Highly Accurate GPS by averaging?

[jarvist]

We (Imperial College CC) are hoping to finally re tie-in the surveys of the caves on our summer expo to a central GPS location. Does anyone have any recent experience (post WAAS & the end of SA) with improving the accuracy of GPS fixes by averaging, and estimates of potential error?

Our current plan is to define a PSS / trig-point on the surface near the cave systems with a good view of the sky, setup our cheap garmin eTrex on a tripod above this point & data-log WAAS/EGNOS GPS locations to a connected laptop once a second.
Currently we don't seem to be able to get DOP (dilution of precision) data to be logged.

Does anyone have any suggestions for methods of discarding or weighting low-quality data, either through knowledge of the predicted DOP or by sampling the scatter in measured signals by time?

I also understand that further increased accuracy can be achieved by post-processing the data + including information from survey ground stations, such as the UK Ordinance Survey RINEX network - does anyone have any experience with this?
 
I also understand that due to the main ionospheric nature of the GPS signal degradation, that readings are most stable during the night - is it worth staying up late to get a better fix?

That said, considering that a single WAAS/EGNOS fix now has an accuracy of <3m, perhaps any higher accuracy is unnecessary when compared to survey errors and the rate of spread of tectonic plates!

[graham]

That said, considering that a single WAAS/EGNOS fix now has an accuracy of <3m, perhaps any higher accuracy is unnecessary when compared to survey errors and the rate of spread of tectonic plates!

Accuracy? or Precision?

That said, do you actually need anything better than that? I am assuming from what you say that you will be mapping all entrances in relation to your PSS by non-GPS means. That will give you what, 0.5 m precision at best? What matters it if you are a bit more than three metres adrift from the rest of the world?

This from someone who spent an afternoon last week wandering round part of Mendip with a borrowed differential GPS picking up - potentially - centimetre accurate readings on cave entrances.

[jarvist]

Well, indeed - of course
Precision I guess is most important, as the motivation of this is to improve the accuracy of the survey tie-ins for far away systems, as a more accurate method than laborious surface surveying.
As a sideline we're also going to try and do some more accurate surface survey work with tripods used on the stations, mounting the normal suunto instruments + laser disto to avoid hand shake and using a card target for the laser beam mounted orthogonal to the leg.

The limiting step for accuracy, at least as far as getting to the registered Gauss-Kruger cave entrance coordinates as required by the Kataster Karst registry, is probably still limited by our imperfect conversion from WGS/lat-long into the local system.

I assume you mean carrier-phase GPS if you're getting cm resolution?

On the subject of ludicrous accuracy surveys, has anyone ever considered the curvature of the earth for a cave? My back of the envelop calculation suggests a 1m vertical error after 3.5km.

[graham]

On the subject of ludicrous accuracy surveys, has anyone ever considered the curvature of the earth for a cave? My back of the envelop calculation suggests a 1m vertical error after 3.5km.

I have, yes, with similar results to you.

[robjones]

On the subject of ludicrous accuracy surveys, has anyone ever considered the curvature of the earth for a cave? My back of the envelop calculation suggests a 1m vertical error after 3.5km.

I was instructed on the basis of "an inch in a hundred yards". 

[kdxn]

An answer that may be too late but thought it worth posting for future.......

Best not to bother with averaging.

If you want more accuracy from a Garmin, try a RINEX logging system for some Garmin receivers and post processing against the IGSCB GNSS receiver network.
Try these links for more info:
http://artico.lma.fi.upm.es/numerico/miembros/antonio/async/
http://igscb.jpl.nasa.gov/network/netindex.html

Alternatively get a geodetic quality GNSS receiver and do Static Network Post Processing or Precise Point Positioning (PPP).

Some factors for you to think about.

What is height ? GNSS very good at spheroidal height differences but these are not the same as water height differences (like mean sea level etc.) you need a geoidal model to convert between the two.

How accurate do you need to be ? How accurate is your cave surveying ? How much money have you got ?

If you have the money, why not contact a Land Surveyor or Geodesist who has a geodetic GNSS receiver and is willing to take your money assist......like me.......

[footleg]

Only just caught up with this thread. 

If you are logging readings every second from one stationary GPS, and you also log readings every second at each of your cave entrances for a few minutes each, what error would be expected in the relative positions of each cave entrance with respect to the stationary receiver? If WAAS gives ~3m accuracy (or do I mean precision? Please remind me!) which is not too different to the probably survey error from in cave surveying, then it only has to be a bit better than this to be as useful as it needs to be. I would assume that you would calculate the relative difference in position between the two GPS receivers for each point in time, and then average these difference readings over the time period of measurement for each entrance. That should be simple enough to do in practice without expensive equipment (well assuming a couple of laptops can be borrowed, or a PDA program written).

[Les W]

Surely if the error is fluctuating you would need to take the corresponding readings at exactly the same time. If you took them at 1 second intervalls but half a second out of sync then the error might be different.

Just a thought.

[footleg]

That is the question. How quickly do they drift? When I fixed all the entrances in West Kingsdale a couple of years ago, I spent a lovely sunny Summer afternoon starting at Valley Entrance, and taking a 1 minute averaged reading at each entrance. Ending up at Valley Entrance a few hours later I repeated the reading there, and got the same reading (OSGB grid to 1m precision). But how do I know if that was a coincidence? Did the readings drift around all over the place all afternoon and I just happened to get the same reading back at the same spot by chance? Or is the error more to do with the conditions on the day and satellite positions at that time, and so 'differential positions over a 4 hour time window' could actually be very accurate? But readings taken on different dates might differ by up to the 3m accuracy quoted for WAAS fixes?

[graham]

Firstly, how do you know for certain that the fluctuations are only time dependant? How many different factors are involved and how will they vary across time as well as space?

[khakipuce]

This gives a pretty good overview of GPS errors
http://www.kowoma.de/en/gps/errors.htm

And I agree with what footleg said, in that probably what really matters to cave surveyors is relative positions of features to each other, rather than exact position on the surface of the earth (which is fraught anyway as the earth is not sphere, the sea isn't level, etc). So it may be better to get a GPS to each entrance and take readings at the same time (better to take many readings say every 5 minutes over an hour) and then rotate the GPSs (i.e use each GPS at each cave entrance) then average the result.

This ought to help compensate for instrument errors as well as atmospheric errors - however the multipath error (in a steep sided valley) may be harder. It may be that getting up out of the valley and fixing the position of a survey station and then using traditional surveying techniques from there to the entrance may be better. But I also guess if you look at the variance of the positions and it is much larger, you know you have a problem.

[Bucket]

New year's eve last year, I bust my toe and couldn't go caving  , so I surveyed between all the cave entrances in Burrington Coombe (using a suunto).  I augmented this with GPS measurements, using a Garmin eTrex, at several points on the hillside  (all with a good clear view of most of the sky).  At each point, I took GPS data for haf an hour on half a dozen different days.  Averaging the data suggested that (a) GPS co-ordinates appear very repeatable to within 2m horizontally but (b) they cycle vertically over periods of 5 minutes and > 1 hour - often varying by as much as 10m about the mean.   Base on that experience I would log data  for an hour or so and repeat this once or twice more if possible.  That should give you more than enough data to average laterally (to within 2m) and give you enough data to work out the vertical variation so that you can guess the mean height.   Overall, I was quite impressed by how repeatable the data was, even over the course of 3 months!  I have the data in a spreadsheet if you want to get an idea of what to expect.

Graham , did you ever try adding my surface data to your Burrington model ?

[graham]

Bucket

I went straight from where we were to adding surface data from NASA satellite data using TerrainTool. However, the next job with that model is to go back to your data and use it to calculate an offset between what we say and what NASA say with regard to entrance heights. Interestingly enough in all the areas where I've done this so far, our data shows the entrances lower than the surface as shown by NASA, especially on/under steeper surfaces. In Cheddar, for example, the swallet entrances are all in close agreement, but the Gorge entrances are all "below ground".

See http://www.ubss.org.uk/resources/surveys/survex/Burrington.lox for the Burrington model and

http://www.ubss.org.uk/resources/surveys/survex/Charterhouse.lox for the Charterhouse/Cheddar one.

Both of these are Therion models and require the loch viewer. Download Therion from http://therion.speleo.sk/

[footleg]

Firstly, how do you know for certain that the fluctuations are only time dependant? How many different factors are involved and how will they vary across time as well as space?

You are making the assumption that I am making assumptions! 

Let assume that I know nothing about errors in GPS, apart from that they are not accurate to the nearest 1m. What I am asking is whether it is possible using two GPS receivers and data logging to determine positions of cave entrances to within 1m relative to each other, using one of the GPS receivers located at a fixed point and measuring the relative position of each entrance to that point? I am not really concerned with what might be causing the variations in the readings. My only concern is the error I could expect in the relative position of each entrance versus any other entrance if I difference readings taken within 0.5 seconds of each other. (i.e. I log readings every second at both locations. So the largest time difference between pairs of readings will be 0.5 sec. ). If I want the relative position of the cave entrance GPS fix compared to the fixed point, then I have to assume the same error at both locations. i.e. If the relative distance between the receivers varies by 1m over successive readings then I have to assume 1m error in the fixed point value I use, and also 1m in the position of the entrance. This is because I am going to repeat the experiment at multiple entrances using the same fixed point in order to place all the entrances relative to each other. So really to get 1m accuracy between different entrances I need to be getting 0.5m accuracy in the relative positioning of each entrance with respect to the fixed point.

The other question is what time period I need to take measurements over the be certain of the accuracy seen. i.e. If the relative positioning of the entrances seen on one day varies only by a small amount over a 1 hour period, but varies by much more over days or months then I might get better accuracy on one day than another. But there will be a maximum error I can expect in readings taken on any random date. Is this going to be <1m?

[khakipuce]

Check the link I posted. There would seem to be two main variables between GPSs at different locations that are read at the same time, firstly are they using the same satelites and secondly is there any multipath error.

Why would they not be using the same satellites? - maybe because you are in a valley in one location and so cannot see all those used by the other GPS.

Multipath error is due to reflected signals, I would think this is unlikely with caves unless you are in something like Trow Gill where a signal reaches you by bouncing of the cliff face rather than coming directly.

You have to remember that you are dealing radio signals from moving satellites. Just like your wireless, somedays the signal will be stronger than others, and when it is weaker the AGC in the GPS will crank up to try to pick up more signal and so may start getting reflections, etc. On another day you will be getting different satellites in different positions.

I think the upshot is there is no easy answer, the pro surveyors use more advanced GPS systems (e.g. Carrier Phase)  that can get down to tens of mm. But it is not a handheld Garmin. You could be better off hiring a 1 second total station instrument for the day and doing it the old fashioned way.

[footleg]

Great link, thanks! In two posts we've gone from 'can I get <1m accuracy from two consumer GPS units with data logging' to an overview of relativity theory and how the speed of motion of the satellites and the person on the surface of the earth causes the apparent speed of the clock in the satellite to be faster to the earth based observer than it really is on the satellite. Gotta love UKCaving!

Having read that whole article I think the answer can best be obtained by collecting some data and analysing it for variations. So now my question is:

Given I have a GPS receiver which can connect to a serial port on my Windows laptop, what software can I use to capture the position data and time for data logging purposes?

[khakipuce]

Sorry to harp on - but I really do not think averaging will get you there. Averaging only works if the error is random and normally distributed. Suppose that at one location the data is always skewed to the north by somehere between 1.9 and 2.7 metres. An average would at best be out by 2.3m.

But I agree, take some readings and check the variance - at least the variance will give you an idea if a particular site is likely to yield accurate results at all. But then presumably your GPS does that any way (mine gives me an accuracy which is constantly updated).

In the tradition of internet forms I hadn't of course read your whole post so did not realise you had a GPS with serial out - the software you need will depend on what sort of GPS it is. Assuming we can get the data off I'm happy to help with some processing software if necessary.

If you have two it is possible to get decent accuracy by taking readings at a base station with a known location (trig pillar?) and at the cave entrance. It is then possible to reverse the calculations for the base station and get the error and then apply this to the readings from the cave entrance GPS. This is done on a per satellite basis, so for each satellite used by the cave entrance GPS a known error can be applied (this is know as differential GPS).

[jarvist]

Given I have a GPS receiver which can connect to a serial port on my Windows laptop, what software can I use to capture the position data and time for data logging purposes?

I've used gps-babel under Linux, but I believe the windows version works similarly.

http://www.gpsbabel.org/

Here's the stuff on real-time tracking:

http://www.gpsbabel.org/htmldoc-1.4.0/tracking.html

If you have an eTrex, the garmin data format contains the most numerical precision in the lat + long, but only the NMEA (ASCII) sentences have any DOP info in them.
You get an update per second, tagged with the GPS-time (for post-processing / combining with an independent station).

I'll try and dig up the magic gpsbabel invocation to get the most data out of an eTrex + spit it out in a sensible format --- I spent a while fiddling with it back in London, but never quite got around to using it on expo.

I found this site very interesting, and may answer some of your questions with respect to increase in accuracy as a function of arithmetic averaging (I recall that 3hrs was a bit of a 'sweet spot'):
http://users.erols.com/dlwilson/gps.htm

If you have two it is possible to get decent accuracy by taking readings at a base station with a known location (trig pillar?) and at the cave entrance.

Hmm, I think a technique like this would be described under quasi-differential GPS.

KDXN's suggestion of getting at the raw data (the satellite pseudo-ranges) + then post-processing seems to make a lot of sense (though I'm not sure if the method he linked to, using an undocumented debug mode of the old garmin GPS 12 works on modern units), but it would also be interesting to see what you can achieve with the minimum of effort / equipment...

[khakipuce]

I have a bare board EM 406 module just for messing with and I use SiRFdemo  http://www.falcom.de/support/software-tools/sirf/. Not sure how it would get on with other brands of GPS though - may be worth a try - I believe it speaks NMEA as well as SiRF.

[footleg]

I have a Magellan Meridian GPS which I believe sends NMEA ASCII data over the serial port cable. I also have a Bluetooth GPS module which I assume sends NMEA data over a bluetooth wireless serial connection as the software I use with it always needs to be set to NMEA format to connect with it. I'll see if I can get GPSBabel to log this NMEA data.

[jarvist]

Hi Footleg,

If it's any use, my GPSBabel command to get info out was:
gpsbabel -T -i garmin -f /dev/ttyUSB0 -F testlog.dat -o xcsv,style=waypoint_data_log.style

The style file is here:
http://gist.github.com/615686

Output looks like this with NMEA input:
1277760772 51.xx6081666666664 -0.xx8856666666667 112.700000 11 5.400000 1.000000 5.500000
1277760774 51.xx6048333333336 -0.xx8883333333333 112.600000 11 2.900000 3.100000 4.300000
1277760776 51.xx6003333333336 -0.xx8911666666667 112.500000 11 2.900000 3.100000 4.300000

- truncation in the 7th decade of degrees, about 4cm.

And with garmin input:
1277761219 51.xx9679420030139 -0.xx2414213831683 95.732574 -1 0.000000 0.000000 0.000000
1277761220 51.xx9553679179760 -0.xx2397661923045 95.686760 -1 0.000000 0.000000 0.000000
1277761221 51.xx9434218338981 -0.xx2381936684230 95.643234 -1 0.000000 0.000000 0.000000

- seemingly more numerical precision in the lat/long, but it could just be because it's transmitted in binary + so not obvious by inspection in decimal the degree of truncation.

(Obv. xx's are to anonymise my secret hideout)

[jarvist]

Oh, and here's an article about why a poor-man's differential GPS (such as subtracting position from a simultaneous fix at a trig point / survey pillar) is unlikely  to give you anything useful:

http://www.oreillynet.com/pub/a/527

- you really do need the raw data.

[footleg]

Thanks Jarvist, a really interesting and clear article. It appears the bottom line is that the errors in the calculated positions recorded at the same time by two different GPS receivers will not be the same, or even have much correlation to each other. So if you just subtract the position calculated by one receiver from another then you are as likely to get a less accurate relative position as a more accurate one. It appears that NMEA data from consumer units does not contain the error data for each satellite which is required to calculate a more accurate relative position. So using two consumer GPS receivers will not gain anything over just averaging the reading from a single receiver at the location and treating the reading as accurate to around 3m.

So given that differential GPS just does not appear possible from consumer receivers, lets just consider the accuracy of a single WAAS enabled GPS. This is quoted as accurate to 3m. This is presumably in ideal conditions. Can I assume that if I have a WAAS average being displayed on my receiver that the calculated position will be within 3m of the real position of the point I am measuring at? If this is the case, then does this mean that on one occasion I might get a reading 3m North of the real position, and on another occasion the reading might be 3m South of the real position? I am always within 3m of the real position, but might see up to 6m difference between readings taken on different days?

Finally, if I log data at my location over a long period (say several hour long sessions on different dates) and plot the positions on a scatter plot, I would expect to get something a bit like this:


Can I then correctly conclude that my real position is roughly in the centre of that splodge of points? Will this be more accurate than +/-3m ?

[kdxn]

Nice thought. Here's some geeky stuff to ponder upon.......

Your cheapie handheld receivers use what we call Coarse Acquisition Code on the L1 frequency. The problem with this is that the signals get delayed by the ionosphere and the delay will depend upon where the satellite is with respect to you and where you are in the world. Low elevation satellite ranges tend to be noisier as they have more stuff to filter through, additional troposphere to deal with. The ionosphere noise varies with latitude, what time of day, what azimuth is has to you and also where we are in the 11 year solar cycle. What I am saying is that your simple handheld receiver has a lot to try and compensate for and it does this with an ionospheric model and a tropospheric model. Not to mention that the signal correlators on your typical handheld are good enough for a handheld - that is the ranges behind the position calculation do not have to be that good because most users are only expecting a few metres of accuracy - why increase the price of the product needlessly ? The WAAS and EGNOS augmentation satellite signals help improve upon these models but they are still models which have been forecast from prior data so your position is probably biased and may be biased for some time so averaging may look good but your average is probably biased. Comparing position fixes between two receivers is very dodgy because the sky view at both receivers is rarely the same so you can not guarantee that both receivers were using exactly the same satellites at the same time. Also you may have different receiver hardware, different firmware and my earlier comment about the fundamental accuracy of these handhelds. When your WAAS and EGNOS position indicates 3m acccuracy, that is based on the least squares fix of all the satellite ranges used with the augmentation signals. If you only have four satellite ranges but they all agree well with one another then the position statistic could be very good, however all four satellite ranges could be biased ! The 3m indication is a statistical amount - it does not mean that all your positions are within 3m - it suggests that a percentage of your position fixes are within 3m. Whats happening with the other percentage of positions ?......................could be anywhere. How big the percentage is depends upon the statistic being used, you often see 1,2...x sigma or CEP Circular Error Probability but here we are perhaps delving too deep.

The only way to get a really good improvement on your fix is to access the individual satellite ranges and preferably the carrier phase(s) too, some of the cheapies will provide low quality L1 phase. Get your data in a RINEX file and see the post processing online links that I posted earlier. These can process your raw data with respect to multiple ground stations equipped with very high quality geodetic receivers. If you wait a little while, you can also use very accurate post processed orbits, ionospheric and tropospheric data all of which can improve your handheld positions. However one last point, a cheapie can only get you so far because you run into the underlying limitations of the silicon and firmware inside. Do not forget you also have the issue of height - GPS gives you a spheroidal height - getting a mean sea level elevation requires the use of  a model - typically this is okay over short distances for relative height differences but there can be some dramatic differences between spheroid height and mean sea level. The UK has an east-west tip of a few metres - India has a 180m difference from south to north.

I am thinking that perhaps a presentation at HE 2011 could be useful. If there is enough interest, I could put one together and do a preliminary run through at the next Cave Electronics and Surveying Group meeting early 2011 with some example data from Mulu 2011 as I will be taking a professional GPS out there and should have the post processed results by then, subject to canopy coverage. GPS signals do not like wet foliage !

[footleg]

Sounds like a great topic for a talk at the next cave tech symposium. I'd certainly find it very interesting.

[kdxn]

OK, looks like I may be doing two talks (if time permits) at the next BCRA cave technology symposium to be held 9-10 April 2011 at Hulland Ward in Derbys. First will be Surface Mapping, second will hopefully be Laser Scanning.

Have dusted off my old GPS Garmin, DeLorme EarthMate and the big bad boy Leica SR530.

Get back from Mulu 31st March so will need to get a move on to include any results...............may have to be preliminary.............full results for HE 2011.

[kdxn]

Thanks to those of you at the BCRA Tech symposium this last weekend.

Given the feedback received, I will propose a Surface Mapping talk for HE2011 and concentrate on practical methods for improving position using handheld (cheap) technology and also professional gear with some comparisons. Hopefully be of interest for UK and expeditions.

[footleg]

I think that would be very interesting. I'll try not to take on too many jobs at Hidden Earth this year so I stand a small chance of being able to get to some talks!

[jarvist]

Given the feedback received, I will propose a Surface Mapping talk for HE2011

That would be fantastic. I will certainly aim to be there.