Evaluation of the Potential of Global Navigation Satellite Systems for

Paper 1084
Evaluation of the Potential of Global Navigation
Satellite Systems for Advanced Driver Assistance
Systems
Doris Schmidt, Hermann Winner,
Technische Universität Darmstadt, Chair of Automotive Engineering, Germany
BIOGRAPHY
Dipl.-Ing., Dipl.-Wirt. Ing. Doris Schmidt is research associate at the Chair of Automotive Engineering at
Technische Universität Darmstadt, Petersenstr. 30, D-64287 Darmstadt, Germany (email: [email protected]).
Prof. Dr. rer. nat. Hermann Winner is Chairman of Automotive Engineering (email: [email protected]).
KEYWORDS – ADAS, Navigation, GPS, GNSS, Error, Sensor Signal Fusion
1. INTRODUCTION
GNSS-receivers are becoming more and more efficient, smaller in size, weight and price which results in the fact
that GNSS-receivers are nowadays a mass product. At present, the number of commercial users is rapidly increasing
and [Bitkom] predicts a further increase (sales increase while the prices decrease).
This growing demand for navigation systems is also monitored in the automobile market. While in 2001 only 9% of
all new vehicles were equipped with a navigation device, already 20% of the new cars had a navigation system in
the year 2004 (see for example [DAT-2002], [DAT-2005]). These are already offered as optional equipment down
to the subcompact-size segment. If this trend continues, the automatic navigation guidance would be part of the
series equipment of new vehicles in the near future just like Anti-lock Braking Systems (ABS), airbags or also
Electronic Stability Program (ESP)1 ([Grell], [Vasek]).
As GNSS-receivers also a large number of Advanced Driver Assistance Systems (ADAS) have been developed and
launched in the market in the last decade. Therefore more and more operations/functions, in former times executed
by the driver, are now taken over from electronic systems. For example 60-70 processors are working in a today’s
upper class vehicle in order to improve comfort and safety ([Grell], [Vasek]). On the one hand these trends result in
more safety and more comfort for passenger cars but on the other hand the complexity of monitoring and
administration of the systems’ functions increases. Considering the ADAS in the long run (see figure 1) the trend
moves towards the integrated ADAS which brings together all available information and data sources as well as the
communication possibilities of the vehicle and carries out its actions on a wide, secured database.
Unlike the long-term consideration, the focus on the short-time view (figure 1) is turned to the development of an
ADAS which supports the vehicle stabilization and vehicle guiding tasks (see [Donges]), simplifies these for the
driver as well as takes over time-restricted control tasks automatically. In this case the system uses all information
provided by internal or external sensors in the vehicle.
Whereas navigation data for automotive applications are mainly used for route guidance nowadays, it is possible to
use these for performance improvement of other ADAS in future. In contrast to vehicle sensor data that make data
permanently available but are subjected to drift effects with increasing driving time, GNSS-data show varying
accuracy and temporary dropouts / unavailability but no drift sensitivity.
Thus it is expected that the mentioned sensor categories may complement each other even more strongly than before
in providing data like the vehicle’s travel or yaw rate. Therefore the two system classes ADAS and GNSS2 may well
supplement each other.
Even if GNSS is continuously improving the 95% precision for the horizontal area is still given as 2.5 m ([Nagle]).
This precision as well as the currently available update rate of 1 Hz is still not sufficient to realize automotive
applications like lane-keeping support3 with GPS only (precision has to be ≤ 0.5 m).
1
It is predicted that each new passenger car has an Electronic Stability Program (ESP) till 2010.
In this paper the term GNSS includes all available and future navigation satellite systems as well as augmentation systems.
3
LKS = Lane Keeping Support is a system which measures the vehicle’s position relative to the lane and offers active support in keeping the
vehicle to the lane.
2
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figure 1: Variety of Driver Assistance Systems (according to [Neunzig])
In non-automotive applications as e.g. precise farming, air traffic or railway-applications (see [Engel], [Dörries],
[Xiaogang], [Kutzbach]) precision is already achieved in the cm-scale. But these results are not directly transferable
to the automotive area, because of other general conditions, e.g. higher speeds, varying dynamic behaviour or no
predetermined fixed lane courses.
In automotive applications for instance [Ryu, J. et al., 2004] and [Bevly] showed the elimination of inertial sensor
errors with the use of GNSS-velocity but in their work there is no estimation how this could influence ADAS. They
and other researchers only use the course angle and the absolute velocity of GNSS-data but do not consider the
position-data, respectively. Furthermore the different chip technology of the GNSS receivers and the different
operating modes are not considered and mostly only very special tests / manoeuvres are realized.
These mentioned and further publications always show only that the researched system has operated once but
explicit statements of reliability of the fusion of GNSS and Inertial-Navigation-Systems (INS) are always missing.
So the research project „GNSS4FAS“ at the Chair of Automotive Engineering of Technische Universität Darmstadt
is going to develop an error model in order to generate statements of reliability of the combined GNSS- INS-system
with this model. This means that the main focus of the project is the investigation of the potential of Global
Navigation Satellite Systems (GNSS) for performance improvement(s) of ADAS (w/o relying on the availability of
digital maps). The following questions are central in this case: Which precision could be achieved by means of
sensor signal fusion of GNSS and ADAS and how can this precision improvement be used for a performance
enhancement of ADAS?
After the methodology and approach in the next section the ADAS are classified by means of relevancy for the
project and the fusion architecture is introduced. Based on this the deduction of characteristics and the typical INS
and GNSS errors are pointed out. This information is necessary for selecting the right vehicle tests which are briefly
presented. The article ends with first test results received from dynamic measurements.
2. METHODOLOGY AND APPROACH
For deducing a method which leads towards the mentioned aim first a selection and a classification of the large
variety of ADAS (see figure 1) is necessary. These as well as the sensor fusion architecture are presented before the
characteristics that are of interest are deduced and possible error types of the two systems are introduced in this
chapter.
2.1. ADAS AND THE CLASSIFICATION
By considering the criteria “not relying on availability of digital maps” and “direct or indirect applications of GNSS
position, speed and course angle”, for this project the large amount of ADAS are structured into two classes:
• sensor adjustment and
• precise localisation.
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Parts of the sensor adjustment-class are systems like the Electronic Stability Program (ESP). ESP is not only used
for the vehicle stabilization in modern vehicles. Their data, primarily the yaw rate information, are also used in
comfort systems as e.g. ACC for curvature determination. Therefore, yaw rate sensor data with a small offset error
have to be achieved for, which is currently only possible by means of offset zeroing of the yaw rate sensors at
standstill condition4. Since these conditions obviously do not exist in the necessary frequency in the normal driving
operation, the long-term offset drift correction could be improved by means of GNSS data.
Systems as e.g. intersection assistance as well as Lane Departure Warning (LDW) und Lane Keeping Support (LKS)
are belonging to the precise localisation-class.
LDW is a mechanism who uses e.g. a camera or a laser and an image processing algorithm. The system registers the
course of the lane in relation to the vehicle. If the warning algorithm predicts an imminent drifting of the current
driving lane, the system warns the driver with haptic, kinestatic, or acoustical feedback.
LKS measures the vehicle position relative to the lane and compared to LDW it additionally offers active support in
keeping the vehicle to the lane. The system recommends steering reactions as a gentle movement of the steering
wheel and the driver has all the time for making the decision if he/she obeys or not ([Continental]).
Whereas in LDW as well as in LKS the relative lateral position, i.e. the offset between the vehicle centre axis and
the ego-lane is base for the functionality of the systems, the exact longitudinal position of the ego-vehicle is of great
importance in the intersection assistant. Just in determination of the ego-position within the lane by means of
systems for lane detection, the quality and the unambiguousness or the visibility has a decisive influence on the
system reliability and therefore on the functionality.
2.2. SENSOR SIGNAL FUSION ARCHITECTURE
To achieve performance improvements or functional expansions for the two ADAS-categories, a sensor signal
fusion of GNSS data and vehicle sensor data is required. Thus, a general sensor signal fusion architecture shown in
figure 2 is presented.
sensor signals
GNSS (SPS, PPS)
inertial sensors
(e.g. ESP)
enhanced signals
sensor fusion
improved position
driver-
error detection
improved speed
error isolation
assistance-
improved yaw rate
functions
surrounding field
(e.g. lane marking
detection)
position in lane
error estimation
integrity
vehicle dynamics and
sensor models
figure 2: System Architecture of Sensor Signal Fusion
By means of the vehicle motion signals provided by CAN interface which are output from inertial sensors, video
camera system as well as GPS receiver a sensor signal fusion is developed under consideration of vehicle movement
and sensor models.
In this research project four different GPS-devices are used. Two of them are representatives of StandardPositioning-Service (SPS)-receivers and the other both are Precise-Positioning-Service (PPS)-receivers. Both PPSreceivers are of the same type. One is an integrated device in the reference system (called PPS 1) and the other
device is an external one (called PPS 2). The PPS-receiver and the two SPS receivers differ in chipset architecture
(PPS 1, PPS 2: patented technology, SPS 1: SirfStarIII chip set and SPS 2: PhaseTrack 125 chip set) as well as in
software technology. Because of the technical differences it is expected that they show different accuracy results as
4
5
This method is obviously not valid for vehicles on ferries or rotating platforms as part of parking towers.
The unit works with 12 channels parallel.
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Paper 1084
well as different dynamic behaviour. On the one hand, the sensor model has to describe the observed errors (e.g.
drift, offset, GNSS characteristical errors) and on the other hand, it is supposed to predict the error quantities for a
fusion system in order to minimize the total error. Thus, improved position, speed, yaw rate data and lateral offset
features can be achieved within the lane and information about integrity can be obtained. Finally, the new improved
data of the different ADAS are available. With this data a detailed analysis of performance improvements of ADAS
is possible.
For the realisation of the shown system architecture the first step for error model development is to figure out the
special parameters with scattering range for the different characteristics which are deduced in the following.
2.3. CHARACTERISTICS AND ERRORS
Based on the mentioned classification and the system architecture the following characteristics for error-model
development are of interest / are deduced:
/ of yaw angle ∆Ψ
• Difference of yaw rate ∆Ψ
• Difference of lateral acceleration ∆a y
•
•
•
Difference of tangential speed ∆v
Difference of displacement (longitudinal, lateral) ∆x, ∆y
Difference of curvature ∆κ .
As some of these are only estimable6 characteristics error propagation has to be considered. table 1 gives a review of
the variables, their symbols and the type of the variable.
table 1: Important variables for performance analysis
Name of variable
symbol
unit
Lateral acceleration
ay
m/s²
Yaw rate
ψ
Rad/s
Tangential Speed
v
m/s
Yaw angle / Course Angle
ψ /Θ
°
Typ of variable
Vehicle
GNSS
measured,
estimated
estimated
measured,
estimated
estimated
measured,
measured
estimated
estimated
measured
Longitudinal Displacement
Lateral Displacement
Curvature
x
y
m
m
m-1
estimated
estimated
estimated
κ
measured
measured
estimated
In normal cases ( a y ≤ 4 m / s ² ) the so-called linear bicycle-model is sufficient for the estimation of the mentioned
variables. The bicycle-model summarizes the lateral properties of an axle and its wheels into one effective wheel.
For further information see [Mitschke].
The measured values are generally not identical to the true values which are necessary for reliable ADAS functions
and differ by an error e . Basically two types of errors occur: systematic and stochastic error. A systematic7 and /or a
stochastic8 error are added to the true value within the sensor unit. For getting the true value it is necessary to
determine the errors. As vehicle sensors and GNSS-receivers use different measuring principles they have different
error sources.
For the estimated characteristics it is necessary to make error propagation for uncertainty examination while the
direct measured characteristics of vehicle sensor according to are composed as follows:
(1)
ψ real ,vehicle (t ) = egain ⋅ψ true,vehicle (t ) + eOffset + enoise + edelay + eNonlinearity
a y real ,vehicle (t ) = egain ⋅ a y true ,vehicle (t ) + egravity + eOffset + enoise + edelay + eNonlinearity
(2)
where egravity = g ⋅ sin ϕ + a y ⋅ cos ϕ (with ϕ roll angle) means the influence of the gravitational acceleration.
The speed signal v is estimated with the information of the four wheel speed sensors n which are composed as
nreal , vehicle (t ) = egain (rdyn = f (v)) ⋅ ntrue, vehicle (t ) + enoise + eNonlinearity
(3).
6
Estimated means that appropriate models are used.
Systematic errors are offsets in measurement which lead to measured values being systematically too high or too low. They are caused by an
unknown but nonrandom fluctuation. If the cause of the systematic error can be identified, then it can usually be eliminated.
8
Stochastic error is caused by random (and therefore inherently unpredictable) fluctuations in the measurement apparatus.
7
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In contrast to the vehicle sensor the GNSS-receiver output is composed as
xreal ,GNSS (t ) = xtrue,GNSS (t ) + eoffset (ionosphere, troposphere) + ...
+ espec ,GNSS (daytime, multipath) + enoise + edelay
(4).
The delay error edelay of the output of the vehicle sensors are <0.1 s while no limit of GNSS-receivers are known.
The latency behaviour of GNSS is presented in this paper. It is common that the offset and the noise are summarized
as error.
These error models (equation (1) - (4)) are based on the mentioned ones in ([Bevly], p.258; [Ryu, J. et al., 2004],
p.245) and are added in this paper.
As the errors of the two systems have different sources it is possible to combine the information of the two systems
in order to improve ADAS. Having a look at the error budget (see table 2) of GNSS it is not possible to use the
GNSS alone. The values given in table 2 are received without augmentation systems. Also if augmentation systems
like EGNOS are used the minimum error is greater than 2.5 m.
table 2: Error Budget of GPS ([Zogg], p.51)
Source of Error
Error [m]
ephemerid data
satellite clocks
ionosphere influcence
trophosphere influence
multipath
receiver influence
total rms-value
total rms-value (filtered, i.e. light averaged)
2.1
2.1
4.0
0.7
1.4
0.5
5.3
5.0
Only by using commercial correction services like SAPOS-EHPS cm-accuracy are obtainable. For using this service
the customer has to pay a fee per month / year. Presumably the consumer (and the OEM9) is not willing to pay a fee,
particularly if the benefit is not obvious for him / her. So to use GNSS in the field of ADAS it is important that
performance improvements are achievable without any additional costs for the costumer.
For figuring out the error components for the vehicle sensors as well as for the GNSS-receivers-output for large
application field, appropriate manoeuvres have to be deduced. Also a reference system is needed as it is in reality
not possible to know the true value of the measured signal. Therefore the measured signals of the reference system
are used as conventional true values as the deviation between true value and conventional true value is observed as
neglectable. So the used reference system is an inertial measurement system with a fibre-optic gyro and the system
is supported by an internal GPS-receiver and an external speed sensor. This system is right now getting validated
with shaving-foam-method and by using calibrated points (with an accuracy of +/- 2cm).
3. MANOEUVERS AND TESTING
For figuring out the potential of GNSS for ADAS it is necessary to consider the challenges of each system (GNSS
and ADAS).
As a result of so-called masking effects the GNSS-system exhibits poor reception and integrity which occur
especially in urban city surroundings where narrow streets are lined by tall buildings. Furthermore dynamic
behaviour e.g. lane changes has also to be considered as till now GNSS was not tested for such dynamic manoeuvres
alternatively the errors are not well known. Therefore the test procedure is divided into two groups. The first group
takes place on the university’s own test track / closed-down airfield in order not to affect the road traffic by dynamic
manoeuvres like slalom or high dynamical braking manoeuvres. Long-time driving in the field is the second group.
Another requirement for doing the test is that they should take place “under real traffic-conditions”, that means in
the field. This specification includes that the selecting course should be representative.
The application area of ADAS causes the type of roads which build the tests. For example ACC is normally used by
fast driving on highways and motorways. The application field of LDW is in cities as well as on high- and
motorways. For a reliable function of LDW it is necessary to have non-ambiguous, clear visible lane markings. The
demands for ESP could not be carrying out in the field because this would cause hazard of other road users.
Therefore the special manoeuvres for ESP have to take place on a test track.
9
OEM = Original Equipment Manufacturer
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Paper 1084
As the paper focuses on dynamic behaviour only those tests are presented. So for studying the dynamic GNSSbehaviour the following tests have been chosen and take place on the test-track:
1) Slalom:
Eleven cones with a distance of 20 m are positioned on a straight line. Between them the test car drives
with a speed of 40 km/h a sinus-like wave and the lateral acceleration is round 4 m/s². figure 3 illustrates
the manoeuvre. This test-layout was chosen for dynamic behaviour research.
20 m 20 m
20 m
20 m
v
Vehicle
cones
figure 3: 20 m Slalom
2) Acceleration-Deceleration:
The vehicle starts in standstill, accelerates to e.g. 40 km/h, then steady-state driving for approximately four
seconds and then again accelerates to e.g. 80 km/h and then the same back. With this test the system
latency of the devices should be tested.
3) Steady-State-Driving:
The car cruises with constant speed (e.g. 50 km/h). This test is necessary in order to do comparisons of
latency of the non steady-state drivings.
All measurements are repeated at least three times.
4. MEASUREMENT EQUIPMENT
All experiments were carried out with the departments own test vehicle, the Mercedes Benz S430 long version
(model series W220, model year 1999) which is shown in figure 4 left. The right picture in figure 4 shows the
antennas of the GNSS units. Three of the four antennas are placed on a luggage rack which is mounted at the front
part of the test vehicle roof. The lateral distance between two antennas was calculated to 47.5 cm which is the
minimum distance to avoid interactions (e.g. signal weakening). The fourth antenna is placed at the rear of the
vehicles roof (see figure 4 right).
SPS 1
PPS 1
PPS 2
SPS 2
figure 4: left: Test Vehicle Mercedes Benz S-Class, right: Antennas of the GNSS-Receivers
In contrast to SPS 1 and SPS 2 which both use only the L1-signal for position calculation (SPS10-units) PPS 1 and
PPS 2 receivers are PPS11-devices. This means that in addition to the L1-signal the phase of the L2-GPS-signal is
used for calculating the position. A further difference is that SPS 1 is the only GPS receiver which has a SiRFStarIII
technology as chip set. The main technical data are listed in table 3. All four receivers are EGNOS enabled.
As the GPS-data are only available on the receiver-serial interface in the NMEA-0183-format a microcontroller
converts the data in a CAN12-compatible format and is directly connected to one of the CAN-Buses in order to
provide the GNSS-receiver output on the CAN. The time-synchronised buses are connected to a notebook where the
measurements are saved. For data recording the software CANalyzer is used.
10
SPS = Standard Positioning Service
PPS = Precise Positioning Service
12
CAN = Controller Area Network is a broadcast, differential serial bus standard for connecting electronic control units. The system uses
digital signals. This system is normally used in the automotive area.
11
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The reference system, the Automotive Dynamic Motion Analyzer (ADMA-G) is a strapdown13 inertial measurement
system equipped with robust fibre gyros, accelerometers and an internal (D)GPS-receiver (called PPS 1). It
measures accelerations and rotation rates in all three directions / axis. As this system is used as the reference system
the system performance has to be guaranteed even during complicated test manoeuvres. Therefore the platform uses
additionally the signal of the speed sensor CORREVIT and the GPS signal (for supporting the inertial measurement
data) in order to reduce drift effects. The GPS-signal could be improved in addition using correction data which are
sent from a GPS-reference station. While the field experiments the reference system is not support with DGPS. This
is only possible at the test track using the department’s own reference station for GPS-correction data.
The reference’s accuracy given by the manufacturer is 1.0° for dynamic roll / pitch and 1.8m (1 σ ) for the position
(single point L1 GPS mode).
table 3: Overview of the main important technical data of the used GNSS-receivers
GNSS-receiver
PPS 1 and PPS 2
SPS 1
SPS 2
Technology
PPS
SPS
SPS
Sampling rate
Frequency
Accuracy Position
Speed accuracy
Time accuracy
Weight
Dimension (LxWxH) [mm]
20 Hz
L1(1575,42 MHz)+L2(1227,60 MHz)
1.8 m (CEP)
0.03 m/s (RMS)
20 ns (RMS)
1000 g
185x154x71
1 Hz
L1(1575.42 MHz)
10 m (2D RMS)
0.1 m/s
1 ms
23 g
43x42x13
0.5 Hz
L1(1575,42 MHz)
<15 m (RMS)
0.05 m/s (RMS)
--.
234 g
157x69x36
5. RESULTS OF DYNAMIC MEASUREMENTS
In this section the first results of the dynamic measurements are presented. As criteria the difference according to
∆ signal data = signal datameasured − signal datareference
(5)
is used as well as the linear regression analysis including residuals and ratios is applied in order to examine the
relation between the measured and the reference data and their dependency. The dependency is described with the
determination coefficient R 2 . The used linear regression equation is defined as
signal data estimated , devicei = mdevicei ⋅ signal dataref + offsetdevicei
(6).
devicei is the parameter for the four GNSS-devices. m devicei and offset devicei are estimated by using the measured
and the reference data for each characteristic. Except for speed signal the data of the inertial measurement platform
are used as reference data. For reference speed data those of a Correvit14-speed sensor which has a uncertainty of
measurement of 0.1% is taken.
Furthermore the root mean squared error RMSE is calculated for the latency-analysis as
(
RMSE = µ ( signalestimated − signalmeasured )
2
)
(7)
where µ is the expected value (mean).
According to the following results it is for the slalom analysis necessary to consider the sideslip angle β 15 as the
maximum over the whole slalom manoeuvres is 1.5°. The course angle Θ and the yaw angle ψ 16 are connected by
Θ = β +ψ
(8).
With this equation it is possible to compare the course-angle-GNSS-data and the vehicle sensor yaw-angle-data.
figure 5 shows the lateral over longitudinal distance for a slalom measurement. The speed for driving through the
cones of the slalom was 40 km/h with a lateral acceleration of circa 4 m/s² and the duration of the manoeuvre itself
amounted circa 40 s.
13
Strapdown inertial systems are rigidly fixed to the moving body. In former times the inertial systems were gimbal-mounted.
The measuring principal of the Corrrevit speed sensor is the optical mouse-principal.
15
Sideslip angle is the angle between the vehicle’s actual movement direction (in the gravity centre) and the longitudinal axis of the vehicle.
16
Yaw angle is the angle between the global longitudinal axis and the vehicle’s actual movement direction
14
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figure 5: left: Lateral Distance over Longitudinal Distance; right ∆ Longitudinal Distance over Time
for Slalom ( v = 40 km / h; a y = 4 m / s ² )
While PPS 1 and PPS 2-units show in figure 5 left no longitudinal shift the SPS 1 and SPS 2 do. So it is expected
that the reason for this behaviour is the narrow sampling rate. Also by having a closer look to the difference between
the measured and the reference values (see figure 5 right) it is seen that on the one hand the SPS 2 has a constant
offset in longitudinal direction while the SPS 1 receiver shows a longitudinal increase over time. On the other hand
SPS 2 shows a step in ∆ longitudinal distance at time=46.5s and 76.3s, these are the points when the dynamic
manoeuvre begins. Looking at the lateral difference the described phenomena could not be observed. It is only
conspicuous that SPS 1 has a larger lateral distance difference than SPS 2 and it is noticeable that the lateral
differences of PPS 2 are smaller than those of PPS 1. One reason for this could be the coupling of PPS 1-receiver
with the INS-sensors in the reference system.
During these dynamic measurements it was observed that both PPS receivers (PPS 1 and PPS 2) show almost an
exact conformity with the reference system for the distance (see figure 5 left) and course angle analysis (see figure
8) but not for the tangential speed (see figure 6 left). Both devices are not able to follow the “sinus-wave”. figure 6
illustrates this aspect and it is also seen in contrast to PPS 1 that PPS 2-unit has lots of peaks, especially at the end
when the sinus-wave runs in a straight line (from 72 s on). The peaks are no typical characteristic of noise and it is
obvious that the peaks are not normal distributed. As the peaks occur during slalom and steady state but not during
accelerated and decelerated manoeuvres the main course for the peaks behaviour is not finally clarified as the peaks
are not reproducible.
figure 6: Tangential Speed over Time for Slalom ( v = 40 km / h; a y = 4 m / s ² ) (left), for accelerated driving
0 km/h – 80 km/h – 0 km/h (right) (Reference: Correvit-sensor)
Also by analyzing the mentioned accelerated driving from 0 km/h – 80 km/h – 0 km/h (figure 6 right) one observed
aspect is that no peaks of PPS 2 data occurred, not even during the steady-state driving. Further, by regarding the
best fit straight line, the residuals and the ratios in figure 7, the second observed aspect is while the best fit straight
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line of all five systems are the same, the residuals and the ratios of SPS 1 and SPS 2 show hysteresis. The negative
residuals and the ratio values <1 are caused by acceleration while the positive residuals and the ratio values >1 are
caused by deceleration. It is also remarkable that with higher speed (>10 m/s) the residuals become in total smaller
and the ratio is almost one. It also seems that the residuals are smaller during acceleration for v >10 m/s than during
deceleration. A possible reason could be the curve progression of the tangential speed (see figure 6 right: from 10
m/s to 22.2 m/s it is a declining curve and back it has more a linear characteristic).
So it is not till now obvious which is in the PPS 2 data the main reason for the peaks. Some experts also assume that
there could be coherence with the measuring principle of the receivers because it is expected that PPS 2 uses the
Doppler-frequency for getting the speed while the SPS-receivers use the deviation of the position. One possible
reason why the PPS 1-receiver shows not the same characteristic as the PPS 2 one is that the reference system where
the PPS 1 is integrated does not display the raw-data, only the processed data. So a more detailed analysis of this
mentioned observation is necessary in order to find the real reason.
figure 7: Tangential Speed, Residuals, Ratios over Tangential Speed Reference for accelerated driving
Analysing course angle Θ and yaw angle ψ 17 by regarding the difference between measured / estimated values and
reference system values figure 8 illustrates the drift of the vehicle sensors (Car-Sext, Car-S) which is caused by the
integration of the yaw rate that is subjected to errors. In contrast to vehicle sensor the PPS-receivers are not drifted
but it is conspicuous that PPS 1 and PPS 2 are time shifted against each other (PPS 2 seems to be earlier even so
PPS 1 has a higher sampling rate). Looking at the course angle itself it is observed that the SPS 1 signal is constantdelayed while the delay of the SPS 2 signal becomes bigger during time. It is assumed that this phenomenon is
associated with the very low update rate of 0.5 Hz.
17
The yaw angle of the vehicle is the integration of the yaw rate.
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figure 8: ∆ Course Angle/ ∆ Yaw Angle (offset corrected) over Time for Slalom ( v = 40 km / h; a y = 4 m / s ² )
So in order to get more information about the delay-time tdelay for different receivers and for different manoeuvres
tdelay is calculated. For slalom the course / yaw angle and the course / yaw rate is considered while for the ac-
/decelerated manoeuvre the tangential speed and the longitudinal acceleration are the relevant signals. According to
(9)
∆Θ devicei < Θ
max, ref ⋅ tdelay , max, devicei
(for the other signals analogue) two methods for calculation are used:
1. Regression analysis
2. Direct calculation by determination ∆Θ max and Θ
max, ref (for the other signals analogue).
As table 4 shows there are different delay times of the receivers for the different manoeuvres.
table 4: Results of the delay time calculation
Slalom - Yaw Angle / Course Angle
Reference
tlatency,regression
tlatency,max
Root Mean Squared Error RMSE
Determination Coefficient R²
Root Mean Squared Error RMSE
(v=const.)
PPS 1 SPS 1 SPS 2 PPS 2 Fzg ext Fzg
0.11
0.407 0.044 0.008 0.027
0.029
0.17
0.46
0.85
1.06
8.2
0.18
1.07
11.3
0.00
0.07
0.52
0.028
0.134
0.90
0.084
0.129
0.92
0.092
0.194
0.315
0.348
0.275
0.229
0.227
Ac-/ Deceleration - Tangential Speed
tlatency,regression
tlatency,max
Root Mean Squared Error RMSE
Determination Coefficient R²
Root Mean Squared Error RMSE
(v=const.)
Reference PPS 1 SPS 1 SPS 2 PPS 2
0.06
0.023 1.14
1.54
0.006
0.07
0.044
0.72
0.13
0.07
0.13
1.32
0.705
0.78
1.60
1.15
0.72
0.058
0.09
0.00
0.043
0.058
0.054
0.068
0.063
10
Paper 1084
Analysing the residuals in figure 9 it is seen that in contrast to the PPS-receivers the residuals of SPS 1 and SPS 2
are stochastically and that they are always available. These SPS 1 and SPS 2 errors of measurement could be
interpreted as typical dynamic effects. Their quantity by using the root mean squared error RMSE is listed in table
4. In contrast to the dynamic effect for the ac- / decelerated driving this effect of the SPS-receivers during slalom is
about factor 10 higher (see figure 10).
figure 9:
∆ Tangential Speed, Residuals over Longitudinal Acceleration for Ac- / Deceleration
(over all test series)
figure 10:
∆ Course Angle/ ∆ Yaw Angle, Residuals over Course Rate / Yaw Rate for Slalom
(over all test series) ( v = 40 km / h; a y = 4 m / s ² )
11
Paper 1084
Comparing these results with a steady-state driving with 50 km/h (figure 11) it is seen that the SPS-receivers as well
as the PPS-units don’t show typical dynamic effect. The Residuals are very small. This observation is the same for
∆ Course/ ∆ Yaw angle.
figure 11: ∆ Tangential Speed, Residuals over Longitudinal Acceleration for steady-state driving (50 km/h)
(for all test series)
6. CONCLUSION
In this paper it was shown that because of the trend of increasing application of (Advanced) Driver Assistance
Systems ((A)DAS) in series vehicles the developments go towards integrated systems. This means that already
equipped systems like ESP or future equipped systems like navigation systems could complement each other and so
improved performance and/or additional functions can arise. Because navigation systems are now affordable mass
products and forecasts say that they become series equipment in cars in 2010, the aim of the project “GNSS4DAS”
is the analysis of the potential of GNSS for ADAS. So at the beginning of this paper a sensible classification for a
number of ADAS are presented. Based on this classification the methodology as well as the approach of the
development of an error model was presented. For figuring out the different error-types of both systems GNSS and
INS the error model of [Ryu, J. et al., 2004] and [Bevly] was expanded. Based on the expanded model specific
manoeuvres were deduced for doing a dynamic research. In this paper the slalom which is the limit range of using
the vehicle in normal mode and the accelerated and decelerated tests were presented and analyzed. While for the
20 m slalom the tangential speed and the course / yaw angle was for four GNSS receivers of interest, the tangential
speed was item of the ac- / decelerated manoeuvre research. According to course / yaw angle analysis it was
observed that the SPS-receivers are not useable for yaw angle prediction compared to PPS. Looking at the tangential
speed the PPS 2 receiver showed an unexpected behaviour especially for slalom. Peaks occurred in the speed signal
during this manoeuvre but not for the ac- / decelerated test while the identical PPS 1 receiver did not show this
behaviour. Till now the main reason is not found as the moose-test analysis does not give the decisive notice. By
doing a regression analysis of tangential speed for an accelerated driving (0 km/h-80 km/h-0 km/h) it was observed
that the SPS-receivers have a hysteretic which becomes smaller with increasing speed.
On possible reason for all this are latency effects. The delay research showed that the latency of the receivers is
dependent on the manoeuvres. Another conclusion is that the error measurements of the SPS-receivers are always
existent and this is interpreted as typical dynamic effects which are also manoeuvre dependent. The RMSE (root
mean squared error) which could be used as a quantity criterion for dynamic effect is for SPS-devices about factor
10 higher for slalom than for ac- / decelerated tests.
12
Paper 1084
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