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## Abstract

This paper proposes precise point positioning (PPP) methods that offer an accuracy of a few decimetres (dm) with triple frequency GNSS data. Firstly, an enhanced triple frequency linear combination is presented for rapid fixing of the extra wide-lane (EWL) and wide-lane (WL) ambiguities for GPS, Beidou-2 and Galileo. This has improved performance compared to the Melbourne-Wübbena (MW) linear combination, and has 6.7 % lower measurement noise for the GPS L1/L2 signals, 12.7 % for L1/L5 and 0.7 % for L2/L5. Analysis with tested data showed a 5–6 % reduction in time required to fix the $N21$ and $N51$ ambiguities.

Once the EWL/WL ambiguities are fixed with the proposed linear combinations, three methods are presented that aim to provide positioning accuracy of a few dm. In the first approach, the three EWL/WL ambiguities in their respective phase equations are used to derive a low-noise ionosphere-free (IF) linear combination. The second method uses a low noise IF combination with two carrier-phase EWL/WL equations and a single pseudorange measurement. The third method uses a low noise IF combination with a single carrier phase EWL equation and two pseudorange measurements. These proposed methods can provide dm level positioning accuracy if carrier phase measurements with mm precision is tracked by the receiver. When comparing these combinations with a combination proposed in [22], it is found that superior performance is achieved with the third method when carrier phase noise is >5–6 mm for GPS and Beidou-2 and >2–3 mm for Galileo. This model only requires the EWL ambiguity to be fixed which typically takes just one epoch of data. Thus, the user achieves instant decimetre level PPP accuracy.

## Abstract

The paper presents a closed-form solution to the point-wise weighted similarity transformation and its variants in the least squares framework under two estimation scenarios.

In the first scenario a target system is subject to random errors whilst in the second one a source system is considered to be erroneous. These transformation models will be named asymmetric in contrast to the symmetrical one solved under the errors-in-variables model where both systems are contaminated by random errors. The entire derivation is based on Procrustes Analysis. The formulas presented herein hold for both 2D and 3D transformations without any modification. The solution uses a polar decomposition to recover the rotation matrix.

## Abstract

Areal deformation monitoring based on point clouds can be a very valuable alternative to the established point-based monitoring techniques, especially for deformation monitoring of natural scenes. However, established deformation analysis approaches for point clouds do not necessarily expose the true 3D changes, because the correspondence between points is typically established naïvely. Recently, approaches to establish the correspondences in the feature space by using local feature descriptors that analyze the geometric peculiarities in the neighborhood of the interest points were proposed. However, the resulting correspondences are noisy and contain a large number of outliers. This impairs the direct applicability of these approaches for deformation monitoring. In this work, we propose Feature to Feature Supervoxel-based Spatial Smoothing (F2S3), a new deformation analysis method for point cloud data. In F2S3 we extend the recently proposed feature-based algorithms with a neural network based outlier detection, capable of classifying the putative pointwise correspondences into inliers and outliers based on the local context extracted from the supervoxels. We demonstrate the proposed method on two data sets, including a real case data set of a landslide located in the Swiss Alps. We show that while the traditional approaches, in this case, greatly underestimate the magnitude of the displacements, our method can correctly estimate the true 3D displacement vectors.

## Abstract

In this work, the direct geodesic problem in Cartesian coordinates on a triaxial ellipsoid is solved by an approximate analytical method. The parametric coordinates are used and the parametric to Cartesian coordinates conversion and vice versa are presented. The geodesic equations on a triaxial ellipsoid in Cartesian coordinates are solved using a Taylor series expansion. The solution provides the Cartesian coordinates and the angle between the line of constant v and the geodesic at the end point. An extensive data set of geodesics, previously studied with a numerical method, is used in order to validate the presented analytical method in terms of stability, accuracy and execution time. We conclude that the presented method is suitable for a triaxial ellipsoid with small eccentricities and an accurate solution is obtained. At a similar accuracy level, this method is about thirty times faster than the corresponding numerical method. Finally, the presented method can also be applied in the degenerate case of an oblate spheroid, which is extensively used in geodesy.

## Abstract

This paper concerns two types of Msplit estimation: squared Msplit estimation (SMS), which assumes normality of observation errors and absolute Msplit estimation (AMS), which applies $L1$ norm criterion. The main objective of the paper is to assess the accuracy of such estimators in vertical displacement analysis by applying Monte Carlo simulations. Another issue is to compare the accuracy of both estimators with the accuracy of the least squares estimation (LS). The paper shows that the accuracy of both Msplit estimates is like the accuracy of LS estimates. However, if some nonrandom errors occur, then accuracy of AMS estimates might be better than the accuracy of the rest of the estimates considered here. It stems from the fact that AMS estimates are robust against disturbances which have a small magnitude. It is also worth noting that the accuracy of both Msplit estimates might depend on the magnitude of the displacement.

## Abstract

Localization in GNSS-denied/challenged indoor/outdoor and transitional environments represents a challenging research problem. This paper reports about a sequence of extensive experiments, conducted at The Ohio State University (OSU) as part of the joint effort of the FIG/IAG WG on Multi-sensor Systems. Their overall aim is to assess the feasibility of achieving GNSS-like performance for ubiquitous positioning in terms of autonomous, global, preferably infrastructure-free positioning of portable platforms at affordable cost efficiency. In the data acquisition campaign, multiple sensor platforms, including vehicles, bicyclists and pedestrians were used whereby cooperative positioning (CP) is the major focus to achieve a joint navigation solution. The GPSVan of The Ohio State University was used as the main reference vehicle and for pedestrians, a specially designed helmet was developed. The employed/tested positioning techniques are based on using sensor data from GNSS, Ultra-wide Band (UWB), Wireless Fidelity (Wi-Fi), vison-based positioning with cameras and Light Detection and Ranging (LiDAR) as well as inertial sensors. The experimental and initial results include the preliminary data processing, UWB sensor calibration and Wi-Fi indoor positioning with room-level granularity and platform trajectory determination. The results demonstrate that CP techniques are extremely useful for positioning of platforms navigating in swarms or networks. A significant performance improvement in terms of positioning accuracy and reliability is achieved. Using UWB, decimeter-level positioning accuracy is achievable under typical conditions, such as normal walls, average complexity buildings, etc. Using Wi-Fi fingerprinting, success rates of approximately 97 % were obtained for correctly detecting the room-level location of the user.

## Abstract

Global Navigation Satellite System (GNSS) and remote sensing Digital Elevation Models (DEMs) represent earth’s surface elevation with reference to ellipsoid and orthometric heights. Proper estimation of the geoid (difference of ellipsoid and orthometric heights) is necessary before comparing data referenced to the different vertical datum. In this paper, an error in estimating EGM96 orthometric height is highlighted, verified by NGA/NASA developed model and MATLAB®. A significant error was found in the ArcGIS derived EGM96 orthometric heights range between ±6.9 meters. In addition, interpolation of low-resolution geoid data also produces significant biases depending on geographic location and the number of the interpolation data point. The bias was maximum negative in the central part of Tibetan Plateau and Himalaya. Therefore, estimation of orthometric height similar to NGA/NASA model precision is necessary for comparison of DEMs for natural resources management, 3D modelling and glaciers mass balance mainly in the mountainous regions.

## Abstract

Satellite navigation systems face different types of errors that affect the positioning accuracy. The tropospheric delay considers one of the major sources of error for the transmitted signal that could face a tropospheric delay of over 2 m at zenith and 20 m at lower satellite elevation angles. A positioning error of 10 m could result from inaccurate mitigation of the tropospheric delay. Two types of models are available; surface meteorological models and global empirical models. Surface meteorological models use surface meteorological data to give accurate mitigation while the global empirical models use global standard atmospheres. Global empirical models are favorable for satellite based augmentation systems such as EGNOS model for the EGNOS augmentation system. Several hybrid neutral atmosphere delay models have been developed (UNB1 through UNB4). The IGGtrop model is initially developed to provide tropospheric delay corrections for the users of Chinese BeiDou Navigation Satellite System (BDS) and its augmentation system. This paper presents an assessment study for the behaviour of IGGtrop model comparing with (EGNOS, UNB3M) models. The behavior of the three models is compared with IGS-tropospheric estimations for two different-latitude IGS stations; (bhr1 and eil1) in the northern hemisphere. This study recommends using IGGtrop model for estimating the zenith tropospheric delay correction for low-latitude regions in northern hemisphere for all seasons with an average zenith tropospheric difference of 0.75 cm. IGGtrop model is also recommended to be used for estimating the zenith tropospheric delay correction for high-latitude geographic regions in northern hemisphere during autumn and spring seasons with an average zenith tropospheric difference of 0.75 cm. While UNB3M model is the best choice for tropospheric delay correction for high-latitude geographic regions in northern hemisphere during winter and summer seasons with an average zenith tropospheric difference of 1.1 cm.

## Abstract

In this contribution, the minimum detectable bias (MDB) as well as the statistical tests to identify disturbed observations are introduced for the Gauss-Helmert model. Especially, if the observations are uncorrelated, these quantities will have the same structure as in the Gauss-Markov model, where the redundancy numbers play a key role. All the derivations are based on one-dimensional and additive observation errors respectively offsets which are modeled as additional parameters to be estimated. The formulas to compute these additional parameters with the corresponding variances are also derived in this contribution. The numerical examples of plane fitting and yaw computation show, that the MDB is also in the GHM an appropriate measure to analyze the ability of an implemented least-squares algorithm to detect if outliers are present. Two sources negatively influencing detectability are identified: columns close to the zero vector in the observation matrix B and sub-optimal configuration in the design matrix A. Even if these issues can be excluded, it can be difficult to identify the correct observation as being erroneous. Therefore, the correlation coefficients between two test values are derived and analyzed. Together with the MDB these correlation coefficients are an useful tool to assess the inner reliability – and therefore the detection and identification of outliers – in the Gauss-Helmert model.