CC BY
97
УДК [528:629.78]+519.688
РАЗРАБОТКА МУЛЬТИСЕНСОРНОЙ СИСТЕМЫ ДЛЯ ОПТИМИЗАЦИИ ОПРЕДЕЛЕНИЯ МЕСТОПОЛОЖЕНИЯ ГИДРОГРАФИЧЕСКИХ СУДОВ
Марк Брайтенфельд
Федеральный институт гидрологии, Кобленц, Ам Майнцер Тор. 1, D-56068 Кобленц, Германия, магистр, тел.: +49 (0261)1306-5285, e-mail: breitenfeld@bafg.de
Аннетте Шайдер
Университет Штутгарта, Институт инженерной геодезии, Гешвистер-Шолль-Штрассе, 24D, D-70174, Штктгарт, Германия, тел.: +49 (0711) 6858-4057, e-mail: annette.scheider@ingeo.uni-stuttgart.de
Фолькер Швигер
Университет Штутгарта, Институт инженерной геодезии, Гешвистер-Шолль-Штрассе, 24D, D-70174, Штутгарт, Германия, доктор наук, профессор, директор института, тел.: +49 (0711) 6858-4044, e-mail: volker.schwieger@ingeo.uni-stuttgart.de
Харри Вирт
Федеральный Институт гидрологии, Ам Майнцер Тор. 1, D-56068 Кобленц, Германия, магистр, тел.: +49 (0261) 1306-5232, e-mail: wirth@bafg.de
Точное позиционирование важно не только для наземных транспортных средств, но и судов. В гидрографии позиционирование гидрографических судов должно выполняться с высокой точностью. В настоящее время приемники GNSS преимущественно используются для определения пространственного положения этих судов во внутренних водных путях Германии.
Среди источников ошибок, влияющих на доступность и точность GNSS измерений, наиболее серьезными являются затенение, рефракция и многопутность. Поэтому потери сигнала ГННС или помехи сигнала приводят к погрешностям измерений. Такие погрешности возникают особенно в регионах с прибрежной растительностью, в долинах с крутыми склонами, внутригородских застройках и под мостами. Целью проекта «HydrOs» является поиск наилучшего решения проблем позиционирования: положения будут определяться более надежным способом и в непрерывном режиме и в итоге будет достигнута точность в пределах нескольких дециметров. Кроме того, система позиционирования должна обеспечить достоверную и целостную информацию. Таким образом, все доступные датчики на борту судна, которые будут задействованы, и еще другие дополнительные датчики будут интегрированы в мультисенсорной системе. Планируется разработка методов, отслеживающих движение судов в пространстве. Динамическая модель движения, которая объединит несколько датчиков, будет использоваться вместе с расширенным фильтром Калмана (EKF). Все доступные наблюдения с заданным уровнем точности будут проходить через фильтр. Движение корабля описывается вектором состояния, который включает трехмерные координаты исходного пункта, пространственное положение судна, скорость и угловую скорость. Сам процесс фильтрации будет поддерживаться с помощью гибкого алгоритма, который автоматически будет распознавать погрешности во входных данных.
Ключевые слова: мультисенсорная системы, фильтр Калмана, кинематическое позиционирование, навигации.
DEVELOPMENT OF A MULTI-SENSOR SYSTEM TO OPTIMIZE THE POSITIONING OF HYDROGRAPHIC SURVEYING VESSELS
Marc Breitenfeld
Federal Institute of Hydrology, Koblenz, Am Mainzer Tor. 1, D-56068 Koblenz, Germany, M.Sc.
phone: +49 (0261) 1306-5285, e-mail: breitenfeld@bafg.de Annette Scheider
Universität Stuttgart, Institute of Engineering Geodesy, Geschwister-Scholl-Str. 24D, D-70174, Stuttgart, Germany, phone: +49 (0711) 6858-4057, e-mail: annette.scheider@ingeo.uni-stuttgart.de
Volker Schwieger
Universität Stuttgart, Institute of Engineering Geodesy, Geschwister-Scholl-Str. 24D, D-70174, Stuttgart, Germany, D. Prof., Director, phone: +49 (0711) 6858-4044, e-mail: volker.schwieger@ingeo .uni - stuttgart.de
Harry Wirth
Federal Institute of Hydrology, Koblenz, Am Mainzer Tor. 1, D-56068 Koblenz, Germany, M.Sc.
phone: +49 (0261) 1306-5232, email: wirth@bafg.de
Precise positioning is important not only for land based vehicles but also for vessels. In the field of hydrography the positions of surveying vessels must be known with a high accuracy. Currently, GNSS receivers are predominantly used to determine the three dimensional position of surveying vessels on German inland waterways.
Availability and accuracy of GNSS positions are influenced by shadowing, refraction, and multipath effects. Thus, the GNSS signal loss or disturbance results in measurement gaps. These gaps occur especially in regions with riparian vegetation, in valleys with steep slopes, intraurban, and under bridges. The project "HydrOs" focuses on the improvement of the positioning solution: The position shall be determined reliably and uninterrupted and at the end of a GNSS gap still with an accuracy of a few decimetres. Moreover, the positioning system shall provide reliable integrity information. Therefore, all available sensors on board of the vessel which might contribute and more sensors shall be integrated in a multi-sensor system.
In the project methods describing the vessels motion in space shall be developed. The dynamic motion model that integrates several sensors is put into effect with an extended Kalman filter (EKF). All available observations with a specified accuracy level are integrated into the filter. The ship motion is described by the state vector which comprises the three dimensional coordinates of a defined reference point, the attitude of the vessel, the velocity, and angular velocity. The filtering process itself will be supported by a flexible algorithm which recognizes automatically gaps of the incoming data.
Key words: Multi-Sensor System, Kalman Filter, Kinematic Positioning, Navigation. 1. PROBLEMS AND OBJECTIVES 1.1Research Issue
One of the main tasks of the Federal Waterways and Shipping Administration (WSV) is to guarantee safety and ease of navigation. Therefore, the acquisition of geospatial data such as shape and depth of inland waterways is essential. These information allow mariners a safe navigation and to calculate the optimal load in
shallow waters. To capture these topographic data, surveying vessels are equipped with multibeam echo sounders. The data captured by the echo sounding systems are georeferenced, processed, and plotted in accurate and reliable charts and maps of the waterways.
Currently, Global Navigation Satellite Systems (GNSS), consisting of the American Global Positioning System (GPS) and the Russian Globalnaja Nawigazionnaja Sputnikowaja Sistema (GLONASS), are used to determine the three dimensional position of the vessel respectively the echo sounder. The GNSS signals are measured and evaluated in Real Time Kinematic (RTK) mode. Thereby, correction data from reference stations are transmitted to the ship receiver and the ambiguities are resolved with special "On-the-fly" algorithms. So the accuracy can be specified to a few centimetres (WANNIGER, 2003). In shadow free areas the reliability, availability, and accuracy of the GNSS positions are satisfactory with long term stability.
Especially in regions with riparian vegetation, in valleys with steep slopes, intraurban, and under bridges the GNSS positions are influenced by shadowing, refraction, and multipath effects. Presently, implausible changes in the positions are not detected and measurement gaps are closed with linear interpolation. Certainly, the interpolation is insufficient because driving dynamics within larger gaps are not considered. Furthermore, the accuracy just before the gaps is inadmissible and unobservable, because the GNSS receivers do not reliably detect the reduced quality.
Alternatively, land-based positioning systems like motorized tachymeters are still used to get accurate positions in the critical areas. However, this sumptuous alternative is time consuming and less efficient. The "HydrOs"-System shall replace this technique.
1.2 Objectives
Due to the positioning problems with GNSS in shadowed areas, it is necessary to draft and develop improved systems and/or substitute methods for real time, post processing, and analysis. Thus, the department M5 (Geodesy) of the Federal Institute of Hydrology and the Institute of Engineering Geodesy of the University of Stuttgart launched the project "HydrOs - Integrated Hydrographical Positioning System" (see, Figure 1). The aim of the project is to develop an integrated system consisting of several sensors (multi-sensor system). In case of GNSS signal loss other sensors measuring independently the attitude and speed of the vessel replace the positioning with GNSS e.g. an Inertial Measurement Unit (IMU) and a Doppler Velocity Log (DVL). Furthermore, the additional sensors improve the accuracy, reliability, and integrity of positioning.
GNSS bow
GNSS stern
Seapath 330+
IMU
GNSS-compass
GNSS centre
DVL
Barometer
Tachymeter
Wind sensor
Propeller angle
Propeller revolution
HydrUs
Integriertes hydrographisches
Data acquisition Data storage Integrated Real time positioning Post processing Integrity key indicators Graphics
Model parameters
Coordinates, velocities,
Water level & flow velocity
■ I I -
Squat
Figure 1: Sensor integration and data flow
The theoretical basis for the data evaluation of a multi-sensor system is the Kalman filter (KALMAN, 1960) which is particularly used in navigation problems (WELCH & BISHOP, 1997). The vessels motion in space is described by a dynamic motion model. The dynamic forces which change speed and direction of the vessel shall be determined by measuring the revolutions (rpm) and orientation of the rudder propeller. Moreover, further regulating quantities like apparent wind and flow velocity can be included in the dynamic model (see, Scheider & Schwieger, 2014). In addition to the Kalman filter a forward-backward smoother (e.g. a RTS-Smoother, RAUCH ET AL., 1965) for post processing applications shall be implemented.
The sensor observations, the hydrological surrounding conditions, and algorithms shall be combined into the prototype software "HydrOs", which is designed for calculating continuously a filtered position with an uncertainty for the height of one decimetre (95% level of confidence) and for the coordinates of three decimetre (95% level of confidence), when the GNSS signal is lost up to 60 seconds. The system integrity information and accuracy information shall be permanently available and represented by user friendly key indicators.
2. SYSTEM DESIGN
In the following chapter the utilised sensors, the use of additional hydrological information, and the integration in the system will be described in more detail. Furthermore, the developed software prototype is shown.
2.1 Integrated Sensors and Models
At the bow and at the stern of the vessel two dual frequency GNSS receivers (SPS855 receivers from Trimble with GA810 antenna types) were installed (see, Figure 2). The output frequency is 10 Hz and the output data formats, as usual in the maritime sector, are NMEA type messages (GGA, VTG, GSA, and GST). This alignment of the GNSS receivers reduces the problem of insufficient GNSS positioning under bridges in some cases: If the bow receiver signal is lost,
sometimes the stern receiver still has an accurate position, and vice versa. This is no solution to the general problem of shadowing, because it only works under very small bridges and for signal losses lasting only a few seconds. The third positioning system, Seapath 330+, is an integrated loosely coupled INS-GNSS system. The system combines inertial measurements (MRU 5+: angular rates and accelerations) and two dual frequency GNSS (GPS-702-GG from Novatel) satellite signals. Output variables are raw angular rates and processed respectively filtered orientation angles (roll, pitch, and heading), horizontal and vertical velocities, three-dimensional coordinates, and heave of the vessel. The Seapath 330+ processes a position solution even if the GNSS signals fails. In the absence of GNSS the positions are calculated with dead reckoning based on the inertial sensor only. Unfortunately, these positions are only short term stable for a few seconds because inertial sensors show drift effects after a short time due to numerical integration (WENDEL, 2007). HENTSCHINSKI & WIRTH (2012) have analysed INS-GNSS coupled systems with the result that these systems do not meet the desired requirements.
To optimize the positioning in GNSS shadowed areas, it is conducive to use a velocity sensor to stabilize the position based on the inertial sensors. A Doppler Velocity Log (DVL) provides flow velocity and speed over ground (SOG) in all three dimensions. Basically, the DVL measures the Doppler shift between transmitted sound at a fixed frequency and received backscatter echoes from small particles or plankton that float in the water respectively echoes from the seabed (cf. Teledyne RD Instruments, 2006). Especially, the SOG reduces drift effects. Therefore a DVL from Teledyne RD Instruments was mounted on the bow of the vessel (see, Figure 2). If the axes of the DVL device are not oriented very precisely according to the axes of the body fixed coordinate system of the vessel, large transversal deviations occur inside GNSS gaps always directing to starboard or port side. The true mounting error is determined by calibration and corrected by rotating the longitudinal and transversal velocity components. Furthermore, the measured speed over ground velocities by the DVL are influenced by bed load transport. The DVL adds the bed loads moving velocity to his speed over ground. Speed through water can be derived from the rpm and angle of the ships propeller. The analogue signals are measured by ammeter. Functional relationships between the amperage and the rpm respectively the velocity through water must be found. The same applies to the orientation of the propeller. Furthermore a wind sensor is installed, that measures the apparent wind velocity and direction. The SOG can also be determined by adding the computed speed through water, the velocity changes caused by wind and the flow velocity.
Although the directly measured SOG by the DVL or from other sensors like wind meter etc. derived SOG stabilizes the position solution, the system drift cannot be eliminated completely. Hence, it is intended to install more absolute positioning sensors which are not affected by signal shadowing. Currently, the suitability of tachymeters mounted on a moving platform is under investigation
Novate! GNSS
MRU 5+ (IMU)
|
| Seapath 330+ | r^si
Figure 2: Overview system design
Figure 3: Barometric heights measured with DIGIQUARTZ Drucktransmitter 1014 A, Co. PAROSCIENTIFIC by SCATTURIN (2013)
The height of the vessels waterline can be determined indirectly with the aid of hydrodynamic numeric models completed with information of the ships vertical movements. The hydrodynamic numeric models provide good approximations for the water level and flow velocity at the position of the vessel. The actual water level is computed by correcting the model water level with the model error. The model error is the difference between the actual height of the vessels waterline derived from the estimated height of the Kalman filter corrected by dynamic draught and heave and the model height of the vessels waterline. So the height of
the vessels waterline is computed by adding the model height, the model error, the dynamic draught, and the heave measured by the IMU.
The dynamic draught is called squat and depends on the ship velocity through water and the under keel clearance which both can be derived from the DVL raw measurements. In the project, investigations are carried out to determine the mathematical functional correlation between squat, speed through water, and under keel clearance for the vessel "Mercator" The resulting characteristic diagram shall be used to calculate the squat in real time.
2.2 Software Design
In Figure 4 the graphical user interface of the "HydrOs" software is shown. In the software application the user can handle the data acquisition by freely definable serial sensor interfaces. The interface parameters as well as the output data formats can be defined individually. So the source code must not be customised if sensors and/or data formats vary.
Figure 4: Graphical user interface of the "HydrOs" software
3. STRUCTURE OF THE KALMAN FILTER
Kalman (1960) developed the Kalman filter (KF) algorithm which represents a very useful and powerful filtering algorithm not only in navigation problems. The typical and characteristic feature of the Kalman filter is the combination of state equations (equations for predicting a future state based on the previous state) and measurement equations (the relationship between current measurements and the target state) (Welsch et al., 2000). Hence, the Kalman filter is a recursive algorithm with two components: system/state equation and measurement equation. The estimation is optimal, if system and measurement equations are linear and the random noise processes in both equation systems are normally distributed. In this context 'optimal' means unbiased estimation with minimal variance. Here, for all sensors white noise is assumed.
Particularly in the case of modelling vessel movements, linearity does not exist. For this purpose the extended Kalman filter (EKF) is used. Inside the EKF algorithm the system and measurement equations have to be linearized to get an approximated linear model. Usually, the equations are expanded into a Taylor series up to terms of first order (van der Merwe, 2004). In Figure 5 the algorithm of the EKF is shown schematically._
Figure 5: Schematic cycle of Kalman filter algorithm (according to WELCH & BISHOP, 1997)
In the time update the non linear function f (•) predicts the state vector xt+l depending on the estimated state vector xk at epoch k. It includes as parameters the regulating quantities and the process noise w;.. The noise process is considered purely stochastically. The Jacobi matrices Tt+1k and BA.+1 k contain the partial derivatives of the linearized function f (•) according to the state vector \k respectively the regulating quantities u, . Ct+1 ¿.contains the partial derivatives of the non-modelled disturbance w;.. These matrices as well as the covariance matrices Z
Xexs.k '
Zuu and Zw are used to calculate the
predicted covariance matrix Z—k+l.
In the measurement update the non linear function a(-) relates the predicted state vector xA.+1 to the current measurements 1A.+1 . Aa.+1 includes the derivatives of a(-) according to the state vector xA.+1. With weighted gain matrix Kt+1, the current measurements \k+l , and the predicted state vector xt+1 the state vector iA.+1 and its covariance matrix Ziii.+1 can be estimated. The precise equations of the EKF algorithm can be extracted e.g. from GELB (1974) or RAMM (2008). 3.1 Motion Model
In the following sections the dynamic motion model of the vessel is described. It is a uniform and linear motion modelled. In consideration of the regulating quantities the motion model is not final.
3.1.1 Coordinate systems and transformations
For a better understanding of the motion model Table 1 shows necessary definitions of used fundamental coordinate systems: the body reference frame of the vessel and the local level (LL) reference Frame. The LL system is true north oriented and horizontal. In consideration of the meridian convergence and the deviations of plumb line, the LL system is transformed to the Universal Transverse Mercator (UTM) system.
All variables being part of the motion model are labelled with upper indexes to specify the coordinate system in which the variable is defined (e.g. vB - velocity in the body frame). Upper indexes of angles
show the direction of rotation (e.g. (pBN : rotation from body system to LL system). The angular rates are additionally labelled with lower indexes (e.g. (oBm ). These indexes describe an angular rate of the body system related to the LL system.
The transformation between these two coordinate systems is described by the three fundamental rotations. The variables q>, 6, i// represent the three orientation angles between the body system and the LL system with the following positive rotational directions:
• X-Axis: Port side moves upwards,
• Y-Axis: Bow moves upwards,
• Z-Axis: Bow moves towards port side.
Table 1: Definition of coordinate systems
Body Reference Frame Local Level Reference System
Axes orientation X-Axis positive to Bow Y-Axis positive to Portside Z-Axis positive to Up/Mast X-Axis positive to East Y-Axis positive to North Z-Axis positive to Up
Notation X B X w
System Right-handed Right-handed
3.1.2 State equation
Most motion models for vessels in the literature are based on the Nomoto-model (NOMOTO ET AL.,
1957) that combines the rudder angle 8 and the angular rate coBBN _ about the Z-Axis to predict the
motion behaviour of the vessel. Some of these extended motion models are described in FOSSEN (2011) or ZIMMERMANN (2000). Nevertheless, all these models only predict the two-dimensional position of the vessel. But the basic idea can be easily transmitted in a three-dimensional prediction (see, Equation 1).
®BN,x,k+\
^ BN,y,k+\ —B
№ T3\! - Uil
VvVl
-TT BN
<Pk+1
e
N U
N k+l N k+l
N
<Pt" 1 sm(^r)tan(0r) cos«)tan «D
0 cos(^D - sin( q>fN )
k J VVJOVVi /""'V'-'A-
cos(éT)
Vt" 0 sm(^r)/cos(^) cos(^)/cos 0™)
+R:{v4nyrMn)-RMnY
(i)
a
a
a
a
a
a
t
fi t
>■ y
>■ y
a
a
a
a
a
a
v
v
y-'X
y y
y-'Z
yx
y y
a
a
a
a
a
a
OJ-V
Cll-V
^ /
^ /
a
a
a
a
a
a
—B
I /'>
V w
va
V
V..V
V..V
y
X-y
X
a
a
a
a
a
a
I <■)
V..W
V..V
v..v
V--X
y y
y--z
yX
yy
a
a
a
a
a
a
— B
I /'I
I I'l
V
V_V
V_V
* y
z y
z
BN
The model parameters a^. must be determined individually for each vessel (ZIMMERMANN, 2000).
Unlike in ZIMMERMANN (2000), here the transversal velocity component vBy is directly predicted (DAVIDSON & SCHIFF, 1946).
The estimated angular rates cbgN xl.,cbgN vl.,cbgNzk and orientation angles (pfN ,0kN ,i]/fN at time step
k are inserted to predict the angles , Q™, i/7B^ at epoch k +1, like it is described in Equation 1
(WENDEL, 2007). Thereby, the angular rates were transformed into the earth-fixed coordinate system. The same applies to the linear approximated position changes which are calculated using the estimated velocity components vyk, vByk, vyk .
In Equation 1 the rudder angle 8 is the only regulating quantity U; in the motion model. In the project it is investigated whether the integration of further regulating quantities (rpm, wind, and flow velocity) improve the system accuracy or not. In this case they shall be included in the vector Uk.
Finally, the disturbance variables must be defined. In general the time derivates of the state variables are the disturbances. Here the time derivates of the angular rates (angular accelerations) and the velocities (accelerations) are defined as disturbance variables. 3.2 Measurement equation
Next to the state equation the second essential component of the Kalman filter is the measurement equation. The final state vector xt+1 can only be estimated, if the predicted state vector xi+1 will be
updated with current observations lk+1. The observation vector depends on the available sensors (see, Section 0). Table 2 gives an overview about all planned observations. The measured heading y/fN must be adjusted for meridian convergence.
Table 2: Observations - "HydrOs": under the dashed line are regulating quantities, the marked observations are used here in the measurement equation (see, chapter 0)_
Observation
s-.BN S->BN S->BN
V.vJr+l>VvJr+l
z,k+1
V.vJr+l?VvJr+l
Z.A'+l
BN nBN „BN
FN NN UN
^ ,
.vv.A'+l
Sensor/Model
IMU
DVL
IMU
IMU
GNSS 1
Supported state variable
— BN —BN —BN y.-. • I " .. '. I " /. '. • I
VB vB
.v.A'+l' v.A'+l' z,k+1
T-.B
' n vB, ,
x.k 1 •> v.A'+l' z.A'+l
7Zbn
(Pk+1
nBN —BN
ük+l 'Vk+l
tN
F" N
UN vB vB
A'+l ? 1 .V.A'+l > 1 V.A'+l
El^NL.Ul^
k+1 ? k+1 ? xy, k+l
GNSS 2
tN
F" N
UN vB vB
U k+13 1 .V.A'+l? ' V.A'+l
T?N ATN tjN ~N
k+l ? k+l ? xy,k+1
GNSS 3
tN
FN Nl k+v.
UN vB vB
^ k+l> 1 .v.A'+l > 1 v.A'+l
^Zk+1' ^A'+l' Sk+1
Tachymeter
E,
A'+l
NN UN
Pk+l Iibar_
Barometer
U
k+l
U
A+l
hydrodynamic numerical model
ammeter
U
A-+1
motion model
1;»r..v.A'+l 3 VStr, v.A'+l 3 VStr,z,k+1
DVL
motion model
wind.xv.k I 1
? Y wind.
A'+l
wind sensor
motion model
B
N
N
N
N
4. Evaluation
Figure 6: Measurement drive in Duisburg - evaluated trajectory segments: None shadowed area (right
box) and shadowed area (left box)
4.1 Data Acquisition and Survey Area
To develop the software "HydrOs" and evaluate the dynamic motion model, real data were captured with the sounding vessel 'Mercator' on the Rhine in Duisburg-Homberg (see, Figure 6). The survey lasted approx. 20 minutes. During this time the vessel passed under bridges five times. Measurement gaps inside the GNSS positions up to 42 seconds are the consequence. Just before and after the gaps, the accuracy of GNSS measurements decreases. Currently these observations are not detected automatically. So implausible observations of the height components are the criterion to handle them manually. At the moment, algorithms for automatic detection are developed and implemented. The algorithms are based on measurements and quality parameters of the several GNSS receivers on the vessel. Information from bow and stern antenna are always compared to those from the centre antenna. Large differences indicate loss of GNSS position (KAUKER, 2014).
4.2 Evaluation
The measured data are processed with a simplified version of the motion model (Equation 1): Because the model parameters a^ have not been determined yet, the parameter matrix is replaced by an identity
matrix and the parameters ajg are set to zero. So the angular rates and the velocity components are modelled as constant variables and the regulating variable 8 was omitted.
For a first evaluation here only one absolute positioning sensor is used: the GNSS receiver at the bow of the vessel. The sensors tachymeter and barometer are not installed yet, and the height of water level from hydrodynamic models is not integrated because the dynamic draught of the vessel is currently unknown.
Accordingly, the observation vector lk+1 is represented by
I L^iV „BN B B B BN ¿jBN ,,,BN TTN T /0x
'k+l - C°zMl V*M1 VvMl VzMl Vk+l Uk+\ Vk+l Lk+1 ^k+l Uk+1 _ <2)
(see also, marked values in the first column of Table 2). Consequently, every state variable is measured directly when GNSS is available. If the GNSS signal is completely lost, the observation vector is reduced by the last three elements.
The measured data are evaluated by using the EKF algorithm. Because there is no reference trajectory, the filtered trajectory is compared to a smoothed trajectory. To smooth the positioning solution with the Rauch-Tung-Striebel (RTS) algorithm (HESSE, 2007 or RAUCH ET AL., 1965), in a second step the smoothed state variables are calculated backwards in time. The RTS algorithm uses the predicted and estimated state vectors, the appending covariance matrices, as well as the transition matrix of the forward
filter. Furthermore already smoothed state vectors are used. Therefore, the smoothing is based on duplicate prediction.
For evaluation, two segments of the complete trajectory have been chosen; each of them has a duration of 90 seconds. One section without any shadowing effects (see, Figure 6, right box) and another section with a measurement gap of 42 seconds for the GNSS positions (see, Figure 6, left box). The gap was extended manually to 60 seconds. By comparing the filter results with the measurements it can be judged if the
requirements are met. Here only the results of the state variables Ek, Nk (horizontal position) and especially Uk (height) are considered, because these are the most relevant parameters.
4.3 Results
To evaluate the results of the Kalman filter the filtered trajectory (EKF) is compared to the smoothed trajectory (RTS). For easier interpretation it is an appropriate action to consider the longitudinal lk,
transversal tk, and height hk deviation at each epoch k referring to the ship's body coordinate system
(see, Figure 7). Therefore the position estimated by EKF at epoch k is transformed on the corresponding body frame at the RTS-position.
Outside the gaps the filtered trajectory is compared with the GNSS trajectory. Figure 8 shows 90 seconds height time series in the non shadowed area (Figure 6, right box). Thus, the GNSS positions are available in the observation vector. It can be seen that the estimated heights (continuous blue line) follow the measured GNSS heights. The height differences between the raw GNSS and the filtered positions are invariably less than 3 cm and show no systematic effects like latency or drift. Furthermore the GNSS noise is reduced by 1-2 cm. The differences in the horizontal components are even smaller. The stochastic input variables shall be adjusted to define the level of filtering.
Figure 7: Longitudinal and transversal deviation (according to Eichhorn, 2005)
Figure 8: Height time series in none shadowed area
In Figure 9 (a) the height time series of the second section is shown (see also, Figure 6, left box). Here the behaviour of the filtered positions in areas with GNSS signal interruption is analyzed. The height deviations between the RTS-smoothed (continuous green line) and the filtered trajectory (continuous blue line) increase systematically linear in time. Figure 9 (b) illustrates exemplary this drift effect for all of the five GNSS gaps. The maximum height deviations at the end of all gaps vary from -12 cm to 14 cm.
711%10 1020 1030 1040 1050 1060 1070 1080 1090 1100 "°'%10 1020 1030 1040 1050 1060 1070 1080 1090 1100 Time [sec] Time [sec]
Figure 9: (a) Height time series in shadowed area. (b) Height deviations between the filtered and the
smoothed trajectory in shadowed area
The drift effects also occur in the longitudinal and transversal directions. Certainly, the maximum deviations between filtered and smoothed positions at the end of the gaps are significantly larger. The longitudinal deviations vary from -28 cm to 38 cm and the transversal deviations from -30 cm to 41 cm.
5. Conclusion and Outlook
In this paper the authors give an outline of the research issue and the objectives in the development project "HydrOs - Integrated Hydrographical Positioning System". The system design, the planned sensors and already used sensors are described and illustrated.
The results of a first investigation based on a simplified dynamic model and a reduced number of sensors show that the desired requirements (see, Section 0) are not yet fully met with these simplifications but they look promising. As indicator the deviations between the filtered and the smoothed trajectory are
considered. If the GNSS signal is lost up to 60 seconds, the longitudinal and transversal deviations arise up to 40 cm and height deviations up to 14 cm.
The full motion model (see, Equation 1) shall be implemented in the near future. Here the parameters e.g. atj that characterize the transmission behaviour between the angular rates and the velocities must be
determined by extensive field tests. Furthermore the model will be extended by more regulating quantities like wind and flow velocity if this improves the system accuracy.
With comprehensive Monte-Carlo-simulations SCHEIDER & SCHWIEGER (2014) came to the conclusion that a curve prediction model can improve the accuracy a little. The currently linear prediction model for the positions shall be used when the vessel moves straight ahead and will be replaced by a curve prediction model during manoeuvres. All described sensors and the hydrological parameters will be integrated in the filter. The sensor redundancies will further improve the accuracy and availability of the positioning system.
6. NOTICE
This paper is published in parallel in the Proceedings of 4th International Conference on Machine Control and Guidance in Braunschweig, Germany.
5 REFERENCES
DAVIDSON, K. S. M.., SCHIFF, L. I.: Turning and Course Keeping Qualities. Transactions of SNAME, Bd. 54, 1946.
EICHHORN, A.: Ein Beitrag zur Identifikation von dynamischen Strukturmodellen mit Methoden der adaptiven KALMAN-Filterung. DGK, Reihe C, Nr. 585, 2005.
FOSSEN, T. I..: Handbook of Marine Craft Hydrodynamics and Motion Control. Wiley & Sons, Ltd, Chichester, 2011.
GELB, A.: Applied Optimal Estimation. The M.I.T Press, Massachusetts Institute of Technology, Cambridge, Massachusetts and London, England, 1974.
HESSE, C.: Hochauflösende kinematische Objekterfassung mit terrestrischen Laserscannern. DGK, Reihe C, Nr. 608, 2007.
HENTSCHINSKI, M., WIRTH, H.: Untersuchung integrierter GNSS-INS-Navigationssysteme. Bundesanstalt für Gewässerkunde, Bericht BfG-1743, Koblenz, 2012.
KAHMEN, H.: Angewandte Geodäsie Vermessungskunde. Walter de Gruyter & Co, Berlin, 2006.
KALMAN, R. E.: A New Approach to Linear Filtering and Prediction Problems. Transactions of the ASME-Journal of Basic Engineering, 82 (Series D), pp. 35-45, 1960.
KAUKER, S.: Detektion von Ortungslücken bei kinematisch erfassten GNSS-Messdaten. Diploma thesis, Universität Stuttgart, not published, 2014.
LÜCK, T., KREYE, C., EISSFELLER, B., MEINKE, P.: Messung von Gleislagefehlern mittels Integration von DGPS und INS. 11. Internationale Geodätische Woche, 2001.
NOMOTO, K., TAGUCHI, K., HONDA, K., HIRANO, S.: On the steering Quality of Ships. International Shipbuilding Progress, Vol. 4, pp. 354-370, 1957.
RAMM, K.: Evaluation von Filter-Ansätzen für die Positionsschätzung von Fahrzeugen mit den Werkzeugen der Sensitivitätsanalyse. DGK, Reihe C, Nr. 619, 2008.
RAUCH, H. E., TUNG, F., STRIEBEL, C. T.: Maximum Likelihood Estimates of Linear Dynamic Systems. AIAA Journal, Vol. 3, No. 8, pp. 1445-1450, 1965.
SCATTURIN, R.: Barometrische Höhenbestimmung in einem hydrographischen Ortungssystem
(HydrOs). Bachelor thesis, Institut für Ingenieurgeodäsie der Universität Stuttgart, 2013.
SCHEIDER, A., SCHWIEGER, V.: Optimierung eines Multisensorsystems zur hydrografischen Positionsbestimmung. Ingenieurvermessung 2014, Wichmann, Heidelberg, 2014.
TELEDYNE RD INSTRUMENTS: Acoustic Doppler Current Profiler. Principles of Operation. A Practical Primer. 2006
VAN DER MERWE, R.: Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic StateSpace models. Phd thesis, OGI School of Science & Engineering at Oregon Health & Science University, 2004.
WANNIGER, L.: Virtuelle GPS-Referenzstationen für großräumige kinematische Anwendungen. ZfV,
3/2003, pp. 196-202, 2003. WELCH, G., BISHOP, G.: An Introduction to the Kalman Filter. Technical Report, Department of
Computer Science, University of North Carolina at Chapel Hill, 1997. WELSCH, W., HEUNECKE, O., KUHLMANN, H.: Handbuch Ingenieurgeodäsie. Auswertung
geodätischer Überwachungsmessungen. Wichmann, Heidelberg, 2000. WENDEL, J.: Integrierte Navigationssysteme: Sensordatenfusion, GPS undInertiale
Navigation. Oldenbourg Verlag, München, 2007. ZIMMERMANN, R.: Repräsentation dynamischer Schiffsmodelle in einem Navigationssystem für die Binnenschiffahrt. Logos-Verlag, Berlin, 2000.
CONTACTS
M.Sc. Marc Breitenfeld,
Federal Institute of Hydrology, Koblenz Am Mainzer Tor. 1, D-56068 Koblenz, Germany phone: +49 (0261) 1306-5285 fax: +49 (0261) 1306-5088 Email: breitenfeld@bafg.de
Dipl.-Ing. Annette Scheider,
Institute of Engineering Geodesy, Universität Stuttgart Geschwister-Scholl-Str. 24D, D-70174 Stuttgart, Germany phone: +49 (0711) 6858-4057 fax: +49 (0711) 6858-4044 Email: annette.scheider@ingeo.uni-stuttgart.de
Prof. Dr.-Ing. habil. Volker Schwieger,
Institute of Engineering Geodesy, Universität Stuttgart Geschwister-Scholl-Str. 24D, D-70174 Stuttgart, Germany phone: +49 (0711) 6858-4041 fax: +49 (0711) 6858-4044 Email: volker.schwieger@ingeo.uni-stuttgart.de
Dipl.-Ing. Harry Wirth,
Federal Institute of Hydrology, Koblenz Am Mainzer Tor. 1, D-56068 Koblenz, Germany phone: +49 (0261) 1306-5232 fax: +49 (0261) 1306-5088 Email: wirth@bafg.de
© Marc Breitenfeld, Annette Scheider, Volker Schwieger, Harry Wirth, 2014
