[*** UNDER CONSTRUCTION ***]

I've been talked into doing an article on Cave Survey analysis and adjustment, with sample code. This, in skimpy form, is my attempt at it. I've just started, so almost everything says "UNDER CONSTRUCTION". However, I am putting it out here so that I can get some feedback on it while it is still easy to change.

Apologies: My apologies to any real surveyors wandering by here. The audience is Cave Surveyors, who have over the years built their own little subculture that references only other cave survey papers, and have drifted quite a ways from the main line survey community.. These pages, therefore, repeat information most surveyors already know.

If you are a real surveyor, you will find this paper pointing out the obvious chronicly, and find that this paper reviews some pretty elementary topics. You should also note that what cavers call a "Survey" is generally a traverse net without triangulations or trilateraliztions, done with hand held instruments under conditions that are less than ideal (Such as a one foot high passage with six inches of water.)

This paper doesn't actually do the derivations of most of what it discusses. Instead it presents the ideas behind it, and then the standard results without derivation, so that the reader with only minimal math may follow it. I generally tell the user where in the general literature they can go to get the full derivations. Generally a reference to the bibliography is made.

Geek Note: There are important ideas, mathematics, etc. that someone really into mathematics should be aware of in this paper. Just putting them in bores the non-mathematical user to tears, and makes them give up. SO... parts of this paper of interest only to the serious math sort are marked (as is this paragraph) with "Geek Note".

Non-Geek Note: It should be the case that if you just ignore most equations the rest of the text will give you the important conclusions that get proved. If equations really bother you, just ignore them and slog on through.

Recent changes to the paper

Recent changes to the code library

- Background
- What is a weight?
- One dimensional weights
- One dimensional weighted averages
- One dimensional example
- Multi-Dimensional weights
- Multi-Dimensional weighted averages
- Two dimensional example
- Some Geek Notes

Dealing with a survey shot:

- Input
- Blunders
- Units conversion.
- computing Weight (Covariance) of a shot.
- full weight of the observations.

Geometry, redundancy, and overdetermined systems.

- The basic problem.
- Connectivity
- Dead ends, dendrites, and equivalent legs
- Matrix methods

Analysis and Adjustment.

- Geometry Analysis.
- Loops, dead ends, and dendrites.
- Traverses and connections.

- Redundancy and Degeneracy.
- Adjustment issues.

Linearization of the problem. This chapter is defunct, and the parts are being moved to other sections.

Adjustments [UNDER CONSTRUCTION]

- [weighted linearized] Least squares
- What it is, What it isn't.
- Adjustment by conditions
- Adjustment by observations

Post processing.

- Observations vs the adjustment.
- Blunders
- Re-linearization.
- Reports
- Accuracy and Precision.
- Apostori [After the fact] Reference variances.

Using canned least squares packages for the task

**Test Data**: Some simple
test surveys designed to exercise Least Squares data adjustment.
Many of these were designed to have answers independent of whatever
the underlying program uses for weights. (Enabling the underlying
adjustment to be tested.)

**Glossary**: a very sketchy
glossary of cave and survey related terminology used in this paper.

**Matrix review**: A very
quick review of the important properties of matrices.

- Numbers
- Rows
- Columns
- Operations on rows and columns
- Matrices
- Matrix Multiplication
- Magnitudes
- Inverses
- Quadratic Forms
- Positive Definite

**Matrix Identities**:
Useful (?) matrix definitions, identities, and facts.

**Statistics review** [ (: Not written yet :) ]

**Code**:
The code directory is sparse at the moment, but
does include some basic 3d weighted network adjustment code.
I'm looking for feedback.
I still reserve the right to change
interface names and arguments, so unless you've checked in with me as a
tester, things will change out from under you.

The bibliography contains pointers to books that cover in detail those things that I only gloss over.

This page is http://www.cc.utah.edu/~nahaj/cave/survey/intro/ © Copyright 2003 by John Halleck, All Rights Reserved. This snapshot was last modified on October 29th, 2003