PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK

PPP-RTK has the potential of benefiting enormously from the integration of multiple GNSS/RNSS systems. However, since unaccounted inter-system biases (ISBs) have a direct impact on the integer ambiguity resolution performance, the PPP-RTK network and user models need to be flexible enough to accommodate the occurrence of system-specific receiver biases. In this contribution we present such undifferenced, multi-system PPP-RTK full-rank models for both network and users. By an application of (Formula presented.)-system theory, the multi-system estimable parameters are presented, thereby identifying how each of the three PPP-RTK components are affected by the presence of the system-specific biases. As a result different scenarios are described of how these biases can be taken into account. To have users benefit the most, we propose the construction of an ISB look-up table. It allows users to search the table for a network receiver of their own type and select the corresponding ISBs, thus effectively realizing their own ISB-corrected user model. By applying such corrections, the user model is strengthened and the number of integer-estimable user ambiguities is maximized

The implications of ionospheric disturbances for precise GNSS positioning in Greenland

Ionospheric irregularities impair Global Navigation Satellite System (GNSS) signals and, in turn, affect the performance of GNSS positioning. Such effects are especially evident at low and high latitudes, which are currently gaining the attention of research and industry sectors. This study evaluates the impact of ionospheric irregularities on GNSS positioning in Greenland. We assess the performance of positioning methods that meet the demands of a wide range of users. In particular, we address the needs of the users of mass-market single-frequency receivers and those who require a solution of high precision provided by geodetic dual-frequency receivers. We take advantage of the datasets collected during three ionospheric storms: the St. Patrick’s Day storm of March 17, 2015, the storm on June 22, 2015, and another on August 25–26, 2018. We discover a significant impact of the ionospheric disturbances on the ambiguity resolution performance and the accuracy of the float solution in Real Time Kinematics (RTK) positioning. Next, assessing the single-frequency ionosphere-free Precise Point Positioning (PPP), we demonstrate that the model is generally unaffected by ionospheric disturbances. Hence, the model is predestined for the application by the users of single-frequency receivers in the areas of frequent ionospheric disturbances. Finally, based on the observation analyses, we reveal that phase signals on the L2 frequency band are more prone to cycle slips induced by ionospheric irregularities than those transmitted on the L1. Such signal properties explain a noticeable decline in the dual-frequency RTK performance during the ionospherically disturbed period and merely no effect for the single-frequency ionosphere-free PPP model.Peer ReviewedPostprint (published version

Method for forecasting ionospheric electron content fluctuations based on the optical flow algorithm

We present the optical flow algorithm for forecasting the rate of total electron content index (OFROTI). It consists of a method for predicting maps of rapid fluctuations of ionospheric electron content in terms of global navigation satellite system (GNSS) dual-frequency phase measurements of the rate of change of total electron content index (ROTI). The forecast is made in space and time, at horizons up to more than 6 h. These forecast maps will consist of the ROTI spatial distribution in the northern hemisphere above 45° latitude. The prediction method models the ROTI spatial distribution as a pseudoconservative flux, i.e., exploiting the inertia of the flux of ROTI to determine the future position. This idea is implemented as a modification of the optical flow image processing technique. The algorithm has been modified to deal with the nonconservation of the ROTI quantity in time. We show that the method can predict both, the local value of ROTI and also the regions with ROTI above a given level, better than the prediction using the current map as forecast, i.e., predicting by a current map from horizons of 15 min up to 6 h. The method was tested on 11 representative active and calm days during 2015 and 2018 from the multi-GNSS (GPS, GLONASS, Galileo, and Beidou) multifrequency measurements of more than 250 multi-GNSS receivers above 45°N latitude, including the high rate (1 Hz) measurements of Greenland geodetic network (GNET) network among the International GNSS Service network.This work is funded by ESA ITT “Forecasting Space Weather Impacts on Navigation Systems in the Arctic (Green-land Area)” Expro+, Activity No. 1000026374. The GNET GNSS observations from Greenland was kindly provided by The Danish Agency for Data Supply and Efficiency, in the Danish Ministry of Energy, Utilities and Climate, Copenhagen, DenmarkPeer ReviewedPostprint (author's final draft

Correlation of morphological and radiological characteristics of degenerative disc disease in lumbar spine: a cadaveric study

Background: Intervertebral disc (IVD) degeneration plays a crucial role in the pathophysiology of low back pain. Several grading systems have been developed for both morphological and radiological assessment. The aim of this study was to assess the morphological and radiological characteristics of IVD degeneration and validate popular radiological Pfirrmann scale against morphological Thompson grading system. Material and methods: Full spinal columns (vertebrae L1-S1 and IVD between them) were harvested from cadavers through an anterior dissection. MRI scans of all samples were conducted. Then, all vertebral columns were cut in the midsagittal plane and assessed morphologically. Results: A total of 100 lumbar spine columns (446 IVDs) were included in the analysis of the degeneration grade. Morphologic Thompson scale graded the majority of discs as grade 2 and 3 (44.2% and 32.1%, respectively), followed by grade 4 (16.8%), grade 1 (5.8%) and grade 5 (1.1%). The Radiologic Pfirrmann grading system classified 44.2% of discs as grade 2, 32.1% as grade 3, 16.8% as grade 4, 5.8% as grade 1 and 1.1% as grade 5. The analysis on the effect of age on degeneration revealed significant, although moderate, positive correlation with both scales. Analysis of the agreement between scales showed weighted Cohen’s kappa equal to 0.61 (p<0.001). Most of the disagreement occurred due to a 1 grade difference (91.5%), whereas only 8.5% due to a 2 grade difference. Conclusions: With the increase of the prevalence of intervertebral disc disease in the population, reliable grading systems of IVD degeneration are crucial for spine surgeons in their clinical assessment. While overall there is agreement between both grading systems, clinicians should remain careful when using Pfirmann scale as the grades tend to deviate from the morphological assessment

Review of code and phase biases in multi-GNSS positioning

A review of the research conducted until present on the subject of Global Navigation Satellite System (GNSS) hardware-induced phase and code biases is here provided. Biases in GNSS positioning occur because of imperfections and/or physical limitations in the GNSS hardware. The biases are a result of small delays between events that ideally should be simultaneous in the transmission of the signal from a satellite or in the reception of the signal in a GNSS receiver. Consequently, these biases will also be present in the GNSS code and phase measurements and may there affect the accuracy of positions and other quantities derived from the observations. For instance, biases affect the ability to resolve the integer ambiguities in Precise Point Positioning (PPP), and in relative carrier phase positioning when measurements from multiple GNSSs are used. In addition, code biases affect ionospheric modeling when the Total Electron Content is estimated from GNSS measurements. The paper illustrates how satellite phase biases inhibit the resolution of the phase ambiguity to an integer in PPP, while receiver phase biases affect multi-GNSS positioning. It is also discussed how biases in the receiver channels affect relative GLONASS positioning with baselines of mixed receiver types. In addition, the importance of code biases between signals modulated onto different carriers as is required for modeling the ionosphere from GNSS measurements is discussed. The origin of biases is discussed along with their effect on GNSS positioning, and descriptions of how biases can be estimated or in other ways handled in the positioning process are provided.QC 20170922</p

An assessment of smartphone and low-cost multi-GNSS single-frequency RTK positioning for low, medium and high ionospheric disturbance periods

The emerging GNSSs make single-frequency (SF) RTK positioning possible. In this contribution two different types of low-cost (few hundred USDs) RTK receivers are analyzed, which can track L1 GPS, B1 BDS, E1 Galileo and L1 QZSS, or any combinations thereof, for a location in Dunedin, New Zealand. These SF RTK receivers can potentially give competitive ambiguity resolution and positioning performance to that of more expensive (thousands USDs) dual-frequency (DF) GPS receivers. A smartphone implementation of one of these SF receiver types is also evaluated. The least-squares variance component estimation (LS-VCE) procedure is first used to formulate a realistic stochastic model, which assures that our receivers at hand can achieve the best possible ambiguity resolution and RTK positioning performance. The best performing low-cost SF RTK receiver types are then assessed against DF GPS receivers and survey-grade antennas. Real data with ionospheric disturbances at low, medium and high levels are analyzed, while making use of the ionosphere-weighted model. It will be demonstrated that when the presence of the residual ionospheric delays increases, instantaneous RTK positioning is not possible for any of the receivers, and a multi-epoch model is necessary to use. It is finally shown that the low-cost SF RTK performance can remain competitive to that of more expensive DF GPS receivers even when the ionospheric disturbance level reaches a Kp-index of 7-, i.e. for a strong geomagnetic storm, for the baseline at hand

Principles of the ground deformation monitoring technology based on GPS satellite measurements in control network

Określanie wskaźników deformacji terenu, takich jak przemieszczenia pionowe i poziome, wymaga wykonywania pomiarów geodezyjnych z dużą dokładnością. W klasycznej geodezji do wyznaczania przemieszczeń pionowych powszechnie wykorzystywana jest metoda niwelacji precyzyjnej, zaś do przemieszczeń poziomych pomiary kątowo-liniowe w sieciach kontrolnych. W pracy zaprezentowano założenia precyzyjnego wyznaczania przemieszczeń pionowych i poziomych z wykorzystaniem statycznych pomiarów GPS. Przedstawiono technologię pomiarów terenowych wraz z konstrukcją satelitarnej sieci kontrolnej i sesji pomiarowych oraz założenia i etapy obliczeń przy wyznaczaniu przemieszczeń punktów ze szczególnym uwzględnieniem strategii opracowania obserwacji satelitarnych w precyzyjnych sieciach lokalnych. Przedstawiono osiągane dokładności wyznaczeń współrzędnych punktów sieci kontrolnej na przykładzie prowadzonych badań deformacji terenu na obszarze Kopalni Węgla Brunatnego „Adamów” S.A. w Turku oraz na obszarze Starego i Głównego Miasta Gdańska. Wyniki wskazują, iż możliwe jest osiągnięcie dokładności wyznaczenia okresowych współrzędnych punktów na poziomie 2-3 mm dla każdej składowej.Determination of deformation indices, like vertical and horizontal displacements, requires high precision geodetic surveys. In the classic surveying, the precise, geometrical leveling is commonly used in order to determine vertical displacements and angle-distance measurements in control network in order to determine horizontal displacements. The paper presents the main principles and steps of precise determination of the 3-D displacements with the use of GPS technology. The technology of field measurements together with the construction of the control network and the observation processing methodology is presented. The emphasis was put on the data post-processing strategy in precise, local satellite networks. The presented achievable accuracy is confirmed after several years of the experience gained during field campaigns at the open pit mine Adamów and the Main and Old City of Gdańsk. The results show that it is possible to achieve 2-3 mm accuracy 3-D coordinates of the monitored points. This in turn allows for high accuracy deformation monitoring

Wstępne badania dokładności nowego modułu ultra-szybkiego pozycjonowania – POZGEO-2 – na obszarach znajdujących się poza granicami sieci ASG-EUPOS

The presented preliminary research concerns the accuracy and reliability of new ultra-fast static positioning module - POZGEO-2 - in case of processing GPS data collected outside the ASG-EUPOS network. Such a case requires extrapolation of the network-derived atmospheric corrections which limits correction accuracy and, therefore, has adverse effect on the carrier phase ambiguity resolution. The presented processing tests are based on processing 5-minute long observing sessions and show that precise positioning can be supported up to 35 km from the ASG-EUPOS borders. This means that precise positioning with POZGEO-2 module can be assured for the most of the border areas of Poland.W pracy prezentowane są badania dotyczące dokładności i wiarygodności pozycji wyznaczanej z wykorzystaniem nowego modułu ultra-szybkiego pozycjonowania - POZGEO-2 opracowanego dla systemu ASG-EUPOS. Przedstawione testy obliczeniowe dotyczą szczególnego przypadku wyznaczania pozycji, gdy użytkownik znajduje się poza granicami sieci stacji referencyjnych. W takich warunkach wymagana jest ekstrapolacja sieciowych poprawek atmosferycznych. Wpływa to negatywnie na dokładność tych poprawek i może doprowadzić do sytuacji, w której wyznaczenie nieoznaczoności będzie niemożliwe. Prezentowane badania oparte są na pięciominutowych sesjach obserwacyjnych i pokazują, że poprawki mogą być ekstrapolowane dla obszarów położonych do około 35 km od granic sieci ASG-EUPOS. Oznacza to, że w praktyce precyzyjne pozycjonowanie ultra-szybkie z użyciem modułu POZGEO-2 może być zapewnione dla niemal całego obszaru Polski

Preliminary results on performance of new ultra-fast static positioning module – POZGEO-2 in areas outside the ASG-EUPOS network

The presented preliminary research concerns the accuracy and reliability of new ultra-fast static positioning module - POZGEO-2 - in case of processing GPS data collected outside the ASG-EUPOS network. Such a case requires extrapolation of the network-derived atmospheric corrections which limits correction accuracy and, therefore, has adverse effect on the carrier phase ambiguity resolution. The presented processing tests are based on processing 5-minute long observing sessions and show that precise positioning can be supported up to 35 km from the ASG-EUPOS borders. This means that precise positioning with POZGEO-2 module can be assured for the most of the border areas of Poland.W pracy prezentowane są badania dotyczące dokładności i wiarygodności pozycji wyznaczanej z wykorzystaniem nowego modułu ultra-szybkiego pozycjonowania - POZGEO-2 opracowanego dla systemu ASG-EUPOS. Przedstawione testy obliczeniowe dotyczą szczególnego przypadku wyznaczania pozycji, gdy użytkownik znajduje się poza granicami sieci stacji referencyjnych. W takich warunkach wymagana jest ekstrapolacja sieciowych poprawek atmosferycznych. Wpływa to negatywnie na dokładność tych poprawek i może doprowadzić do sytuacji, w której wyznaczenie nieoznaczoności będzie niemożliwe. Prezentowane badania oparte są na pięciominutowych sesjach obserwacyjnych i pokazują, że poprawki mogą być ekstrapolowane dla obszarów położonych do około 35 km od granic sieci ASG-EUPOS. Oznacza to, że w praktyce precyzyjne pozycjonowanie ultra-szybkie z użyciem modułu POZGEO-2 może być zapewnione dla niemal całego obszaru Polski