DARMSTADT
`UNIVERSITY OF
`TECHNOLOGY
`
`PROGRESS IN AUTOMOBILE LIGHTING
`
`Department of Lighting Technology
`September 28/29, 1999
`
`FOUNTAIN AT MATHILDENHOHE, DARMSTADT
`
`
`
`
`
`
`
`
`
`
`
`Mercedes EX1027
`U.S. Patent No. 11,208,029
`
`
`UNIVERSITY OF
`TECHNOLOGY
`
`PROGRESS IN AUTOMOBILE LIGHTING
`
`Department of Lighting Technology
`September 28/29, 1999
`
`FOUNTAIN AT MATHILDENHOHE, DARMSTADT
`
`
`
`
`
`
`
`
`
`
`
`Mercedes EX1027
`U.S. Patent No. 11,208,029
`
`
`
`jo"1deqQSUINIOA
`AySJAUAyeIsWUeG‘ABojouyoe|Bunybry
`
`
`
`
`628e9
`SCHI ~j~
`09
`~ t,
`:)
`'
`
`+--
`...c
`0)
`_J
`,.._
`0
`
`+-'
`0..
`Q)
`0
`
`(0
`
`(I)
`E
`::J
`.g
`
`\
`
`f7
`
`,·~
`
`.
`
`
`
`dedicated to
`
`Mr. Reinhard Ropke
`
`
`
`28 I 29 September, 1999
`
`Proceedings of the Conference
`
`Lichttechnik Darmstadt
`
`Published by
`
`Prof. Dr.-lng. H.-J. Schmidt-Clausen
`Darmstadt University of Technology
`
`Eigentum der
`AUDIAG
`D-85045 lngolst.R..-,1,
`
`UTZ
`Herbert Utz Verlag - Wissenschaft
`Mi..inchen 1999
`
`
`
`ISBN 3-89675-920-5
`
`PAL '99: 2 Volumes, Vol. 5 & Vol. 6; not to be sold separately
`
`Die Deutsche Bibliothek- CIP-Einheitsaufnahme
`Progress in automobile lighting/ Darmstadt, University of Technology,
`Department of Lighting Technology. Publ. by. H.-J. Schmidt-Clausen. -
`Munchen : Utz, Wiss.
`Vol. 6. PAL '99 : 28./29. September, 1999 ; proceedings of the conference/
`Lichttechnik Darmstadt. - 1999
`ISBN 3-89675-920-5
`
`Das Werk ist urheberrechtlk:h geschutzt. Die dadurch begrundeten Rechte, insbesondere die der Ober(cid:173)
`setzung, des Nachdrucks, der Entnahme von Abbildungen, der Funksendung, der Wiedergabe auf photo(cid:173)
`mechanischem oder ahnlichem Wege und der Speicherung in Datenverarbeiturigsanlagen bleiben, auch
`bei nur auszugsweiser Verwertung, vorbehalten.
`
`Die Wiedergabe von Gebrauchsnamen, Handelsnamen, Warenbezeichnungen usw. in diesem Werk
`berechtigt auch ohne besondere Kennzeichnung nicht zu der Annahme, daB solche Namen in Sinne der
`Warenzeichen- und Markenschutz-Gesetzgebung als frei zu betrachten waren und daher von jedermann
`benutzt werden durften.
`
`Copyright © 1999 Herbert Utz Verlag GmbH
`
`Druck: drucken + binden gmbh, Munchen
`
`Herbert Utz Verlag GmbH, Munchen
`Tel.: 089-277791-00
`Fax: 089-277791-0.1
`utz@utzverlag.com
`www.utzverlag.com
`
`
`
`Evaluation of the applicability of digital maps for the
`reconstruction of the real street shape
`
`Alejandro Vukotich
`
`Darmstadt University of Technology and Audi AG
`
`Abstract
`
`This paper focuses on the applicability of digital road maps, as they are used in
`
`commercial navigation systems, for the reconstruction of the street geometry. It
`
`points out a procedure to predict the accuracy of calculated curve radii
`
`depending on the quality of database. To obtain a satisfying approximation of
`
`the real street shape, approprjated interpolation and spline methods are used.
`
`Finally, an algorithm for radii calculation is demonstrated.
`
`1 Introduction
`
`With the advances and proliferation of navigation systems, the efforts of the
`
`automotive industry in making use of the employed geographical databases for
`
`different . comfort and security applications, such as "Advanced Frontlighting
`
`System" (AFS) and "Automatic Cruise Control" (ACC), has grown in meaning
`
`and importance. Both systems can be improved with regard to functionality and
`
`robustness by evaluating the geometrical description of the forthcoming lane.
`
`This paper demonstrates a procedure for a quantitative evaluation of the
`
`suitability of digital databases for the geometrical description of roads. The
`
`investigation efforts reported in this paper do not focus on the navigation system
`
`as a whole but on the underlying digital road map.
`
`In chapter 2
`
`the basics of digital road maps are presented, chapter 3
`
`demonstrates a method to evaluate and compare existing databases. An
`
`example of evaluation is given in chapter 4, where different methods of
`
`774
`
`
`
`interpolation and an algorithm for radius calculation are demonstrated based on
`a selected test track.
`
`2 Basics
`
`2.1 Navigation System
`
`SateUite navigation systems are characterised by low positioning accuracy (100
`integrity owing to masking effects. For
`limited availability, and
`meters),
`exactness, these deficiencies have to be compensated for by complementary
`sensor data, such as velocity and yaw rate [8]. Therefore, once the actual
`position of the car is determined through the "Global Positioning System"
`(GPS), it can be matched to the database by using additional sensors, and so,
`the adequate route from point A to B can be calculated on basis of the digital
`map.
`
`The use of the determined route for AFS and ACC goes along with high
`demands concerning availability and accuracy of the predicted lane, which
`leads to severe requirements on the vehicle positioning and the map matching
`algorithms, and clearly differ from the original purpose of navigation systems.
`After matching the actual position to the map, the shape of the street is to be
`derived by evaluating the corresponding extract of the database. For this
`procedure, it is a prerequisite that the digital road map is as accurate and
`updated as possible.
`
`2.2 Digital Road map
`
`The database installed within the car is generated in two steps.
`
`First, the European streets are digitised by two main suppliers according to their
`rules and methods, which are company dependent. The digital data are then
`encoded in a standard "Geographic Data File" (GDF) format [2].
`
`The second step comprises the reduction and conversion of the GDF database
`by the navigation system manufacturer into a system specific format where
`redundant information concerning navigability is removed.
`
`775
`
`
`
`In commercial digital road maps, streets are represented by polygons, where
`the spots represent the shapepoints and the interconnecting lines the street
`vectors. To each of them, additional information concerning specific properties
`is stored in form of attributes.
`
`To generate the shapepoints and attributes, the database providers make use
`"
`of two methods.
`
`The first procedure consists of the extraction of information of detailed road
`maps that are available at public offices. These maps, mainly in the scale of
`1 :5000, are processed and evaluated with computers. Afterwards, a trained ·
`employee sets the shapepoints manually on the road map, and annotates the
`attributes. In this case, a certain subjectivity remains in the positioning of the
`shapepoints due to the influence of the human factor.
`
`The second method to digitise a road network is by recording the geographical
`position delivered by a "Differential Global Positioning System" (DGPS) [6] while
`driving along the routes; In this case, an accuracy of one to three meters can be
`achieved, while the shapepoints are recorded in steps of one to two seconds.
`Usually, only a small number of the· recorded shapepoints is stored in the final
`GDF database.
`
`In both digitising methods no altitude information is collected. In this respect, to
`guaranty the quality of digitalisation, a subsequent verification of the data
`generated is done on field.
`
`In order to run through all the stages described above, a year is required until a
`database can be commercially released. Taking into account that 20 percent of
`the street geometry changes each year, several problems concerning the
`information value of the digital map have to be expected. Furthermore, it has to
`be considered when applying such systems that large areas are only partially or
`not at all digitised.
`
`The matter about how precise the database does match the real street
`geometry is analysed in the following steps.
`
`776
`
`
`
`Procedure
`
`. The procedure illustrated in this chapter aims at a quantitative evaluation of the
`accuracy of digital maps concerning their capability to give information about
`the real street shape. The goal is to get a global value and an evaluation
`method that can be given to a database manufacturer to test their digital map
`concerning the applications needs, without having to know the exact algorithms
`used by the applications. Figure 1 demonstrates the proceeding while the single
`steps are explained in more detail in chapter 4.
`
`digital maps
`
`real street
`
`f
`
`smooting
`--·-
`interpolation
`
`........
`
`-
`
`r·-------· -~
`
`lateral deviation \
`
`Fig. 1: Block diagram of proceeding.
`
`777
`
`
`
`The standard deviation of the distance between digital map and real street
`characterises how well the digital data matches the street geometry concerning
`shape.
`
`The calculated radius of a curve, which is extracted from a digital map by using
`specific algorithms, can be used as reference for the evaluation of the
`'---.__
`underlying database. Specially, the mean error of the determined radius
`represents a value that differs clearly between different databases and
`algorithms that are applied for the calculation of the curvature.
`
`A description of the functional dependency between the above demonstrated
`values, allows a deduction of a relatively simple to measure value to a complex
`one which represents the more appropriate criteria to describe the accuracy of a
`digital map in connection to a certain algorithm. In this investigation, the
`standard deviation of the lateral distance to the real street represents the
`simple, and the mean error of the determined radius stands for the complex
`value ..
`
`By analysing different databases without changing the algorithm for the radius
`calculation, a comparison between different digital maps can be achieved.
`
`3 Investigation
`
`3.1 Test course
`
`is used as reference for , the following
`track of 2.5 kilometres length
`A
`investigations. The country road segment disposes of three left and right
`curves, in order to avoid possible shape dependent influences on the evaluation
`and interpretation of the database.
`
`Three digital road maps, named map A, B and C, are used and matched with
`the actual street shape. The description was taken from corresponding map
`material that was obtained from survey offices in the scale of 1 :5000. Maps A
`and B correspond to the original GDF databases, while map C represents a
`possible navigation system specific road map.
`
`778
`
`
`
`- - -~ - ----- j - - - - - · - - r - - - - - - , . - - - - - · - - - - - · - - - - - - - - - - - -
`
`2199
`
`1896
`
`_1185
`
`. 1024
`
`1585
`
`756
`
`·-_ 505
`
`y/m
`
`1400
`
`---,------,--(cid:173)
`! --- street i
`
`L .. - - - - . - -
`
`1200
`
`1000
`
`800
`
`600
`
`400
`
`200
`
`i _______________ , _________________
`-200
`-400
`-600
`
`,f_,_ 0
`0
`
`__ -----------------, - - - ' - - - - -~ ' - - - - - - - - - '
`1200
`1000
`800
`600
`400
`200
`
`x/m
`
`Fig. 2: Representation of the entire test track.
`
`In Figure 2, the reference road segment is shown in its integrity. The track is
`exposed in a Cartesian system, where the axes are given in meters. The
`numbers beside the track represent the distance, measured along the course,
`from the lowest point of the track. Tbe real street is drawn by the left and right
`delimiting survey points. Figure 3 shows the two curves at a distance of 1024
`metres in more detail.
`The individual points represent the shapepoints, the connecting lines, the street
`vectors. To describe a curve with similar lateral deviation values as in straight
`segments it is necessary to place a higher number -of shapepoints. It can be
`clearly observed, that the density of shapepoints increases in Cllrves.
`
`779
`
`
`
`y/m
`
`'
`f
`I 1 - - - · - - - - -~ - - .
`'' ·------ digital map A
`1
`-------- digital map B
`'
`. _ · -------- digital map C
`street
`1000 r-; -
`
`950 ,-
`
`900 :--
`
`850 :_
`
`800'
`
`-100
`
`~,:-::____c""-----~----·-- -· · - - - - - - · - - - - - - -~ - - - I
`150
`100
`50
`0
`-50
`
`I
`__________ r ______________ j
`200
`250
`
`x/m
`
`Fig. 3: Detailed representation of curves.
`
`3.2 Interpolation
`
`In order to achieve a good approximation of the real street course, interpolation
`methods are used to generate additional points between the shapepoints given
`
`by the database.
`
`this context are the cubic and cubic spline
`in
`The methods analysed
`interpolation [7]. The linear interpolation was not considered due to the fact that
`it gives no further information about the curvature of the street. Figure 4 and 5
`show the individual interpolation results based on map A. As reference, the
`street median was computed and also graphically represented.
`
`The cubic and the cubic spline interpolation fits polynoms of third degree
`between the base points. Equation 1 shows the fitting function
`
`(1)
`
`780
`
`
`
`Both interpolation methods demand continuity in the first derivation at the
`transition points (equation 2 and 3), while the cubic spline sets additional
`limiting conditions on the second derivation (equation 4).
`
`(k = 1, ... , n -1).
`
`( k = 1, ... , n - 1) .
`
`( k = 1, ... , n - 1) .
`
`(2)
`
`(3)
`
`(4)
`
`--- ~-------------------------.--------------· 7,_,---------~----,-
`
`____ ,.-
`
`y / m
`7001 ·1-- 0 shapepoints
`linear interpolation
`,
`, ·------ cubic interpolation
`690! l ·---- cubic spline interpolation
`: : ==--~ubic int~olation after smoothihg
`6801 !
`I
`670[-
`
`.
`
`·
`
`'
`6601'·
`
`650:·
`
`640i
`
`!
`520:-
`
`6101
`i
`I
`600i
`
`'
`· - - ~ - - I - - - - · - - · - - - - · - - - - - - - - - · · - - - - - - - - - - , - ~ - - - -
`-200
`
`-260
`
`-240
`
`'
`-220
`
`~
`'
`
`-'180
`
`-160
`
`-140
`
`x Im
`
`Fig. 4: Interpolation results, demonstrated based on map A.
`
`781
`
`
`
`y Im
`
`; _ --,---·--------,---·-··-----·
`. r-~-------~---
`shapepoints
`o
`linear interpolation
`! : -------- cubic interpolation
`,
`1000 [ • ---·-·-·· cubic spline interpolation
`; ~-=-:::._t::ubic interpolation after ~ri:!<?_<?thing__J
`
`.---- ·-·, --------···-··-, ________ ,---
`
`i
`
`990 ;·
`
`980 ,-
`
`970'
`
`960 i
`
`950 ,-
`
`·-.___
`
`/'/1,:·
`;!'/ /
`; /
`
`;
`
`:"
`
`r \\
`
`. ~ · - - - - - - - ______ _!" _________________ ~ - - -~
`130
`140
`120
`110
`100
`90
`80
`
`150
`
`160
`xlm
`
`Fig. 5: Interpolation results, demonstrated on basis of map A.
`
`Strong deviations of the expected course can be observed for the cubic and
`cubic spline interpolation at curve entrances and exits which is explained by the
`irregular spaced data. Lengths between 20 and more than 450 metres can be
`found in map A for the corresponding test course.
`
`The overshoots caused by the cubic interpolation are smaller than those
`produced by the cubic spline interpolation, leading to the conclusion, that the
`'
`cubic interpolation represents the best match to the real street geometry.
`
`3.3 Smoothing
`
`To improve the interpolation of the data a smoothing of the calculated track has
`to be achieved. This can be done either by adding shapepoints at suited
`positions, or by formulating special conditions to be fulfilled by the spline
`function. For the following analysis, the first method is used.
`
`782
`
`
`
`By subdividing the long street vectors in equally spaced parts, the overshoots
`can be suppressed. Figure 6 demonstrates the length of each street vector
`depending of the distance, once for the smoothed and once for the original
`shapepoints of map A. The solid line in Figure 4 and 5 represents the best
`match, achieved by smoothing and interpolating the data.
`
`vector length / m
`1· - - - -T .
`
`.
`
`I
`
`:
`
`- , - - - - - - : - -~ ·
`
`---r--··-----;
`
`i r
`.. original database
`'
`:
`:
`i _ ~- __ smoot.hed datr_a_base-,-,· ... ------,-. - - - - - -~ ·
`1000•
`i
`.
`'
`!
`I
`aoo;--··· ----r
`i
`'
`/
`
`.
`
`i
`/I
`
`: ------ ; //_ ... · +--- . ----- -
`
`11
`
`4 0 0 ~ -
`;
`I
`i
`2oor- --, /
`
`f ...
`
`!
`
`·
`
`li
`
`;:
`
`~
`
`)
`
`• ,
`
`--
`
`i
`
`.
`
`-
`
`'
`i
`'
`i
`'
`'
`------------,--- ---.-,--------,-----t--------,----1
`.
`!
`
`I
`
`' ...... -··
`0 ~ --
`
`1;
`. ;
`.
`; ____________ L_ -------+-
`
`',' ~ - -~~ - - - - -+ - -~
`! ___ _! ____ L_ ______ :-- j _____ , ___ : -
`-200/--
`\
`i
`l
`'
`l
`!
`:
`.
`I
`1
`i
`·
`·
`I
`. 7 --~-----1-----
`-j
`-400!--- - - ~ - 7---< - - - - :
`:
`'
`I
`i
`!
`i
`:---- : -- _ _:_ ____ j ______ ~ - - - - - -L - ___ J ____ L ____ _:___ -~--;
`-~~±___
`
`1
`
`7
`
`:
`
`!
`
`'
`
`'
`
`.
`
`l
`
`'
`
`I
`
`-6001 __
`
`200
`
`400
`
`600
`
`800
`
`1000
`
`1200
`
`1400
`
`1600 1800 2000
`
`2200
`
`Fig. 6: Vector length of map A before and after the smoothing.
`
`distance Im
`
`3.4 Lateral deviation
`
`is defined as the shortest distance between one
`lateral deviation
`The
`shapepoint on the digital map and the street median. In Figure 7 the <;:Jefinition is
`graphically demonstrated.
`
`783
`
`\
`
`.
`
`,
`,:
`
`,
`
`~ '
`!
`
`l,·
`
`,
`
`r· !
`
`I
`
`:
`
`I
`
`I
`
`.
`;
`
`.
`'
`
`1
`!
`~--~------: -----~-----+-: ~
`
`;
`
`'
`1 ·
`
`:
`!
`·
`
`:
`;
`
`1
`
`1-
`
`i
`
`
`
`base point
`
`digital
`
`---------------
`
`street
`
`lateral deviation
`
`Fig. 7: Definition of the lateral deviation.
`
`In order to achieve a homogeneous ponderation of the lateral deviation over the
`entire test track, base points are generated on the interpolated map at constant
`distances to each other. The lateral deviation to the street median is calculated
`for each of these base points.
`
`In the following the lateral deviation is used as a criterion for the fitting quality of
`the digital road map to the street. A quantitative comparison between the
`different maps is made possible by the mean and the standard de,viation of the
`lateral deviation. The probability distribution function of the lateral deviation is
`represented in Figure 8 for map A.
`
`784
`
`
`
`probability/ 1
`1 · --------r----
`
`.----, --~------- ; -- ·----~------.---·-·-- ------------ ---·---- ----- ----·-·------
`
`'
`
`'
`
`'
`
`,.-P
`
`1
`
`0.9971--
`1
`0.99 ~- · ·
`i
`0.98 t-· ·
`
`0.95:
`0.90; ..
`i
`
`0.75
`
`0.50
`
`'
`0.25,!-
`
`0.10 !
`0.05 !· · ·
`·
`0.02;
`:
`0.01
`
`---'.t-
`
`,·
`'
`,:
`
`- ..... : -
`
`::.~l.
`
`0.003(- ·
`'
`!
`! _______ i --·· - - - - - - - - - - - - - - - : - - - - · · - - - - - - - - - - - - - - - - - · - - - - - - - - :
`5
`0
`-5
`-10
`
`.
`
`.
`:
`- - - ----- · - - - - - - - - - - - · · --------·
`15
`10
`lateral deviation/ m
`
`Fig. 8: Laterai deviation of map A.
`
`It can easily be recognized that the function above represents a Gaussian
`for map B and C. Table 1
`result
`distribution. Similar representations
`summarizes the mean and standard deviation values for the lateral deviation of
`map A, B and C.
`
`map A
`
`mapB
`
`mapC
`
`mean Im
`
`standard deviation / m
`
`2.44
`
`-1.97
`
`0.92
`
`5.76
`
`5.23
`
`10.36
`
`Table 1: Statistical values for the lateral distribution of map A, Band C.
`
`785
`
`
`
`For long test courses it is expected to get mean values of zero. Due to the
`limited length of the analysed street this effect could not be observed. Future
`investigations shall demonstrate this _context.
`
`A digital map can have a constant offset to the real street without having effect
`. on the quality of shape prediction. The standard deviation gives further
`particulars about the shape fidelity of the digital map.
`
`·.___
`
`For map C the standard deviation determined is almost twice as high as for map
`A and B. This leads to the presumption that map C delivers the worst
`description of the forthcoming lane.
`
`3.5 Street geometry - curve radius
`
`According to RAS-L [1] modern streets are composed of three different types of
`segments. These are straight lines, clothoids and circles. The transition of a
`straight part into a curve with constant radius is smoothed by clothoids, where
`the radius changes continuo!,.lsly along the street. In order to reproduce this
`effect, the selected method of radius calculation retrieves a radius for each
`shapepoint. Figure 9 demonstrates how the algorithm works.
`
`d
`
`\\
`
`d
`
`-I
`
`--.;:::
`
`r
`
`s~apepoint '-~,\
`\
`)
`I
`//
`"~---~
`
`\
`
`Fig. 9: Algorithm for radius calculation.
`
`For each shapepoint, two virtual points are generated in a defined distance (d)
`along the polygon. The three points define a circle, the radius (r) of which is
`
`786
`
`
`
`determined and associated to the original shapepoint. Ideally d is to be chosen
`as small as possible, but with the decreasing of d, the calculated radius
`becomes more noisy. This occurs due to the measuring and positioning errors
`during the generation of the digital map. In this investigation a distance of 40
`metres was chosen. The direction of the curve has no influence on the
`evaluation of the radius and therefore was not considered in this investigation.
`
`radius/ m
`r-
`
`..
`
`i
`
`.
`
`l
`
`-
`
`---
`
`.
`
`.
`
`,
`
`-
`
`;/"
`
`600
`
`!
`J ··t
`,.,
`.f
`
`,= - - - , - ·
`
`1
`
`1
`j
`. - - - -+ - - - ______ ; · - - - - -~ - - - ·
`
`1 oo ~----"----
`I
`0(-- ---·-,--·--·--r
`!
`I
`f
`'
`.. ----- --·-· --· ___ .. _, ______ _
`500
`400
`
`600
`
`700
`
`800
`
`900
`
`1000
`
`1100
`
`1200
`
`1300
`
`distance Im
`
`Fig. 10: Calculated radii for maps A, B, C and for the real street shape.
`
`Figure 10 demonstrates the radii generated by the algorithm shown above for
`each of the digital maps and for the real street. It can be observed, that the
`minimum of radii are very similar for all maps, while the location .of the minimum
`,
`varies.
`
`Figure 11 shows the difference between the radii calculated for the digital maps
`A, B and C and the radii for the real test course.
`
`787
`
`
`
`deviation of radius / m
`600,-
`i ; -
`d~g~tal map A
`' : ················ d1g1tal map B
`' [ :=:.=~ital map C
`,_:_ -·----'-· ·-
`
`400
`
`200 !- --·--- - - -
`
`r
`
`. r - - -
`
`J --,----,
`
`: / \ , _,
`
`/ \ -
`
`:
`
`. !
`
`' \
`
`/
`
`: \\
`
`O· .. kt/ ' ~.//
`-200 - · -u · ----·-·---------------·--·· __ , __ -·-··---· -·-
`\
`/
`
`!
`
`!
`
`:
`
`'
`
`\ _____ : ___ /
`
`-400 :-- · · · - - - - - - - · - - · - ·
`
`-600. ·-- ---···-·-'-·--··- ·- ·----·----'·-------- L · - · - - - -~ - - - -~ - - -~ - - -~
`500
`600
`700
`800
`900
`1000
`1100
`1200
`1300
`distance/ m
`
`Fig. 11: Calculated deviation of the radii for maps A, B, C from the radii
`calculated for the real street shape.
`
`In Table 2 the mean value of radii difference is represented for the digital maps.
`
`mean of radii difference / m
`
`map A
`
`mapB
`
`mapC
`
`-34.1
`
`-32.3
`
`89.1
`
`Table 2: Mean values of the distribution of the radii difference of map A, B
`
`andC.
`
`788
`
`
`
`It can clearly be seen that the radii retrieved by map C is the worst concerning
`accuracy. The mean deviation of the radii to the target value is more than twice
`as high as for map A and B.
`
`3.6 Functional dependency
`
`Comparing the results of Table 1 and 2, it can be seen that the standard
`deviation of the distance between digital map and real street is correlated to the
`quality radius calculated by the demonstrated method.
`
`This investigation demonstrates that with an increasing of factor 2 of the
`standard deviation of the lateral deviation, the error in radius determination
`increases by nearly factor 2.5.
`
`4 Summary and Conclusion
`
`The presented investigation represents an evaluation method, exemplified for a
`selected test course. For a secure statistical statement, additional tracks must
`be used and examined.
`
`Further, particular algorithms such as the smoothing can be extended and
`improved. Other procedures like Bezier curves must be tested concerning their
`applicability. The influence of different types of streets such as motorway and
`highway has to be considered.
`
`The error generated' in the calculation of the street radius depends on the.
`absolute radius value of the respective curve. This functional dependency has
`to be analysed in order to get a mean error for different radii.
`
`Nevertheless, a correlation between the lateral deviation and the calculated
`street radius was found.
`
`the procedure shown
`Furthermore,
`comparison of different road maps.
`
`in
`
`this paper allows a quantitative
`
`789
`
`
`
`Reference
`
`[1]
`
`[2]
`
`[3]
`
`[41
`
`[5]
`
`[6]
`
`[7]
`
`Bundesministerium tor Verkehr
`Richtlinien fur die Anlage von Straf.sen, Teil: Linientohrrung (RAS-L), StB
`13/38.50.04/728F95, Bonn, 1995
`
`European Committee for Standardisation
`Geographic Data Files, CEN TC 278, 1995
`
`Hamberger, Werner
`Verfahren zur Ermittlung und Anwendung von pradiktiven Streckendaten
`for Assistenzsysteme in der FahrzeugfOhrung, VOi-Veriag, DOsseldorf,
`
`1999
`
`Hamberger, Werner; Cremers, Rolf; Willumeit, Hans-Peter
`Verbesserung der aktiven Fahrzeugsicherheit durch fortschrittliche
`Navigationssysteme;, 1998. - 14 Abb. : 5 Abb., 14 Lit.
`
`Lehn, J.; Wegmann, H.
`EinfOhrung in die Statistik, B. G. Treubner Stuttgart, 1985
`
`Seeber, Gunter; Schmitz, Martin
`Methodik der GPS- und DGPS-Messung, lnstitut tor Erdmessung,
`
`Hannover, 1996
`
`Spath, Helmuth
`Spline-Algorithmen zur Konstruktion glatter Kurven und Flachen, R.
`Oldenbourg Verlag MOnchen Wien 1986
`
`[8] Weisser, Hubert; Schulenberg, Peter J.; Bergholz, Ralf
`Autonomous Driving on Vehicle Test Tracks: Overview, Motivation, and
`Concept, IEEE International Conference on Intelligent Vehicles, 1998
`
`790
`
`
Accessing this document will incur an additional charge of $.
After purchase, you can access this document again without charge.
Accept $ Charge
Still Working On It
This document is taking longer than usual to download. This can happen if we need to contact the court directly to obtain the document and their servers are running slowly.
Give it another minute or two to complete, and then try the refresh button.
A few More Minutes ... Still Working
It can take up to 5 minutes for us to download a document if the court servers are running slowly.
Thank you for your continued patience.
This document could not be displayed.
We could not find this document within its docket. Please go back to the docket page and check the link. If that does not work, go back to the docket and refresh it to pull the newest information.
Your account does not support viewing this document.
You need a Paid Account to view this document. Click here to change your account type.
Your account does not support viewing this document.
Set your membership
status to view this document.
With a Docket Alarm membership, you'll
get a whole lot more, including:
- Up-to-date information for this case.
- Email alerts whenever there is an update.
- Full text search for other cases.
- Get email alerts whenever a new case matches your search.
One Moment Please
The filing “” is large (MB) and is being downloaded.
Please refresh this page in a few minutes to see if the filing has been downloaded. The filing will also be emailed to you when the download completes.
Your document is on its way!
If you do not receive the document in five minutes, contact support at support@docketalarm.com.
Sealed Document
We are unable to display this document, it may be under a court ordered seal.
If you have proper credentials to access the file, you may proceed directly to the court's system using your government issued username and password.
Access Government Site
