VEHICLE LOCALIZATION IN URBAN CANYONS USING GEO-REFERENCED DATA AND FEW GNSS SATELLITES Cleent Fouque Philippe Bonnifait Heudiasyc UMR CNRS 6599, Universite de Technologie de Copiegne, France. firstnae.nae@hds.utc.fr Abstract: Global Navigation Satellites Systes (GNSS) alone can provide very accurate positioning - few centieters in real-tie if the satellites visibility is very good and if there is no ulti-track or refraction of the RF signals. Unfortunately, when a vehicle evolves in urban areas these conditions are rarely satisfied: the coputed location can be uch debased and even not possible, if less than four satellites are directly visible or if the geoetry is badly configured with a poor GDOP. A way to tackle such a proble can consist in using the pseudo-ranges easured by the GNSS receiver (instead of using its navigation solution) and in fusing the with other data sources like for instance proprioceptive sensors. In this paper, we study the use of a priori charted data anaged by a Geographical Inforation Syste (GIS). We focus here on the use of a road network provided by cartographers like NavTeQ or TeleAtlas. We explain how to use such inforation in the coputation fix: the geo-referenced data is odeled as a linear segent that can be used as a constraint or fused with the pseudo-ranges. The underlying proble of choosing the good segent (known as the road selection proble) is also treated in this paper. We proposed a new ethod that uses the residuals to do this selection. Experiental results perfored in Copiegne illustrate the interesting perforance of this approach since the ap-atched location can be coputed using only 3 satellites and a usual 2D ap in urban canyons. Keywords: Outdoor Localization, Global Navigation Satellites Systes, GIS data, tightly coupled data fusion 1. INTRODUCTION The positioning of an intelligent vehicle with respect to a given ap is an iportant issue for any robotics applications. For instance, the ap inforation is very useful for trajectory planning (Jabbour et al., 2006) or for contextual inforation retrieval. In soe applications, this inforation can be natural landarks stored as Geographical Inforation and used for a precise positioning (Reazeilles et al., 2004). Global Navigation Satellites Systes (GNSS) like GPS, Glonass or Galileo are very proising and affordable technologies for robotics. We can iagine that each vehicle will be soon equipped with a GNSS receiver. The proble that consists in localizing a vehicle with respect to a ap is known as apatching. Usually this proble is tackled using GNSS fixes, i.e. position solutions coputed using pseudo-ranges and epheeris data. This approach has the ain drawback to need at least four satellites in line of sight.this condition is rarely satisfied in urban canyon (Georgiev and Allen, 2004). An alternative consists in using a tightly coupled approach in which the ap inforation is used in
the coputation of the fix. This is the approach considered in this paper. We focus here on the use of a road ap provided by cartographers. The available inforation describes the centerline of the carriageways in a 2D representation. The ain difficulty consists in using such inforation in the GNSS coputation. We propose in the following an approach to reach this goal. We show how to construct a navigation frae in which the position of the satellites at their eission tie is known. By supposing first that the road is known, we show how to copute a location. Then, we propose a strategy to select the ost likely road by using the residuals of the coputation. Experiental results carried out with our experiental show the perforance of the approach: the ethod is able to work in an urban canyon using only 3 satellites. The paper is organized as follows. Section 2 will reind how a stand-alone GPS fix is coputed, then several ethods for ap-aided GPS positioning will be presented in Section 3. In Section 4 a siple road selection algorith will be presented. To conclude, Section 5 will show soe experiental results obtained using the presented road selection algorith and the ap-aided GPS positioning. 2. STAND-ALONE GPS POSITIONING GNSS positioning is based on the ultilateration principle: easuring the tie of flight between a receiver and four SVs (Space Vehicles), it is possible to copute the 3D position of the receiver in a ECEF (Earth Centered, Earth Fixed) frae using the WGS84 geodetic syste. In this section, we present a ethod to copute an approxiate position of the satellites before carrying out the localization coputation, under the hypothesis that the receiver clock is approxiately synchronized with the GPS tie. This ethod is not necessary for GNSS stand alone coputation. It will be useful for the fusion with the Geographical Inforation Syste (GIS) data. 2.1 SV estiated positions SVs broadcast in real-tie epheerids data that contains Keplerian paraeters describing their orbits. Given a GPS tie-stap t i e, it is possible to copute an estiate position of the SV at this tie index in the ECEF(t i e), since ECEF rotates with the earth. The receiver has to solve the following probles: (1) What is the eission tie t i e of the sequence sent by SV i? (2) What was the position SV i at tie t i e in ECEF(t i e )? (3) What is this position in the current ECEF? The receiver estiates the tie of flight t i flight of a sequence broadcast a SV, by easuring the shift between the eitted frae and its locally generated replica (C/A code): t i flight = t r t i e (1) Where t r is the reception tie and t i e is the eission tie in the GPS tie reference syste. t i flight is in the order of 70s. Unfortunately, there is an internal clock bias in the receiver copared to the GPS reference tie. At the reception tie, the receiver reads its clock t u (t r ). We have: t r = t u (t r ) + dt u (2) The eission tie is therefore given by: t i e = t u(t r ) + dt u t i flight (3) If the internal clock bias of the receiver is kept sall, then t i e can be approxiated by ˆt i e = t u(t r ) t i flight,easured (4) Using ˆt i e, it is possible to copute an estiated position Xsat i = ( x i (ˆt i e ), yi (ˆt i e ), zi (ˆt i e )) of SV i in the frae ECEF(t i e) using the broadcast epheeris. See (Kaplan, 2000) for details. Now, we need to express the SV position X i sat in ECEF(t r ). If we odel the earth rotation by a siple 24 hours periodic rotation around z axis (ECEF coordinates), then the earth rotation angle between eission and reception ties is: α i earth = ω earth t i flight,easured (5) Using the angle express in 6, a single yaw rotation between ECEF(t i e ) and ECEF(t r) is done. 2.2 Receiver position coputation To copute the position of the receiver, let consider now the pseudo-range easureent ρ i done by the receiver on SV i: ρ i = c t i flight,easured (6) where t i flight,easured is the easured tie of flight. Like the receiver, SV i has an clock offset: t i e = t s(t r ) + dt i s (7) So, we can rewrite the pseudo-range easureent as: ρ i = c (t r t i e ) + c (dt u dt i s ) (8)
Where c is the speed of light in vacuu. Let denote R i the geoetrical distance between SV i and the receiver in ECEF(t r ) frae: R i = (x+x i (t i e)) 2 +(y+y i (t e )) 2 +(z+z i (t e )) 2 (9) R i = c (t r t i e ) (10) For siplification, let us assue that dt i s can be precisely known using the epheerids data. The corrected pseudo-range ρ i c is given using Eq.8: ρ i c = Ri + c dt u (11) Using Eq.9 and Eq.11, a relationship between corrected pseudo-range easureent for a SV and the receiver position and its internal clock bias has been built. Assuing n visible SVs, we can write a state vector X an observation vector Y : X = [x, y, z, dt u ] t, Y = [ρ 1 c,, ρ n c ] t (12) A non-linear equation syste is obtained. If n > 4, then the syste is also redundant. It is a static positioning proble that can be solved using an iterative least squares ethod or a Bancroft non-iterative ethod. Those ethods are not explained here. We invite readers to refer to (Kaplan, 2000) and (Yang and Chen, 2001). 3. USING A ROAD SEGMENT IN THE POSITIONING COMPUTATION We now intend to introduce the geographical inforation in the position coputation. To illustrate this concept, let us use a digital road ap. Under the hypothesis that the current evolution segent is known, we present in this section two ways to use the cartographic data. 3.1 Road aps A road ap is a database that contains a vectorial description of the road network. Roads are described in a discrete way by their center-line. The data associated with a road is classified in three groups: Geographical inforation: a segent set describing the geoetry road Topological inforation: description of connectivity between roads segents Seantic inforation: Road nae, speed liit, etc... Actually, nuerical road aps can achieve a etrical precision, which is sufficient to any navigation tasks, like route planning. 3.2 Working Frae In order to copute a valid tightly coupled GNSS/ap-atching positioning solution, a coon working frae is necessary. Let recall that GPS provides epheerids data in the WGS84 Cartesian frae whereas aps depict earth surface using planar projection such as Labert93 in France (conforal conic projection). Using the geographical data of the ap, let us deterine a tridiensional local frae such as (O, i, j) is tangential to the WGS84 Earth reference ellipsoid, since the elevation is not available in an usual ap. Suppose the syste has in eory a cache of the roads around the current position of the vehicle. The origin O is chosen to be the origin of the first node. The x axis is defined as the first following shape point of the first road. The plane (O, i, j) is defined by a shape point of another road (in the working frae, all the ap points have z = 0). An hoogeneous transfor is therefore coputed to obtain a WGS84 Cartesian position in the local frae: x y z 1 loc x = T WGS84 loc y z 1 WGS84 3.3 Plane Constraint for Coputation (13) Let suppose that the good road segent has been selected fro the road points given by the GIS. The constraint defined by this selected segent is a piece of a vertical plane (in the working frae), since the elevation of the ap is unknown. In practice, we consider the whole plane and we check afterwards that result atches with the segent. Taking A(a 1, a 2 ) and B(b 1, b 2 ) as the extreity of the segent, the segent defines a straight line: y = b 1 + b 2 a 2 b 1 a 1 (x a 1 ) (14) The geoetrical equation of the constraint eans that only the coputation along (x, y) is constrained: { y = f1 (x) (15) z = var 3.4 First ethod: Unknown Eliination This ethod has been proposed by Cui and Ge in (Cui and Ge, 2003). The idea is to eliinate
the positions of which are projected onto the twodiensional ap frae thanks to their aziuth and elevation angles. Theirs easureents can be copared to circles of radii ρ ± ǫ where ǫ defines the uncertainty of the easureent. Assuing the vehicle is oving on a charted road, the longitudinal precision provided by the GNSS is ore iportant to achieve a good positioning. According to Fig.1, one can intuitively notice that if the SVs are located in the direction of the road, they provide a better positioning inforation than those orthogonal to the road. Fig. 1. Incertainity aera according to SV position regarding the road direction: on the left, 2 satellites are seen transversally; on the right, they are seen in the direction of the road. a variable using the constraint equation. Introducing Eq.15 in Eq.9, the geoetrical distance between the receiver and SV i can be rewritten as: R i = (x+x i (t e )) 2 +(f 1 (x)+y i (t e )) 2 +(z+z i (t e )) 2 (16) This new expression of the geoetrical distance gives a new non-linear syste: ρ i c = h i (x, z, dt u ), i = 1,,n (17) The proble diension is now reduced and the inial nuber of needed SVs to achieve the coputation of positioning solution is now 3. Since the constraint is strong, the coputed position belongs to the constraint plane. Please note that its projection onto the ap can be outside of the segent. 3.5 Second ethod: Plane Fusion This ethod has been proposed by S. Syed and M.E. Cannon in (Syed and Cannon, 2004). Using the segent paraeters, a new observable is built. Therefore, it is possible to add a new equation to the observation odel defined using Eq.14: (b 1 a 1 ) a 2 +(a 2 b 2 ) a 1 =(b 1 a 1 ) y+(a 2 b 2 ) x ρ n+1 c = h n+1 (x, y, z, dt u ) (18) With this additional easureent and at least three SVs, the positioning solution can be coputed. Contrary to the unknown eliination ethod, the coputed solution doesn t belong to the constraint plane defined by the road segent. 3.6 SVs position relative to road heading The geoetrical configuration of the SV versus the current segent is crucial. Let consider 2 SVs 4. ROAD SELECTION ALGORITHM We have seen how a road segent inforation can be introduced into the positioning solution coputation. A road selection algorith is proposed in order to select the evolution segent that best atches the current GNSS observations. In order to reduce the road selection algorith processing tie, a road cache has been extracted fro the ap around a first GNSS fix. 4.1 Candidate segents extraction For each segent in the road cache, a tightly coupled positioning solution is coputed using the unknown eliination ethod described previously in Section 3.4 in order to deterine the corresponding atched point. Therefore, a nonlinear equation syste like Eq.17 is solved for each segent. A fix solution is coputed using the Newton-Raphson Least Squares iterative solver. A segent can be considered as a candidate if: The projection of the fix onto the reference plane (0, i, j) belongs to the considered segent. The fix elevation is close to 0 in the local frae (i.e. lower than an user s defined threshold). Please note that this stage can provide no segent. This can indicate large ap errors or bad GNSS observations. 4.2 Positioning solution residuals As the positioning solution is coputed using a Newton-Raphson iterative solver with a fixed nuber of iterations, we suggest to use the residuals. Indeed, they allow defining a consistency value in order to choose the ost probable segent: where: Res = Y H dx (19)
Selected road and Matched Points in Local frae Selected road and Matched Points in Local frae 60 12 9 6 60 12 9 6 40 15 PRN: 24 40 15 20 20 0 PRN: 4 PRN: 13 18 9 6 0 PRN: 4 18 9 6 20 40 60 PRN: 2 15 Candidte Seg. Chosen Seg. Unknow Eliination 12 Plan Fusion GPS Fix 9 PRN: 23 6 PRN: 20 20 40 60 PRN: 2 15 Candidte Seg. Chosen Seg. Unknow Eliination 12 Plan Fusion GPS Fix 9 6 PRN: 20 80 80 100 80 60 40 20 0 20 40 60 80 100 Fig. 2. Road selection results and positioning solution using all visible SVs Y is the easureent H is the Jacobian atrix of the observation equation dx is the residuals vector of the coputation. 4.3 Most likely segent selection Without any a priori inforation on the vehicle position, the segent with the better consistency is chosen as the ost likely segent. Otherwise, if the vehicle position on a segent is known with good accuracy at one oent, then a connex candidate segent is preferred. 5. FIRST EXPERIMENTAL RESULTS 5.1 Methodology Experients have been carried out in two stages. The first stage dealt with data recording and the second with data exploitation. Data has been recorded using our laboratory experiental vehicle strada and a GPS receiver type Trible 5700 in a stand-alone ode. The data recording has been done on a road next to the lab and this road has been well identified in the geographical database. SVs easureents were recorded using Rinex 2.10 observation file forat and the corresponding navigation file has been used. We analyze in this section the road selection algorith and the tightly coupled GNSS-Map fusion using a single fix. For siplicity, the local frae has been set along the current evolution segent. Therefore, the (O, i) axle coincides with the good segent. Please notice that this segent in reality is not East oriented. Moreover, the SVs used in the position coputation have been superposed on the ap using a skyplot graphic which allows to estiate their elevation and aziuth angles respectively with the origin of the local frae. 100 80 60 40 20 0 20 40 60 80 100 Fig. 3. Road selection and position using three SVs near to the road axle 5.2 Results using 6 SVs As shown by Fig.2, let consider what happens if all the 6 visible SVs are used for the coputation. 4 segents are claied to be candidate (those plotted in dash) and the current evolution segent has been correctly chosen as the ost likely segent (plotted in bold). As presented in Section 3, the positioning solution coputed using the unknown eliination ethod has correctly eliinated the incorrect segents, because they have provided solutions outside of the segents or too far fro the horizontal frae of the ap. Moreover, if we exaine the result of the autonoous GNSS fix, we can observe a significant bias in the ap data (about 12 eters). This result show that the presented algorith is efficient for a siple road selection since there is little abiguity due to the other candidate segents. The relevance of the proposed tightly coupled GNSS-Map atching using the constraint plane is therefore shown. 5.3 Ipact of SVs configuration in the position coputation Let us now appreciate experientally the ipact of SVs configuration with respect to the road in the positioning solution coputation. As shown on Fig.3, only the SVs with aziuth near to road heading are used where as, on Fig.4, the SVs used are orthogonal to road direction. We can see that, when the SVs are spread along the segent axle, the correct evolution segent is the only one claied to be a candidate (and obviously selected). When using the SVs that are not along the segent axle, the correct evolution segent doesn t belong to the candidate segents list and the result of the coputation is incorrect. Further ore, we can notice that all the candidate segents direction are near to the axis ade by
60 40 20 0 Selected road and Matched Points in Local frae 9 12 6 15 PRN: 24 PRN: 13 9 6 18 this research is on the use of a dynaic state observer (for instance a Kalan filter) to take benefice of the road connectedness, particularly while approaching junction. Moreover, we plan also to use WAAS/EGNOS corrections to increase the reliability of the ethod. 20 40 60 80 15 Candidte Seg. Chosen Seg. Unknow Eliination 12 Plan Fusion GPS Fix 100 80 60 40 20 0 20 40 60 80 100 9 PRN: 23 Fig. 4. Road selection and position using three SVs orthogonal to the road axle the SVs and, in this case, orthogonal to the evolution segent. This result proves experientally the analysis done on Fig.1: in a urban canyon the visible satellites are naturally well configured for a tightly coupled GNSS-Map coputation and only 3 are sufficient. We have also rearked that, when using few SVs, the positioning solution coputed with both ethods introduced in section 3 are equivalent. This coes fro the fact, that when using few SVs, the weight of the constraint plane in the observation odel grows up and so attracts the atched point next to the road segent. 6. CONCLUSION AND FUTURE WORK In this paper, we have described two ethods to fuse road ap data with GNSS rough easureents (L1 pseudo-ranges). This approach has several advantages. First, as shown by the experients, it is possible to use only three satellites to copute a fix. Secondly, since the selection of a segent is necessary, the ap-atching proble is can be solved using the residuals of this coputation. The ain difficulty arises fro the need to copute a GNSS fix using the pseudo-ranges and particularly to locate the satellites thanks to the epheerid data in a frae attached to the ap. We have proposed a ethod that supposes that the clock drift of the receiver is sall. Therefore, the position of the satellites at their eission ties can be easily deterined in the frae of the ap. In order to solve the segent selection proble, we have proposed a siple search strategy. The results that we have obtained are very encouraging since the ethod is able to retrieve the good segent. We have also confired experientally that the satellites that are the ost interesting for the solution coputation are those that are in the axle of the road, which is the situation occurring in urban canyons. The perspective of 6 REFERENCES Cui, Y.J. and S.S. Ge (2003). Autonoous vehicle positioning with gps in urban canyon environents. IEEE Transactions on Robotics and Autoation 19, 15 25. Georgiev, A. and P. K. Allen (2004). Localization ethods for a obile robot in urban environents. IEEE Trans. on Robotics and Autoation 20, 851 864. Jabbour, M., Ph. Bonnifait and V. Cherfaoui (2006). Manageent of landarks in a gis for an enhanced localisation in urban areas. In: IV2006 IEEE Intelligent Vehicle Syposiu. Tokyo, Japan. Kaplan, Elliot D. (2000). Understanding GPS: principles and applications. Artech House. Reazeilles, A., F. Chauette and P. Gros (2004). Robot otion control fro a visual eory. IEEE Int. Conf. on Robotics and Autoation, ICRA 04 4, 4695 4700. Syed, S. and M.E. Cannon (2004). Fuzzy logicbased ap-atching algorith for vehicle navigation syste in urban canyons. Proceeding of th ION National Technical Meeting. Yang, M. and K-H. Chen (2001). Perforance assessent of a non-iterative aglorith for global positioning syste (gps) absolute positioning. Proc. Natl. Sci. Counc. ROC(A) 25, 102 106.