Boris Kargoll

• Professor at Anhalt University of Applied Sciences

Geodetic measurements rely on high-resolution sensors, but produce data sets with many observations which may contain outliers and correlated deviations. This paper proposes a powerful solution using Bayesian inference. The observed data is modeled as a multivariate time series with a stationary autoregressive (VAR) process and multivariate t-distr...

Many geodetic measurement data can be modelled as a multivariate time series consisting of a deterministic (“functional”) model describing the trend, and a stochastic model of the correlated noise. These data are also often affected by outliers and their stochastic properties can vary significantly. The functional model of the time series is usuall...

In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patte...

In the article On the impact of correlations on the congruence test: a bootstrap approach, Table 1 should be corrected to.

The detection of deformation is one of the major tasks in surveying engineering. It is meaningful only if the statistical significance of the distortions is correctly investigated, which often underlies a parametric modelization of the object under consideration. So-called regression B-spline approximation can be performed for point clouds of terre...

In this contribution, we extend the Gauss-Helmert model (GHM) with t-distributed errors (previously established by K.R. Koch) by including autoregressive (AR) random deviations. This model allows us to take into account unknown forms of colored noise as well as heavy-tailed white noise components within observed time series. We show that this GHM c...

Today, short- and long-term structural health monitoring (SHM) of bridge infrastructures and their safe, reliable and cost-effective maintenance has received considerable attention. From a surveying or civil engineer’s point of view, vibration-based SHM can be conducted by inspecting the changes in the global dynamic behaviour of a structure, such...

The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (in J Geod 92(3):271–297, 2018. https://doi.org/10.1007/s00190-017-1062-6), is extended to multivariate approaches. Multivaria...

This Special Issue focusses on algorithms and methods related to 3D models, defined as mathematical representations of surfaces of objects in three-dimensional Euclidean space. Although the methodology and software for the processing of remotely sensed point clouds has matured considerably throughout the last decade, numerous challenges remain, rel...

The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (2018a), is extended to multivariate approaches. Multivariate models are used to describe the behavior of multiple observables...

The choice of an appropriate metric is mandatory to perform deformation analysis between two point clouds (PC)-the distance has to be trustworthy and, simultaneously, robust against measurement noise, which may be correlated and heteroscedastic. The Hausdorff distance (HD) or its averaged derivation (AHD) are widely used to compute local distances...

In this paper, we propose a new technique—called Ellipsoidal and Gaussian Kalman filter—for state estimation of discrete-time nonlinear systems in situations when for some parts of uncertainty, we know the probability distributions, while for other parts of uncertainty, we only know the bounds (but we do not know the corresponding probabilities). S...

In this study, the feasibility of Micro-Electro-Mechanical System (MEMS) accelerometers and an image-assisted total station (IATS) for short- and long-term deformation monitoring of bridge structures is investigated. The MEMS sensors of type BNO055 from Bosch as part of a geo-sensor network are mounted at different positions of the bridge structure...

In this contribution, a robust Bayesian approach to adjusting a nonlinear regression model with t-distributed errors is presented. In this approach the calculation of the posterior model parameters is feasible without linearisation of the functional model. Furthermore, the integration of prior model parameters in the form of any family of prior dis...

In this paper, we intend to test whether the random deviations of an observed regression time series with unknown regression coefficients can be described by a covariance-stationary autoregressive (AR) process, or whether an AR process with time-variable (say, linearly changing) coefficients should be set up. To account for possibly present multipl...

In this contribution, a procedure for deciding, whether the oscillation of a surveyed structure is damped or not, is proposed. For this purpose, two bootstrap tests under fairly general assumptions regarding auto-correlation and outlier-affliction of the random deviations ("measurement errors") are suggested. These tests are derived from an observa...

B-spline surfaces possess attractive properties such as a high degree of continuity, which is important for computing curvature. Since the local support of the basis functions allows to control the shape of the estimated surface, they are increasingly used in the field of geodesy, where their main application is the fitting of surfaces to, e.g., 3D...

Terrestrial laser scanners (TLS) are powerful instruments that can be employed for deformation monitoring due to their high precision and spatial resolution in capturing 3D point clouds. Deformation detections from scatter point clouds can be based on different comparison methods, among which the geometry-based method is one of the most popular. Co...

A stochastic process can be represented and analysed by four different quantities in the time and frequency domain: (1) the process itself, (2) its autocovariance function, (3) the spectral representation of the stochastic process and (4) its spectral distribution or the spectral density function, if it exits. These quantities and their relationshi...

In the last two decades, the integration of a terrestrial laser scanner (TLS) and digital photogrammetry, besides other sensors integration, has received considerable attention for deformation monitoring of natural or man-made structures. Typically, a TLS is used for an area-based deformation analysis. A high-resolution digital camera may be attach...

We investigate a time series model which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance stationary autoregressive (AR) processes whose white noise components obey independent scaled t-distributions. These distributions enable the stochastic modeling of heavy...

In engineering practice, usually measurement errors are described by normal distributions. However, in some cases, the distribution is heavy-tailed and thus, not normal. In such situations, empirical evidence shows that the Student distributions are most adequate. The corresponding recommendation – based on empirical evidence – is included in the I...

Automatically modeling and intelligently monitoring composite tunnel structures is of great significance considering the development of composite and diverse tunnel construction materials. Therefore, how to efficiently analyze the deformation of all kinds of tunnel structures with its expanding application is becoming increasingly important. In thi...

This version merges, extends and replaces the previously uploaded four parts. New material was added to most chapters.

Today, short- and long-term structural health monitoring of bridge infrastructures and their safe, reliable and cost-effective maintenance have received considerable attention. For this purpose, image-assisted total station (here, Leica Nova MS50 MultiStation) as a modern geodetic measurement system can be utilized for accurate displacement and vib...

Deformation monitoring of structures is a common application and one of the major tasks of engineering surveying. Terrestrial laser scanning (TLS) has become a popular method for detecting deformations due to high precision and spatial resolution in capturing a number of three-dimensional point clouds. Surface-based methodology plays a prominent ro...

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student’s) t-distribution. This error model allows f...

In this contribution, we consider an expectation conditional maximization either (ECME) algorithm for the purpose of estimating the parameters of a linear observation model with time-dependent autoregressive (AR) errors. The degree of freedom (d.o.f.) of the underlying family of scaled t-distributions, which is used to account for outliers and heav...

We investigate a time series model which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance-stationary autore-gressive (AR) processes whose white noise components obey independent scaled t-distributions. These distributions enable the stochastic modeling of heavy...

We study a time series model which can generally be described as the additive combination of a multivariate, nonlinear deter-ministic model with multiple univariate, covariance-stationary autore-gressive (AR) processes whose white noise components follow independent scaled t-distributions. These distributions allow for the stochastic modeling of he...

Until now, methods of gravity field determination using satellite data have virtually excluded robust estimators despite the potentially disastrous effect of outliers. This paper presents computationally-feasible algorithms for Ruber's M-estimator (a classic robust estimator) as well as for the class of R-estimators which have not traditionally bee...

In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system. The main loop of this algorithm includes one prediction step and one correction step with measurement informat...

With the development of city constructions, tunnels are becoming important structures for underground transportation. Tunnels constitute layered composite structures with concrete, reinforcement, waterproof layers, etc. Deformation monitoring of this kind of wide-ranging composite structure is significant to assure their safety considering the deve...

In this paper, we show that empirical successes of Student distribution and of Matern’s covariance models can be indirectly explained by a natural requirement of scale invariance – that fundamental laws should not depend on the choice of physical units. Namely, while neither the Student distributions nor Matern’s covariance models are themselves sc...

We derive an expectation conditional maximization either (ECME) algorithm for estimating jointly the parameters of a linear regression model, of a time-variable autoregressive (AR) model with respect to the random deviations, and of a scaled t-distribution with respect to the white noise components. This algorithm is shown to take the form of itera...

In the field of engineering geodesy, terrestrial laser scanning (TLS) has become a popular method for detecting deformations. This paper analyzes the influence of the uncertainty budget on free-form curves modeled by B-splines. Usually, free-form estimation is based on scanning points assumed to have equal accuracies, which is not realistic. Previo...

This paper is concerned with the spectral analysis of stochastic processes that are real-valued, one-dimensional, discrete-time, covariance-stationary, and which have a representation as a moving average (MA) process. In particular, we will review the meaning and interrelations of four fundamental quantities in the time and frequency domain, (1) th...

To visualize the surface of an object, laser scanners determine the rectangular coordinates of points of a grid on the surface of the object in a local coordinate system. Vertical angles, horizontal angles and distances of a polar coordinate system are measured with the scanning. Outliers generally occur as gross errors in the distances. It is ther...

GOCE satellite gravity gradiometry (SGG) data are strongly autocorrelated within the various tensor components. Consideration of these correlations in the least-squares adjustment for gravity field determination can be carried out by digital decorrelation filters. Due to the complexity of the correlation pattern the used decorrelation filters consi...

Many years of intensive research led to the realization of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission (cf. ESA 1999), which was launched on 17 March 2009. The primary goal of this mission is the determination of the static component of the Earths gravity field with the unprecedented global accuracy and re...

An adaptive robust estimation for the linear model using the t-distribution is available. Unknown weights for the observations to identify outliers are introduced, i.e. the variance-inflation model is applied. The EM (expectation maximization) algorithm is used for the estimation of the unknown parameters and results in an iteratively reweighted le...

In this paper, we review a data-adaptive class of robust estimators consisting of convex combinations of the loss functions with respect to the L-1- and Huber's M-estimator as proposed by Dodge and Jureckova (2000). The great advantage of this approach in comparison to the traditional procedure of applying a single estimator is that the optimal wei...

GOCE satellite gravity gradiometry (SGG) data are strongly autocorrelated within the various tensor components (of which we use Vxx, Vyy and Vzz). In order to determine and refine the stochastic model necessary for the determination of the gravity field parameters from these data, we use the Tuning Machine, developed within the GOCE High-level Proc...

The goal of the current REAL GOCE project, which is funded throughout the years 2009 - 2012 by the Federal Ministry of Education and Research (BMBF) of Germany through the Geotechnologien Programme, is the complete implementation of a GOCE data processing chain and its application to the GOCE real data within the framework of a cooperative scientif...

The goal of this chapter is to describe an in-situ approach to determine a global Earth gravity model and its variance/covariance information on the basis of calibrated measurements from the GOCE mission. As the main characteristics of this procedure, the GOCE data are processed sequentially on a parallel computer system, iteratively via applicatio...

Until now, methods of gravity field determination using satellite data have virtually excluded robust estimators despite the potentially disastrous effect of outliers. This paper presents computationally-feasible algorithms for Huber’s M-estimator (a classic robust estimator) as well as for the class of R-estimators which have not traditionally bee...

This paper discusses numerical and statistical techniques used to recover the gravity potential from GOCE mission data. In particular, in a closed loop simulation, it is shown that two completely different and independent solution strategies, i.e. the direct method and the semi-analytic approach, lead to essentially identical results. Both methods...