# Robust Estimators in Geodetic Networks Based on a New Metaheuristic: Independent Vortices Search  
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1 Graduate Program in Applied Computing, Unsinos University, Av. Unsinos, 950, Sao Leopoldo 93022-000, RS, Brazil; iekoch@edu. flexibility in network design, and the achievable accuracy has also helped the densification of classical first-order geodetic networks [2]. Most geodetic networks have been established using GNSS signals, which are available all over the Earth's surface. They are defined by several materialized points with high precision and their co-ordinates serve as a basis in a wide variety of applications. Some examples are: support and basic control for surveying and mapping projects; implementation and maintenance of infrastructure works; monitoring of structural deformations; land cadastre and management; and monitoring of geodynamic events, such as earthquakes, landslides, and volcanoes. The study of Mt. Etna is a good example; two GNSS-based networks found a motion pattern of the active Nizzei faults [3]. In addition, a geodetic network design was applied to find optimal ground locations for interferometric synthetic aperture radar (InSAR) devices [4]. To establish a geodetic network using GNSS, the receivers need to be placed at benchmarks and record satellite tracking data over a given period. Then, baseline vectors are determined between pairs of receivers, based on ranging and phase observations to the satellites. Once the vectors are computed, they become the new observations of the network and need to be adjusted to get the final point co-ordinates [1]. Although most of the GNSS observation process does not require much direct human influence, the vectors may not be free of blunders. There are sources of error that may cause significant deviations (e.g., multipath signal propagation error, cycle slips, and ionospheric anomalies). The electromagnetic wave assumed to propagate along the line of sight between the satellite and the receiver might be reflected or scattered by obstructions before reaching the instrument [5]. Other error sources are more mundane, such as mistakes in measuring the height of the antenna above the marker. Although random errors are inherent to observations, outliers should be detected, identified, and adapted for better determination of the co-ordinates [6]. An outlier is better not to be used (or not used as it is) in an adjustment process because it has a high probability of being caused by a gross error [7]. In geodesy, outliers are mostly produced by gross errors, and gross errors most often lead to outliers. As outliers in observations affect the accuracy, those errors need to be identified or minimized [8]. In standard geodetic adjustments, a least squares (LS) process is often applied, as it is the best linear unbiased estimator, assuming that no outliers and/or systematic errors are present in observations [1; 9; 10]. If the data are contaminated, however, such an estimation will lead to biased parameters [11]. Alternatively, the adjustment can be based on Robust Estimators (REs), which are less sensitive to outliers. If some observations contain blunders or even systematic errors, the REs will be insensitive to those non-random errors when estimating the parameters [11]. REs have a wide range of applications; for example, in [12], a robust parameter-estimation method for a mixture model working with the weights of samples is presented. Furthermore, applications of non-Gaussian distributions on multipass SAR Interferometry have been presented in [13], and new methods for geodetic observations have been presented in [14]. Therefore, they need to be investigated for a better understanding of their capabilities and limitations in geodetic networks. The minimizing objective functions associated with REs are not linear and, therefore, iterative processes or smart techniques are required to solve them. One approach is to combine metaheuristic algorithms (MHs), to optimize the objective function.