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 GPS altitude : wgs84 / msl / geodetic corrections
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rwcx183

81 Posts

Posted - 05 juin 2004 :  19:25:22  Show Profile  Reply with Quote


Translating WGS84 coordinates
Many GPS users may not be aware of a potential discrepancy between the altitude reported by their GPS and their actual altitude. GPS receivers calculate position first in a coordinate system known as ECEF XYZ. That just means Earth Centered Earth Fixed xyz. The WGS84 defined center of the earth is given the coordinates 0,0,0. The x-axis extends from that center, to a point at the equator where the longitude is 0 and of course, in the negative direction to a point at the equator where the longitude is 180 degrees. The y-axis extends from the origin at the center of the earth, to a point at the equator where the longitude is 90 degrees east (for the + direction) and longitude 90 degrees west (for the -direction). Lastly, the z-axis is the same as the earth's polar axis. That is, it extends to the north pole (+) and to the south pole (-). This is all fine and dandy, but if I gave you coordinates of a position in this coordinate system, few people would be able to tell even roughly where that was. We're all much more familiar with latitude, longitude and elevation. So usually, GPS manufacturers will translate the ECEF XYZ coordinates to lat/lon/elev coordinates that we can understand. For latitude and longitude, this is not so hard to convert for those of us that still remember high school geometry.

The trouble with altitude.
We have to make some assumptions about the shape of the earth. WGS84 has defined that shape to be an ellipsoid, with a major and minor axis. The particular dimensions chosen are only an approximation to the real shape. Ideally, such an ellipsoid would correspond precisely to "sealevel" everywhere in the world. As it turns out, there are very few places where the WGS84 ellipsoid definition coincides with sealevel. On average, the discrepancy is zero, but that doesn't help much when you're standing at the water's edge of an ocean beach and your GPS is reading -100ft below sealevel. The deviation can be as large as 300ft in some isolated locations. When the National Marine Electronics Association came up with the NMEA standard, they decreed that altitudes reported via NMEA protocol, shall be relative to mean (average) sea level. This posed a problem for GPS manufacturers. How to report altitudes relative to mean sea level, when they were only calculating altitude relative to the WGS84 ellipsoid. Ignoring the discrepancy wasn't likely to make GPS users very happy. As it happens, there is actually a model of the difference between the WGS84 ellipsoid and mean sea level. This involves harmonic expansions at the 360th order. It's a very good model, but rather unusable in a handheld device. It was determined that this model could be made into a fairly simple lookup table included in the GPS receiver. The table is usually fairly coarse lat/lon wise, but the ellipsoid to mean sea level variation, known as geoidal separation, varies slowly as you move in lat/lon. So, the GPS receiver calculates an ellipsoidal elevation and then applies an interpolated correction to that, from the lookup table and the result is reported via NMEA protocol. Additionally, NMEA allows the reporting of the geoidal separation, as a separate parameter, for folks that might want to do their own ellipsoidal to geoidal corrections. Simply adding the altitude above mean sea level reported, to the geoidal separation value reported, nets the original ellipsoidal altitude. From that point, the user (with lots of time on his hands) can re-calculate the altitude above mean sea level, using whatever model he wishes. Very few of us would ever do that, as the GPS receiver calculated and corrected altitudes are plenty good enough.

The trouble with SiRF - UPDATED 02/2006 : starting with V2.3.3 on SiRFII , V2.1.1 on XTrac, and V3.1.0 with SiRFstarIII, the Geoid separation is now reflected in GGA field 9 to show MSL altitude.

Enter SiRF. SiRF, until very recently, have not bothered to do the ellipsodal to mean sea level correction, to altitudes reported in NMEA protocol. SiRF admits that, so there's no controversy there. Eventually, SiRF got tired of listening to complaints about altitude discrepancy and they did finally release new firmware that includes the corrections from ellipsoidal to mean sea level altitudes. I don't remember exactly what version it occured on, but somewhere between 2.20 and 2.30 (ed #1 - 2.30 introduced that). If you have an older firmware, the reported altitudes will be ellipsoidal and you will probably notice that when you're standing on any ocean beach in North America, the displayed altitude is below sea level, since for the whole of North America, mean sea level is higher than the WGS84 ellipsoid. You can usually tell whether a GPS receiver is reporting true altitude above mean sea level, or ellipsoidal altitude by examining the NMEA sentences. Example:

$GPGGA,192435.716,3340.9130,N,11740.0502,W,2,08,1.2,211.6,M,-34.1,M,1.3,0000*46

The field immediately following the "M", specifies the geoidal separation value. If a GPS receiver is reporting a value there, then that usually indicates that the the field just before the "M" is the altitude above mean sea level. So, in this case, we're fine. (ed #2 - except that contrary to NMEA rules, SiRF receievers do not deduct the geoidal separaration to calculcate the msl)


Here's another example:

$GPGGA,161618.123,3343.5789,N,11747.9085,W,1,04,3.5,137.5,M,,M,,0000*5F

In this case, the field following the first "M" is null, indicating that the GPS receiver did not report geoidal separation, most likely because it did not know what the value was. So, we can assume that this GPS receiver is reporting ellipsoidal altitudes. Technically, that's in violation of the NMEA protocol, but it's a pretty minor violation.

There are of course, exceptions to the rule. Two that come to mind are, my old Lowrance GM100 (non-SiRF based)GPS receiver that calculated and reported altitudes above mean sea level, via some clever programming tricks, yet did not (could not) report a geoidal separation value. Then there was the newer SiRF based Lowrance iFinder, that managed to report the goeidal separation value, but still was reporting ellipsoidal altitudes. I guess SiRF and or Lowrance was a little confused on that version of firmware, since it was corrected in a later firmware release (see ed #2 - I suppose that the lowrance having another software layer unlike a standalone receiver like a Bluetooth GPS could fix the SiRF discrepancy)

SiRF binary mode notes
One final not here. In SiRF binary protocol, positions are reported exclusively in ECEF XYZ coordinates and it's the responsibility of whatever software you're using, to translate from ECEF XYZ to lat/lon and (we hope) altitude above mean sea level. SiRF did add conventional lat/lon/alt coordinate reporting via SiRF binary protocol (MSG ID 41), to the most recent firmware releases, but MSG ID 41 is not enabled by default. MSG ID 41 does supposedly report both ellipsoidal and altitude above mean sea level.

There is a similar story behind SiRF supporting magnetic variation reporting.

J.G.

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gpspassion

93998 Posts

Posted - 05 juin 2004 :  19:42:59  Show Profile  Visit gpspassion's Homepage  Reply with Quote
Excellent stuff!
I took the liberty of doing some formatting and addind a few notes. Note #2 is really something SiRF need to fix. What they haven't done it yet is rather odd!

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rwcx183

81 Posts

Posted - 06 juin 2004 :  08:12:51  Show Profile  Reply with Quote
I think that SiRF did fix #2, though the fix may have not yet propagated to all of the SiRF based receiver implementations. I'll have to double check, but I'm pretty certain that in addition to my Lowrance iFinder, the latest EarthMate also does the proper adjustment of ellipsoidal altitude, into altitude above mean sea level. I don't know about the BlueLogger though, since I suspect that one comes from a different OEM than the regular EarthMate.

Also, I did verify that MSG ID 41 does indeed report both ellipsoidal altitude and MSL altitude. This time they took no chances and simply reported both, but no separation value. Of course, anyone could calculate the separation value from the two, if needed for some reason. I was disappointed to find that once again, SiRF fumbled the documentation. The documentation of MSG ID 41 is hopelessly fouled up. I ended up sorting it out the hard way.

J.G.
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gpspassion

93998 Posts

Posted - 06 juin 2004 :  11:13:44  Show Profile  Visit gpspassion's Homepage  Reply with Quote
I discussed this with Delorme actually after testing the BlueLogger and it still does not follow the NMEA rules by deducting the correction from field #9 but it is firmware 2.31 so it's not the latest. I'll check on the FW2.32 units I've had come my way ;-)

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rwcx183

81 Posts

Posted - 06 juin 2004 :  17:47:30  Show Profile  Reply with Quote
I went back and checked the EarthMate again. Comaparing the altitude reported via NMEA $GPGGA, to the two altitudes reported via binary msg ID 41, I was surprised to find, that the EarthMate IS reporting ellipsoidal altitude via NMEA. I even cross-checked it, by converting the ECEF XYZ coordinates to lat/lon/alt. That altitude agrees with the NMEA and ellipsoidal. Not trusting my memory by this time, I fired up the iFinder and lo and behold, it too reports ellipsoidal altitude via NMEA. I don't know what I was thinking. I have some dim memory now, of one version of firmware that recorded the correct MSL altitude with waypoint records, but displayed on the screen, ellipsoidal altitude. Then that was changed and now display and recorded altitudes are both MSL, but NMEA is still ellipsoidal altitude.

So, at this point, I don't have any evidence to suggest that SiRF ever got it right, with respect to NMEA report altitudes.

J.G.
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gpspassion

93998 Posts

Posted - 06 juin 2004 :  17:54:03  Show Profile  Visit gpspassion's Homepage  Reply with Quote
Ok, thanks for checking, I will check with 2.32 to see if there's any change here, I doubt it ;-)

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gpspassion

93998 Posts

Posted - 11 juin 2004 :  18:46:06  Show Profile  Visit gpspassion's Homepage  Reply with Quote
News item on the front page ;-)

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igalan

Spain
358 Posts

Posted - 14 juin 2004 :  13:30:51  Show Profile  Reply with Quote
Very interesting article. I wasn't aware of the difficulties of calculating the altitude above MSL.

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Walter W. Kruer

USA
4 Posts

Posted - 18 août 2004 :  04:13:21  Show Profile  Reply with Quote
I'm evaluating the purchase of a BT GPS and think the best route is a SIRF unit. The problem is that I will use almost exclusively in aviation so the altitude reporting is very important. The last reference I saw was that GPSPassion was going to evaluate the 2.32 firmware units. My questions are do they report the corrected altitude in NMEA mode? How can I verify the firmware version before making a purchase? And finally, can I update the firmware when a new version is available.

Thanks for the help

Willie
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paulkbiba

USA
5064 Posts

Posted - 18 août 2004 :  05:38:48  Show Profile  Reply with Quote
The "driving" type of units, be they CF, Bluetooth or mouse, are NOT good enough to use for altitude information if you are using them for aviation. I have a number of the latest units and they will vary from as much as 100 feet from unit to unit. Altitude is NOT what these units were designed to measure.

This is your first post and we would like you to make some more in the future, so NO, NO, NO if you want altitude.

By the way, did I say NO? If I didn't, well then here it is: NO!

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gpspassion

93998 Posts

Posted - 18 août 2004 :  12:01:46  Show Profile  Visit gpspassion's Homepage  Reply with Quote
Actually, this lack of accuracy is a limitation of the GPS system in itself, which is not hard to figure out when you look at the way it works, hard to get very good accuracy when your altitude is x meters when the satellites are at 20,000 kms! SBAS is supposed to improve that, haven't really read any reports that it does.

On the 2.32 questions:
1. Still same as 2.3, not in GGA field #9
2. If you can connect to the GPS before buying it, use CE Monitor to check the vetrsion
3. Upgrade: no

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DaleDe

USA
10 Posts

Posted - 14 déc. 2005 :  23:42:38  Show Profile  Visit DaleDe's Homepage  Reply with Quote
The lack of accuracy is a limitation of the GPS system but not for the reason you suggest. If the distance to the satellites were an issue then the horizontal accuracy would be just as bad. The limitation in accuracy is caused by the geometry of the situation. For horzontal positions it is possible to get a diversity of satellite positions distrbuted around you but for vertical accuracy you have all of the satellites on one side (above) you. The earth itself blocks the other satellites.

In addition hills or in some cases simply mask angle reduces the vertical accuracy even more by limiting the sky view. When flying the hill problem is generally not a problem so GPS with a low mask angle can provide better accuracy in flying than you will typically get on the ground. With a reasonable sky view, and I haven't any idea what the sky view of the original poster was or what terrain he was in, you can achieve 1.5 times to 2 times worse accuracy than your horizontal accuracy at the same location. In addition some satellite receivers tend to favor (weigh more heavily) satellites that produce a good horizontal DOP if they are not using all of the satellites in the solution.

Yes, SBAS like WAAS do improve things, particularly for planes. The spec for vertical accuracy is about 7 meters for aircraft using WAAS and they are typically better than this. Note that GPS units designed for aircraft use should have a mask angle of zero to achieve this number. A negative angle can improve things even more if the antenna can receive the lower satellites.

Dale
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gpspassion

93998 Posts

Posted - 15 déc. 2005 :  00:09:04  Show Profile  Visit gpspassion's Homepage  Reply with Quote
Welcome to the forums.
Old message you've dug out there, I agree that my explanation lacked some detail and clarity, I do seem to remember I had the distibution/angles in mind. Giving it some more thought I'd say that the fact that the GPS satellites are all at an altitude of 20,000 kms doesn't help. If they were staged at different altitudes then it might be different with more triangulation "material" available.

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DaleDe

USA
10 Posts

Posted - 15 déc. 2005 :  01:21:16  Show Profile  Visit DaleDe's Homepage  Reply with Quote
Sorry, I hadn't check the date but I was following a more recent thread and 43472 http://www.gpspassion.com/fr/articles.asp?id=43472 that shows that GPS altitude cannot be trusted and it referenced this discussion. I hadn't realized that I have switched to a really old thread. I am not used to this discussion group. I will pay more attention. However the topic really pertains to the other thread so I will pursue it a bit more.

I do not see how altitude would change the DOP which is the dominant factor in predicting accuracy. It would however make the calculations a bit more difficult. Today all of the satellites are on then canopy surrounding the earth and the angles are all relative to this canopy. If there were different alitutudes of satellites it would make DOP a bit tougher to compute but not likely to change the outcome. It is DOP itself that predicts that vertical accuarcy is usually less.

By the way, if altitude of the satellites mattered then SBAS systems would get an added boost since they are twice as far out. I guess I need to move back to the original thread and leave this one alone.

Dale

quote:
Originally posted by gpspassion

Welcome to the forums.
Old message you've dug out there, I agree that my explanation lacked some detail and clarity, I do seem to remember I had the distibution/angles in mind. Giving it some more thought I'd say that the fact that the GPS satellites are all at an altitude of 20,000 kms doesn't help. If they were staged at different altitudes then it might be different with more triangulation "material" available.

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gpspassion

93998 Posts

Posted - 15 déc. 2005 :  01:28:20  Show Profile  Visit gpspassion's Homepage  Reply with Quote
No that's fine, forums offer this type of flexibility, most people just like to start new threads though, I'm happy when I see a new one coming back to life! You don't need to quote a thread above yours though, just type your text in the box of hit "Reply"

Yes, I did have these geo-stationary SBAS satellites in mind, but that's not the way the GPS sytem was designed so it's OT really, but one senses that having different ranges of altitudes would help with triangulation in the same way a horizontal distribution does.

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DaleDe

USA
10 Posts

Posted - 15 déc. 2005 :  01:30:11  Show Profile  Visit DaleDe's Homepage  Reply with Quote
Oops I got the link wrong (need to learn how to do this correctly).
It should have been http://www.gpspassion.com/forumsen/topic.asp?TOPIC_ID=43272.
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