System Testing

Abstract

One important aspect in the design and development of a positioning system is the performance testing to ensure the actual equipment meets the design requirements. While this testing would include the testing of all the subsystems (including the RF receiver and transmitter, analog baseband components, digital signal processing, and processor software), this chapter concentrates on the overall integrated performance testing.

Annex A—Accuracy Evaluation of Differential GPS

11.1.1 Introduction

This annex provides an accuracy evaluation of Differential GPS (DGPS) system with one Base and one Rover unit. The motivation for this objective is associated with the determining the accurate positions of Base Stations for outside positioning systems. Ideally, a system would need very accurate positions of Base Stations and this could be obtained by standard surveying methods (millimeters accuracy), such as using a Theodolite (angle measurements) or a Total Station which incorporates both a angle and distance measurements. This is a very time-consuming and expensive method, so a more elegant approach is to use GPS for the surveying task. Due to the accuracy limitation (3—15 m) an ordinary GPS system (Selective Availability inactive) would be inadequate. Therefore, Differential or Kinematic versions of GPS are to be considered. DGPS improves the accuracy of the non-differential version by 5—10 times. This is achieved by applying differential corrections to the measured pseudoranges of the rover GPS unit. The following provides information on the expected accuracy of DGPS based on test measurements.

For the simplest version of Differential GPS (shown in Fig. 11.29) a Base unit and a Rover unit is required. The Base unit is positioned at a known (surveyed) location. Differential corrections are generated as the difference between the currently calculated Base position and the fixed (surveyed) position. Corrections are then transmitted (by cable or radio) to the Rover unit to correct currently measured Rover position.

Fig. 11.29

Setup for Differential GPS

Accurate Base positions can be obtained either by classic surveying methods (Theodolite/Total Station equipment) or by long-term averaging using the GPS receiver itself. As mentioned above, the first method is expensive requiring specialist surveying equipment. The second method on the other hand takes a long time, but can use relatively cheap GPS units. To get a reasonably accurate positions the Base GPS unit has to be in “self-surveying” mode for about 24 h.

11.1.2 Measurements

Several tests were carried out with an initial setup with the units only a few meters apart, and thus could be connected by a cable. The measurements were performed on the flat roof of a building, but it is surrounded by other low-rise buildings and large trees which could partially obscure the path to GPS satellites. The initial test was aimed at determining how long the DGPS measurements need to be averaged to obtain a sufficiently accurate measurement of the Rover position. The initial tests used 15 min of averaging. However, to obtain a good initial reference for the Base unit, 24 h of positional data were averaged. In three 15 min measurements (taken at different times of day) the obtained accuracies were 0.2, 0.23 and 0.35 m. Figure 11.30 shows an example plot of the variation in measured positions over the 15 min period. As can be observed there is a generally chaotic variation over time, with no real pattern or correlation between the two units, and with considerable error from the 24 h average.

Fig. 11.30

Base and Rover units’ positions recorded over 15 min; averaged Rover position has a 0.2 m error in distance from the Base unit

Quite clearly the 15 min averaging interval is not long enough to get reasonable accuracy but it improves the instantaneous readings significantly. However, changing the averaging time will not necessarily improve the accuracy of the position. In one particular measurement the estimate of accuracy was getting worse with longer averaging. This is shown in table below.

Averaging time (min)	Distance (m)	Error (m)
5	84.12305	−0.80695
10	84.17194	−0.75806
15	83.94985	−0.98015
20	83.52374	−1.40626
25	83.32507	−1.60493
30	83.26382	−1.66618

In the second part of the testing, a similar test-setup was used but this time with a pair of radios so that differential corrections could be sent over a longer distance. Position measurements of Rover unit were taken at 2, 5, 10, 20, 40 and 80 m from the base station. The results were shown in Fig. 11.31. It is somewhat inconclusive that accuracy decreases with the bigger separation between Base and Rover units.

Fig. 11.31

Average error with 15 min of averaging as a function of the separations distance. Observe the errors are not particularly correlated with separation distance

The final test was carried out at a race course, which is largely free of obstacles. The separation distance between Base and Rover unit was 671.9 m. The true distance between Base and Rover antennas was measured with a Total Station to millimeters accuracy. The Base GPS unit was given roughly the correct position coordinates and differential corrections were transmitted to the Rover unit using a radio link. Position data were logged over 1 h. The differential distance between the Base (given coordinates) and Rover unit (recorded data) was calculated with 5, 10, 15…60 min averaging times. The measurement error is then calculated as difference between true (Total Station) distance and differential distances calculated from position averages. The results are shown in Fig. 11.32. This measurement suggests that after 15 min, differential accuracy is better than 0.8 m in an open field situation.

Fig. 11.32

Differential error between DGPS base and rover unit; error is calculated after 5, 10, 15…60 min of averaged positions