STAR*NET V6 - Circe

Chapter 5 Preparing Input Data
5.11 Using Standard Errors to Weight Your Observations
What do weights mean?
STAR*NET allows you to individually weight each observation in the adjustment. This
feature provides you with great flexibility in performing adjustments. However, it also
requires a basic understanding of the concepts involved. Otherwise, you may adversely
affect the quality of the adjustment results. STAR*NET’s statistical tests will usually
indicate a problem with observation weights, but you should still understand the
implications of your inputs. Therefore, the next few paragraphs present a brief
description of weights and their meaning.
Throughout the discussion, we will refer to the sample distance input line below:
D TOWER-823 132.34 0.04 5.4/5.1
The distance has a standard error of 0.04 in whatever linear units are set in the project
options. The standard error is the square root of the variance of the input value. They are
both measures of the precision with which the input value was derived. A small variance
and standard error indicate a precise measurement, and a large value indicates an
imprecise measurement. Note that a small variance does not necessarily indicate an
accurate measurement. Rather, it indicates that multiple readings of, for example, a
single distance, clustered closely together. If the measuring instrument had a large
systematic error, then this precise measurement may be rather inaccurate. For example,
ten measurements of a distance made with an EDM that is out of calibration may agree
closely, but may all be significantly different than the true value.
Another way to state the precision of an observation is its weight. Weight is inversely
proportional to variance: as the variance decreases, the weight increases. In other words,
a precise measurement with a low variance should be given a large weight in the
adjustment so that it will have more influence. When you indicate the standard error of
an input value (0.04 in the example above), STAR*NET converts it internally to a weight
by squaring the value to compute the variance and then inverting it. This results in a
value of 625 for the example.
Theoretically, though, the weight and variance are inversely proportional to each other.
STAR*NET assumes the proportionality constant to be 1.0. How does this assumption
affect you? If the standard errors that you assign to your observations are not realistic,
and the constant should have had a value significantly different from 1.0, the adjustment
will frequently fail the Chi Square statistical test. This situation may not affect your
computed coordinate values very much, but you should always investigate the reasons
for an adjustment failing the Chi Square test. This topic is explained in more detail in
Chapter 8, “Analysis of Adjustment Output .”
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