781
1 INTRODUCTION
Inland shipping is an important pillar of the European
transport system. Nevertheless, it needs to compete
with other modes of transport like road and rail
transport. In order to increase both efficiency and
safety of inland navigation, advanced driver assistant
functions are currently being developed. Two of the
most challenging phases of inland navigation are the
bridge passing and the passing of waterway locks. For
the entering of a waterway lock typically a vessel with
a width of 11.4 m and a length of 100 m (or even 200
m) needs to pass a 12 m wide lock chamber. This
results in very tight requirements for the
determination of position, heading and velocity of the
vessel. Bridge passing additionally yields to tight
requirements on the height determination, namely
10 cm [5].
In order to reach these accuracies, phase-based
positioning needs to be applied. One can distinguish
between relative positioning by means of RTK (Real
Time Kinematic) using correction data of a nearby real
or virtual reference station and absolute positioning
by means of PPP (Precise Point Positioning) using
corrections from a global network of reference
stations. PPP [20] enables accurate positioning for a
single receiver without the need for differential
techniques by modelling and correcting for the
different error sources. State-of-the-art algorithms
such as the Canadian Spatial Reference System Precise
Point Positioning (CSRS-PPP) of the Canadian
Geodetic Survey of Natural Resources Canada [17]
can be freely used to analyse measurements in
postprocessing and to have an accurate reference. On
the 20th of October 2020 it was upgraded to version 3
Development of Precise Point Positioning Algorithm to
Support Advanced Driver Assistant Functions for Inland
Vessel Navigation
C. Lass & R. Ziebold
German Aerospace Centre (DLR), Neustrelitz, Germany
ABSTRACT: Bridge passing and passing waterway locks are two of the most challenging phases for inland
vessel navigation. In order to be able to automate these critical phases very precise and reliable position,
navigation and timing (PNT) information are required. Here, the application of code-based positioning using
signals of Global Navigation Satellite Systems (GNSS) is not sufficient anymore and phase-based positioning
needs to be applied. Due to the larger coverage area and the reduction of the amount of correction data Precise
Point Positioning (PPP) has significant advantages compared to the established Real Time Kinematic (RTK)
positioning. PPP is seen as the key enabler for highly automatic driving for both road and inland waterway
transport. This paper gives an overview of the current status of the developments of the PPP algorithm, which
should finally be applied in advanced driver assistant functions. For the final application State Space
Representation (SSR) correction data from SAPOS (Satellitenpositionierungsdienst der deutschen
Landesvermessung) will be used, which will be transmitted over VDES (VHF Data Exchange System), the next
generation AIS.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 15
Number 4
December 2021
DOI: 10.12716/1001.15.04.09
782
and since then allows for ambiguity resolution for
data collected on or after 1st of January 2018.
For real-time application other methods have to be
applied. Here, the convergence time is of upmost
importance as we cannot wait an hour for the float
ambiguities to converge before beginning operation.
This can be achieved by PPP-RTK [19] which uses PPP
based on a network of local reference stations like in
RTK to derive the real-time corrections, so called State
Space Representation (SSR) correction data, of
individual error components like satellite clock and
orbit, tropospheric and ionospheric errors as well as
code and phase biases. Due to accounting for the
ionospheric delay, one can use the undifferenced code
and phase observations with true integer ambiguities
which can be fixed without requiring a long time to
converge [10]. This enables horizontal positioning
close to sub-cm level in a multi-GNSS scenario [9]. An
example of a nationwide PPP-RTK service is the
Centimeter Level Augmentation Service (CLAS) of
Japan’s Quasi-Zenith Satellite System (QZSS) which
provides corrections via QZS L6 signals. CLAS was
upgraded on the 30th of November 2020 with a new
atmospheric correction message.
Due to the fact that the service area is significantly
enlarged for PPP-RTK (100-1000 km) compared to
RTK (1-20 km) while also requiring a smaller data
rate, PPP-RTK is seen as the key enabler for highly
automatic driving for both road and inland waterway
transport. The project SCIPPPER (2018-2021) aims the
application of PPP-RTK for the automatic
entering/exiting of a waterway lock [13]. This is a pilot
project for the usage of SSR corrections provided by
the SAPOS (Satellitenpositionierungsdienst der
deutschen Landesvermessung) reference station
network. The correction data will be broadcasted by
using the new communication channel of VDES [6, 11]
(VHF Data Exchange System) – the next generation of
the AIS (Automatic Identification System). As the
decoding of the SSR corrections in the proprietary
SSRZ format [10] is in development, we will present a
PPP algorithm using methods which can also be
applied or easily adapted to the real-time PPP-RTK
case.
The paper is organised as follows: In section 2 we
discuss the driver assistant functions and their
requirement on the position, navigation and timing.
Afterwards, section 3 explains the associated system
design. In section 4 we describe the PPP algorithm
and will also put emphasis on accurate velocity
estimation. The algorithm is then applied to an inland
water measurement campaign which is disseminated
in section 5. The final section summarises the paper
and gives outlook to further activities associated with
the SCIPPPER project.
2 REQUIREMENTS ON PNT PROVISION FOR
DRIVER ASSISTANT FUNCTIONS
Unlike the maritime domain, where the requirements
for radio-navigation systems have been clearly
defined by the International Maritime Organization
(IMO) [11] [12], the navigational specifications for
inland waterway scenarios have not been addressed
by any international committee. Therefore, the
requirements for the provision of the position,
navigation and timing (PNT) data have to be derived
from the functional requirements of the different
driver assistant functions. In [5] this has been done for
assistant functions like the bridge-collision warning
system, automatic guidance and the mooring
assistant. For the automatic entering of a waterway
lock these requirements have been deduced in the
SCIPPPER project and shall be described here.
For the development of the requirements typical
dimensions of the waterway lock and the inland
vessel are assumed. In Figure 1 a true to scale sketch
of the lock chamber together with the inland vessel is
shown. The narrow gap between the vessel and the
lock chamber of ideally 30 cm on both sides is hardly
visible.
Figure 1. True to scale sketch of a typical lock chamber and
inland vessel (ship width: W = 11.4 m, ship length: L = 100
m, chamber width: 12 m)
The accuracy requirements for the provision of
position, velocity and orientation differ for the
different phases of an automated passing of a
waterway lock. At the beginning of the manoeuvre,
there is more space available for manoeuvres in the
outer harbour of the lock than at the time of the
manoeuvre when the vessel is fully inside the lock
chamber. In order to adapt the accuracy requirements
to the available manoeuvring space, the entry and exit
manoeuvres shall be divided into five phases as can
also be seen in Figure 2:
− Phase 1: Start of the manoeuvre in the outer
harbour, alignment of the position and orientation
of the vessel with the lock gate or the central axis
of the lock, approach in the direction of the lock
gate.
− Phase 2: Achieving the required position and
orientation accuracy before the actual entry into
the lock. If the accuracy is not reached at the end of
phase 2, an alarm is issued. The skipper must then
abort the manoeuvre and take over control
completely.
− Phase 3: Passing through the lock gate,
manoeuvring in the lock chamber, stopping the
ship.
− Phase 4: Exit from the lock.
− Phase 5: Manoeuvring in the outer harbour, taking
over of control by the skipper or stopping.
Figure 2. Schematic overview of the different phases of
passing a waterway lock
The resulting accuracies for the position, heading,
rate of turn (ROT) and velocity are summarised in
783
Table 1. The numbers have been derived by allocation
of the available space between the measurement
system and the control system with its actuators.
Table 1. Requirements on PNT provision for the different
phases of passing a waterway lock
_______________________________________________
Phase 1,5 Phase 2 Phase 3, 4
_______________________________________________
Horizontal positioning 10 1 (Bow), 1
accuracy [cm] 10 (Stern)
Heading accuracy [°] 11°/L(m) 11°/L(m) 0.5°/L(m)
L=100m 0.1° 0.1° 0.005°
ROT[°/min] 0.3 0.3 0.3
Velocity [cm/s] 1 1 1
_______________________________________________
The highest position accuracies of 1 cm are
required when the whole vessel (phase 3,4) or parts of
the vessel like the bow in phase 2 are in the lock
chamber. Here, the shadowing and multipath of
satellite signals by the up to 30 m high metallic walls
like in the locks in the Main Danube Channel, will
jeopardise satellite-based positioning. Therefore,
close-range sensors, like LIDAR, are required here on
bow and stern for local positioning in the lock
chamber. The focus of this paper lies in the pure
GNSS based PNT provision. The according
requirements for GNSS based positioning can be
found in the phases 1 and 5. Besides the high accuracy
of 10 cm for the position, also the tight requirements
for heading and rate of turn (ROT) and velocity need
to be mentioned. The required heading accuracy
scales with the length of the vessel and results in 0.1°
for a length of 100 m and 0.05° for 200 m. This is one
order of magnitude tighter than accuracies achievable
by state of the art GNSS compass systems used on
inland vessels so far. Due to the fact, that the
controller for rudder, engine and thrusters mainly
controls the very low longitudinal and transversal
speed at bow and stern the measurement accuracy of
the velocities is also of upmost importance. The
required 1 cm/s is a demanding target.
Table 2. Requirements for GNSS based determination of
position, height, heading and velocity for the different
assistant functions developed in the projects LAESSI [5] and
SCIPPPER [13]
_______________________________________________
Lock Bridge- Mooring Automatic
entering height assistance guidance
(GNSS warning
only)
_______________________________________________
Horizontal 10 20 10 30
positioning
accuracy [cm]
Height - 10 - -
accuracy [cm]
Heading 11°/L(m) 0.3° 0.07° 0.1°
accuracy [°] 0.1°
L=100m
Velocity 1 - - -
[cm/s]
_______________________________________________
Table 2 summarises the different requirements for
GNSS based PNT provision for the different driver
assistant functions. The most stringent requirements
concerning positioning of 10 cm arises from the lock
entering and the mooring assistance. As expected the
bridge height warning is the only assistant function
with tight requirements on the height. Due to the fact,
that for the lock entering not only the rudder angle
but also the engine and thrusters have to be steered it
is the only assistant function which requires highly
accurate velocity measurements. For all assistant
functions the heading accuracy is very important.
3 SYSTEM DESIGN FOR PNT PROVISION
Figure 3 gives an overview of the system design for
the driver assistance functions. It can be divided into
the three segments: i) shore side services, ii) onboard
systems and iii) the communication link. While this
paper focusses on the GNSS based PNT provision, for
reasons of completeness in the figure also the other
modules relevant for the driver assistant functions are
shown. These are the waterway information (mainly
from waterway locks) and the onboard system with
the control system together with the nautical display
and the closed range sensors.
Figure 3. Schematic overview of system concept for the
driver assistance function
3.1 Shore side service
For the GNSS based PNT provision the reference
station network of the Surveying Authorities of the
Laender of the Federal Republic of Germany is used.
For the surveyors they provide as a standard product
a network solution for the provision of virtual
reference station correction for RTK positioning. As a
pilot project in individual regions like Bavaria the
same reference station network is used to provide SSR
corrections to enable PPP positioning in the service
area. Transmission of SSR correction data requires less
capacity than RTK corrections and can be applied in a
larger region. Thus, this is the ideal candidate for a
broadcast service on a carrier with limited bandwidth.
The shore side service is complemented by Integrity
monitoring station and the server for shore side
services which sends the SSR correction data together
with the integrity information to the vessels by using
the communication link.
Unfortunately, the standardisation of all required
SSR correction within RTCM is still pending. Only
corrections for satellites clocks and orbits as well as
the code biases are described in the current RTCM
784
Standard 10403.3 in section 3.5.13. Therefore, the
standardisation of the corrections for the tropospheric
delay, the ionospheric delay and the phase biases are
not finalised yet. In the SCIPPPER project the
corrections are designed in the proprietary SSRZ
format [4] by Geo++ which is flexible and compact but
complex to decode. The content of the SSR correction
data will be described in more detail in section 4.
3.2 Communication link
For the communication the transmission capabilities
of the new VDE system (VDES) will be used together
with the mobile internet connection. One part of the
new VDE system is a high-speed data channel with
100 kHz bandwidth on the VHF transmission side.
This data channel will be used to broadcast PPP
correction data. Combining the high-speed data
channel with the reduced bandwidth requirements of
PPP may generate a precision navigation service that
has the potential to significantly enhance accuracy of
navigation on inland waterways.
3.3 Onboard systems
The onboard system for the GNSS based PNT
provision consists of a VDES transceiver together with
a mobile internet router for the reception of the SSR
correction data, a setup of two GNSS antennas +
receivers and an inertial measurement unit (IMU). The
two GNSS antennas will be placed on the bow and
stern respectively. This setup enables on the one hand
the realisation of the high heading accuracy which
scales with the length of the vessel. On the other hand,
it should help to improve the continuity of the
positioning while passing a waterway bridge.
Assuming a vessel with a length of 100 m the GNSS
antenna on the stern still receives signals from all
satellites while the bow antenna is under the bridge
and vice versa. The aim of the IMU is the provision of
a short-term backup mainly for the orientation
(heading) of the vessel but also for the positioning.
4 PPP ALGORITHM DEVELOPMENT
4.1 Problem formulation
For PPP we consider both code and phase
observations with regards to frequency fi and satellite
s.
( )
( )
( )
, 2 , ,
, 2 , , , ,
Φ
i s s s s i s i s
i s s s s i s i s i s s i s
R x x c t t T I
x x c t t T I A w
= − + − + + +
= − + − + − + + +
(1)
The variables are the receiver position x, satellite
position xs, speed of light c, receiver clock offset δt
depending on which GNSS satellite s belongs to,
satellite clock offset δts depending on satellite s,
tropospheric delay Ts, ionospheric delay Is, wave
length λi, phase wind-up w, integer ambiguity Ai and
the remaining errors εi,s, ϵi,s such as multipath and
receiver noise.
To fulfill the requirements derived in section 2 we
need precise satellite position information as well as
correction data for the different error sources
associated with the GNSS signals. For real-time
applications, we use SSR corrections [4] which consist
of
− Orbit corrections, every 30 s
− Clock corrections, every 5 s
− Ionosphere and troposphere delays, every 30 s
− Code and phase biases, every 30 s
The orbit and clock corrections refer to a specific
broadcast ephemeris and are given as coefficients of a
linear (orbit) and a quadratic (clock) polynomial,
respectively. The issue of data of the broadcast
ephemeris (IODE) can be found in the header of the
orbit correction.
The SSR messages also contain an epoch time (GPS
seconds of week or GLONASS seconds of day) and an
update interval which define the optimal time frame
the corrections should be applied. First tests showed
that the corrections are received with a positive delay.
Hence, old corrections, i.e. the time of application
does not lie in the optimal time frame, have to be
applied. This necessitates managing the corrections as
well as the broadcast ephemeris they refer to. Also, a
warning flag should be given if the correction is
considered too old so that the observation can be
downweighted or even discarded.
As the decoding for the compact but complex
SSRZ format [4] is in development, a postprocessing
PPP algorithm was developed which can be used or
adapted to the real-time case. Hence, all methods
derived here are with real-time application in mind
and will use as little postprocessing knowledge as
possible.
The following corrections are used in our
algorithm:
− Precise satellite orbits and clocks from final
products (IGS, GFZ)
− Satellite antenna phase center offset and variation
(IGS)
− Tide displacements caused by sun and moon
− Phase windup
For postprocessing we use the ionosphere-free
linear combination of (1) and separate the
tropospheric delay into the dry (hydrostatic) and wet
zenith delay Zh, Zw. The zenith delays are used in
conjunction with Vienna mapping functions mh, mw [2]
which depend on the elevation of satellite s, the
receiver position and the time. All in all, we have:
(2)
Note that the first equation defines the operator for
the iono-free linear combination which is applied to
the different terms. The dry zenith delay is computed
using the receiver position whereas the wet zenith
delay is estimated in the Kalman filter.
785
The Kalman state X consists of the receiver
position x, velocity v, receiver clock offset cδt, receiver
clock drift
ct
, wet zenith delay Zw and the float
ambiguities (λA)IF. We assume a constant velocity and
constant clock drift for the state transition. With NG
being the number of GNSS and NA the number of float
ambiguities, this can be summarised as:
( )
( )
33
3
1
GG
G
A
t
t
t
NN
tt
t
N
t
w
N
IF
x
II
I
v
II
ct
X F X
I
ct
Z
I
A
+










==










(3)
We included the clock drift since it is a by-product
of the velocity estimation described in subsection 4.2
and also allows for accurate prediction of receiver
clock offset as the drift is quite stable over time.
Furthermore, this can be used to have an accurate a
priori estimate of the receiver clock offset even in case
of a clock jump. For our JAVAD DELTA-3 and
TRIUMPH-1M receivers the clock offset can have
values up to ± 0.5 ms. If a clock jump is detected an
accurate a priori clock offset can be obtained as
follows:
0.001 s 0.001 s
t t t
c t c t c t c c t
+
= + −
A receiver clock jump is detected by comparing the
a priori estimate to either an SPP solution or by
calculating a least squares fit of the clock offset from
the a priori Kalman state and the code observations.
Here, it is assumed that the position change and the
sum of all the other errors is far less than 300 km
which is the approximate size of a clock jump.
Figure 4. Histogram for difference of a priori and a
posteriori clock offset for a 24 hour measurement campaign,
1 Hz, median receiver clock drift of about -692.86 m/s
In Figure 4 we can see that epochs with clock
jumps (red bins) have a similar Gaussian white noise
behavior with regards to the difference of a priori and
a posteriori clock offset as all the other epochs (yellow
bins) if the clock drift is considered. If the clock drift is
not considered (blue bins), the difference will not
have a mean of zero in epochs with a clock jump. As
the estimates using (4) are as good as the a priori
estimates in epochs without a clock jump, a reset of
the uncertainties of the clock offset for the Kalman
state is not needed.
4.2 Considerations for accurate velocity estimation
As described in Table 2 of section 2, we have tight
requirements on the GNSS based position as well as
on the velocity when entering a waterway lock. To
guarantee a high accuracy in the velocity estimation as
well as having a low uncertainty in the Kalman Filter
which can then be used for the automatic steering,
further thoughts have to be put into the velocity
determination.
If we derive the velocity just by using the Kalman
Filter as described in (3), the uncertainty of velocity
will mostly depend on the trust in the state-transition
model with regards to position and velocity. This has
the disadvantage that if the velocity changes from one
epoch to another, then the a priori estimate will be off
and if additionally, too much trust is put into the
state-transition, the a posteriori velocity will be off as
well. On the other hand, if we put little trust into (3),
then the uncertainty of the velocity in the Kalman
filter will always be high regardless of its actual
accuracy which would imply that the automatic
steering cannot trust the PPP velocity.
Another way to estimate the velocity is using
Doppler measurements which have an accuracy of a
couple of cm/s [14], i.e. worse than the accuracy
derived by (3) in case the constant velocity
assumption holds. Nonetheless, it has the advantage
of estimating instantaneous velocity without requiring
any information from previous epochs. Therefore, we
use them to have an a priori estimate of the velocity
and clock drift in the first epoch or in case of a full
reset of the Kalman filter. Otherwise, they are not
used in our algorithm at all.
A third method are the time-differenced carrier
phase measurements (TDCP) [3] which allow for
calculating the relative change in position between
two epochs. They are known [14] to have an accuracy
of less than 1 cm/s without having to determine the
ambiguities of the phase observations as long as they
are constant for the two epochs considered. Therefore,
cycle slip detection is of upmost importance as phase
observations with cycle slips must be discarded for
the computation of the TDCP and in the Kalman filter
as well. As cycle slip detectors we use the Melbourne-
Wübbena linear combination [1] and the geometry-
free linear combination [15].
22
,,
2 2 2
22
2
ΦΦ
tt
tt
t t t
i s i s
s
s
t
tt
s
xx
v v c t
ct
xx




++
++
+ + +
++

−
−

− +

−

−
(5)
Note that (5) is abbreviated and also includes the
time difference for the satellite clock offset, the
tropospheric and the ionospheric delay from (1). For
the delays we use the models from Saastamoinen [12]
and Klobuchar [7]. In the real-time application the
appropriate SSR corrections will be used. In case a
receiver clock jump occurs, ± c⋅0.001 s has to be added
in the nominator on the left-hand side of (5). Should
computation time be a critical point in the real-time
application, we found that it suffices to use linear
interpolation to estimate the intermediate satellite
position xs and velocity vs without having a significant
786
impact on the accuracy. The unknown receiver
velocity v and clock drift
ct
are calculated using a
weighted least squares fit with the weights being the
inverse of the sum of the noises of the phase
observations in the Kalman filter divided by the time
difference of the epochs.
( )
( ) ( )
2
,
22
100
sin sin
t
TDCP s
ss
ct
tt

−−
−
=
++
Here, αs(t) is the elevation angle of satellite s at
time t. For GLONASS satellites the weights are
divided by five. The weights imply that the values
derived from (5) depend on the sampling frequency
and will be worse with higher sampling frequency.
On the other hand, the approximation error of the
constant velocity model (3) will decrease. The optimal
sampling rate is up for discussion which has to
consider the requirements of the automatic steering.
The accuracy of the TDCP with regards to the
sampling frequency will be examined in section 5.
Once computed the a priori state estimates for the
Kalman filter are as follows:
2
2
2
2
t
tt
t
t
t
tt
t
t
x x v
vv
c t c t c t
c t c t
+
+
+
+
+
+
+
+
=+
=
=+
=
(7)
Figure 5. Histogram for difference of a priori and a
posteriori clock offset for a 24 hours measurement
campaign, 1 Hz, with and without TDCP
As can be seen in Figure 5 the inclusion of TDCP in
the state-transition allows for a more accurate
prediction of the clock offset which decreases the
noise of the a priori residuals. This can be helpful in
detecting outliers or cycle slips in the phase
observations. Note that Figure 4 was produced
without using those new a priori values based on
TDCP.
5 RESULTS
For a measurement campaign associated with the
SCIPPPER project a vessel, the MS NAAB in
Regensburg as displayed in Figure 6, was equipped
with two antennas which were connected to a JAVAD
DELTA-3 and a JAVAD TRIUMPH-1M receiver. Note
that for this campaign the antennas were not mounted
at the stern and bow of the vessel. In future
measurement campaigns of the project it is planned to
mount the antennas as described in section 2.
Furthermore, RTCM SSR corrections were recorded
which can later be used for the real-time algorithm
development. As explained in section 4, in the
following final products are used for the
determination of precise satellite clock and orbits in
our PPP algorithm. Unless stated otherwise we use
observations from GPS, GLONASS and Galileo.
Figure 6. MS NAAB with two GNSS antennas (red circles)
mounted on top
As a first accuracy test, we check the position
difference of our postprocessing algorithm and the
Canadian service in a quasi-stationary environment,
that is the vessel was attached to a small pier as
depicted in Figure 6. Therefore, the position is not
fixed as there is influence from the current, the water
level and the wind. As a reference we took the
position calculated by the Canadian Spatial Reference
System (CSRS) Precise Point Positioning service [17]
at 4 a.m. and compare it to positions calculated
between 0:00 and 4:00. The results can be seen in
Figure 7.
Figure 7. Portside antenna position difference with regards
to CSRS position at 04:00, Regensburg, 25th of September
2019; Right-hand side: Zoom in of East component between
2:00 and 2:30 marked by black ellipsis on left-hand side
With regards to convergence we can see that it
takes about 12 minutes in the East and 23 minutes in
the North component until we have an estimated
accuracy of less than 10 cm. The Up component takes
about 51 minutes to reach the same levels of accuracy.
In both algorithms we observed the same current
motions in the East and North component starting
from 1:40 a.m. which are emphasised on the right-
hand side of Figure 7 though there seems to be a slight
787
offset of a couple of cm in the North and partially the
East direction between the two PPP methods. In
general, once the floating ambiguities have converged
the results are at an acceptable level and lie in the
requirements as mentioned in section 2.
Figure 8. Baseline length of the two antennas in Regensburg
campaign in the first four hours of 25th of September 2019;
Standard deviation calculated for baseline between 1:00-4:00
As the vessel was equipped with two antennas, we
can do an integrity test by comparing the baseline
between the antennas. As a reference we used the
RTKLib [16] software package in the differential
”Moving-Base” positioning mode. In Figure 8 we can
see that after about 45 minutes the baseline length
derived from the PPP algorithms are quite similar
though our method has a slight offset compared to the
RTKLib reference and calculates a longer baseline
length. In both methods the root-mean-square error
(RMSE) with regards to the median solution from
RTKLib considering all epochs between 1:00 and 4:00
is less than 2 cm. Therefore, both methods show a
sufficient accuracy. The higher RMSE and variance of
our postprocessing algorithm can be explained by the
use of the iono-free linear combination which is
known to increase the noise of the code and phase
observations [15]. Furthermore, we only estimate float
ambiguities instead of the integer ambiguities of (1)
which can be fixed by introducing phase biases and
using algorithms such as the LAMBDA method [18].
Furthermore, as our algorithms are developed with
real-time application in mind, we cannot use methods
such as a backward Kalman Filter which would help
in finding cycle slips as well as improving the results
in the first hour.
Figure 9. Position difference with regards to RTK reference
of starboard antenna, 25th of September 2019
The second scenario considered is a dynamic one
where the vessel is leaving the pier. As a reference we
used Real Time Kinematic (RTK) by taking
observations from a virtual reference station
computed from several IGS stations which is two
kilometres away from the position of the vessel at
5:00. The MS NAAB then moves in the direction of the
reference station. We can see in Figure 9 that there is
only a couple of a cm difference between the two PPP
methods with our algorithm being closer to the RTK
solution in the East component whereas the Canadian
service is better in the North component. Note that the
calculation started prior to 5 a.m. to allow our PPP
algorithm to converge.
Figure 10. Left-hand side: Velocity of starboard antenna,
25th of September 2019; Right-hand side: Difference to
velocity derived from RTK Position
Besides the position, the velocity is of high interest
for the advanced driving assistance functions. Figure
10 shows the velocity in East (E), North (N), Up (U)
for the dynamic scenario. We can see that the TDCP
derived velocity is closer to the RTK solution than the
one calculated from the Doppler measurements
regardless whether we have a quasi-stationary or a
dynamic scenario. Note that in the JAVAD receivers
the Doppler smoothing bandwidth was set to 3 Hz
which is the default value to avoid noisy velocity
without having latency problems [8]. If we take a look
at the velocity in the up direction on the left-hand side
of the figure, the TDCP velocity is quite close to the
RTK solution and it can be difficult to deduce what is
the better solution of the two. To make a more
accurate assertion of the accuracy, we will consider a
static scenario where we have a reference velocity in
all directions of zero.
Figure 11. RMSE of Doppler and TDCP derived velocity for
different sampling frequencies, 28th of August 2019,
Neustrelitz
As a stationary scenario we used the GNSS
measurements of an antenna which was mounted on
the roof of the Institute of Communication and
Navigation of the German Aerospace Center (DLR) in
Neustrelitz, Germany. To consider different sampling
frequencies, the measurements were downsampled
from 2 Hz to 1 Hz, 0.5 Hz, 0.2 Hz and 0.1 Hz. The
results of three hours of data can be seen in Figure 11
788
and Table 3. To make a fair comparison between the
different sampling frequencies we only analysed the
results of the common epochs, i.e. the measurements
of every 10 seconds.
Table 3. RMSE of 3d velocity [mm/s] with regards to
different sampling frequencies, 28th of August 2019,
Neustrelitz
_______________________________________________
0.1 Hz 0.2 Hz 0.5 Hz 1 Hz 2 Hz
_______________________________________________
Doppler 13.25 13.25 13.25 13.25 13.25
TDCP 2.00 2.19 2.72 3.66 5.96
_______________________________________________
We can see that the accuracy of the TDCP velocity
is far better than the one derived from the Doppler
measurements, especially for low sampling
frequencies, and it seems to scale linearly with the
sampling frequency with regards to the RMSE of the
different ENU velocities. The Doppler results are the
same for all epochs as the calculated velocity is
instantaneous and does not depend on prior data and
the time between epochs like the TDCP. While we do
not have a reference at millimetres-per-second-level
for the dynamic scenario shown in Figure 10, we are
confident that the accuracy of the TDCP derived
velocity is in the same regime as the algorithms used
for both scenarios are identical. All in all, the time-
differenced carrier phase measurements provide an
accurate way to estimate the a priori velocity in a
Kalman filter without requiring the convergence of
ambiguities as long as we are able to detect cycle slips.
6 CONCLUSIONS AND FUTURE WORK
In this paper we presented the current status of our
PPP algorithm which will be used for advanced driver
assistance functions for inland waterway navigation.
Here, the focus was on the bridge height warning
system and the automatic passing of a waterway lock
which lead to very stringent requirements on
determination of position, orientation and velocity of
the vessel. The requirements were deduced in the
paper and overall system concept was described. The
currently developed PPP algorithm, which is in detail
described in the paper, shows an acceptable accuracy
of the horizontal position of 10 cm which lies within
the requirements of the driver assistant functions but
the convergence time needs to be improved for real-
time application. This will be done by using real-time
SSR corrections which also allow for fixing the integer
ambiguities. Besides the position, we have shown a
highly accurate way to determine the velocity of the
vessel at a millimetres-per-second-level even without
knowing the ambiguities which, apart from the
position and heading, is crucial for entering a
waterway lock. We aim to conclude the development
of the real-time PPP algorithm and also plan to fuse
GNSS with IMU data which can help with potential
GNSS errors or outage when passing a bridge.
As the next step within the project SCIPPPER the
individual technology developments need to be
finalised. These are the global PPP based positioning,
the local positioning by using LIDAR, the automatic
steering of the vessel and the new communication
channel by using VDES. Finally, the system will be
tested and validated with all components working
together and a demonstration (see [13]) of the full
system on the Main-Danube channel will be
organised.
ACKNOWLEDGEMENTS
The authors would like to thank all project partners within
the project SCIPPPER which are Argonics GmbH, ArgoNav
GmbH, Alberding GmbH, Weatherdock AG, Federal
Waterways Engineering and Research Institute (BAW) and
the Federal Waterways and Shipping Administration for the
fruitful collaboration within the project. Furthermore, we
thank the crew of the MS NAAB for their support during
the measurement activities. We also thank SAPOS and
GEO++ for the provision of the SSR correction data.
This work was partially funded by the German Federal
Ministry of Economic Affairs and Energy (grant number
03SX470E).
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