GPS Location Precision

[gplracerx]

Here's a plot of GPS position data from a VBOX Sport at a fixed location:
The reason that there are four series in the plot is Excel's limit of 32,000 data points in a series.

The collection time was about 1 hour and 45 minutes. The average number of satellites used was 7.8. The standard error was about 5 feet (1.5 m) NS and EW so 67% of the measurements should be within 10 feet of the true position. Sort of. The problem being that on the short term, the next reading is highly dependent on the previous reading. This is referred to in statistics as serial autocorrelation and is probably caused by filtering the data in the device to remove noise. What that means to the user is that to improve the precision of the location requires a lot more averaging than you might think. For the VBOX Sport with a 20Hz update rate, you would need to average for at least 200 seconds. Also, the error in the difference between two measurements well separated in time, like a POI and the car position is the square root of the sum of the squares of the standard errors or ~1.4 times the standard error of an individual measurement, 7 feet or 2.1m. Averaging to get a precise location for the POI can at best reduce that error to the error in an individual measurement. So my thought that HLT needs an averaging function for POI location wouldn't help enough to be worth it.

I need to run a few more of these to see if long term drift is significant compared to the single point measurement error. An averaging function or app would help to correct POI's if there is indeed significant drift. I'm also planning on testing other GPS units if I can figure out a way to log that much data.

[gplracerx]

Also, there was no warmup period. The device was turned on and logging started as soon as a lock was achieved. You can see the initial location at about 14 feet NS and -3 feet EW if you look closely. It's inside the range of all the measurements, barely. The device was out in the sun and the internal temperature increased to 49.5C from an initial 23.1C.

[Harry]

Interesting data... Referring to the thread on long term drift (viewtopic.php?f=10&t=1651&p=8438#p8423) it would be really interesting to see what happens within 5 or 6 hours... Inaccuracies in the range above would not generate detection problems like that described in the other thread...

- Harry

[gplracerx]

I've run the same experiment with the external magnetic antenna. The standard errors were more than twice as large. The antenna was on the roof of my car, so there should have been a sufficient ground plane. I have only run each experiment once, so it could possibly be day to day variation, but I don't think so. I thought the magnetic antenna would have been better rather than worse than the internal antenna.

The VBOX Sport has the advantage of internal data logging at ten significant figures. Using HLT, I can only get eight. I'm also wondering if there is GPS data filtering in iOS or HLT because eyeballing the data, the serial autocorrelation of the Emprum Ultimate was very high and I saw no variation at all for the XGPS160. Now if I had an iPad, I might be able to use the XGPS160's internal data logging capability now that the app is out.

[Harry]

Every GPS sensor applies some filtering on GPS data (Kalman or variant of Kalman filter). My observation is iOS applies a very "strong" filtering like seen in this picture on top of that:

LapTimer does not apply filtering on top of that applied by the sensors (or iOS) themselves (version 17.5 will have an option to further "soften" positions using a Kalman filter - but only as a Recalculate function to be applied manually). I assume it will be hard / next to impossible to find out what VBOX, XGPS, UltiMate apply here, I'm not even sure they do anything on top of what the chipset does.

iOS's filtering for all data going through Location Service are one of the reasons I strongly prefer sensors being connected directly.

On the magnetic antenna: I have a different perception here. Not motivated by the drift (which I have never measured), but by accuracy reported while driving, the VBOX with external antenna generates great accuracy on Nordschleife (which has difficult receiving conditions), while it nearly fails without this external antenna. Not sure you had the same weather and sun activity conditions when doing the tests?

- Harry

[gplracerx]

I've only run the two experiments with the VBOX Sport. I need to try the experiment with the device on the dashboard of the car rather than outside on the ground, which is near ideal, and I need to repeat the original experiments at least once. The other thing to do is look at the signal to noise for the satellite data. The Emprum Ultimate will definitely stream NMEA data to a computer and I think the XGPS160 will too. So I just need a program to log the data and translate it. I found some Java programs that might do the trick, but I haven't tried them yet.

[gplracerx]

Here's a different look at stability for an Emprum Ultimate. These are time series of latitude and longitude converted to meters. The data were obtained by using the Sensor Data app logging at 5 Hz on an iPod Touch v4.





The Emprum was not powered before connection to the iPod and logging was started as soon as it was connected. It looks like it takes at least 6 minutes of on time before the results begin to be stable. The interesting question is whether the glitches starting at 570 and 1040 seconds are random or correspond to changes in which satellites are included in the calculation. If it's satellites, then there is some chance that you could improve precision after the fact by comparing the record from the moving receiver with a similar receiver in a fixed location. The problem would be that conditions might not be the same for the moving receiver, trees beside the road or some other obstruction, for example. Synchronization would be done using the UTC timestamps from each receiver.

I'll post the equivalent charts for the VBOX sport experiment above in meters. Eyeballing the XY chart, it looks like the Emprum is much more heavily filtered than the VBOX Sport. However, that may also be a result of Sensor Data going through iOS Location Services.

[gplracerx]

And here's the data from the VBOX Sport:





While the Emprum looks more stable after a long warmup, stability has its cost in slow response to movement, as pointed out by Harry above. Based on this data, the VBOX Sport will be more accurate when moving even if the individual readings are less precise. The VBOX Sport does not appear to require any significant warmup either.

Maybe I can use HLT in manual timing mode to get a true comparison between the Emprum, the Dual XGPS160 and the VBOX Sport.

[Harry]

Do you have the same thing for the XGPS160? It's pretty interesting to see the different smoothing characteristics for the GPS chips used. I doubt it is influenced by the dongle models / providers, to my knowledge this type of smoothing algorithms are applied and decided on chip set level.

- Harry

[gplracerx]

Here's the plots for the XGPS160. I used HLT in manual timing mode to acquire the data. I need to repeat the experiment with Location Services off just to make sure that iOS isn't doing something weird and with the VBOX Sport to compare the internal logging with HLT.





The accuracy of an individual reading is about the same as for the VBOX Sport, but the serial autocorrelation is a lot higher for the XGPS160, probably a function of the filtering. That would make calculating speed and acceleration from the position data a lot less noisy than with the VBOX Sport data. Or, to put it another way, the VBOX Sport data would need to be filtered before differentiation. OTOH, the position data may lag more with the XGPS160. The XGPS160 data were acquired at night and the VBOX Sport data during the day. That might make a difference too.