DARMSTADT
`UNIVERSITY OF
`TECHNOLOGY
`
`PROGRESS IN AUTOMOBILE LIGHTING
`
`Department of Lighting Technology
`September 28/29, 1999
`
`FOUNTAIN AT MATHILDENHOHE, DARMSTADT
`
`VWGoA 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
`
`VWGoA EX1027
`U.S. Patent No. 11,208,029
`
`
`
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`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
`
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`
`Copyright © 1999 Herbert Utz Verlag GmbH
`
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`
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`
`
`
`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 ,-
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`·-.___
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`; /
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`
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`
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`
`. ~ · - - - - - - - ______ _!" _________________ ~ - - -~
`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
`'
`/
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`.
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`i
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`: ------ ; //_ ... · +--- . ----- -
`
`11
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`; ____________ L_ -------+-
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`-200/--
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`
`200
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`400
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`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
`
`\
`
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`
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`
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`~ '
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`~--~------: -----~-----+-: ~
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`1 ·
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`:
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`:
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`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
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`'
`0.25,!-
`
`0.10 !
`0.05 !· · ·
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`:
`0.01
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`---'.t-
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`- ..... : -
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`! _______ 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
`
`-
`
`---
`
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`1 oo ~----"----
`I
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`f
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`.. ----- --·-· --· ___ .. _, ______ _
`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
`
`
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