Testing Theory

As in other physical sciences, empirical data are used in geodesy to make inferences so as to describe physical reality. Many such problems involve the determination of unknown parameters from a set of redundant measurements. Measurements are said to be redundant when they exceed the minimum necessary for a unique determination of the parameters. There are two main reasons for collecting redundant measurements. First the requirement to be able to check for mistakes or errors. Second the wish to increase the accuracy of the results computed. As a consequence of measurement uncertainty (exact measurements do not exist), the redundant data are usually inconsistent in the sense that each sufficient subset yields results which will differ from the results obtained from another subset.

To obtain a unique solution, consistency needs to be restored by applying corrections to the data. This computational process of making the measurement data consistent with the model such that the unknown parameters can be determined uniquely, is referred to as adjustment. Adjustment theory therefore deals with the optimal combination of redundant measurements together with the estimation of unknown parameters. An introductory course on adjustment was presented in Adjustment theory. This theory is extended in this book to the case of time-varying or dynamic parameters with an emphasis on their recursive estimation.

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