Simulation:
Effect of RF Noise on Position Accuracy
Now that the autocorrelation process is understood a little better, it is now time to see how the inaccuracies caused by noise in the autocorrelation process transfers to position inaccuracies. This part of the project was done in the GPS lab at the Center For Space Research. The equipment that was used was the Global Simulations Services GPS simulator, the Mitel Architect receiver, and the IntegriNautics pseudolite. Other miscellaneous equipment was a RF combiner to combine the one signal from the simulator with the pseudolite signal, and a supply of attenuators. These were both 10 dB in line attenuation, and a dial attenuator that ranged from 0 to 33dB in 3dB increments. The original plan was to investigate the effects of the near-far problem in addition to the cross correlation properties by transmitting the pseudolite at too high of a power level. However, the pseudolite uses a PRN that is not recognized by the receiver. After a few unsuccessful attempts to modify the software, the topic was shifted and the pseudolite was then used as a noise source.
Procedure
First, a baseline is established by attenuating the pseudolite to the approximate power level of the received signals from the satellites. Position information was taken for approximately thirty minutes. This procedure was repeated three more times at different pseudolite attenuation levels. The second test removed an additional 18 dB of attenuation. This level was chosen because that was the level where the received signal to noise ratio of was seen to drop. The third test saw a further reduction of the attenuation by another 10dB. This was estimated to be the tracking threshold. The final test involved turning the dial one notch to remove an additional 3 dB of attenuation.
Results and Discussions
The first test was fairly uneventful. It established a baseline for which to compare all the other readings. A plot of individual axis errors and the 3-axis error compared with the other cases is shown in Figure 1. The mean and the standard deviation of the position error turned out to be fairly good, with a 3-axis mean residual of 12.34 meters, and a standard deviation of 2.72 meters. These numbers can be compared with the values taken in the following cases in Table 1.
For the second test, the attenuation was dropped until the point where the signal to noise ratio was first noticed to change. This ended up being at 42 dB of attenuation. The results match the ones taken in the previous test. This was to be expected since the signal to noise ratio at the receiver dropped by less than 10%.
Next, in the third test an additional 10 dB of attenuation was removed to provide 32 dB still on the line. It should be noted that this test was run twice. The first time it was run the receiver ended up taking a long time to lock onto the satellites. In one case, it took an extra 12 minutes to find one satellite. In that case, the satellite was low on the horizon and the signal to noise ratio was low. As the elevation increased, so did the signal to noise ratio, and lock was finally acquired. Because it took so long to acquire the satellites, and since the time spans of the data collection needed to be similar, it was decided to increase the attenuation until all of the satellites were acquired at which time the attenuation would be returned to its testing level. You can see from the graph and from the data that the position accuracy decreased dramatically. One thing that was interesting to note was that towards the end of the data collection, there is a huge jump in the data. This was caused by SV 9, which had the lowest signal to noise ratio, and was constantly dropping in and out. At that point, the pseudorange reading for that satellite went to 250 meters. This reading throws off the mean and the standard deviation for this case, and without it the values would be about 25 meters for the mean 3-axis error, and 18 for the standard deviation.
For the last cast there is not much to report. The same procedure that was used in the previous case for acquiring the satellites was used here. However, shortly after the start of the data taking, SV 9 gave another erroneous pseudorange reading, this time at 593 meters. After that there was only one more data point before all of the satellites were lost. Throughout the short time of the data collection, satellite kept dropping in and out until the receiver lost all of them.
Figure 1 Effect of Varying the Pseudolite Attenuation on the Position Accuracy
Table 1 Position Accuracy with Various Attenuation Levels on the Pseudolite
Conclusions
This part proved helpful in understanding how high interference affects the position estimate. I had already known that as the signal to noise ratio decreased, the measurements would get more noisy until it reached a point where the receiver would lose lock. The part that I was unaware with was what happens when the signal to noise tracking threshold was reached. I can see that there were some false positive correlations from the noise spikes that should have been removed, but weren’t. In that case it is better to just not have the satellite with the low signal to noise ration corrupting the information. From one bad data point in the 32 dB case, the mean 3-axis error was 6 times greater than expected and the 3-axis standard deviation ended up 50 times higher than expected. I can now see there is good reason to have elevation masks, where satellites reading are rejected if they fall below a certain elevation, and signal to noise masks.