Blunder Detection and Data Snooping in LS and Robust Adjustments

There are many procedures for adjusting data and detecting the presence of blunders in a set of observations. Most such procedures involve examining the adjustment results for residuals whose magnitude is in some sense "large." In data snooping, each residual is divided by its own standard deviation, resulting in a statistic whose distribution is known. Thus blunder detection becomes a statistical hypothesis testing problem. In iterated data snooping, only the observation with the largest normalized residual is deleted at each iteration. The residuals may be either from a conventional least-squares LS adjustment or from an "L1 norm" adjustment that seeks to minimize the sum of absolute values of residuals. Iterated data snooping with the LS residuals is at least as effective as any other method of detecting blunders. We show by example that it can produce much better results than the L1 norm adjustment. Both forms of data snooping are superior to the many empirical or approximate methods that are still widely used.