GIS-BASED REAL-TIME CORRECTION OF DEVIATION ON VEHICLE TRACK *

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1 Proceedins of the 004 International Conference TP-038 on Dynamics, Instrumentation and Control, Nanin, China, Auust, 004 GIS-BASED REAL-TIME CORRECTION OF DEVIATION ON VEHICLE TRACK YUANLU BAO, YAN LIU Department Automation, USTC Hefei, Anhui, 3006, China SHENG-GUO WANG Department Electrical and Computer Enneerin, UNCC 90 University City Blvd, Charlotte, NC ,USA This paper introduces some innovative techniques used for GPS Intellient Vehicle Naviation System. It is very important to obtain on time correction of deviation on vehicle trac at roads because there exist both vector map error and GPS vehicle position error. The paper develops three important technical approaches: Dital Map Generation with linear eo-adustin; Dital Map Geo-adustin by nonlinear rectification; and Real-time Deviation Correction for vehicle trac based on the traffic vector map.. Introduction Dital Times in modern city brins Intellient Transportation System (ITS). ITS needs dital map based on Georaphic Information System (GIS). As an important application, Intellient Vehicle Naviation System (IVNS) [] has developed rapidly on the world. This paper deals some techniques used in IVNS developed by University of Science and Technoloy of China GPSLab [-4]. The paper develops three important technical approaches on IVNS: Dital Map Generation with a linear adustin; Dital Map discrete nonlinear Geo-adustin; and Real-time Deviation Correction of drivers trac at the traffic roads. An example for user interface on IVNS is shown in Fi.. This wor is supported by NSFC Grant of the National Science Foundation of CHINA. Wor partially supported by NSF under Grant CCR of the USA National Science Foundation.

2 . Dital Map Generation with linear eo-adustin In the followin subsections we discuss the dital map eneration. The dital map s database structure is described in details of Ref. []. The procedures and software of GIS-DMG (Dital Map Generation) is shown in Fiure. Raster Map Map Layers Extraction Map Layers Vector- main Vector Map Used Map Map layer Map Geo-adustin & GIS data-addin User interface (Vector map show) GPS or GIS Application system (ITS, AVL, Naviation, IVMS, etc) Fiure. The user interface on IVNS Fiure. The bloc diaram for DMG.. Dital Map Generation from the Printed Map A usual way to enerate a dital map is throuh dital instrument [5], but it costs much time and labor. In order to improve the precision and efficiency, new software named as DMG (Dital Map Generation) is developed and used successfully. The whole process has three main steps: Map Layer Extraction, includes road networ extraction; Map Layer Ditization or Vector-main; Vector Map Geo-adustin. On vector map, the main idea is to determine and store the nodes that represent the road curves by the lines connectin the correspondin nodes. If the orinal raster map has exact proportion then the enerated vector map has only linear error with its node topoloy. The linear error can be revised perfectly by a lobal linear eo-adustin. However, enerally the produced vector map has nonlinear error, thus a new nonlinear eo-adustin procedure should be used... Automatic Map lobal linear Geo-adustin Map eo-adustin is for improvin vector map accuracy. The method is to use the recorded road locus by GPS to automatically adust the vector traffic map. Select a roup of n nown points set G with their accurate position set G: G =,, L, } = { ( x, y ), ( x, y ), L, ( x, y )} () G { n n n n = { n n n n,, L, } = { ( x, y ), ( x, y ), L, ( x, y )} ()

3 3 Definition. An automatic vector map linear eo-adustment should adust a selected roup of pointsg to Ĝ, for Ĝ closes to their nown exact positions G as nearly as possible and simultaneously eepin the map topoloy. The problem becomes to find a mappin M ( ) from points to ) i, e.. M G) = Gˆ = { ˆ, ˆ, L, ˆ } = { M ( ), M ( ), L, M ( )} (3) ( n n Fiure 3a. Usin road locus to adust a dital map 3b. Adusted dital map after Geo-adustin The mappin M ( ) should be a composition mappin and include only two inds of mappins: a linear mappin M L ( ) for expansion/contraction and movement, and a conformal mappin M R ( ) for rotation, e.. M ( ) = M R ( ML( )) : M L( ): M [( ( x, y)] = ( K x + m, K y + m ) = ( x, y ) = ρ θ L x x y y (4) M R( ) : M ˆ R ( ρ θ ) = ( K ) ( r ) ˆ ρ ρ θ + θ = ρ θ = ˆ( xˆ, yˆ) = M( ) (5) Because all mappins include movin factors, the pole in M R ( ) is selected as the superposition of the orin of that in M L ( ) and has x = ρ cos(θ ), y = ρ sin(θ). Throuh minimizin optimal performance index n ˆ i i i i i J = G G = = [( x xˆ )) + ( y yˆ ) ] (6) The parameters V = [ Kx, mx, Ky, my, Kρ, rθ ] can be obtained for eo-adustin. Let the mappin M ( ) actives all nodes of the vector map, denoted by P, the vector map lobal linear eo-adustin is accomplished. M ( ) : P ˆ = {ˆ p } = M( P) = { M( )} for all nodes p on vector map (7) p

4 4 Note that M ( ) always eeps vector map topoloy, an example for dital map linear eo-adustin of city Hefei is show in Fi. 4. The most simple case is n =, then the procedure become only lobal eolocatin, the result Ĝ = G can be always obtained. Usin exact location {, } of two points {, }, we can et an initial eo-locatin for the vector map. The linear adustin procedure can always done by two steps as followin: Step : Move whole map area S for ( x, y) ( x, y ) by mappin M ( ) : p( x, y) M( p) = pˆ(ˆ, x yˆ) = pˆ( x + x x, y + y y) Where point p ( x, y) is any point on map and p (ˆ, x y) is the mapped point. Step : Rotate and resize the new map area S (except the fixed point ) for by M (): p( x, y) pˆ(ˆ, x yˆ ) as follows: ( yˆ y ) /( xˆ x ) = tan{ α + arctan[( y y ) /( x x )]} ( xˆ x ) + ( yˆ y ) = β ( x x ) + ( y y ) Where enlarement factor α and rotation anle β around point ˆ ˆ are [ y y )/( x x )] tan [( y y )/( x )] α = = tan x (0) ( (8) (9) β = y () = ( x x ) + ( y y ) ( x x ) + ( y ) 3. Dital Map Discrete Nonlinear Geo-adustin Dital map accuracy depends only on all nodes location precision. A strict automatic vector map eo-adustment should adust a selected roup of points to their nown exact eo-data (lontudes and latitudes). The vector map linear eo-adustment could only adust the selected roup of pointsg to Ĝ nearin to their exact positions G. Thus we need to develop innovative techniques to eoadustment G exactly matchin its exact positions G. 3.. Structure of nonlinear adustment alorithm Definition. An automatic vector map nonlinear eo-adustment should adust a selected roup of points G in Eq. () to their exact location G in Eq. () and simultaneously eepin the vector map topoloy. The oal is to find a transformation or mappin M ( ) to map G onto G: M ( ) : M G) = G = {,, L, } = { M( ), M( ), L, M( )} ( n n ()

5 Then, apply this mappin M( ) on all nodes P on the vector map to et P = M (P) as in Eq. (7). The new alorithm adusts a sample by a sample point. At the time of adustin one point, the alorithm also automatically adusts all its neihborin area points within a bloc eepin their topoloy. If the selected sample point set has enouh distribution, then the vector map will have an accurate adustment because of the limited nodes on vector map. 3.. Dynamic discrete bloc area (polyon S ) Assume the selected sample set G has n points. At the bennin of the -th step, the alorithm has accurately adusted sample points {,, L, } {,, L, } (3) They are and should be the fixed points durin the followin adustment steps. The -th step mappin M ( ) adusts the point to and its neihborin bloc/area (polyon) S, e.., : x, y ) = M [ ( x, y )] And all points ( p at S, is mapped to p : p x, y ) = M [ p( x, y )] ( (4) 5 Half Plane H ( i ) L i i Map Area L A E L 5 L 5 G B S 6 3 L 3 C D L 4 4 Fiure 4. Bloc S and adusted points ( i < ) i Fiure 5. Construction of bloc The sample point distribution is the ey factor to determine the boundary of dynamic neihborin reon S. The first bloc S and the second S are ust the map area as described in Sec. and the mappin procedures are Eqs. (0-3). The -th bloc S ( 3) is determined by the followin rules shown in Fi. 5. S U H ( ),,, L, n i= i = (5) S

6 6 The constructin reon S by m-lines L i may not be a bounded reon. Then the bloc S is constructed as shown in Fi. 6, S [ = i= i i I H ( ) IH ( )] (6) Where H ( ) is a half plane with point constructed by the line i L. i 3.3. Discrete nonlinear adustment alorithm Step (=3,4,,n): Do mappin M to topolocally map all points in S and complete as follows. From the above, S is a convex m-polyon (or m-polyon) with m. Note that bloc S in Fi. 5. is always a convex quadrilateral and and are always both within the bloc S. Connectin point to all vertexes of the polyon S divides S into m trianles L, i {,, } L and = L,, m. In the same way, Connectin point to all vertexes of polyon S divides S into other m trianles L. It leads to m m S = U = L = U = L, i {,, } L (7) 4 L 4 L F E L 3 A L 5 L L 5 3 S 6 L 3 B C L Fiure 6. Construct S from unbounded area D A G Fiure7 Mappin p ˆ p AB= L L i to p ĝ pˆ i L B i In some situations, the bloc S may be m-polyon, the alorithm principle is the same, ust replacin m by m. Thus for simplicity, we address the case with m-polyon. The mappin M is a mappin on S onto S itself. It consists of m (or m) mappins on m (m) trianles of S, e.., M ( S ) U m m = = M ( L ) = = L U. (8) The nonlinear mappin M maps m trianles their correspondin m trianles: L respectively onto i

7 M =, {,,, } ( L ) L 7 i L (9) Mappin M uarantees maintainin the topoloy because all neihborin trianles share their common sides in the mapped imae space. Fi. 7 shows the mappin rules of M on m trianles. Without loss of enerality, assume a point p in AB and its imae p ' in AB by the mappin M, e.., p L i = AB S M ( p) = p L = AB S, i Extend the line p to cross the line AB at point G and connect and G. The mappin rule lets the imae point p be on the line sement and G p' G p G (0) = It uniquely determines the imae point p from point p. Eq. (9) uniquely determines the mappin M on AB. Similarly define the mappin M on all other trianles of S. The nearer a point p to is, the larer adustment effect on p is. The mappin M in Step adusts the bloc S and also eeps its topoloy. The whole discrete nonlinear eo-adustment M ( ) consists of the above described mappin M, =, L, n, in sequence, e.., M( ) = M L M M L M M () n Because each mappin M eeps the map topoloy and adusts selective point to its accurate position, therefore the whole map M ( ) also eeps the map topoloy and satisfies the required mappin Definition.

8 8 Fi.8. Hefei vector map after adustin via the new method on 4 points 3.4. Example for city Hefei map This section shows effectiveness of the new approach by an example. Fi. 8 shows Hefei city vector map after discrete nonlinear adustin via the new method on 4 points and their correspondin neihborin areas topolocal discrete nonlinear adustment. While Fi. 3a shows Hefei vector map before adustin and Fi. 3b shows Hefei vector map after only lobal linear adustin. In the fiures, the points mared by + are correct points, and the points mared by are their correspondin points i before adustin on the vector map. More examples are also available at 4. Rear-time Correction of Deviation of Vehicle Position An important characteristic of the IVNS is its Real-time Correction of the Deviation (RCD) of vehicle position. The deviation is resulted from orinal satellite data errors, as well as the vector map errors. 4.. Basic idea and main procedure of the RCD alorithm The RCD alorithm is a computer realization of the state estimation problem for a discrete-time system, which is described by the followin state equations: i Fi.9. GPS-measured position and adusted p pˆ x( ) px( ) + [ νx( ) + νx( )]/ pˆ( ): = = pˆ y( ) py( ) + [ νy( ) + νy( )]/ ()

9 9 p p( ) : = p x y ( ) pˆ = ( ) pˆ x y ( ) + ε x ( ) ( ) + ε ( ) y (3) e e( ) : = e ˆ x y ( ) p = [ p( ) ( )] = ( ) p x y ( ) ( ) x y ( ) ( ) (4) Where p ( ) denotes the estimated vehicle position on the dital map at time, they are calculated based on the previous instant time position and an averae speed of the current time and previous time, p () denotes the adusted vehicle position on the dital map at time, ε () is an adustin factor, e.., a position shift correction, at time used to force the movin vehicle icon to eep alon the road at the dital map. The vehicle position at time, obtained and recorded by the GPS-receiver in the movin vehicle, is denoted as (). The velocity v () of the movin vehicle on the earth surface is measured by the GPS-receiver at time with its eastward speed v x () and northward speed v y (). In addition, e () is the tuned error between the adusted map location p () and the GPS measured location ()? The reason to introduce ε () it is to eliminate those anti-facts described above, such as a movin vehicle umps from one road to another. It is the RCD alorithm discussed in the next subsection to calculate ε ( ) or e (). Here we ust describe the eneral idea and concept of the RCD. Fis.9-0 shows those perceivable senses and intuitive senses. The artificial position adustment factor ε () is used to force the movin vehicle onto the road of the dital map. The error e ( ) reflects the effects of both the GPS measure-error and the dital map precision error.

10 0 Fi.0. Effect of Rear-time Correction of Deviation 4.. Some consideration and artifice with the RCD alorithm When a vehicle runs on the road-arc AB, the RCD alorithm is perfectly effective for eepin the vehicle on the same road-arc AB as shown in Fi.9. Suppose a vehicle startin point error is e )] T ( o) = [ ex( o), ey ( o (5) With the startin position p )] T ( o) = [ px( o), py( o (6) on the map. On that road-arc, either with a normal or slowdown acceleration, the dynamic movement process of the vehicle can be described by equations () and (3). Thus, an important problem is how to et the precise e ( o ) with the p ( o ) on some basic points such as the startin point A in Fi.9 at the time 0. Then, a further problem is how to determine these basic points? Obviously, an intersection point (such as point A or B in Fi.9) is the best candidate. When a vehicle passes the intersection, it may slow down, stop, or turn riht or left. Then, the velocity vector v ( o ) v( o ) should evidently be chaned. When this is accurately found at an intersection point, toether with the location information of that intersection in the dital map database, we can tae a new p ( o ) ust at the intersection, and ben a new innovative procedure of the RCD alorithm. Then, we can record this new e ( o ) in Eq. (4) with a hih precision. References. Bao Yuanlu, Xia Bin, Bao Yuanhui. Three ey techniques on exploitation of GPS vehicle monitorin systems [J]. China Hihway (3), 4(00). Shen-Guo Wan and Yuanlu Bao. New intellient method to enerate vector maps for GPS naviation [C]. IFAC World Conress 0. Paper number: 57(00) 3. Jiamin Ye, Yuanlu Bao, Aipin Liu. Road Extraction from Color City Map [A]. ICCA 0, C60(00) 4. Guo Jiehua, Yao Zhenwan, Bao Yuanlu, Zhan Wanshen. An autoproofreadin alorithm of eoraphic vector map [J]. Journal of Imae and Graphics, 43(999)

11 5. Wenzhon Shi and Chanqin Zhu, The Line Sement Match Method for Extractin Road Networ From Hih-Resolution Satellite Imaes [J]. IEEE Trans. Geoscience and Remote Sensin. CA5(00)