Darko Anđić

The purpose of this study is to develop and evaluate a decision-making framework for selecting the optimal measurement accuracy of geodetic instruments used in engineering structure displacement monitoring. The study investigates whether integrating multiple Multi-Criteria Decision-Making (MCDM) methods with different preference structures can provide reliable and robust support for this complex engineering geodesy problem under an unfavourable geodetic control network configuration. To address this question, the proposed framework combines the SWING weighting method with four MCDM methods, namely Proximity Indexed Value (PIV), Preference Analysis for Reference Ideal Solution (PARIS), Measurement of Alternatives and Ranking according to COmpromise Solution (MARCOS), and COmplex PRoportional ASsessment (COPRAS). Six total station alternatives were evaluated using criterion functions representing measurement precision and reliability characteristics under four preference structures represented by ordered 8-tuples of criterion weights. The framework was validated through comparative analysis using TOPSIS as the benchmark method, while ranking robustness and consistency were further examined through a leave-one-out sensitivity analysis. The results demonstrate that all four MCDM methods successfully addressed the considered optimization problem and consistently identified the same two best-performing alternatives. The comparative analysis revealed a high degree of agreement between PIV, PARIS, COPRAS, and the TOPSIS benchmark, whereas MARCOS exhibited slightly greater ranking variability while preserving the identification of the optimal solutions. Furthermore, the sensitivity analysis showed that ranking stability was influenced more strongly by the adopted preference structure than by the particular MCDM method employed. These findings are significant because they establish a comprehensive and reproducible framework for optimizing measurement accuracy in engineering geodesy, demonstrate the applicability of four MCDM methods not previously employed for this optimization problem, and provide broader methodological insight into the importance of combining multiple preference structures, comparative analysis, and sensitivity analysis when evaluating MCDM performance.

Only a few studies have so far addressed the applicability of Multi-Criteria Decision-Making (MCDM) methods in the optimization of geodetic control networks. For instance, the methods such as Višekriterijumsko Kompromisno Rangiranje/Rešenje (VIKOR) (in english: Multi-Criteria Optimization and Compromise Ranking/Solution), Analytic Hierarchy Process (AHP), Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Multi-Attributive Border Approximation Area Comparison (MABAC), Multi-Attributive Ideal-Real Comparative Analysis (MAIRCA), Combined Compromise Solution (COCOSO), Range of Value (ROV) can be mentioned. Among them, the VIKOR method, it can be said, proved to be the most suitable tool in the mention area of engineering geodesy as it allows treating alternative solutions identified in a specific task in a desired way by using different preferential approaches represented by sets of criterion weights. Thus, the VIKOR method is used as a reference herein, and methods whose applicability is tested are four novel methods that have been used in some other areas, different from geodesy. It is about Multiple Criteria Ranking by Alternative Trace (MCRAT), Ranking the Alternatives by Perimeter Similarity (RAPS), Ranking by Alternatives Median Similarity (RAMS) and Ranking by Alternatives Using the Trace to Median Index (RATMI). The subject of this study is optimization of a 2D geodetic control network established to provide information regarding horizontal movements of a dam. The dam is located in Montenegro. The optimization is performed considering several pre-set constraints related to precision and reliability in the corresponding geodetic network. It turned out the four tested MCDM methods provided exactly the same results that were highly correlated with those obtained using the selected reference method. This fact led to the conclusion those four novel methods could be equally used in tasks similar to the one presented herein.

This study deals with the use of VIKOR method in finding the optimal solution for a special-purpose geodetic network design. It is about a multi-criteria compromise ranking method developed in 1986. Based on previously defined criteria functions related to precision and reliability, four acceptable alternative solutions were firstly established. Then, with the aim of finding the optimal one, those solutions were subjected to VIKOR method. The geodetic micro-network used in this study was simulated as a trilateration one and consisted of six control points discretizing a structural geometry as well as four, five or six reference points (pillars), depending on what alternative solution it was about. The optimal network design should have ensured the detection of deviations of the control points' positions in accordance with a priori introduced tolerances and constraints. It turned out the approach based on VIKOR method is a very efficient tool in tasks involving multiple conflicting requirements referred to a geodetic engineer and in the cases when the decision must be made in a short term.

The study presented sampling interval impacts on variance components of the epoch-wise residual errors in relative GPS positioning. In the process of estimates of variance components, the2-way nested ANOVA method was used. For that purpose, GPS observation data during four months at two permanent GPS stations, establishing a 40-km-long baseline as a part of the Montenegrin permanent network (MontePos), were used. The study results showed that there is no statistically significant impact of sampling interval changes on epoch-wise variance components related to the residual tropospheric and ionospheric delays(effect xf061;) when it comes to such a baseline. However, it is not the case with epoch-wise variance components related to the interstation-distance-independent residual ‘far-field’ multipath effect (effect xf062;). It turned out that the absolute values of relative differences of standard deviations of the effectxf061;xf020;on the relative GPS coordinates (e, n and u) had maximum values 11.1%, 10.2% and 8.9%, respectively. Keeping the same order of presentation for the effectxf062;, the values of 5.9%, 9.9% and 12.5% were obtained. In addition, absolute values of relative differences of standard deviations of horizontal and vertical position had maximum values of 3.8% and 7.7%, respectively.

In this paper, a new two-stage approach, involving an integral treatement of all quasi-random effects limiting the accuracy of relative GPS positioning and the method of moments to obtain final variance components regarding the effects of short-term (“far-field”) multipath (factor b), joint action of long-term (“near-field”) multipath and receiver antenna phase center offset and variations (factor a1), as well as joint action of tropospheric and ionospheric refraction (factor a2), is presented. In the study, GPS data collected on five baselines were used. Variance components of the quasirandom effects were obtained for the three relative GPS coordinates (e, n and u) using individually monthly datsets including daytime- and those including nighttime-wise ambiguity-fixed baseline solutions. The related results show that statistically significant inequality exists when comparing corresponding variances obtained for daytime and nighttime periods. It turned out that the following standard deviation estimates intervals are present (by the coordinates e, n and u, respectively): (a) daytime period: 3.3–6.9, 4.6–9.0 and 9.1–20.3 mm (factor b); 1.5–4.7, 1.9–7.0 and 3.4–21.9 mm (factor 1a ); 0.0116– 0.3282, 0.0103–0.2365 and 0.1222–0.7818 mm/km (factor a2); (b) nighttime period: 3.2–4.9, 4.7–7.3 and 8.4–15.4 mm (factor b); 0.8–3.8, 2.1–5.0 and 3.1–15.8 mm (factor a1); 0.0118–0.2734, 0.0097–0.2289 and 0.0752–0.6315 mm/km (factor a2).