GPS World - May 2008 - (Page 50)

INNOVATION | Algorithms & Methods of the final solution is required for aborting processing when the expected precision exceeds a user-defined threshold. Ambiguities are assumed to be time-invariant during calculations. However, this is only true provided there is constant phase lock during . Cycle slips are discontinuities in the phase measurements caused by a temporary loss-of-lock in the carrier-tracking loop. Hence, the detection and exclusion of such slips and other outliers has to be ensured when working with time differences. FIGURE 1 illustrates the algorithm chosen to meet the abovementioned concerns. At the beginning of the trajectory section to be analyzed, a starting point at is determined via codebased single-point processing. The position of this point is accurate only to within a few meters and therefore offset by from the true track (grey line). All subsequent epochs, , are processed with respect to using time differences and the resulting track (black line) is precise relative to this starting point. If maneuvers causing loss-of-lock on too many satellites are performed (like the Immelmann loop aerobatic maneuver shown by the dashed red line), processing has to be aborted. A new base position at can be imported from the single-point solution right after the maneuver (no re-initialization) and processing can be continued relative to the new base epoch. Such an event will inevitably cause a gap in the resulting trajectory. In the example, the solution fails again between the base epoch, , and the current time, . However, this time there are enough healthy satellites observed at and to calculate the baseline between these two points (referred to as an inter-epoch solution later in this article). A base-epoch handover preventing a gap in the solution can be realized and processing is hereupon continued to . Quality of Results. Integrity and precision monitoring is realized through residual analysis. The (unbiased) residuals, , are the differences between the observed time-differenced phase ranges and the estimated ones; that is, the ranges dropping out from the last iteration step of the non-linear least-squares procedure. For more than four used satellites, the variance of the measurements, , can be estimated from an analysis of the residuals according to Å FIGURE 1 Basic principle of time differences. 0.4 (1) 3D offset (meters) 0.3 (1.1) (2) (2.1) 0.2 (3) (4) 0.1 0 0 2 4 6 8 10 (5) 3D offset (meters) 1.5 (6) 1.0 0.5 0 0 2 4 Time (minutes) 6 8 10 Å FIGURE 2 Static test 3D error: (1) best solution, (1.1) uncertainty estimate of best solution, (2) best solution with handover, (2.1) uncertainty estimate of best solution with handover, (3) no high-rate clocks, (4) broadcast ephemeris, (5) no ionospheric correction, (6) no tropospheric correction. the size of the residuals Ð which can, in principle, be used as a flag for detecting such bad measurements. As error drift raises the residual level over time, outliers run the risk of being buried by systematic errors. However, the residual level for a solution between subsequent epochs is very low as error drift has virtually no effect over small time intervals. The time-difference approach permits us to use the inter-epoch residual time history for outlier detection and classification. We are currently developing an algorithm to automate this process. where is the number of observed satellites. The Jacobian needed for linearizing the navigation equations is constructed using the line-of-sight unit vectors as in the single-point processing procedure. Therefore, the known concept of position dilution of precision (PDOP) can be applied to estimate the precision of the resulting baseline between and : Using this metric, the expected precision of the solution can be monitored at any time. The quality estimation is made less transparent in the case of a base-epoch handover, as the residual level drops down close to zero for such events. For this reason, handovers should be handled with care! Cycle slips or outliers increase 50 GPS World | May 2008 Practical Validation We will illustrate both the potential and the limitations of the time-difference approach using data gathered by a single-frequency receiver module during one static and two dynamic experiments. The receiver module has a footprint of 25 × 25 millimeters and a mass of 3 grams. For the tests, we used an evaluation kit offered by the manufacturer with an active 25 × 25 millimeter patch antenna. An RTK solution generated by TU Delft served as a reference for the dynamic tests. Static Test. A static test was performed on July 17, 2007, at the www.gpsworld.com http://www.gpsworld.com

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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

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