Backsights and default accuracy estimates

[John Halleck]

On Fri, 31 May 2002, Martin Green wrote:

> Date: Fri, 31 May 2002 03:21:19 +0100
> From: Martin Green <mjg54@cam.ac.uk>
> To: John Halleck <John.Halleck@utah.edu>
> Cc: survex@survex.com
> Subject: Re: Backsights and default accuracy estimates
> 
> Hi,
> The grade system was made up by the BCRA, I do not why they made there
> decisions, but it is common practice here to use them.

  I didn't question their use.  Only
     1) Their being from the cave survey community instead of from
        the survey community.  (Which being BCRA would seem to
        confirm.)
  and
     2) Whether they made the claim that fore- and back-sights
        had to agree within a degree in a grade 5 instead of
        just being accurate within a degree.  (Which was your
        claim.)

>   I can not find a
> link to a BCRA set of definitions, but here is a similar one.
> http://malaysiancave.tripod.com/cave_maps_survey_grading.htm

  Thank you.
  But I don't see any requiremement that foresights and backsights have
  the one degree agreement...  It only requires that angles be accurate
  to one degree.

  So my question still stands.  Can someone please do me the favor of
  checking that the grade 5 actually requires fore and backsight agreement
  within a degree (as Mr. Green stated) instead of just having a requirement
  that the compass measurements are accurate within a degree?

> My comments on the accuracy was a fairly hand wavy order of magnitude
> approach, to demonstrate that the errors can get big quick, ie if your
> errors manage to swing the cave around. 

  Only if you ignored the Azimuth data.  We do, after all, have the
  original azimuth data and not just the computed turned angles.

  Yes, there are adjustment analysis techniques that suffer from that
  problem.  But I fail to see any reason that the usual techniques
  would have that problem.

> Therefore it is best to avoid that approach unless it will give more
> accurate results.

  You keep making that claim.  I keep pointing out that (at least
  with loops, the case you claimed was "touchy") this is horseshit.

>  After all in a long enough cave, with an inaccurate
>  enough measuring system, with 15 degree  magnetic shifts, it is still
> more accurate to assume that magnetic north is
> absolute north than it is to measure angles.

  Only if you make a number of assumptions that I haven't seen made
  in this discussion. (Such as blunders not being in a loop, and
  the distribution of both blunders and anomalies being uniform)

> To properly solve the problem
> would require a Baysian logic approach, with prior probabilities for
> magnetic variations determined from a suitable geologist, and well
> determined probability distributions of the surveyors when they read
> instruments, then solved using a suitable optimisation alogrithem.

  I assume you mean Baysian statistics.  (Since I can't really see
  how Baysian logic is applicable here) But bringing in yet another
  statistcal method doesn't change the problem.  Surveyors have
  been dealing with this problem (Successfully) since about the time
  of Gauss.  Admittedly some of the papers are obscure (surveyors
  resurvey blunders...) they are around, and readable by people
  with basic skills.

> Any way we seem to be talking about the same things, and disagreeing.

  I begin to wonder if we are talking about he same things.

> But I would like to say that I think that a measurement of a position is
> useless with out an estimation of the associated error.  Otherwise how can
> you tell blunders from errors?

  And you are saying don't use the very tests that would allow you
  to tell which are wich.

>   Wheather you are 10m from another cave or within a hundred meters
> in some direction?

  Huh?

> So trying to determine the error
> in the general case scenario for people adhering to BCRA grade 5 surveying
> is not at all moot, as they are unlikely to do it themselves, nor is the

  1) I don't think the question is moot.  I don't, however, agree with
     what you said about fore and back sights.
  2) Why would they not do it themselves?
     I've yet to see any notible project where the people couldn't find
     someone who could do so, and didn't use that person to tell them
     about what they had.

> volume of blunderless data available to make generalisation for all cavers.

  If you are looking for the standard deviation of the data, and the 
  data typically contains blunders, then they need to be included.
  (Just what do you think "standard deviation of the data" means?)

  And the question of what the Grade 5 survey says is still open, since
  the URL you posted doesn't agree with your statement of it.

> Martin
> (I am just about aware that n^1=n,

  Then why did you give n^1 instead of n?

>  and that the problem is a system of
> probabalistic non-linear 3d equations,

  Your original statement is not compatable with this.

>  but aren't they ever so hard to solve
> with out the odd approximation).

  Yes, that's why the linearized system is used by any least squares network
  adjustment that I've ever seen used on real data. 
  I looked back on the discussion, and I said I was dealing with X, Y, Z's
  derived from a non-linear transformation.  I can't find anywhere that I 
  said that I advocated trying to solve the non-linear equations.