Overdetermined system

As an over-determination is in areas of mathematics and geodesy refers to the presence or the additional measurement of geometrical parameters such as directions or routes which go beyond the necessary determination pieces of a model.

The simplest example is the measurement of the third angle in the triangle, which would be complementary to the other two to 180 °. More complex cases are geometric body or surveying networks in which excess measurements or data are available.

This redundancy can serve several purposes:

• To control the system, such as when joining several Operate or in the presence of different processing methods
• To increase the accuracy because each additional observation can reduce the effect of small, unavoidable measurement errors
• For statements about the certainty and reliability of a system.

In an overdetermined system more conditional equations than there are unknowns. The additional equations and measurements there is small inconsistencies in the system, which stiffen, but have to be processed appropriate.

The mathematical tools for proper handling of excess provisions are the compensation calculation and the analysis of variance. They are based on the statistical distribution imperceptible influences ( see normal distribution ) and minimize the contradictions between small supernumerary measurements or data with the least squares method.

As a result, we obtain the most probable values ​​of the unknowns and the so-called residuals (residual variances) between the final values ​​and the individual Bestimmungssgrößen. From these residuals individually effective error components can be factored out and used for a refinement of the mathematical-physical model.

• Geodesy
• Compensation calculation