O independent vortices search no controle de qualidade em redes Geodésicas: uma avaliação de estimadores robustos otimizados por meta-heurística para o ajustamento de redes geodésicas

Abstract

Geodetic networks are the basis not only for mapping activities, geoinformation, land registry and other location-based services, but also provide an important role in society as infrastructure works (roads, bridges, tunnels, water supply, sewage, electricity networks, telecommunications, etc.) which are directly dependent on highly accurate three-dimensional control points. Given the importance of this reference points, a precise computation and adjustment is highly necessary in the establishment of this networks. Most of them are settled using GNSS (Global Navigation Satellite System) signals which are available all over the Earth surface. The geodetic networks based on GNSS techniques have their points’ coordinates estimated from the relative distances between them, called observations, through adjustment processes. When it comes to adjust all the observations to form a network, the least squares (LS) method is often applied because it is the best linear unbiased estimator, assuming that no outliers and/or systematic errors exist. Outliers may occur in practice, however, and cause such estimation to fail and leading to unprecedented errors over many points in the network. Alternatively, Robust Estimators (ERs) can be applied as to be insensitive to the presence of outliers. Such ERs can be implemented through metaheuristic algorithms (MHs) to solve the estimator’s function, often complex and not solvable by equations. This approach has already been brought by other studies, however, they were not widely explored, mostly in very specific and limited scenarios. This work brings a new research of this strategy, analyzing the behavior of several ERs known in the literature, through the application of a new meta-heuristic called Independent Vortices Search, besides a new strategy for the search space definition. A large number of error scenarios were generated to test the ERs, along with a classic iterative and robust method, which does not require any MH algorithm. In addition, we also tested the median and cut position of some estimators to verify the impact of this adjustment on the solutions. Results indicate that the new MH—IVS—is superior to the original algorithm and all other modification proposals. In network adjustments, the ERs tested present better results than the LS method in the presence of large-scale outliers, however, they demonstrate a lower solution in scenarios with no outlier or small magnitude gross errors. For the detection of outliers, the LS method has great difficulties in scenarios with small errors, whereas for situations with large outliers, both LS and other ERs present good results.