A review of outlier detection procedures used in Surveying Engineering

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.