. Additionally, the data is linked to thecorresponding locality by geo-referencing throughvehicle-mounted position sensors, determining thescanners position and orientation at the time of
measuring (see (Paffenholz 2012)).
Due to the dimensions of the mounted sensors
and the subsequent restricted maximum speed,
a survey cannot be performed without interfering with the traffic flow. To solve this issue theFraunhofer Institute of Physical Measurement
Techniques (IPM) developed the Profile Pavement Scanner (PPS) (fig. 1), the first scanner tobe certified by BASt for use in public spaces forthis purpose.
In combination with a suitable measurement
vehicle a sensor platform is created that allows
for speeds of up to 100 km/h. Due to the fusionof high movement speed and the flexible deploy-1

Fig. 1 Fraunhofer Profile Pavement Scanner (PPS)
for pavement inspection

Fig. 2 Used GNSS-Array to determine absolute
angles as observations for the sensorfusion

ment the documentation of the road conditions
is achieved without hindering the traffic flow.
The sole positioning of the scanner could in
principle be achieved by using GNSS only. But
in the actual target environment signal loss due
to signal shading cannot be ruled out. To deal
with this and to determine the needed exteriororientation of the sensor an IMU is used as additional sensor system. Since the IMU acts as
autonomous system and provides data in a highfrequency independently from the GNSS receiver,
it is an optimal supplement. To achieve an optimal position and orientation for the scanner,
the measurements of both the IMU and GNSS
sensors are combined.
This paper focuses on a fundamental case studyof direct geo-referencing in post-processing as
preliminary stage for the long-term objective ofdeveloping an adequate geo-referencing of highest
accuracy for use with the PPS.
Consequently, different algorithms for the sensor fusion were tested with both simulated data
and a practical experiment and evaluated for theirsuitability. Goal was to fully utilize the existing
low-cost hardware and to ensure an optimal result in the sensor fusion. Therefore the state
estimation is aided by a GNSS array (fig. 2), that
not only allows positioning and the calculation of
speed but also for the first time gives information
about the orientation.
Based on the existing hardware and the intention to prevent avoidable surveys the goal wasto achieve a lane precise positioning, which requires an accuracy of below 1.75 m. This is due
to generate adequate approximation coordinates,
which would be sufficient for the referencing offor example an image giving sensor system.
The paper is structured as follows: After classifying this contribution in the research context
of kinematic multisensory systems section 3 explains the used approaches with regards to inertial
navigation and Kalman-Filters. Following this,section 4 illustrates the application and the results are compared. Finally, section 5 discusses
the results.

2 Related Work
The challenge of direct geo-referencing has been
approached in the early 90s (e.g. (Cannon 1991)).
The focus has been the direct geo-referencing of
airborne surveys (see (Skaloud 1999), (Schwarz2001)). Therefore Cramer (2001) analysed the attainable accuracy. Basis were always high quality
sensors and the EKF as fusion algorithm.
One trend in regards to algorithms was started
by Julier and Uhlmann (2002) with the UKF. A
comparison between UKF and EKF can be foundin (Wendel et al. 2005) and (El-Sheimy, Shin, andNiu 2006). Subsequently, the emphasis changed
to the realization of systems with low-cost sensors(e.g. (van der Merwe and Wan 2004) and (Shin2005)).
Another trend in present science is the improvement of sensor fusion with more than one
GNSS antenna (e.g. pioneering work by (Böder
2002), further approaches by (Wieser and Aschauer 2011), (Paffenholz 2012) and (Eling, Klingbeil, and Kuhlmann 2015)).
This paper focuses on the cost-effective realization of a multi-sensor system for direct georeferencing based on the combination of a low-cost

2

MEMS-IMU and a GNSS array with four antennas. This not only allows an update of the IMU
based estimations of position and velocity but
also of the orientation.
Both sensors are fused in an EKF and an UKF.
Based on El-Sheimy, Shin, and Niu (2006) the
UKF was additionally chosen because of its ability
to handle large attitude errors in an appropriate
way. In this respect this paper is an extension of
their contribution by concerning the assistanceof the orientation estimation by using an GNSS
antenna array.
In contrast to Skaloud (1999), Schwarz (2001)
and Böder (2002) the sensor platform is a landbased vehicle. And unlike van der Merwe andWan (2004) a GNSS array instead of a single
antenna is used. Furthermore, the results fromthe UKF are compared to those of the EKF. The
difference to Wendel et al. (2005) lies in the useof a loosely coupled architecture for the sensor
fusion.

3 Methods
In this section the basic principles of inertial navigation, as well as EKF and UKF are explained.

3.1 Inertial Navigation
To describe the movement of a sensor platform
with IMU measurements the formulation in thelocal, topocentric navigational coordinate system
is chosen (see also (Wendel et al. 2005)). This
results in navigation equations that are shown in
the equations (1)-(8). To indicate the position ina higher coordinate system the WGS-84 ellipsoid
in combination with latitude, longitude and elevation ϕ, λ and h are used. Rn and Re describe thencorresponding ellipsoidal half-axes and veb,dthesensor platforms speed along the local verticaldirection.

λ̇ =

1
ϕ̇ =
Rn (ϕ) − h(1)1(Re (ϕ) − h) cos(ϕ)(2)

nḣ = veb,d(3)

The differential equation for the speed follows
asv̇neb = Rnb abib − (2 ω ie + ω en ) × vneb + gnl(4)Here Rnb is the rotation matrix from the body
fixed in the navigational coordinate system andabib is the measured acceleration. Furthermoreω nie describes earth’s rotation rate, ω nen is thetransportation rate and gnl is the local gravity
vector.
T
gnl = 0, 0, g(ϕ, h)(5)The gravity vector is not assumed as a constant and instead depends on the longitude λ andthe ellipsoidal height h. The calculation follows
the normal gravity formula after Somigliana (see(Torge 2002)).
The last navigation equation is the equationof orientation.
nΨ̇ = Rnb ω bib − ω nie − ω nen(6)

The equations 4 and 6 need the earth rotationand the transportation rate. Those can be formulated in the navigational coordinate systemasω nie = ωe cos(ϕ)
and asnω nen = veb,east

Re (ϕ)−h0vn− Reb,northn (ϕ)−h−ωe sin(ϕ)

T

(7)

vn
tan(ϕ)− eb,east
Re (ϕ)−hT(8)

3.2 Kalman-Filters
This by Rudolf Emil Kalman described algorithm
is used for optimal estimations of the state ina linear or linearised system based on measurement data (see (Kalman 1960)). A distinction
is made between the prediction, based on thesystem equation (9), and the filtering, based on
the measurement equation (10).
x̃ = Tx̃ + Bũ + Sw

(9)l̃ = Ax̃

(10)

The matrix T describes the transition matrix,
x the state vector, B the outer input matrix, u
the outer input vector, S the noise matrix, w thenoise vector, l the measurement vector and A thedesign matrix. The system and the measurements
are subject to noise that within the algorithm isreferred to as Gaussian White Noise (GWN).
In the prediction step the state x is extrapolated based on the corresponding variance propagation Qx̂x̂ . In the filtering step a control and3correction takes place by determining the covariance matrix of the innovation D and the Gain
matrix K. Based on these the weighted mean of
the innovation between the measurement l andthe predicted state x̄ can be computed. In another step the corresponding variance-covariancematrix (VCM) Qx̂x̂ can be calculated.

λUKF = α2 (n + κ) − n

With it the sigma points of the prediction follow as
X 0 = x̂p(n + λUKF ) Qx̂x̂

3.2.1 Extended Kalman-Filter

X i = x̂ +Since the Kalman-Filter loses the characteristic ofa Best Linear Unbiased Estimator (BLUE) whenused with nonlinear problems a linearisation of
the nonlinear transfer function f is needed (see(Eichhorn 2005) and (Paffenholz 2012)).

i = 1, . . . , np
X i = x̂ −(n + λUKF ) Qx̂x̂∂fk+1,k (xk , uk , wk )∂xk
xk =x̂k∂fk+1,k (xk , uk , wk )Bk+1,k =∂uk
uk =uk∂fk+1,k (xk , uk , wk )Sk+1,k =∂wk
wk =wk∂hk+1,k (xk+1 , vk+1 )Ak+1,k =∂xk+1
xk+1 =x̄k+1
Tk+1,k =

(11)
(12)
(13)
(14)

3.2.2 Unscented Kalman-Filter
An alternative approach to use a Kalman-Filter
with a nonlinear problem was publicized by Julier,Uhlmann, and Durrant-Whyte (1995). The UKF
is a special case of the Monte Carlo Simulationthat allows updating the mean value and the
VCM of a state based on deterministically chosen
sigma points. The used number of sigma points isvariable and can be chosen based on the application (see (Julier and Uhlmann 2002) and (Julier
2003)).
The advantage of this approach is that thenonlinear functions from the prediction as well as
the measurement equations can be used directly
and therefore making linearisation unnecessary.
Additionally, it has to be noticed that moments up
to third order are included in the UKF approach.
This paper uses the scaled unscented transformation (see (Julier 2002)), since it allows foradaption of scattering range and weightings. For
the distribution of the sigma points both (Julier
2002) and (van der Merwe and Wan 2004) recommend the parameters α = 10−3 , β = 2 and κ = 0
based on the assumption of normally distributed
errors. The number of points should be 2n + 1
with n = rg(x). Initially the scaling parameter
λUKF has to be calculated

(15)

(16)
(17)
i

(18)
i

i = n + 1, . . . , 2nFurthermore, the corresponding equations are
distinguished by the weights of the mean value
Wm and those of the VCM Wc .
λUKF
+ (1 − α2 + β)(n + λUKF )
λUKF
Wc0 =
(n + λUKF )
λUKF
c
Wm
i = Wi =2(n + λUKF )
Wm
0 =

(19)
(20)
(21)

Following this the sigma points of the prediction step are transferred with the nonlinear system equation f ().
yP = f (X P )(22)

Based on that the predicted state is calculated
from the weighted mean .
x̄ =

2n
X

Wci yPi(23)

i=1

The corresponding VCM results from the variance of the transferred sigma points. Due to theassumption of GWN the noise term Q is added.
!
2n
1 X c
T
Qx̄x̄ =W (y − x̄)(yPi − x̄)+ Qk
2n i=1 i Pi
(24)
For the filtering step the calculations are analogical to those of the prediction step. The sigma
points are transferred based on the nonlinear measurement h().
yF = h(X F )(25)

In the same way the weighted mean value andthe VCM Qyy of the transferred sigma points are4

calculated. The cross-correlation matrix Qxy isdetermined here, too.
ȳF =

2n
X

Wm
i yF

(31)

and gyroscopes (e.g. (Wendel 2007) and (van der
Merwe and Wan 2004)).
As aiding absolute sensor a GNSS array consisting of four PG-S1 antennas and two MR-1
receivers on a quadratic platform was used. Thisnot only allows to aid the position and velocity
estimation but the orientation estimation, which
otherwise can not be controlled directly. The twoantennas connected to the same receiver were diametrically positioned, so that there was a lengthwise and a crossways pair. Furthermore, for theprocessing of the position, velocity and angular
output each pair was divided into a primary anda secondary antenna. The output of the receivercontains the position and velocity of the primary
and the internally calculated angle between bothantennas, which could directly be used as observed quantities.
Additionally, the precision of the systems was
examined to obtain a reliable stochastic modelfor the sensor fusion. To minimize the costs theuse of SAPOS-correctional data was omitted andinstead only single point code solutions were used.
Consequently, the position precision was determined to spos = 2.325 m. For the orientation measurements the output of the receivers was compared with laser tracker measurements. The orientation precision was determined to sΨ = 1.2016◦ .
The output rate of this absolute sensor system
was 10 Hz.

(32)

4.1 Prediction

(26)

i=1
2n

Qyy =

1 X c
W (y − ȳF )(yFi − ȳF )T
2n i=1 i Fi
(27)

Qxy =

2n
X

1
Wc (xFi − x̄F )(yFi − ȳF )T
2n i=1 i(28)

Parallel to the prediction the filtering takes
the measurement noise Qll as additive term into
account.
D = Qyy + Qll(29)

In contrast to the EKF the Gain matrix K is
calculated by multiplying the covariance matrix
with the inverse cofactor matrix of the innovation.
K = Qxy D−1(30)

The final calculation of the filtered state andthe filtered VCM are analogical to those of the
EKF.
x̂ = x̄ + K (l − A ȳF )TQx̂x̂ = Qx̄x̄ − KDK

4 Application
To minimize the cost for the system a MEMSIMU of the type SBG System IG-500E, with thespecifications as show in table 1 and a sample
rate of 20 Hz, was used.
Table 1 Specification of the IMU SBG IG-500E

Accelerometers Gyrocopes
dynamic range
inital bias
noise density± 5g± 5 mg √0.25mg/ Hz± 300 ◦ /s
± 0.5 ◦ /s√
0.05◦ /s/ Hz

The results of the factory-calibration were stored
inside and automatically used to correct the raw
measurements. Nevertheless since IMUs basedon MEMS designs show significant offsets during
use even after calibration, the state vector wasaugmented with the biases of the accelerometerTo fuse the measurements of these complimentary
systems an EKF as well as an UKF, both in aloosely coupled architecture, are used.
The EKF had the design of an error state filter as described in Wendel (2007) and therefore
estimates the errors produced through state estimation based on pure IMU measurements.
∆x = ∆p ∆v ∆Ψ ∆ba ∆bω
(33)
In contrast to that the UKF had the design of a
total state filter based on the nonlinear navigation
equations and estimates the wanted quantities
directly.

x = p v Ψ ba bω
(34)
While the estimation of the position and velocity in the UKF do not need special consideration,
there is a challenge in the selection of orientation
parameters and the modelling of the IMU error
characteristics with respect to the intended task.

5

A proper description of the platform’s orientation is given with quaternions. These have theadvantage that a singularity free description oforientations is guaranteed.
Following van der Merwe and Wan (2004) for
the total state UKF the nonlinear propagation
equation of the quaternions is used as1sin(s)
qk+1 = I cos(s) − Ω(ω) ∆t
qk (35)
2
s
with
1
2

s=

q
(ωx ∆t)2 + (ωy ∆t)2 + (ωz ∆t)2

(36)

and


0
1 
−ω
 x
Ω(ω) =
2 −ωy
−ωz

ωx
0
ωz
−ωy

ωy
−ωz
0
ωx


ωz
ωy 

−ωx 
0

(37)

Finally a model for the IMU errors has tobe chosen. In this paper it is modelled as random walk. Consequently the measurements are a˜ b , thesuperposition of the true measurements (.)
iboffsets b(.) and the GWN w(.) .
abib = ãbib + ba + wa

(38)

ω bib = ω̃ bib + bω + wω

(39)



p̄IMU − 21 (pGNSS1 + pGNSS2 )lEKF =  v̄IMU − 12 (vGNSS1 + vGNSS2 ) Ψ̄IMU − ΨIn case of the UKF the measurements are directly used in the observation vector l.

12 (pGNSS1 + pGNSS2 )(43)lUKF =  21 (vGNSS1 + vGNSS2 ) ΨAt first simulations based on artificial data of
a 7.6 km trajectory with variations in all orientational dimensions were carried out. Therefore
the error-free accelerations and gyroscopic measurements in the named respective output rates
were created and superpositioned with offsets asstated in tab. 1 and GWN as follows
σΨ = 1.5 ◦(44)

σv = 2.5 m/s(45)

σp = 2.5 m(46)

To judge the results they were transformed toa local topocentric coordinate system with the car
as origin as in Eichhorn (2005) with the lengthwise component lk, the crossways component qk
and the height component h (see fig. 3).
xk+1

4.2 Filtering
To be precise, the lever-arm lb between the GNSS
and the IMU must be taken into account by correcting the measurements of position and velocityof each main antenna according to equations (40)and (41). The corresponding lever-arms between
the main antennas and the case of the IMU were
determined with a laser tracker to be each 0.840 m± 0.002 m before the experiment took place.
pIMUi = pGNSSi − Rnb lbi
vIMUi = vGNSSi − Rnb (ω bib × lbi )(42)(Ỹ , X̃)k+2

lk k+1

qk k+1(Ỹ , X̃)k+1
d k+1(Ŷ , X̂)k+1(Ỹ , X̃)k
(40)
(41)

After relating the GNSS measurements to the
IMU the respective observation equations can begenerated. In case of the error state EKF, where
only differences between the prediction and themeasurements are processed, the corresponding
observation equation results from the differenceof the predicted states reduced by the averaged
measurements as follows.

yk+1
Fig. 3 Local coordinate system as proposed by
Eichhorn (2005)

The simulation showed, that the approach using the EKF resulted in a mean position deviationof dp = 0.796 m ± 0.876 m, while the approachwith the UKF yielded a mean position deviation dp = 0.699 m ± 0.536 m in post-processing.
Accordingly, a significant advantage of one algorithm over the other could not be detected. After6the successful simulations a practical experiment
was carried out.
The focus of this experiment was to test thesystem in a “high-kinematic” scenario to ensurethat both the sensors and the algorithms work
under extreme circumstances. Regarding thesimulations the difference were the tighter turns
with a partial curb turning raidus of only 10 m.
The gathered data was again analysed in a postprocessing step.
The reference trajectory was generated fromdata gathered by another multi-sensory system
consisting of a navigational class iMAR iNav
RQH-1003 IMU in combination with a dual band
GNSS receiver with carrier-phase based correctional data. It was processed with the commercial
software solution KingsPad and can be seen in fig.
4. As measurement equipment of superior category this solution has an deviation of ca. 0.002 m.

ϕ [m]

300
200

n
X
¯ lk = 1
˜ i − lk
ˆi
∆
lk
n i=1
v
u n
u1 X
rmslk = tv2
n i=1 lki

(47)

(48)

The tables 2 and 3 summarize the results.
Hereby it has to be mentioned, that the yaw angle
is intentionally not listed in the tables. This isdue to a problem with the mechanisation of thez-gyroscope, which led to an fluctuation rangeof the rms between 80◦ -100◦ in case of the unaided respectively between 10◦ -14◦ in case of the
aided orientation, without significant differences
between the chosen algorithms. It has to be underlined that in this case the reductions of therms is achieved through the use of additional observation information and not through the choiceof the processing algorithm. Apart from that thedimensions of the results correspond with thosefrom the simulations.
Table 2 Results of processing the field data using
the EKF

100
0deviation with corresponding root mean square(exemplary in equations 47 and 48) were chosen.

0

200
λ [m]

unaided ori.
¯
∆
rms

400

Fig. 4 Reference trajectory created with a navigational grade IMU, differential GNSS andprocessed with KingsPad

Due to the highly kinematic trajectory withvery tight turns the EKF diverges soon after thestart of the movement depending on the attitude
error at initialization. But because of the highupdate rate of the GNSS even initialization errorsof over 30◦ can still be compensated, but degrade
the navigation solution significantly. Therefore a“pre-zero“-epoch with adjacent averaging of themeasurements is required.
In contrast to that the UKF processes the data
successfully and is able to compensate even large
initialization errors in a minimum of time.
For an appropriate comparison and analysisof the proposed approach for each algorithm two
different cases were processed: On the one hand
without aiding through absolute orientation measurements and on the other hand with aiding. As
appropriate operating figures the mean positionlk [m]
qk [m]
h [m]
α
β

0.620
4.420
0.012

[◦ ]
0.1457[◦ ] −2.8932

0.449
2.083
1.131

aided ori.
¯
∆
rms
0.575
3.942
0.006

0.386
1.778
1.060

3.5769 0.2145
2.5899 −2.6715

1.6424
1.1711

Table 3 Results of processing the field data using
the UKF

unaided ori.
¯∆rms
lk [m]
qk [m]h [m]αβaided ori.
¯
∆
rms

0.724
0.782
0.053

0.449
0.565
0.289

0.675
0.563
0.045

0.500
0.477
0.289

[◦ ] −5.6236[◦ ] −3.4452

2.33921.16080.21310.10570.15030.1178In case of the unaided orientation it can beseen, that using the EKF results in inhomogeneous estimated position components, which is

7

30

30

20

20

[%]

[%]

10
0

0

10
0

1 2
[m]

[%]

(a) Histogram of ∆lk

0 1 2 3
[m]

60

60

40

40

[%]

[%]

shown by a considerable deviation in the crossways component qk. In contrast to that the UKF
provides a more homogeneous output regarding
the lengthways and crossways components.
In case of the additional aided orientation theaccuracy of the position estimations slightly improve for both algorithms. But more importantthe orientation estimations can be significantly
improved. For the EKF the effect mainly manifests in a reduced standard deviation, while anunexpected high estimation error of the crossways component qk still remains. This is caused
through an error in the initial point, which degrades the whole navigation solutions. In case of
the UKF the additional aiding of the orientation
manifests as an improvement of both the accuracy
and the precision.
One reason for this outcome is found in the
choice of the platform. By using a land vehicle thechanges in roll and pitch are quite small comparedto those in the yaw axis. Since the experiment was
conducted on a trajectory with many sharp turns
to ensure working algorithms, drastic changes
were detected by the yaw axis gyroscope. In
combination with the mechanical inconsistency
the detected errors occured.
As it can be seen in table 3, the use of the UKF
provides better results in post-processing. But aninspection of the associated histograms (figures
5 and 6) reveals that a normal distribution can
only be assumed for modelling the orientation
errors.

20
0

−1

0
[◦ ]

(a) Histogram of ∆α

1

20
0

−0.5 0 0.5[◦ ](b) Histogram of ∆βFig. 6 Histograms of the orientation errors for the
aided UKF result

5 Conclusion
To detect the locations in need of rehabilitation
in a time- and cost-efficient way with a position in the world coordinate system a direct georeferencing of the PPS is needed. As preliminary
stage a low-cost system was successfully developed, that enables direct referencing at any given
time through fusion of a GNSS array and MEMSIMU measurements. It could be shown, that with
the inclusion of the IMU as support for the GNSS
array the target of a lane precise positioning could
be achieved in more than 99 % of the time.
For the future development of this system, theassumption of normally distributed measurement
noise has to be replaced by correlated noise andshould be taken into account accordingly. Additionally, for the long-term objective of developing
an adequate geo-referencing of highest accuracy
for use with the PPS, changing the fusion architecture to a tight coupling, meaning a centralized
processing of the raw GNSS data in the form ofpseudoranging and doppler measurements, could
be a promising way of maxing out the potentialof the system. Furthermore, for higher accuracies, the MEMS-IMU has to be replaced with asuperior sensor and differential GNSS positioningor real time GNSS corrections need to be applied.

(b) Histogram of ∆qk

30

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