Abstract:
The method of least squares is the most widely used parameter estimation tool in
surveying engineering. It is implemented by minimizing the sum of squares of weighted
residuals. The good attribute of the method of least squares is that it can give an unbiased and
minimum variance estimate. Moreover, if the observation errors are normally distributed
identical results to the maximum likelihood method can be obtained. However, the method of
least squares requires gross error and systematic bias free observations to provide optimal
results. Unfortunately, these undesired errors are often encountered in practice. Therefore,
outlier diagnosis is an important issue in spatial data analysis. There are two different
approaches to deal with outliers: statistical outlier test methods and robust estimation. Baarda
and Pope methods are well known hypothetical testing methods. On the other hand, there are
numerous robust methods to eliminate or reduce disruptive effects of outliers, such as Mestimation
method, L1 norm minimization, the least median squares and the least trimmed
squares. Robust methods are useful to locate multiple outliers. Yet, statistical testing approach
can also be generalized to multiple outliers. Furthermore, reliability measures and robustness
analysis enable us to assess the quality of our networks in terms of gross error detection and the
effect of undetected errors. In this study, a review of outlier detection procedures is given. The
main features of the methods are summarized. Finally, statistical test for multiple outliers is
applied to a GPS network.
