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1

Research on general theory and methodology in geodesy in Poland in 2019–2022

Klos Anna, Ligas Marcin, Trojanowicz Marek

Advances in Geodesy and Geoinformation

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2023

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Vol. 72, no. 1

art. no. e40, 2023

EN

We present a summary of research carried out in 2019–2022 in Poland in the area of general theory and methodology in geodesy. The study contains a description of original contributions by authors affiliated with Polish scientific institutions. It forms part of the national report presented at the 28th General Assembly of the International Union of Geodesy and Geophysics (IUGG) taking place on 11-20 July 2023 in Berlin, Germany. The Polish authors developed their research in the following thematic areas: robust estimation and its applications, prediction problems, cartographic projections, datum transformation problems and geometric geodesy algorithms, optimization and design of geodetic networks, geodetic time series analysis, relativistic effects in GNSS (Global Navigation Satellite System) and precise orbit determination of GNSS satellites. Much has been done on the subject of estimating the reliability of existing algorithms, but also improving them or studying relativistic effects. These studies are a continuation of work carried out over the years, but also they point to new developments in both surveying and geodesy.We hope that the general theory and methodology will continue to be so enthusiastically developed by Polish authors because although it is not an official pillar of geodesy, it is widely applicable to all three pillars of geodesy.

2

Absolute Msplit estimation as an alternative for robust M-estimation

Duchnowski Robert, Wyszkowska Patrycja

Advances in Geodesy and Geoinformation

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2022

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Vol. 71, no. 1

art. no. e17, 2022

EN

The problem of outlying observations is very well-known in the surveying data processing. Outliers might have several sources, different magnitudes, and shares within the whole observation set. It means that it is not possible to propose one universal method to deal with such observations. There are two general approaches in such a context: data cleaning or robust estimation. For example, the robust M-estimation has found many practical applications. However, there are other options, such as R-estimation or the absolute M split estimation. The latter method was created to be less sensitive to outliers than the squared M split estimation (the basic variant of Msplit estimation). From the theoretical point of view, the absolute M split estimation cannot be classified as a robust method; however, it was proved that it could be used in such a context under certain conditions. The paper presents the primary comparison between that method and a conventional robust M-estimation. The results show that the absolute M split estimation predominates over the classical methods, especially when the percentage of outliers is high. Thus, that method might be used to process LiDAR data, including mismeasured points. Processing synthetic data from terrestrial laser scanning or airborne laser scanning confirms that the absolute M split / estimation can deal with outliers sufficiently.

3

An adjusted Grubbs' and generalized extreme studentized deviation

Alrawashdeh Mufda Jameel

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

548--557

EN

Detecting outlier data is an interesting subject in the statistical field. Grubbs’ test is one of the common detection methods of outlier observation at univariate data sets. This approach is based on the mean and standard deviation of univariate data, and hence, these data are highly affected by the presence of outliers. An improvement for Grubbs’ test is proposed in this paper to increase the power of detecting data.

4

Accuracy Characteristics of the Selected Diagnostics Methods and the Adjustment of Geodetic Observations

Kulupa Martyna, Magda Paulina, Mrówczyńska Maria

Civil and Environmental Engineering Reports

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2021

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Vol. 31, no. 4

167--183

EN

The article presents the results of the adjustment of the experimental horizontal geodetic network using the classical method and the estimation of strengths in identifying observations with gross error and analyzing the accuracy of the obtained results. The presented analyses were made considering the possibility of their use in implementation networks and measurement and control networks used for monitoring building structures. The paper's subject was a horizontal network established on the Morasko campus (Poznań). While creating it, the practical needs and economics of measurements were taken into account. The obtained results of numerical analyzes confirmed the benefits of using the methods of estimating strengths in the equalization process, which give satisfactory results in the case of outliers.

5

Application of Robust Estimation Method for Establishing 3D Combined Terrestrial and GNSS Network: A case of a Quarry in Lang Son, Vietnam

Luu Anh Tuan, Hoang Ngoc Ha, La Phu Hien, Pham Van Chung

Inżynieria Mineralna

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2020

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no. 2, vol. 1

57--64

EN

Recently, in Vietnam, the detection of geodetic measurements that contain rough errors as well as such data processing method has been considered as a key step in geodetic data processing, especially for large geodetic networks with many different types of measurements like 3D - Global Navigation Satellite Systems (GNSS) network. On the other hand, mines in Vietnam often have complex terrains, so it is necessary to apply modern and flexible surveying methods in combination with ground and space measurements to build 3D coordinates control networks for management and exploitation to ensure sustainable development. Therefore, this research developed a Robust estimation method based on empirical weighting function for establishing 3D geodetic network combining terrestrial observation and GNSS vectors. The experiment on processing the combined network in Lang Son limestone quarry, Vietnam showed that the proposed method could be an effective solution for processing 3D terrestrial – GNSS geodetic network for mine surveying in Vietnam.

PL

Niezawodność osnowy geodezyjnej wynika z niezawodności układu obserwacyjnego, który tę osnowę wyznacza oraz wyraża możliwość jego kontroli na wypadek zaistnienia błędów grubych, szczególnie w przypadku dużych osnów składających się z tradycyjnych sieci zintegrowanych z GNSS obserwacjami. Z drugiej strony, ponieważ tereny kopalni odkrywkowych w Wietnamie są często o silnie zróżnicowanej morfologii utworzone w wyniku eksploatacji górniczej a sieci kontrolne na obszarach górniczych powstawały w różnych okresach o różnych figurach geometrycznych i różnych metodach pomiarowych, wiec jest zintegrowanie klasycznych sieci z GNSS obserwacjami zostało koniecznym zagadnieniem. W artykule, przedstawiono wyniki badania nad zastosowaniem metod estymacji odpornej w sieciach geodezyjnych zintergrowanych z 3D obserwacjami GNSS w kamieniołomie Lang Son. Eksperyment dotyczący przetwarzania połączonej sieci w kamieniołomie wapienia Lang Son (Wietnamie) wykazał, że proponowana metoda jest odpowiednim rozwiązaniem do przetwarzania tradycyjnej naziemnej sieci z 3D GNSS-owskimi obserwacjami w osnowie geodezyjnej służącej skutecznie do prac geodezyjnych w kamieniołomie Lang Son a w innych kopalniach odkrywkowych generalnie mówiąc.

6

Geodesy: General theory and methodology 2015–2018

Borkowski Andrzej, Kosek Wiesław, Ligas Marcin

Geodesy and Cartography

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2019

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Vol. 68, no. 1

145--162

EN

The summary of research activities concerning general theory and methodology performed in Poland in the period of 2015–2018 is presented as a national report for the 27th IUGG (International Union of Geodesy and Geophysics) General Assembly. It contains the results of research on new or improved methods and variants of robust parameter estimation and their application, especially to control network analysis. Reliability analysis of the observation system and an integrated adjustment approach are also given. The identifiability (ID) index as a new measure for minimal detectable bias (MDB) in the observation system of a network, has been introduced. A new method of covariance function parameter estimation in the least squares collocation has been developed. The robustified version of the Shift-Msplit estimation, termed as Shift-M*split estimation, which enables estimation of parameter differences (robustly), without the need of prior estimation of the parameters, has been introduced. Results on the analysis of geodetic time series, particularly Earth orientation parameter time series, geocenter time series, permanent station coordinates and sea level variation time series are also provided in this review paper. The entire bibliography of related works is provided in the references.

7

Study on detection of gross error in geodetic network adjustment

Kim J. H., Kim C. J., Li R. J.

Geodesy and Cartography

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2018

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Vol. 67, no. 1

57--69

EN

Generally, gross errors exist in observations, and they affect the accuracy of results. We review methods to detect the gross errors by Robust estimation method based on L1-estimation theory and their validity in adjustment of geodetic networks with different condition. In order to detect the gross errors, we transform the weight of accidental model into equivalent one using not standardized residual but residual of observation, and apply this method to adjustment computation of triangulation network, traverse network, satellite geodetic network and so on. In triangulation network, we use a method of transforming into equivalent weight by residual and detect gross error in parameter adjustment without and with condition. The result from proposed method is compared with the one from using standardized residual as equivalent weight. In traverse network, we decide the weight by Helmert variance component estimation, and then detect gross errors and compare by the same way with triangulation network In satellite geodetic network in which observations are correlated, we detect gross errors transforming into equivalent correlation matrix by residual and variance inflation factor and the result is also compared with the result from using standardized residual. The results of detection are shown that it is more convenient and effective to detect gross errors by residual in geodetic network adjustment of various forms than detection by standardized residual.

8

Adaptive data processing in the presence of outliers with unknown stochastic characteristics

Griszin J.

Przegląd Elektrotechniczny

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2017

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R. 93, nr 12

14--17

EN

The paper presents a new adaptive algorithms of data processing when observed data are corrupted by pulse interferences which cause outliers in measurements. It is assumed that stochastic characteristics of the outliers are unknown. The algorithm is based on the nonlinear filtering approach and procedure of on-line calculation of the stochastic characteristics of the outliers described by the Markov chains. The simulation results are presented.

PL

W artykule został przedstawiony nowy adaptacyjny algorytm przetwarzania danych zniekształconych zakłóceniami impulsowymi które skutkują anomaliami w pomiarach. Algorytm został opracowany z wykorzystaniem metod oceny stochastycznych parametrów anomalii opisanych łańcuchami Markowa. Przedstawiono wyniki symulacji.

9

Application of square Msplit estimation in determination of vessel position in coastal shipping

Zienkiewicz M. H., Czaplewski K.

Polish Maritime Research

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2017

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nr 2

3--12

EN

The main aim of this paper is to assess the possibility of using non-conventional geodetic estimation methods in maritime navigation. The research subject of this paper concerns robust determination of vessel’s position using a method of parameters estimation in the split functional model (Msplit estimation). The studies performed will help in finding out if and in which situations the application of Msplit estimation as the method for determining vessel’s position is beneficial from the perspective of navigation safety. The results obtained were compared with the results of traditional estimation methods, i.e. least squares method and robust M-estimation.

10

Comparison of robust estimators for leveling networks in Monte Carlo simulations

Pokarowska M.

Reports on Geodesy and Geoinformatics

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2016

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Vol. 101

70--81

EN

We compared the method of least squares (LS), Pope’s iterative data snooping (IDS) and Huber’s M-estimator (HU) in realistic leveling networks, for which the heights or the vertical displacements of points are known. The study was conducted using the Monte Carlo simulation, in which one repeatedly generates sets of observations related to the measurement data, then calculates values of the estimators and, finally, assesses it with respect to the real coordinates. To simulate outliers we used popular mixture models with two or more normal distributions. It is shown that for small, strong networks robust methods IDS and HU are more accurate than LS, but for large, weak networks occurring in practice there is no significant difference between the considered methods in the accuracy of the solution.

11

The proposition of a new damping function for outliers in the adjustment process

Gargula T.

Geomatics, Landmanagement and Landscape

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2015

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no. 2

21--31

EN

This study proposes of new damping function in the robust estimation process. The formulae for a behaviour of the damping function were provided and a diagram of adjustment process was presented. The numerical examples are given in order to assess the efficiency of the proposed computational algorithm in accomplishing a typical geodetic task with outliers or gross errors.

12

Theoretical geodesy

Borkowski A., Kosek W.

Geodesy and Cartography

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2015

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Vol. 64, no. 2

261--279

EN

The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011-2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-Msplit estimation, which allows to estimate a vector of parameter differences and the Shift-Msplit(+) that is a generalisation of Shift-Msplit estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2nd, 3rd and 4th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.

13

Data driven tests for univariate symmetry about an unknown median

Inglot T., Janic A.

Probability and Mathematical Statistics

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2014

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Vol. 34, Fasc. 2

317--336

EN

We propose new data driven score rank tests for univariate symmetry about an unknown center. We construct test statistics, state assumptions and define estimators of nuisance parameters. We prove that the test statistics are asymptotically distribution-free under the null hypothesis. Using simulations, we verify these asymptotic results for finite samples and show that, under the assumptions and when they are somewhat violated, the size of the test is stable when changing the null distribution. We also compare the empirical behaviour of the new tests with those proposed in the literature. We show that for families of distributions commonly applied to model asymmetry the new tests overcome their competitors on average and for most individual alternatives.

14

Robust fault-tolerant control for a multi-tank system

Buciakowski M., Witczak M., Luzar M.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 1

39--44

EN

The paper deals with the problem of robust fault-tolerant control for non-linear discrete-time systems. The main part of this paper describes sensor a fault diagnosis scheme using virtual sensors, which recover the measurement of the fault sensor based on the fault-free ones. The virtual sensor is designed in such a way that a prescribed attenuation level is achieved with respect to the fault estimation error while guaranteeing the convergence of the robust observer underlying the virtual sensor. The subsequent part of the paper deals with the design of robust controller as well as the proposed fault-tolerant control scheme. The final part of the paper shows the experimental results regarding the multi-tank system, which confirm the effectiveness of proposed approach.

PL

Artykuł przedstawia problem odpornego sterowania tolerującego uszkodzenia układem nieliniowym w czasie dyskretnym. Głowna część artykułu opisuję diagnostykę czujników pomiarowych z wykorzystaniem wirtualnych czujników. Wirtualny czujnik został zaprojektowany w taki sposób, aby dla określonego poziomu tłumienia zakłóceń uzyskać możliwie mały błąd estymacji stanu oraz zapewnić dobra zbieżność obserwatora, na którym bazuje wirtualny czujnik. Kolejna część artykułu opisuję metodę projektowania odpornego regulatora oraz proponowaną metodę detekcji uszkodzeń. W końcowej części artykułu przedstawiono wyniki eksperymentalne dotyczące układu wielu zbiorników. Zastosowany układ wielu zbiorników charakteryzuję się nieliniowością, przez co może zostać wykorzystany do weryfikacji przedstawionych w artykule techniki sterowania tolerującego uszkodzenia. Przedstawione wyniki potwierdzają skuteczność proponowanego podejścia bazującego na detekcji uszkodzeń czujników pomiarowych z wykorzystaniem wirtualnych czujników pomiarowych. Wyniki obrazują działanie układu w przypadku wystąpienia uszkodzenia przy braku sterowania tolerującego uszkodzenia oraz działanie układu w przypadku zastosowania sterowania tolerującego uszkodzenia.

15

Example of Robust Free Adjustment of Horizontal Network Covering Detection of Outlying Points

Zienkiewicz M. H., Bałuta T.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2013

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nr 16(3)

179--192

EN

This paper presents the method of detecting outlying reference points by applying robust free adjustment. The article contains the theoretical basis of the robust free adjustment. Theoretical considerations are supplemented by a numerical example showing the possible practical applications. In this paper is also included example, which presents detecting of reference points contaminated by gross error, in the case of existence gross errors in observation sets.

16

Zastosowanie metody Hampela do aproksymacji modelu teoretycznego chłodni kominowej w podejściu dwuwymiarowym

Muszyński Z.

Archiwum Fotogrametrii, Kartografii i Teledetekcji

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2013

|

Vol. 25

117--126

EN

Correct assessment of construction safety requires reliable information about geometrical shape of the analyzed object. The least square method is the most popular method to calculate object deviation between theoretical geometry and the real object shape measured with geodetic methods. The paper presents the possibility of using robust estimation methods on the example of Hampel’s method. Deviation values obtained in this way are resistant to outliers influence and are more reliable. This problem is illustrated by a hyperbola which is approximated in survey points (measured by terrestrial laser scanning) localized on the generating line of the cooling tower shell in one of its axial vertical cross-section.

PL

Bezpieczna eksploatacja cienkościennych konstrukcji powłokowych, do których należą hiperboloidalne chłodnie kominowe, wymaga okresowej kontroli ich stanu geometrycznego. Powszechnie stosowaną technologią pomiarową jest w tym przypadku precyzyjna tachimetria bezreflektorowa. W niniejszym artykule przedstawiono możliwości i zalety wykorzystania naziemnego skaningu laserowego do pomiaru geometrii płaszcza chłodni kominowej. Zniekształcenia geometryczne chłodni wyznacza się poprzez wpasowanie modelu teoretycznego konstrukcji w zbiór punktów pomiarowych opisujących jej stan rzeczywisty. W przypadku braku dokumentacji projektowej, parametry modelu teoretycznego określa się poprzez aproksymację, stosując zazwyczaj metodę najmniejszych kwadratów. W artykule przeanalizowano możliwość wykorzystania w tym celu metody Hampela, jako przykładowej metody estymacji odpornej. Otrzymane wyniki potwierdzają skuteczność tej metody w przypadku występowania znacznych lokalnych zniekształceń geometrycznych konstrukcji. Parametry modelu teoretycznego, uzyskane z wykorzystaniem metody Hampela, pozwalają wyznaczyć bardziej wiarygodne wartości imperfekcji geometrycznych, które wykorzystywane są później przy sporządzaniu ekspertyz budowlanych.

17

Fuzzy adaptive Kalman filter for the drive system with an elastic coupling

Serkies P. J., Szabat K.

Archives of Electrical Engineering

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2013

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Vol. 62, nr 2

251--265

EN

In the paper issues related to the design of a robust adaptive fuzzy estimator for a drive system with a flexible joint is presented. The proposed estimator ensures variable Kalman gain (based on the Mahalanobis distance) as well as the estimation of the system parameters (based on the fuzzy system). The obtained value of the time constant of the load machine is used to change the values in the system state matrix and to retune the parameters of the state controller. The proposed control structure (fuzzy Kalman filter and adaptive state controller) is investigated in simulation and experimental tests.

18

A review of robust estimation methods applied in surveying

Banaś M.

Geomatics and Environmental Engineering

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2012

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Vol. 6, no. 4

13--22

EN

This paper provides a review of popular outlier-robust methods used in surveying. The presented methods have been divided into two groups i.e. active and passive methods. The first group comprises the following methods: the Huber Method, the Hampel Method, the Danish Method, the Gaździcki Method, the Least Absolute Deviation and a Choice Rule of Alternative. The second group of methods is represented by the so called iterative data snooping (IDS) and τ-test. There are M-estimation rules presented in the introduction to the review of active methods.

PL

Praca zawiera przegląd popularnych metod odpornych na błędy grube stosowanych w geodezji. Metody te podzielono na dwie grupy, tj. aktywne oraz pasywne. W pierwszej z nich znalazła się metoda Hubera, Hampela, duńska, Gaździckiego, liniowa, najmniejszych odchyleń absolutnych oraz zasada wyboru alternatywy. Druga grupa zawiera metodę Iterative Data Snooping (IDS) oraz τ-test. Wstęp do metod aktywnych stanowi przedstawienie zasad M-estymacji.

19

Effectiveness of chosen robust estimation methods compared to the level of network reliability

Kwaśniak M.

Geodesy and Cartography

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2011

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Vol. 60, no 1

3-19

EN

The work presents the results of studies on dependence of effectiveness of chosen robust estimation methods from the internal reliability level of a geodetic network. The studies use computer-simulated observation systems, so it was possible to analyse many variants differing from each other in a planned way. Four methods of robust estimation have been chosen for the studies, differing substantially in the approach to weight modifications. For comparative reasons, the effectiveness studies have also been conducted for the very popular method in surveying practice, of gross error detection basing on LS estimation results, the so called iterative data snooping. The studies show that there is a relation between the level of network internal reliability and the effectiveness of robust estimation methods. In most cases, in which the observation contaminated by a gross error was characterized by a low index of internal reliability, the robust estimation led to results being essentially far from expectations.

PL

W pracy przedstawiono wyniki badan nad zależnością skuteczności wybranych metod estymacji odpornej od poziomu niezawodności wewnętrznej sieci geodezyjnej. W badaniach wykorzystano symulowane komputerowo układy obserwacyjne, dzięki czemu możliwe było przeanalizowanie wielu wariantów różniących się w zaplanowany sposób. Do badan wybrano cztery metody estymacji odpornej różniące się istotnie podejściem do modyfikacji wag. Dla porównania, badaniom skuteczności poddano również popularna w praktyce geodezyjnej metodę wykrywania błędów grubych bazująca na wynikach estymacji MNK, tzw. metodę Baardy. Z przeprowadzonych badan wynika, ze istnieje związek pomiędzy poziomem niezawodności wewnętrznej sieci a skutecznością metod estymacji odpornej. W większości przypadków, w których obserwacja obarczona błędem grubym charakteryzowała się niskim wskaźnikiem niezawodności wewnętrznej, estymacja odporna prowadziła do uzyskania wyników istotnie odbiegających od oczekiwanych.

20

Robust data processing i the presence of outliers

Griszin J.

Przegląd Elektrotechniczny

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2010

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R. 86, nr 3

25-27

EN

The paper presents a robust algorithm for data processing in discrete-time dynamic systems when observed data are corrupted by outliers. The algorithm has been developed using non-linear filtering theory and the Gaussian approximation method. The simulation results are presented.

PL

W artykule został przedstawiony algorytm estymacji stanu dyskretnych liniowych systemów dynamicznych odporny na obecność anomalii w pomiarach. Algorytm opracowano w oparciu o teorię filtracji nieliniową z wykorzystaniem metody aproksymacji gaussowskiej. Przedstawiono wybrane wyniki symulacji zaproponowanego algorytmu.