[Proj] Using Proj.4 to compress a 10-parameter Molodensky-Badekas datum shift into 7 parameters

[Noel Zinn (cc)]

Mikael / Cliff,

I am sympathetic to Cliff's suggestion that the M-B evaluation/rotation 
point be the datum origin.  Regrettably, I don't have a copy of John 
Badekas's 1969 Ohio State monograph, "Investigations related to the 
establishment of a world geodetic system", in which the transformation was 
proposed and which may have Badekas's advice on the matter.  However, I do 
have Claude Boucher's (IGN) 1979 paper ("Investigations on geodetic 
applications of satellite Doppler observations for control networks")  from 
the 2nd International Geodetic Symposium in Austin (which I attended and at 
which I met John Snyder).  Boucher's advice for the M-B evaluation/rotation 
point is the barycenter (in ECEF) of all the points in the adjustment. 
Bruce R. Harvey (UNSW) has an 1986 paper ("Transformation of 3D 
Coordinates") in the Australian Surveyor in which he offers the same 
barycentric advice for M-B.   My own explorations with M-B presented to the 
Americas Petroleum Survey Group in 2004 (cited by Mikael below) used the XYZ 
barycenter, which is why it's below the surface of the Earth.  Of course, 
these were simulations and there were no datum origins.

As an aside, Boucher's 1979 paper presented the Bursa-Wolf 7-parameter 
transformation with the position-vector rotation sense and that may be the 
first time Bursa-Wolf was associated with position-vector rotations.  Some 
years ago Malcolm Jones of Australia gave me a copy of Milan Bursa's 1966 
paper, "Fundamentals of the Theory of Geometric Satellite Geodesy".  Bursa 
employed the coordinate-vector rotation sense!

As a further aside, and getting back to my original point, it's clear from 
the titles, dates and readings of these papers that the issues of the day 
involved relating a proliferation of new, global satellite datums to one 
another.  The 7-parameter transformation is well suited for that purpose 
because on a global scale the correlations among the 7 parameters is near 
zero.  The Molodensky-Badekas is better suited for small terrestrial datums 
where 7-parameter correlations are high.  We've made a wrong turn 
geodetically by deriving 7-parameter transformations in small areas.

Proj.4 should support M-B despite our new-found ability to compress 10 
parameters into 7.

Regards,
Noel

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)


--------------------------------------------------
From: "Mikael Rittri" <Mikael.Rittri at carmenta.com>
Sent: Wednesday, October 13, 2010 4:03 AM
To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org>
Subject: Re: [Proj] Using Proj.4 to compress a 10-parameter 
Molodensky-Badekas datum shift into 7 parameters

> Clifford,
> thanks for your comments.
>
> You wrote:
>> In regard to the "unexplained" difference in ellipsoid height results,
>> my guess is the approximations made by the inverse algorithm
>> from Geocentric coordinates.
>
> Well, I hope it is just something like that.  But I don't know how
> accurately cs2cs implements this inverse algorithm.
>
>> The "evaluation point" is the Datum Origin, a rather important item.
>
> "Evaluation point" is the term used in the EPSG database, but I see
> that they sometimes call it "rotation point" in their Guidance Note 7.2.
>
> No, it isn't.
>
> I mean, the datum origin may be important, but the origin of the
> La Canoa datum is at
>
> 63° 51' 34.880" W, 08° 34' 17.170" N
> (source: your column on Venezuela, 
> http://www.asprs.org/resources/grids/12-2000-venezuela.pdf )
>
> And when I convert the evaluation point of my example datum shift
> to long/lat, I get a different location:
>
>>cs2cs +ellps=intl +proj=geocent +to +ellps=intl +proj=longlat
> 2464351.59   -5783466.61   974809.81
> 66d55'15.629"W  8d52'22.857"N -16138.645
>
> which is about 340 km west of the datum origin, and nearer
> the centre of Venezuela.
>
> Rather, I think the evaluation point in this example
> might be the average of all observation points used
> to derive the datum shift.  Noel used this approach in
> pages 45 - ... of 
> http://www.hydrometronics.com/downloads/Molodensky-Badekas.pdf
> That could also explain why the evaluation point is 16 km
> below the ellipsoid surface (caused by the curvature of the
> Earth).
>
>> ...and Prof. Molodensky preceeded them [Dr. Kumar and Prof. Badekas]
>> on another continent by some years if not decades.
>
> That reminds me of something I have wondered about:
> Wasn't Helmert much earlier than Burša and Wolf?
>
> Regards,
>
> Mikael Rittri
> Carmenta AB
> Sweden
> www.carmenta.com
> ________________________________
>
> From: proj-bounces at lists.maptools.org 
> [mailto:proj-bounces at lists.maptools.org] On Behalf Of Clifford J Mugnier
> Sent: den 12 oktober 2010 16:37
> To: PROJ.4 and general Projections Discussions
> Subject: Re: [Proj] Using Proj.4 to compress a 10-parameter 
> Molodensky-Badekas datum shift into 7 parameters
>
>
> The "evaluation point" is the Datum Origin, a rather important item.  In 
> regard to the "unexplained" difference in ellipsoid height results, my 
> guess is the approximations made by the inverse algorithm from Geocentric 
> coordinates.
>
> Personally, I prefer the elegance of incorporating the Datum Origin.
>
> I have also been told by Dr. Muneendra Kumar that Badekas had nothing to 
> do with Molodensky's original method.  I believe they were in school 
> together at the same time, and Prof. Molodensky preceeded them on another 
> continent by some years if not decades.
>
> Clifford J. Mugnier, C.P., C.M.S.
> Chief of Geodesy,
> Center for GeoInformatics
> Department of Civil Engineering
> Patrick F. Taylor Hall 3223A
> LOUISIANA STATE UNIVERSITY
> Baton Rouge, LA  70803
> Voice and Facsimile:  (225) 578-8536 [Academic]
> Voice and Facsimile:  (225) 578-4578 [Research]
> Cell: (225) 238-8975 [Academic & Research]
> Honorary Life Member of the
> Louisiana Society of Professional Surveyors
> Fellow Emeritus of the ASPRS
> Member of the Americas Petroleum Survey Group
>
>
> ________________________________
>
> From: proj-bounces at lists.maptools.org on behalf of Mikael Rittri
> Sent: Tue 12-Oct-10 03:45
> To: PROJ.4 and general Projections Discussions
> Subject: [Proj] Using Proj.4 to compress a 10-parameter Molodensky-Badekas 
> datum shift into 7 parameters
>
> [see post at 
> http://lists.maptools.org/pipermail/proj/2010-October/005436.html ]
>
>
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