Converting between WGS60 & WGS84 and between AGD66 & GDA94?

[Son of a Beach]

I'm writing some mapping/navigation software at the moment, and it's currently working very well, except that the maps I'm using are a little out of date, and the locations are consistently wrong by the exact same amount. From my research so far, it appears that this is because the maps are based on 'the old system', and the coordinates I'm using are for 'the new system'.

I've never used GPS before in my life, so please excuse my ignorance. I've been reading up and trying to learn, but there's a few things I've been unable to ascertain, and would appreciate advice.

From another topic I read the following:

it looks like you are using AGD66 as your datum. If that is so and I add 112m to the Easting and 183m to the Northing to convert to GDA94/WGS84

• Is AGD66 based on WGS60? It appears that GDA94 is based on WGS84. Is this correct?
• This conversion between AGD66 and GDA94 (112 east, 183 north)... is that only for our local (AGD66/GDA94) maps, or does that also work world wide for converting between WGS60 and WGS84 by the same numbers of metres?
• I can find web sites with tools do convert between the various standards, but I've not been able to find information on how to do the conversions manually yourself (apart from MJD's reference above). Can anyone point me in the right direction to find this information which I could then use to build the conversions into my software?

Thanks in advance!

[loric]

Lifted from: http://jevans.pcug.org.au/Pages/Map%20Reading.htm , as i think it gives a good simple explanation in a few sentences.


The map coordinates are anchored to the real earth via a complicated system of fixed points and a mathematical model of the earth's surface. In Australia, the anchoring system adopted in 1966 was called the Australian Geodetic Datum 1966 (AGD66). Maps based on this datum use the Australian Map Grid 1966 (AMG66 or just AMG). An updated version of the datum (AGD84) was adopted by some States in 1984, but for map reading and navigational purposes, can be regarded as being the same as AGD66.

From 2000, all Australian mapping authorities are using a new datum, the Geocentric Datum of Australia (GDA). This datum was defined in 1994. Maps based on this datum use the Map Grid of Australia 1994 (MGA94 or just MGA). The main reason for its introduction was the wide-spread use of satellite-based navigation systems such as Global Positioning System (GPS). GPS is based on the World Geocentric System 1984 (WGS84). For most practical purposes, WGS84 and GDA coordinates are the same.

GDA coordinates (both latitude and longitude, and eastings and northings) differ from AGD coordinates by approximately 200 metres in a north-easterly direction. So, to convert GDA94 to AGD66, decrease the Northing by 184 metres and decrease the Easting by 113 metres.


The definitive answers can be found here, though requires a bit of trolling around:
http://www.ga.gov.au/geodesy/datums/calcs.jsp#trans

Also states the official definitions of the datum(s).

Another good site:
http://www.icsm.gov.au/icsm/gda/

[tastrax]

Here is another quick reference for you Nik

http://www.dpiw.tas.gov.au/inter.nsf/We ... 3M66D?open

Another good reference is the datum list from Oziexplorer (if you use that) - in the development version you can see all the parameters behind each datum. This allows you to see how different they are...

Datum1.jpg (94.9 KiB) Viewed 26704 times

Datum2.jpg (99.41 KiB) Viewed 26704 times

[Son of a Beach]

Thanks guys... that's all good info. The confirmation of converting between AGD66 & GDA94 is good (nice to see from an authoritative source).

And that their coordinates essentially means that they map nicely to WGS60 & WGS84 respectively.

However, I'd still like to see some confirmation that I can use the AGD66/GDA94 conversion maths world wide for WGS60/WGS84 conversion. Makes sense to me that I should be able to, but for all I know, this conversion only applies to our part of the world, or something. Since the software I'm writing is for an international audience, I have to make sure it is WGS-based, rather than just AGD/GDA based. (I think?)

[loric]

May i ask why you want to use an Australian geo datum OS?
If it's for OS nav purposes, it'd be more useful to apply the regional datum.

[photohiker]

May i ask why you want to use an Australian geo datum OS?
If it's for OS nav purposes, it'd be more useful to apply the regional datum.

That's a good point.

In the UK, all the Ordnance Survey maps use OSGB-36 datum. If the purpose of the nav app is to give a valid grid reference that can be shared with someone using a map then you really need to support the local datum. The OSGB-36 dataum is supported by any handheld navigator I have been able to play with long enough to verify - definitely Garmin.

[Son of a Beach]

I DON'T want to support the Australian datum (actually, I should say, I don't want to support ONLY the Australian datum). That's why I'm asking about converting between WGS60 and WGS84.

I've merely been using the Australian datum as an example, because that's the maps I've got handy.

Here's the common data that the application currently supports (copy/pasted directly from the code):

Code: Select all

    [Ellipsoid ellipsoidWithId:-1 name:@"Placeholder" radius:0 ecc:0],
    [Ellipsoid ellipsoidWithId:1 name:@"Airy" radius:6377563 ecc:0.00667054],
    [Ellipsoid ellipsoidWithId:2 name:@"Australian National" radius:6378160 ecc:0.006694542],
    [Ellipsoid ellipsoidWithId:3 name:@"Bessel 1841" radius:6377397 ecc:0.006674372],
    [Ellipsoid ellipsoidWithId:4 name:@"Bessel 1841 (Nambia] " radius:6377484 ecc:0.006674372],
    [Ellipsoid ellipsoidWithId:5 name:@"Clarke 1866" radius:6378206 ecc:0.006768658],
    [Ellipsoid ellipsoidWithId:6 name:@"Clarke 1880" radius:6378249 ecc:0.006803511],
    [Ellipsoid ellipsoidWithId:7 name:@"Everest" radius:6377276 ecc:0.006637847],
    [Ellipsoid ellipsoidWithId:8 name:@"Fischer 1960 (Mercury] " radius:6378166 ecc:0.006693422],
    [Ellipsoid ellipsoidWithId:9 name:@"Fischer 1968" radius:6378150 ecc:0.006693422],
    [Ellipsoid ellipsoidWithId:10 name:@"GRS 1967" radius:6378160 ecc:0.006694605],
    [Ellipsoid ellipsoidWithId:11 name:@"GRS 1980" radius:6378137 ecc:0.00669438],
    [Ellipsoid ellipsoidWithId:12 name:@"Helmert 1906" radius:6378200 ecc:0.006693422],
    [Ellipsoid ellipsoidWithId:13 name:@"Hough" radius:6378270 ecc:0.00672267],
    [Ellipsoid ellipsoidWithId:14 name:@"International" radius:6378388 ecc:0.00672267],
    [Ellipsoid ellipsoidWithId:15 name:@"Krassovsky" radius:6378245 ecc:0.006693422],
    [Ellipsoid ellipsoidWithId:16 name:@"Modified Airy" radius:6377340 ecc:0.00667054],
    [Ellipsoid ellipsoidWithId:17 name:@"Modified Everest" radius:6377304 ecc:0.006637847],
    [Ellipsoid ellipsoidWithId:18 name:@"Modified Fischer 1960" radius:6378155 ecc:0.006693422],
    [Ellipsoid ellipsoidWithId:19 name:@"South American 1969" radius:6378160 ecc:0.006694542],
    [Ellipsoid ellipsoidWithId:20 name:@"WGS 60" radius:6378165 ecc:0.006693422],
    [Ellipsoid ellipsoidWithId:21 name:@"WGS 66" radius:6378145 ecc:0.006694542],
    [Ellipsoid ellipsoidWithId:22 name:@"WGS-72" radius:6378135 ecc:0.006694318],
    [Ellipsoid ellipsoidWithId:23 name:@"WGS-84" radius:6378137 ecc:0.00669438]


hmmm... if 'Australian National' here refers to AGD66, then I need to figure out what to add to this list for GDA94 (and other such more modern international standards). Then I won't need to worry about conversions at all.

Yes, I think I've got it all wrong. What I really need is a more modern or more complete list to replace or supplement this one!

[Son of a Beach]

OK, so more on the conversion. It is NOT universal, and is local to Australia, if I'm reading this correctly (from http://www.icsm.gov.au/icsm/gda/faq.html#WGS84 ):

Q7. What is the difference between the existing AGD and the new GDA coordinates?
The Australian Geodetic Datum (AGD) was established before satellite techniques were available and was based on a model of the Earth, that is best suited the Australian region at the time. GDA is based on an international mathematical model which 'best fits' the shape of the whole earth, with its centre coinciding with the earth's centre of mass. Coordinates on the earth's surface change approximately 200 metres in a north easterly direction with the new datum (GDA). The exact change and orientation of the change will vary slightly from area to area.

That last sentence implies that this conversion is for a specific location, and varies more the further you are from that location. This is what I thought might be the case all along, and it means that I cannot use this location to convert between WGS 60 and WGS84.

However, this may not be a big deal, as I have both of those catered for directly anyhow. I just need to figure out the ellipsoid definitions for both of the Australian standards to be truly useful for Australians, and perhaps for other international ellipsoid standards that I'm missing.

Does anyone know where there's a more comprehensive list of ellipsoid definitions than the list I posted above? (preferably showing radius and eccentricity squared)

[Son of a Beach]

AHA! Finally, I think I have found the answers I need!

It looks like the Ellipsoids list I have is the same as the ones I can find elsewhere, but there are a variety of data sets based on each ellipsoid. I now have found a list of these data sets, and a definition of each datum and how they differ from each other in a format that I think I can turn into logic in my application. PHEW! What a long painful search it has been to track this information down.

I eventually found it towards the end of the PDF document here.

I will look at how to translate this information into logic and then into code in my application over the next few days.

[north-north-west]

Could you please convert this thread title from Gibberish to something with a slightly closer resemblance to English?

Thanks.

[Son of a Beach]

Heheh... yeah none of these terms meant anything to me until a couple of weeks ago when I needed to learn them in order to write mapping/navigation software. I've never used a GPS in my life, and when I do start, it will likely be on a device running software I've written.

[north-north-west]

Ahhh, that should be fun. I'm picking mine up from the PO tomorrow, so we can take it in turns to make silly mistakes. But I'll stick to the supplied software. I can manage to turn on the PC but that's about as far as my skills go - I'm a fully paid up member of Cybercretins Anonymous.

[Son of a Beach]

OK, I've now found what I thought would be a fairly authoritative map datum list (used for GRASS, aparently) in the PDF linked to above. I've coded it into my application, and it is getting close, but still out by a bit. If I hard code the offset for AGD mentioned in the first post of this topic (112, 183) into my program it gets it exactly right on the map. So that is the correct offset.

So why is the offset for AGD66 different in the list I found: (-133, -48)
If this is wrong for AGD66, then I guess I can't trust the list for any of the other data?

The entire list is shown below (copy/paste from my program code):

Code: Select all

         [Datum datumWithName:@"wgs84" description:@"World Geodetic System 1984" ellipsoid:@"wgs84" dx:0.0 dy:0.0 dz:0.0],
         @"wgs84",
         [Datum datumWithName:@"wgs72" description:@"World Geodetic System 1972" ellipsoid:@"wgs72" dx:0.0 dy:0.0 dz:5.0],
         @"wgs72",
         [Datum datumWithName:@"nad27" description:@"North American 1927" ellipsoid:@"clark66" dx:-22.0 dy:157.0 dz:176.0],
         @"nad27",
         [Datum datumWithName:@"nad83" description:@"North American 1983" ellipsoid:@"grs80" dx:0.0 dy:0.0 dz:0.0],
         @"nad83",
         [Datum datumWithName:@"a-can" description:@"Alaska and Canada NAD27" ellipsoid:@"clark66" dx:-9.0 dy:151.0 dz:185.0],
         @"a-can",
         [Datum datumWithName:@"eur" description:@"European" ellipsoid:@"international" dx:-84.0 dy:- 103.0 dz:-127.0],
         @"eur",
         [Datum datumWithName:@"tokyo" description:@"Tokyo mean" ellipsoid:@"Bessel" dx:-128.0 dy:481.0 dz:664.0],
         @"tokyo",
         [Datum datumWithName:@"aus" description:@"Australian Geodetic" ellipsoid:@"australian" dx:-122.0 dy:-41.0 dz:146.0],
         @"aus",
         [Datum datumWithName:@"osgb36" description:@"Ordnance Survey of Great Britain" ellipsoid:@"airy" dx:368.0 dy:- 120.0 dz:425.0],
         @"osgb36",
         [Datum datumWithName:@"sam69" description:@"South American 1969" ellipsoid:@"sam69" dx:-77.0 dy:3.0 dz:-45.0],
         @"sam69",
         [Datum datumWithName:@"sad-69" description:@"SAD-69/Brasil" ellipsoid:@"SAD-69" dx:-60.0 dy:-2.0 dz:-41.0],
         @"sad-69",
         [Datum datumWithName:@"pulkovo" description:@"Pulkovo 1942" ellipsoid:@"krassovsky" dx:28.0 dy:-130.0 dz:- 95.0],
         @"pulkovo",
         [Datum datumWithName:@"eur50" description:@"European 1950 mean" ellipsoid:@"international" dx:-87.0 dy:-98 dz:-121],
         @"eur50",
         [Datum datumWithName:@"eur79" description:@"European 1979 mean" ellipsoid:@"international" dx:-86 dy:-98 dz:-119],
         @"eur79",
         [Datum datumWithName:@"agd66" description:@"Australian Geodetic 1966" ellipsoid:@"australian" dx:-133 dy:-48 dz:148],
         @"agd66",
         [Datum datumWithName:@"agd84" description:@"Australian Geodetic 1984" ellipsoid:@"australian" dx:-134 dy:-48 dz:149],
         @"agd84",
         [Datum datumWithName:@"gda94" description:@"Geocentric Datum of Australia 1994" ellipsoid:@"wgs84" dx:0.0 dy:0.0 dz:0.0],
         @"gda94",
         [Datum datumWithName:@"grs80" description:@"Geographic Reference System 1980" ellipsoid:@"wgs84" dx:0.0 dy:0.0 dz:0.0],
         @"grs80",
         [Datum datumWithName:@"rome40" description:@"Rome 1940" ellipsoid:@"international" dx:-225 dy:-65 dz:9],
         @"rome40",
         [Datum datumWithName:@"Sasia" description:@"South Asia" ellipsoid:@"fschr60m" dx:7.0 dy:-10.0 dz:- 26.0],
         @"Sasia",
         [Datum datumWithName:@"s-42" description:@"S-42" ellipsoid:@"krassovsky" dx:28.0 dy:-121.0 dz:- 77.0],
         @"s-42",
         [Datum datumWithName:@"potsdam" description:@"Potsdam Rauenberg 1950 DHDN" ellipsoid:@"bessel" dx:606.0 dy:23.0 dz:413.0],
         @"potsdam",
         [Datum datumWithName:@"carthage" description:@"Carthage 1934 Tunisia" ellipsoid:@"clark80" dx:-263.0 dy:6.0 dz:431.0],
         @"carthage",

[Son of a Beach]

PS. And here is another list which agrees with the one above for AGD66. So why do these offsets not work for me in practice, and the ones in the OP do?

PPS. To summarise... why does the ADG66 to GDA94/WGS84 offset on this page work correctly, and why is it different to the offset on every other list I've found (which do NOT work correctly).

[Son of a Beach]

I think I'm talking to myself here, but hey, it's good to say (type) these things 'out loud' sometimes as having to form it into words helps to clarify the thinking about the problem.

I lay awake most of last night thinking about this problem, and have formed a conclusion that may or may not be correct, and may or may not be obvious to others. I think that the 'dx', 'dy', and 'dz' are not actually what I thought (assumed) they were. They are definitely delta in metres. However, I don't think that dx/dy relates directly to the easing/northing offsets, which is what I had assumed.

I need to figure out what they really do mean. I'm now guessing that the dx/dy/dz triplet defines an effective phase-shift of the entire ellipsoid in 3 dimensions, in which case there's going to be some complicated formula to derive the actual easting/northing offsets for a particular datum's dx/dy/dz triplet for any given point on the earths surface. This would explain why the easting/northing offsets are different for different parts of the earth and that the offset provided for AGD66 & GDA94 are regarded as being near enough for most places in Australia.

So now I've got to try to confirm my theory, and if I do then I need to find out the formula (my maths is nowhere near good enough to figure this sort of thing out on my own).

[tastrax]

Hi Nik,

You lost me a couple of posts ago but I assume you also checked out this page..

http://www.utas.edu.au/spatial/locations/spaconv.html - a few leads there to calculators etc

I also have a spreadsheet somewhere that I found on the web years ago that has all the formulas for conversions. I will see if I can find it in my archives.

[Son of a Beach]

Yes, I've got a lot of good information from that page, and seen a lot of calculators. But what I really need is the formula(s) required to build a calculator into my own software.

To be precise, what I really need to know is how to convert eastings/northings from WGS84 (which is what my source gives me) into any other mapping datum. I have the ellipsoid definitions, and the datum definitions (in dx/dy/dz), but I don't know what to do with them after that.

(I've already build a calculator for converting lat/long into eastings/northings in WGS84, based on free code I found elsewhere).

[Son of a Beach]

Ah, I was right, it seems. This FAQ answer explains the basics of what is required, without actually providing the formula, but gives the impression that it's very complicated.

Essentially, you have to:

• convert that Latitude/Longitude coordinates into ECEF (I've yet to come to grips with what this means) according to the ellipsoid definition the lat/long coordinates were derived from
• apply the dx/dy/dz parameters so some complex formula or other for the datum conversion
• convert from ECEF to Latitide/Longitude for the ellipsoid you want to end up on
• convert from lat/long to eastings/northings

I've got the last step down no worries at all. The rest of it is still a mystery to me, but at least I'm making progress again, albeit very slowly.

[loric]

http://www.ga.gov.au/nmd/products/fwdpr ... liggda.jsp
See "Geoscience Australia's coordinate conversion tables."
It's a zip folder with a whole bunch of excel sheets to do transformations.


EarthCentreEarthFixed (ECEF)
http://www.satsleuth.com/GPS_ECEF_Datum ... mation.htm

Does this help any?

Your problem isn't technically difficult - essentially a whole bunch of trig and cartesian transformations. You sure are keen to get this baby off the ground huh!?

[Son of a Beach]

Thanks loric. The first link I've looked at before, and it's all very Autralian (AGD/GDA) centric. I need something that I can apply to any datum (defined by ellipsoid/dx/dy/dz).

That second link looks promising in helping me understand the geometry better.

I've also now got enough of an understanding of the process above to realise that the sample code that I noticed some days ago on wikipedia here may actually be of some use in all this.

EDIT: Yes, that second link explains ECEF very well, and it looks like it even provides the formulas I need to convert between Lat/Long and ECEF in both directions. These formulas, combined with the information I found earlier for the steps for converting between one datum and another, should do the trick. Now I should be able to write some code which implements this (and maybe compare with that code on Wikipedia to see if I'm doing it right). Thanks heaps for this pointer, loric.

[Son of a Beach]

DONE IT!!! It flippin' works!!! (sorry, I'm very excited... can you tell?)

Thanks to everyone for your advice and pointers to several helpful web pages. It took a long time for me to put together the various sources enough to understand what was really required, and then to write the code to implement it.

My little mapping program now includes an (OOP) "datum" object that can be instantiated for any known map datum and can convert coordinates to any other known map datum (ie, any datum for which I've coded knowledge into the application). I've coded in all the datums I could find, and it appears to work very well for AGD66, at least. It certainly shows my current location on the map to within just a few metres.

Now I can finally get on with the rest of the application, and try to make it look a little more pretty, and work in a more user friendly manner.

[tastrax]

Well done Nik - great to see such persistence. Just remember the day that you finish the project someone will ask for some obscure datum and projection (or a renaming of one of your so it works with other programs). If its a possibility...give them at least one place to add in their own parameters.

[Son of a Beach]

Yes, you're right. The most challenging part of application development is often figuring out how to deal with the exceptions to the rule. Sometimes it seems like the majority of the work goes into the elements of the software that will get used the least.

[north-north-west]

I still don't understand any of this. I mean - it's English but it just doesn't make any normal sense . . .

. . . which is bad news for me given one of my most recent purchases . . .

[MJD]

The most challenging part of application development is often figuring out how to deal with the exceptions to the rule.

And then there's all those different and sometimes unforeseen ways that your customers will test, sorry I meant use, your software.

[bahkyp]

Remember UTM (Universal Transverse Mercator) and a datum in DMS (Degrees M S) are different shapes, and while you can have GDA94 & WGS84 datum (DMS), it is not a UTM WGS84 map. Most maps with northings and eastings are UTM. UTM tries to overlay a square grid on a round globe. This is why the metres offset for AGD66 to WGS84 UTM conversion for me here in Sydney is different to TAS. This is also why all maps have a convergence (the lats and longs line up on one side and make a triangle with the map edge on the other) and why realistically ~200m NE is generally good enough. (Oh and why Royal Greenwich Observatory is now at 0 0'2.5" west according to WGS84! and 51.477653,-0.000732 on Google!)

I know Geosience Australia has a list of all Australian maps and their AGD-GDA offsets. http://www.ga.gov.au/geodesy/datums/agd-gda94.xls. Adjacent maps differ generally by 0 to 1m.

The calculation the other spreadsheets I've seen in this thread should be doing are UTM AGD66 to DMS AGD66, then AGD66 to GDA94 (Accurate to 2 cm of WGS 84), then DMS GDA94 to UTM GDA94. You should not convert directly, when you do this you ironically get bigger errors. (because the grids on the globe bend!)

Oh and note that your GPS in forested areas will be accurate to ~50m anyway. And has an absolute accuracy of ~15m for cheap models and ~3m for expensive ones with a full constellation and stationary observation. You need a known, fixed point and 2 GPS to get better.

Michael

[Son of a Beach]

Yes, it is rather complicated. The software I wrote for this converts everything to latitude and longitude first then to the desired datum then to UTM grid references. It works very accurately as as far as my own testing goes.

I learned most of what I needed to know by following links posted on this topic, plus doing some further research on the actual maths of the conversions from there (much of the maths is still over my head).

[frenchy_84]

sounds like you have turned in to a full blown geodesist. Are you ready for the next realisation of GDA?

[Son of a Beach]

sounds like you have turned in to a full blown geodesist. Are you ready for the next realisation of GDA?

It's been a very steep learning curve! I'm certainly no expert, but I've got a much better grasp than what I had before posting this topic (at which time I knew nothing, and had never even used a GPS).

Yes, I can easily add datums to the list supported by Bit Map (the iPhone application). In fact, I've just added the Old Israel Datum today, ready for the imminent release of version 1.3.

Each datum is simply defined by an ellipsoid definition, and an offset of the ellipsoid's centre from the wgs84 ellipsoid's centre (in 3 dimensions: dx, dy & dz). The ellipsoid definition can be either by name (to a known ellipsoid which is already defined within the software), or by radius and flattening. Optionally, the ellipsoid eccentricity can also be included (can be good to get more accurate results than if calculating the eccentricity on the fly with computer's limited decimal places, which can be further reduced during some calculations).

[frenchy_84]

im glad you understand it, cause i did a degree on it and still dont understand it. i forwarded the link to Bit Map to my mates who have an Iphone, it looks good.