Sensors and Methods for Mobile Robot Positioning

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74 Part I Sensors for Mobile Robot Positioning Figure 3.6: Typical GPS static position error with SA "On." (Courtesy of [Byrne, 1993].) Figure 3.7: Typical GPS static position error with SA "Off". (Courtesy of Byrne [1993]).
Chapter 3: Active Beacons 75 All of the error sources listed in Table 3.3 are further influenced by the particular geometry of the four reference satellites at time of sighting. Ignoring time synchronization needs for the moment (i.e., so only three satellites are required), the most accurate three-dimensional trilater-ation solutions will result when the bearing or sight lines extending from the receiver to the respective satellites are mutually orthogonal. If the satellites are spaced close together in a tight cluster or otherwise arranged in a more or less collinear fashion with respect to the receiver as shown in Figure 3.8, the desired orthogonality is lost and the solution degrades accordingly. Terms used to describe the strength of the position fix based on the geometry include: Dilution of Precision (DOP), Horizontal Dilution of Precision (HDOP), Geometric Dilution of Precision (GDOP), Position Dilution of Precision (PDOP), Time Dilution of Precision (TDOP), and Vertical Dilution of Precision (VDOP). The various DOPs are error multipliers that indicate the accuracy of a particular type of position fix based on a certain pseudo-range error. For instance, if the pseudorange measurements are accurate to 10 meters (33 ft) and the HDOP is equal to 3.5, the horizontal position accuracy would be 10 × 3.5 = 35 meters (100 ft). A PDOP of 2 or 3 is fairly good, while a PDOP of 10 is not so good. Certain geometries can cause the DOP to become very large (infinite). Two useful DOP identities are shown in Equations (3.2) and (3.3). 2 2 2 PDOP = VDOP + HDOP (3.2) Acronyms used in this section 2 2 2 GDOP = PDOP + TDOP (3.3) Kihara and Okada [1984] show that the minimum achievable (best-case) value for GDOP is 1.5811. This optimal constellation occurs when the four required GPS satellites are symmetrically located with an angle of 109.47 degrees between adjacent bearing lines as shown in Figure 3.9. With the exception of multi-path effects, all of the error DOP dilution of precision GDOP geometric dilution of precision HDOP horizontal dilution of precision PDOP position dilution of precision TDOP Time dilution of precision VDOP vertical dilution of precision SA selective availability sources listed in Table 3.3 above can be essentially eliminated through use of a practice known as differential GPS (DGPS). The concept is based on the premise that a second GPS receiver in fairly close proximity (i.e., within 10 km — 6.2 mi) to the first will experience basically the same error effects when viewing the same reference satellites. If this second receiver is fixed at a precisely Figure 3.8: Worst-case geometric dilution of precision (GDOP) errors occur when the receiver and satellites approach a collinear configuration as shown [Everett, 1995].
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7KH8QLYHUVLW\RI0LFKLJDQ Where am I?
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Acknowledgments This research was s
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2.4.2.2 Watson Gyrocompass ........
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6.4 Summary .......................
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INTRODUCTION Leonard and Durrant-Wh
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Part I Sensors for Mobile Robot Pos
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14 Part I Sensors for Mobile Robot
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CHAPTER 5 ODOMETRY AND OTHER DEAD-R
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132 Part II Systems and Methods for
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R e t r o r e f l e c t i v e m a r
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CHAPTER 8 MAP-BASED POSITIONING Map
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218 Appendices, References, Indexes
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220 Appendices, References, Indexes
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Systems-at-a-Glance Tables Odometry
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Systems-at-a-Glance Tables Global N
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Systems-at-a Glance Tables Beacon N
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Systems-at-a-Glance Tables Landmark
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REFERENCES 1. Abidi, M. and Chandra
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238 References 31. Boltinghouse, S.
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240 References MOBOT-IV.” Proceed
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242 References 90. Dahlin, T. and K
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244 References 120. Fisher, D., Hol
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246 References 156. Janet, J., Luo,
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248 References 187. Larsson, U., Ze
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250 References 220. Nolan, D.A., Bl
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252 References 249. Sanders, G.A.,
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254 References 278. Turpin, D.R., 1
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256 References 309. EATON - Eaton-K
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258 References 349. SPSi - Spatial
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260 References 380. MacKenzie, P. a
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262 Index AC ..............47, 59,
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264 Index Datums ..................
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266 Index glass ...................
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268 Index lateral-post ............
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270 Index NPN .....................
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272 Index signal ..... 17, 31, 38,
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274 Index Abidi ...................
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280 Index Video Index This CD-ROM c
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282 Index Paper 52 Paper 53 Paper 5
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