Courses - GPS 403
GPS 403 Quality Control with
Adjustments (catalog description): Geometry of
least-squares, definition of network coordinate systems,
singularities, probability regions, minimal and inner constraints,
invariant quantities, multivariate normal distribution, relevant
statistical tests, type I/II errors, internal and external
reliability, absorption of errors, blunder detection,
decorrelation, inversion of patterned and large matrices,
numerical aspects; Kalman filtering. GPS 401, equivalent or
consent. Lec 1. Cr 1
Unfortunately, many people think
that "adjustments and high accuracy go together" somehow. We will
stress in this unit that adjustment is best viewed as a tool for
objective quality control and that the respective techniques and
rules apply equally to high-accurate or low-accurate applications.
An undetected blunder in a low-accurate survey can potentially be
very damaging.
This unit addresses statistics in
detail as it applies to least squares. We introduce the
multivariate normal distribution and derive the relevant
statistical tests. After discussing type-I and type-II errors we
introduce internal and external reliability as major tools of
quality control, followed by a discussion of strategies for
blunder detection. This includes recognizing the fact that
least-squares solutions tend to absorb parts of the blunder, i.e.
making residuals to reveal only the "visible part" of the actual
errors.
Minimal and inner constraints are
ways to define the coordinate system in networks. For example, a
plane distance network can be translated and rotated without
changing the distances and angles; we say that distances and
angles are invariant with respect to translation and rotation.
Another example is a GPS vector network that is invariant with
respect to translation. Introducing minimal and inner constraints
is a general way of dealing with this invariance, or the lack of
coordinate system definition. The effect of these constraints on
the size and shape of the probability regions will be discussed in
the context of the over-all geometry of an adjustment as implied
by the stochastic and mathematical models.
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