KSCE Journal of Civil Engineering (2008) 12(6):401-408 DOI 10.1007/s12205-008-0401-9
Surveying and Geo-Spatial Information Engineering
www.springer.com/12205
A GIS-based Simulation to Predict GPS Availability along the Tehran Road in Seoul, Korea Yang-Won Lee*, Yongcheol Suh**, and Ryosuke Shibasaki*** Received April 18, 2008/Accepted August 26, 2008
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Abstract GPS (Global Positioning System) availability is somewhat limited in urban areas because portions of the signals are blocked, reflected, and diffracted by obstructions like buildings. This has been well known through a number of on-site surveys, and recent GIS (Geographic Information System) approaches also simulate the urban GPS availability using 3-D (three-dimensional) terrain data. However, such simulation for skyscraper areas in Seoul, Korea has not been reported yet. Hence, we built a GIS-based prediction model to analyze the GPS availability in terms of LOS (Line of Sight) and DOP (Dilution of Precision), and conducted a simulation for the Tehran Road in Seoul, according to time and location. Our prediction model can show spatiotemporal aspects in GPS availability and apply to examine when and where the navigation services are usable in dense urban areas. Keywords: Global Navigation Satellite System (GNSS), Global Positioning System (GPS), satellite availability simulation, Geographic Information System (GIS) ···································································································································································································································
1. Introduction Navigation is the science of guiding a vehicle or person from one place to another (Kaplan, 2006), and the GNSS (Global Navigation Satellite System) is a key component of modern navigation services. The American GPS (Global Positioning System) and the Russian GLONASS (Global Navigation Satellite System) are currently operational while the European Union’s GALILEO will be fully operational by the mid-2010s. As an RNSS (regional navigation satellite system) that covers Asia and Oceania, the Japanese QZSS (Quasi-Zenith Satellite System) is expected to be launched by the mid-2010s. It is obvious that the integration of multiple GNSSs (including RNSS) will advance the usability of navigation services (Dellago et al., 2003; Kawano et al., 2004; Seynat et al., 2004; Wu et al., 2004; Lee et al., 2005; Bae et al., 2006; Feng and Wang, 2007; Januszewski, 2007; Lavrakas, 2007). However, in dense urban areas, benefits from such integration may be somewhat limited because portions of the signals are blocked, reflected, and diffracted by obstructions like buildings. When evaluating the GNSS availability in urban canyons, local terrain variations should be taken into account since the satellite visibility and the user/satellite geometry are highly dependent on surrounding geographic features (Li et al., 2006). Recent GIS (geographic information system) approaches have used 3-D (three-dimensional) terrain data to predict GPS availability, for
example, in Tokyo (Suh et al., 2004; Lee et al., 2006; Suh and Lee, 2007; Suh and Shibasaki, 2007) or in London (Taylor et al., 2005; Li et al., 2006; Taylor et al., 2007). The simulation results were almost in agreement with on-site surveys, which indicates that GIS methods can be of help especially for dense urban areas. Such simulation for skyscraper areas in Seoul, Korea has not been reported yet. Thus, in this paper, we present a GIS-based simulation to predict GNSS availability along the Tehran Road in Seoul. The GPS availability is explored here, and the availability of an integrated GNSS (e.g., GPS, GALILEO, and QZSS) will be dealt with in our next paper. In order to estimate spatiotemporal variations in GNSS availability, we built a prediction model to analyze LOS (line of sight) and DOP (dilution of precision) according to time and location. The LOS and DOP analyses are based on the geometric relationships among satellites, a receiver, and an obstruction. Satellite positions were modeled using the almanac of GPS, and 3-D obstruction objects were created from 1-m resolution DEM (digital elevation model) and DSM (digital surface model). Our simulation can apply to show when and where the navigation services are usable in dense urban areas.
2. GPS Availability Prediction Model GPS availability changes over time and space because satellites rotate around the Earth and the obstructions in urban areas can block the signal against a user. To account for such spatiotemporal
***Postdoctoral Researcher, Center for Spatial Information Science, The University of Tokyo, Tokyo, Japan (E-mail:
[email protected]) ***Member, Assistant Professor, Dept. of Satellite Information Sciences, Pukyong National University, Busan 608-737, Korea (Corresponding Author, Email:
[email protected]) ***Director and Professor, Center for Spatial Information Science, The University of Tokyo, Tokyo, Japan (E-mail:
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Yang-Won Lee, Yongcheol Suh, and Ryosuke Shibasaki
Fig. 1. Coordinate Transformation for Determination of Satellite Position
variability, our prediction model includes three parts: (1) determination of satellite position, (2) obstruction modeling, and (3) LOS and DOP analyses. 2.1 Determination of Satellite Position Satellite positions are usually expressed in LTP (local tangent plane) coordinate system because a satellite position and a user position should be comparable in the same geodetic coordinate system. We derived LTP coordinates of a satellite from the Keplerian orbital elements, by the following steps (Fig. 1). 2.1.1 Satellite Position in Geocentric Perifocal Coordinates The geocentric perifocal coordinate system has its origin at the center of the Earth. The X-Y plane coincides with the satellite orbital plane, where the X-axis is directed toward the vernal equinox and the Y-axis is 90° from the X-axis in the direction of satellite motion. The position of a satellite can be expressed as xp = r cos v ,
(1)
yp = r sin v, and
(2)
zp = 0 ,
(3)
using the radius ( r ) and the true anomaly ( v ). The radius is 2 defined as a ( 1 – e )/ ( 1 + e cos v ) , where a is the semi-major axis and e is the eccentricity. 2.1.2 Geocentric Perifocal Coordinates to Geocentric Equatorial Coordinates The geocentric equatorial coordinate system also has its origin at the center of the Earth, but the X-Y plane coincides with the Equator. The X-axis points in the direction of the vernal equinox and the Zaxis is directed to the North Pole. We converted the geocentric perifocal coordinates to geocentric equatorial coordinates, using the following transformation matrix: cosΩ cos ω – cosi sinΩ sin ω – cos Ω sin ω – cos i sin Ω cosω sinisinΩ R = sinΩ cos ω + cosicosΩ sinω –sinΩ sin ω + cos icosΩ cosω –sinicosΩ sinisin ω –sin icosω cosi
(4) where Ω is the RAAN, ω is the argument of perigee, and i is the inclination. Here, the position of a satellite ( xe, ye, ze ) is expressed as xe = R11 xp + R12 yp + R13 zp ,
(5)
ye = R21 xp + R22 yp + R23 zp , and
(6)
ze = R31 xp + R32 yp + R33 zp .
(7)
2.1.3 Geocentric Equatorial Coordinates to ECEF Coordinates The ECEF (Earth-Centered, Earth-Fixed) uses a threedimensional Cartesian coordinate system so that it can describe the position of a satellite in meters from the center of the Earth. The XY-axis defines the equatorial plane, and the Z-axis pierces the North Pole. These axes are fixed with respect to the Earth. The ECEF coordinates can be converted from the geocentric equatorial coordinates, using the rotation rate ( θ ) of a satellite. The ECEF coordinates of a satellite ( Xe, Ye, Ze ) are derived from the geocentric equatorial coordinates ( xe, ye, ze ) : xE = cos θ xe + sin θ ye ,
(8)
yE = – sin θ xe + cos θ ye , and
(9)
zE = ze .
(10)
2.1.4 ECEF Coordinates to LTP Coordinates The LTP is also known as the NED (North-East-Down) that uses the orientation of north, east, and down in a regional coordinate system. The down indicates the height below WGS84 (World Geodetic Datum 1984) ellipsoid. The three components can be represented in meters, and the ECEF coordinates ( xE, yE, zE ) are transformed to the LTP coordinates ( xL, yL, zL ) as follows: xL = sin ϕo cos λ o xE + sin ϕo sin λo yE – cos ϕo zE ,
(11)
yL = – sin λo xE + cos λ o yE , and
(12)
zL = cos ϕo cos λo xE + cos ϕo sin λ0 yE + cos ϕo zE – aW ,
(13)
where ϕo and λo are the latitude and longitude of the origin of a regional coordinate system, and aW is the semi-major axis of the WGS84 ellipsoid. 2.2 Obstruction Modeling To model the obstructions such as building and tree in a 3-D object, we used 1-m resolution DEM and DSM created from LiDAR (light detection and ranging). The height difference between DEM and DSM can be interpreted as the height above ground level; hence, we defined an obstruction as the grid cell that was at least 2 m higher than the ground level (Fig. 2). Remaining parts were regarded as ground surfaces.
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A GIS-based Simulation to Predict GPS Availability along the Tehran Road in Seoul, Korea
Fig. 2. Creation of 3D Obstruction Objects using DEM and DSM
Fig. 3. DEM and DSM Coordinate Transformation into LTP
The DEM and DSM used in this study are based on the TM (Transverse Mercator) coordinate system with WGS84 ellipsoid. For the comparisons with satellite positions, we converted the TM coordinates to the LTP coordinates (Fig. 3) through TM to LLA (latitude-longitude-altitude) transformation (Snyder, 1987), LLA to ECEF transformation, and ECEF to LTP transformation1). 2.3 LOS and DOP Analyses Using the coordinates of satellites and obstructions in the LTP coordinate system, an LOS analysis was conducted using a ray tracing technique. Ray tracing is a general method borrowed from geometrical optics that models the path of light by following the light rays as they interact with optical surfaces. The same principle applies to the path of electromagnetic signals (e.g., Wang and Yang, 2003; Diskin and Brennan, 2005; Jo et al., 2006; Kikuchi et al., 2006), and we employed a ray tracing technique to examine the paths of GPS signals in various local terrain conditions that were represented in 3D obstruction objects. We considered a satellite to be visible if the satellite-user segment does not intersect with any surrounding obstruction. The intersection between a ray and a 3-D object was computed using the methods in a Java library named “ j3d.” From the visible satellites, we filtered out those with an elevation lower than a given mask angle (e.g., 15o). This is because a low-elevation satellite is possibly prone to the signal contamination by reflections from buildings (Ward et al., 2006) as well as by atmospheric delays (Conley et al., 2006). Hence, the number of visible satellites in this simulation refers to that of relatively high-elevation satellites. 1)
IEEE Aerospace and Electronic Systems Society, http://psas.pdx.edu/ CoordinateSystem/Latitude_to_LocalTangent.pdf
Vol. 12, No. 6 / November 2008
Once visible satellites are identified for a user location, DOPs can be derived as the measure of user/satellite geometry. When visible satellites are adequately far apart in the sky, the geometry is regarded as favorable, and the DOP value is calculated as low; when close together, the geometry is unfavorable, and the DOP value is high. Thus, a low DOP is associated with better accuracy due to the wider angular separation among satellites. Several DOP parameters are used to characterize the accuracy components of GPS, and these are termed GDOP (geometric DOP), PDOP (position DOP), HDOP (horizontal DOP), VDOP (vertical DOP), and TDOP (time DOP). The PDOP is commonly used in evaluating the position solution of GPS because it represents the user/ satellite geometry in terms of a 3-D user position.
3. GPS Availability Simulation 3.1 Study Area We conducted a simulation experiment to evaluate the GPS availability for the Tehran Road in Seoul where many high buildings are located. In Fig. 4, our target area was represented in red while the green part denoted the obstructions that were identified using the height difference between DEM and DSM. To reflect local terrain variations in the simulation results, we divided the target area into grid cells of 1 m × 1 m. The simulation time was between 09:00 and 18:00 on 15 June 2007 (local time equals GMT + 9 h), and 30 satellites were operational at the date. 3.2 LOS and DOP Analyses For the GPS availability simulation in terms of LOS and DOP, we first tested our prediction model using four sample points on
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Yang-Won Lee, Yongcheol Suh, and Ryosuke Shibasaki
Fig. 4. Study Area: Tehran Road in Seoul, Korea
the Tehran Road (Fig. 5). The LOS and DOP were calculated for 12 hours at intervals of 1 hour because the repeat cycle of GPS is 11 hr 58 min. The four points were closely located, but the number of visible satellites (Fig. 6) and the PDOP values (Fig. 7) were quite different, which shows the spatial and temporal variations in the GPS availability in urban canyons. The mask angle used was 15o like ordinary GPS receivers. The PDOP values within 1σ were used in the DOP analysis. Suppose n ( n ≥ 4 ) satellites are visible to a user; then, the possible
n
nCi , where C is number of satellite constellation subsets will be i∑ =4 the combination noperator. In the same way, n visible satellites nCi values for a receiver location. We simply produce PDOP ∑ i= 4 derived the minimum, maximum, and mean of the PDOP values within 1σ. Then, we calculated the number of visible satellites and the mean PDOP values for the whole target area. The length of the Tehran Road is 4000 m and the width is 50 m while the target area in this simulation was set to approximately 3600 m × 60 m,
Fig. 5. Four Sample Points around the Yoksam Station on the Tehran Road − 404 −
KSCE Journal of Civil Engineering
A GIS-based Simulation to Predict GPS Availability along the Tehran Road in Seoul, Korea
Fig. 6. Number of Visible Satellites According to Simulation Time
Fig. 7. PDOP Values According to Simulation Time
including parts of the pavements. The number of visible satellites with a mask angle of 15o was estimated for 09:00, 12:00, 15:00, and 18:00 on 15 June 2007. Four or more satellites were available for almost all grid cells on the target area, but the visibility showed some spatial and temporal variations according to the distribution of buildings and Vol. 12, No. 6 / November 2008
to the orbital movements of satellites. At 09:00, ten satellites were visible in two thirds of the areas while seven or fewer satellites were available at 12:00 and 15:00. The number of visible satellites increased again at 18:00. The visibility at 21:00 would be similar to that of 9:00 because of the repeat cycle of GPS constellation (Table 1). The area around the Yoksam Station
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Yang-Won Lee, Yongcheol Suh, and Ryosuke Shibasaki
Table 1. Number of Visible Satellites According to Simulation Time (Mask angle = 15°) No. of satellites
09:00
12:00
15:00
18:00
Fewer than 3
0.0%
0.0%
0.2%
0.0%
4
0.0%
2.7%
1.9%
0.6%
5
0.2%
6.5%
6.1%
1.4%
6
0.9%
14.5%
12.5%
7.2%
7
6.3%
76.3%
79.3%
17.1%
8
12.4%
0.0%
0.00%
73.7%
9
13.9%
0.0%
0.00%
0.0%
10
66.3%
0.0%
0.00%
0.0%
09:00, 12:00, 15:00, and 18:00 on 15 June 2007. If more satellites are visible, there is a possibility that a position solution can have a lower PDOP value (that is, higher accuracy). Similar to the results of the visibility simulations, the mean PDOP was favorable at 09:00, but getting worse in the afternoon, and then recovered around 18:00. The area close to the Yoksam Station was also vulnerable to the PDOP (Fig. 9).
4. Conclusions
showed worse visibility for the four simulations (Fig. 8). The mean PDOP with a mask angle of 15o was estimated for
We built a GIS-based prediction model for the GPS availability in terms of LOS and DOP, and presented a simulation for the Tehran Road in Seoul. Our prediction model includes (1) determination of satellite position, (2) obstruction modeling, and (3) LOS and DOP analyses. The coordinates of moving satellites and the obstructions on the ground were compared using the
Fig. 8. Number of Visible Satellites on the Tehran Road − 406 −
KSCE Journal of Civil Engineering
A GIS-based Simulation to Predict GPS Availability along the Tehran Road in Seoul, Korea
Fig. 9. Mean PDOP on the Tehran Road
almanac of GPS and the 3-D terrain data from LiDAR, and we derived the satellite-obstruction-user geometry to calculate the number of visible satellites and the mean PDOP. The simulation results in the Tehran Road showed some spatial and temporal variations according to the orbital movements of GPS satellites and the distributions of buildings. Our prediction model can reveal the spatiotemporal aspects in GPS availability and apply to examine when and where the navigation services are usable in dense urban areas.
Vol. 12, No. 6 / November 2008
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