Courses - GPS 402
GPS 402 Adjustment Algorithms
(catalog description): Error ellipses and ellipsoids,
propagation of estimated quantities, a priori information on
parameters, adjustment of implicitly related observations and
parameters, mixed model, condition equation model, sequential
solutions, testing conditions on nonlinear parametric functions.
Prerequisites: GPS 401, equivalent or consent. Lec 1. Cr 1
The mixed model, which deals with
observations and parameters that are implicitly related, is at the
center of this unit. This is the most general adjustment model and
is often easy to relate to specific applications. An example is
fitting a circle through observed points. Applying simple
specifications to the mixed model allows us to derive the
observation equation and the condition equation model. The
condition equation model, the third adjustment model that is being
discussed, applies when there are no parameters involved, e.g.
adjusting a leveling network.
We use the mixed model for
developing sequential solutions for all three models. The
sequential solutions, also referred to as adjustments in steps,
refer to the same set of parameters but to different observations.
Additional specifications yield the models that allow
incorporation of a priori information on parameters, or the
testing of conditions between parameters. We consider nonlinear
conditions between parameters, and then apply the General Linear
Hypothesis Model after the linearization. Statistical tests for
testing conditions will be presented but not derived in this unit.
Ellipses of standard deviation,
often referred to as error ellipses for brevity, are introduced as
a simple form of higher-dimensional probability regions. The
magnification of these regions to assure that a certain
probability is included and the shapes of these regions as a
function of correlation will be studied.
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