GPS World - May 2008 - (Page 54)

INNOVATION | Algorithms & Methods 0.25 3D offset (TD - RTK) 3D error estimate (TD) 0.20 0.15 0.10 0.05 0 20 40 60 80 100 120 140 160 180 Å FIGURE 7 Flight test/take-off: 3D offset of the time-difference solution from the RTK solution with error estimation. 7.0 6.5 6.0 100 80 60 Time (seconds) 5.5 5.0 4.5 4.0 400 0 40 20 g (me ters) 3.5 3.0 2.5 -20 -40 -200 200 Northing (meters) -400 -600 0 -800 Å FIGURE 8 Flight test/dynamic curve: 3D trajectory color-coded with PDOP. 0.4 3D offset (TD - RTK) 3D error estimate (TD) off in local topocentric coordinates, color-coded with PDOP values. With the number of used satellites dropping from six to five after 116 seconds, PDOP rises from 2.0 to 2.25. This moderate increase only marginally affects precision itself but has a negative impact on its estimation. The 3D offset between the time-difference solution and the RTK solution stays within 2 decimeters during 3 minutes and 20 seconds of processing (see black line in FIGURE 7). During the first 170 seconds, the estimate of the error (grey line) agrees well with the observed offset. This is not true for the last 30 seconds. Here, the residual level drops to low values, which directly affects the precision estimate. Even though the true trajectory is not known, this effect is most likely caused by the low number of used satellites, which impedes the proper estimation of the measurement variance in this case. A second section, as depicted in FIGURE 8, was processed with time differences. Here, a dynamic soaring-like maneuver was flown with a bank angle of approximately 50 degrees in an upward curve. This trajectory caused the number of used satellites to drop from six to five after 12 seconds and a base-epoch handover after 16 seconds. PDOP values rose from 2.1 to 2.85 after 12 seconds. Following the base handover, the geometry of the visible constellation remained poor with only five satellites available (PDOP of 7.1). Due to the adverse visibility conditions, measuring the described maneuver is difficult and the time span which can be processed with satisfactory precision is limited to half a minute. The low number of used satellites and the base-epoch handover after 16 seconds (error estimate drops to zero) reduce the reliability of the error estimation. This is confirmed by the grey line in FIGURE 9. In this case, the error estimate is very unsteady and too pessimistic Ð a result which can only be confirmed by comparison with a reference. During the considered time-span, the RTK and time-difference solutions coincide with less than a 2 decimeter offset (see black line in Figure 9). Up (meters) 3D offset and error estimate (meters) 3D offset and error estimate (meters) 0.35 Eastin 0.3 0.25 0.2 0.15 0.1 0.05 0 0 5 10 Time (seconds) 15 20 25 Å FIGURE 9 Flight test/take-off: 3D offset of the time-difference solution from the RTK solution with error estimation. precise ephemerides and tropospheric and ionospheric corrections were used to process the cycle-slip-and-outlier-corrected data. FIGURE 6 shows the resulting 3D trajectory for taxi and take54 GPS World | May 2008 Conclusions The time-difference approach is a true L1-only phase-observation processing method for measuring kinematic trajectories. Only one, low-cost, single-frequency GPS receiver is required to obtain decimeter or sub-decimeter precision relative to a starting point for trajectory sections lasting up to several minutes. The temporal limitation represents the main downside of the approach. Further, one has to be aware that phase-data observables are very sensitive to signal obstruction and antenna tilting. This is a disadvantage faced by every type of phase-based processing. The user must always be aware of what he or she is actually doing with the receiver. However, no additional effort such as initialization, implementing a nearby base station, surveying a reference point, or making use of a satellite- or ground-based augmentation system is required for the time-difference method. The technique permits trajectory determination virtually (Continued on page 57) www.gpsworld.com http://www.gpsworld.com

Table of Contents Feed for the Digital Edition of GPS World - May 2008

GPS World - May 2008 Contents Out in Front Letters to the Editor Expert Advice GPS III Contract Award Now a Reality? Near-Space Location Boost RTK Crops Up in Precision Ag Safety Afoot 50+ Leaders to Watch Making a Difference with GPS Product Showcase Advertisers Index & Company Directory Marketplace Classifieds Seen & Heard

GPS World - May 2008

For optimal viewing of this digital publication, please enable JavaScript and then refresh the page. If you would like to try to load the digital publication without using Flash Player detection, please click here.