Volume 13, Issue 1

Least-squares collocation (LSC) is a crucial mathematical tool for solving many geodetic problems. It has the capability to adjust, filter, and predict unknown quantities that affect many geodetic applications. Hence, this study aims to enhance the predictability property of LSC through applying soft computing techniques in the stage of describing the covariance function. Soft computing techniques include the support vector machine (SVM), least-squares-support vector machine (LS-SVM), and artificial neural network (ANN). A real geodetic case study is used to predict a national geoid from the EGM2008 global geoid model in Egypt. A comparison study between parametric and soft computing techniques was performed to assess the LSC predictability accuracy. We found that the predictability accuracy increased when using soft computing techniques in the range of 10.2 %–27.7 % and 8.2 %–29.8 % based on the mean square error and the mean error terms, respectively, compared with the parametric models. The LS-SVM achieved the highest accuracy among the soft computing techniques. In addition, we found that the integration between the LS-SVM with LSC exhibits an accuracy of 20 % and 25 % higher than using LS-SVM independently as a predicting tool, based on the mean square error and mean error terms, respectively. Consequently, the LS-SVM integrated with LSC is recommended for enhanced predictability in geodetic applications.

This study investigates the development and testing of an approximation method for the Mine Surveyor to calculate meridian convergence . This study, a detailed review of experimental techniques, follows a statistical experimental approach to establish how accurate an alternative method performs against traditional methods of meridian convergence calculation used by the Mine Surveyor. The spatial study is defined by the geographical range of the existing Schreiber Geodetic Tables, ranging from 70 km south of Ndola (Zambia) to 10 km north of De Aar (South Africa). The sample size is established under the constraint of an infinite population. Linear regression in collaboration with the hold-out validation technique is adopted to statistically refine the alternative method of calculation. The computational outcomes of the refined alternative method in comparison to the unrefined method are predominantly closer to the traditional outcomes. Computational outcomes specific to the hold-out validation set demonstrate a maximum sub-1″{1^{\prime\prime }} variance of 0.650″{0.650^{\prime\prime }}. A sub-variance of 0.650″{0.650^{\prime\prime }} satisfies the South African Mine Survey limits of error. The subsequent clustering of variances at specific variance intervals are similar to comparative studies conducted by T. Soler and R.J. Fury with respect to meridian convergence .

The main mathematical problem in the planar three point resection problem of surveying is to find a necessary and sufficient condition that a point on a plane is uniquely determined if the directions from that point to three given points are known only up to an unknown offset. It will be shown in this paper that such a condition is the applicability of Willerding’s formula for computing the point in question, and that this condition is equivalent to the well-known necessary condition that the four considered points are not located on a circle or a line. Because of this result, the easy evaluation and the short derivation of Willerding’s formula, it can be expected, that this formula will be widely used in surveying, and also for autonomous robot localization.

The determination of the oceanic Moho (or crust-mantle) density contrast derived from seismic acquisitions suffers from severe lack of data in large parts of the oceans, where have not yet been sufficiently covered by such data. In order to overcome this limitation, gravitational field models obtained by means of satellite altimetry missions can be proficiently exploited, as they provide global uniform information with a sufficient accuracy and resolution for such a task. In this article, we estimate a new Moho density contrast model named MDC2018, using the marine gravity field from satellite altimetry in combination with a seismic-based crustal model and Earth’s topographic/bathymetric data. The solution is based on the theory leading to Vening Meinesz-Moritz’s isostatic model. The study results in a high-accuracy Moho density contrast model with a resolution of 1° × 1° in oceanic areas. The numerical investigations show that the estimated density contrast ranges from 14.2 to 599.7 kg/m 3 with a global average of 293 kg/m 3 . In order to evaluate the accuracy of the MDC2018 model, the result was compared with some published global models, revealing that our altimetric model is able to image rather reliable information in most of the oceanic areas. However, the differences between this model and the published results are most notable along the coastal and polar zones, which are most likely due to that the quality and coverage of the satellite altimetry data are worsened in these regions.

Random and systematic errors affect navigation satellite observations on both pseudo-range and carrier phase. These errors are originated at satellites, propagation path and receivers. This study focuses on the GNSS receiver internal delay determination resulting from the receiver’s electronics circuit. The characterisation of the delay in the GNSS geodetic receivers is essential to enhance the accuracy for the time transfer and time comparisons as part of GNSS integrity chain determinations. The purpose of GNSS receiver internal delay at the National Institute of Metrology (Thailand), NIMT, is to estimate the characteristics and performances of the GNSS geodetic receiver used for international time comparisons. The experiments are simultaneously observed GNSS satellites by a GPS and a GNSS receivers and two separate antennas with short baseline (around 6 metres), where both receivers are connected to the identical external caesium frequency standard maintained as time and frequency standard of Thailand. The GPS receiver is well-defined for its receiver internal delay on the pseudo-range observation of C1, through comparisons using an internationally recognised method, while the geodetic GNSS receiver is to be defined on its receiver internal delay. These experiment observations started from 26 December 2017 to 17 January 2018 at NIMT, Pathumthani, Thailand. The determined unknowns are receiver position, receiver clock offset, tropospheric delay through the geodetic technique of static Precise Point Positioning observations with Bernese GNSS software version 5.2. Later the receiver internal delay of NIMT is computed and analysed. The receiver internal delay on GPS C1 code is successfully characterised, resulted as 346.0 nanoseconds as of this experiment.

More and more sensors and receivers are found nowadays in smartphones which can enable and improve positioning for Location-based Services and other navigation applications. Apart from inertial sensors, such as accelerometers, gyroscope and magnetometer, receivers for Wireless Fidelity (Wi-Fi) and GNSS signals can be employed for positioning of a mobile user. In this study, three trilateration methods for Wi-Fi positioning are investigated whereby the influence of the derivation of the relationship between the received signal strength (RSS) and the range to an Access Points (AP) are analyzed. The first approach is a straightforward resection for point determination and the second is based on the calculation of the center of gravity in a triangle of APs while weighting the received RSS. In the third method a differential approach is employed where as in Differential GNSS (DGNSS) corrections are derived and applied to the raw RSS measurements. In this Differential Wi-Fi (DWi-Fi) method, reference stations realized by low-cost Raspberry Pi units are used to model temporal RSS variations. In the experiments in this study two different indoor environments are used, one in a laboratory and the second in the entrance of an office building. The results of the second and third approach show position deviations from the ground truth of around 2 m in dependence of the geometrical point location. Furthermore, the transition between GNSS positioning outdoors and Wi-Fi localization indoors in the entrance area of the building is studied.

If the associated differential inter-system biases (DISBs) are priori known, only one common reference satellite is sufficient, which is called the inter-system model. The inter-system model can help to maximize the redundancy of the positioning model, and thus can improve the positioning performance, especially in harsh environment. However, in practice use not all receivers can be calibrated with DISBs in advance. In this paper, taking combined GPS and BDS pseudorange positioning as the example, we compare three positioning models and their positioning performance. One is traditional intra-system model, and the other two belongs to the inter-system models, i. e. the model with calibration of DISB and the model with real-time estimation of DISB parameter. Positioning performance using the three models is evaluated with simulated obstructed environments. It will be shown that besides the model with calibration of DISB, the model with real-time estimation of DISB parameter can also effectively improve positioning accuracy and reliability compared with the traditional intra-system model, especially for the severely obstructed environment with only a few satellites observed. When no more than 7 satellites visible, the positioning accuracies in each directions can be improved by no less than 15 %. The proposed model can be used alternatively when no priori DISB calibration is available.