On the effects of hard and soft equality constraints in the iterative outlier elimination procedure.

Reliability analysis allows for the estimation of a system's probability of detecting and identifying outliers. Failure to identify an outlier can jeopardize the reliability level of a system. Due to its importance, outliers must be appropriately treated to ensure the normal operation of a system. System models are usually developed from certain constraints. Constraints play a central role in model precision and validity. In this work, we present a detailed investigation of the effects of the hard and soft constraints on the reliability of a measurement system model. Hard constraints represent a case in which there exist known functional relations between the unknown model parameters, whereas the soft constraints are employed where such functional relations can be slightly violated depending on their uncertainty. The results highlighted that the success rate of identifying an outlier for the case of hard constraints is larger than soft constraints. This suggested that hard constraints be used in the stage of pre-processing data for the purpose of identifying and removing possible outlying measurements. After identifying and removing possible outliers, one should set up the soft constraints to propagate their uncertainties to the model parameters during the data processing.

Robust Estimators in Geodetic Networks Based on a New Metaheuristic: Independent Vortices Search.

Geodetic networks provide accurate three-dimensional control points for mapping activities, geoinformation, and infrastructure works. Accurate computation and adjustment are necessary, as all data collection is vulnerable to outliers. Applying a Least Squares (LS) process can lead to inaccuracy over many points in such conditions. Robust Estimator (RE) methods are less sensitive to outliers and provide an alternative to conventional LS. To solve the RE functions, we propose a new metaheuristic (MH), based on the Vortex Search (IVS) algorithm, along with a novel search space definition scheme. Numerous scenarios for a Global Navigation Satellite Systems (GNSS)-based network are generated to compare and analyze the behavior of several known REs. A classic iterative RE and an LS process are also tested for comparison. We analyze the median and trim position of several estimators, in order to verify their impact on the estimates. The tests show that IVS performs better than the original algorithm; therefore, we adopted it in all subsequent RE computations. Regarding network adjustments, outcomes in the parameter estimation show that REs achieve better results in large-scale outliers' scenarios. For detection, both LS and REs identify most outliers in schemes with large outliers.