General Algorithm for Gross Error Filtering Utilizing Weighted Arithmetic Mean Value Preceding Least Square Adjustment

Abstract

In the context of error detection in measurements, various methods are available depending on the magnitude of the errors. Very large gross errors, often coming from mistakes, typically need to be removed before the adjustment process. In fields such as photogrammetry and geodesy, these errors, among others, can include swapping of coordinates and misidentification of measurement points. The next two categories consist of moderate and small gross errors, which are more challenging to identify, as they result inaccuracies rather than mistakes. Assuming we have redundancy in measurements for the computation of unknown parameters, we solve the task through adjustment using the least squares method. Faulty measurements are characterized by multiples of the mean error of unit weight. We consider measurements burdened with small gross errors as those where the error magnitude exceeds three times the mean error of unit weight, but does not reach twenty times. Most established methods aim to identify and filter out these errors during the adjustment process, either in a single step or through iterative refinement by modifying the weight functions. This paper introduces an error-filtering algorithm capable of identifying small, moderate, and large gross errors before executing the adjustment. The sole requirement is that the given task can be solved with the minimum necessary number of measurements, i.e., without redundancy in measurements. After presenting the general algorithm, the effectiveness of the method is demonstrated through one example.