The Impact of Orbital and Clock Errors on Positioning from LEO Constellations and Proposed Orbital Solutions

Two approaches are discussed for the estimation and prediction of the orbits of low earth orbit (LEO) satellites that can be used for navigation. The first approach relays on using a ground monitoring network of stations. The procedures to generate the LEO orbital products in this approach are proposed at two accuracy levels to facilitate different positioning applications. The first type targets producing orbits at meter-level accuracy, defined here as LEO-specific broadcast ephemeris. The second type of products would produce orbits with an accuracy of cm as polynomial corrections to the first type of orbits. Real and simulated LEO satellite data is used for testing, mimicking LEO satellites that can be used for positioning. For the first type of products, it was found that orbital prediction errors play the dominant role in the total error budget, especially in cases of mid and long-term prediction. For the second type of products, the predicted orbits within a short period of up to 60 s generate errors at a few cm, and fitting the corrections with a quadratic polynomial reduced the fitting range errors to the cm level compared to the case of applying a linear polynomial. This level of accuracy can fulfill the requirement for precise point position ing (PPP). The second approach is computing the orbits in real time applying the kinematic or reduced-dynamic mode, where the orbits are computed in the PPP mode using GNSS observations collected onboard LEO satellites and the GNSS orbits and clock products are received through inter-satellite links such as the free-access SouthPAN service in Australia, Galileo HAS, or Beidou (BDS-3, PPP-B2b service). The limitations of this approach and preliminary results are given. Furthermore, the LEO satellite clocks determined together with the orbits in the reduced-dynamic LEO satellite orbit process in near-real-time are also analysed. Finally, the impact of possible orbital and clock errors in the range of decimetres to several meters of LEO satellites on positioning performance is analysed

THE IMPACT OF ORBITAL AND CLOCK ERRORS ON POSITIONING FROM LEO CONSTELLATIONS AND PROPOSED ORBITAL SOLUTIONS

Two approaches are discussed for the estimation and prediction of the orbits of low earth orbit (LEO) satellites that can be used for navigation. The first approach relays on using a ground monitoring network of stations. The procedures to generate the LEO orbital products in this approach are proposed at two accuracy levels to facilitate different positioning applications. The first type targets producing orbits at meter-level accuracy, defined here as LEO-specific broadcast ephemeris. The second type of products would produce orbits with an accuracy of cm as polynomial corrections to the first type of orbits. Real and simulated LEO satellite data is used for testing, mimicking LEO satellites that can be used for positioning. For the first type of products, it was found that orbital prediction errors play the dominant role in the total error budget, especially in cases of mid and long-term prediction. For the second type of products, the predicted orbits within a short period of up to 60 s generate errors at a few cm, and fitting the corrections with a quadratic polynomial reduced the fitting range errors to the cm level compared to the case of applying a linear polynomial. This level of accuracy can fulfill the requirement for precise point positioning (PPP). The second approach is computing the orbits in real time applying the kinematic or reduced-dynamic mode, where the orbits are computed in the PPP mode using GNSS observations collected onboard LEO satellites and the GNSS orbits and clock products are received through inter-satellite links such as the free-access SouthPAN service in Australia, Galileo HAS, or Beidou (BDS-3, PPP-B2b service). The limitations of this approach and preliminary results are given. Furthermore, the LEO satellite clocks determined together with the orbits in the reduced-dynamic LEO satellite orbit process in near-real-time are also analysed. Finally, the impact of possible orbital and clock errors in the range of decimetres to several meters of LEO satellites on positioning performance is analysed

Maintaining real-time precise point positioning during outages of orbit and clock corrections

The precise point positioning (PPP) is a popular positioning technique that is dependent on the use of precise orbits and clock corrections. One serious problem for real-time PPP applications such as natural hazard early warning systems and hydrographic surveying is when a sudden communication break takes place resulting in a discontinuity in receiving these orbit and clock corrections for a period that may extend from a few minutes to hours. A method is presented to maintain real-time PPP with 3D accuracy less than a decimeter when such a break takes place. We focus on the open-access International GNSS Service (IGS) real-time service (RTS) products and propose predicting the precise orbit and clock corrections as time series. For a short corrections outage of a few minutes, we predict the IGS-RTS orbits using a high-order polynomial, and for longer outages up to 3 h, the most recent IGS ultra-rapid orbits are used. The IGS-RTS clock corrections are predicted using a second-order polynomial and sinusoidal terms. The model parameters are estimated sequentially using a sliding time window such that they are available when needed. The prediction model of the clock correction is built based on the analysis of their properties, including their temporal behavior and stability. Evaluation of the proposed method in static and kinematic testing shows that positioning precision of less than 10 cm can be maintained for up to 2 h after the break. When PPP re-initialization is needed during the break, the solution convergence time increases; however, positioning precision remains less than a decimeter after convergence

Fast precise point positioning: a system to provide corrections for single and multi-frequency navigation

Fast Precise Point Positioning (Fast-PPP) provides Global Navigation Satellite System corrections in real-time. Satellite orbits and clock corrections are shown to be accurate to a few centimeters and a few tenths of a nanosecond which, together with the determination of the fractional part of the ambiguities, enable global high-accuracy positioning with undifferenced Integer Ambiguity Resolution. The new global ionospheric model is shown to provide corrections accurate at the level of 1 Total Electron Content Unit over well-sounded areas and Differential Code Biases at the level of tenths of a nanosecond. These corrections are assessed with permanent receivers, treated as rovers, located at 100 to 800 kilometers from the reference stations of the ionospheric model. Fast-PPP achieves decimeter-level of accuracy after few minutes, several times faster than single- and dual-frequency ionospheric-free solutions, using a month of Global Positioning System data close to the last Solar Maximum and including equatorial rovers.Postprint (author's final draft

Effects of Parent and Peer Behaviors on Adolescent Sexual Behavior: Are Positive and Negative Peer Behaviors Moderators?

Adolescents and young adults account for a significantly high proportion of unintended pregnancy and sexually transmitted infection cases in the United States. According to Jessor\u27s Problem Behavior Theory, combined protective factors, such as exposure to positive parenting and peer behaviors, create an environment that is supportive of conventional behaviors and discouraging of problem behaviors. There is an extensive amount of literature on parent and peer influences on adolescent sexual behavior but few studies address the interactive influence of both parent and peer behaviors on adolescent sexual risk-taking. The purpose of this study was to examine the relationship between maternal supportiveness and strictness on adolescent sexual risk-taking, as well as the moderating influence of peer involvement in positive or negative activities. A sample of 14-16 year old adolescents was drawn from the National Longitudinal Survey of Youth-1997 (NLSY-97; N = 4,008, 50.5% male, 59.4% White, 26.5% Black, and 13.3% other). Higher levels of maternal supportiveness, maternal strictness, and positive peer behaviors were each associated with lower levels of sexual risk-taking two years later. High levels of negative peer behaviors were related to high sexual-risk taking two years later. No interaction terms were significant. Important implications for positive peer relationships were also found. Future research should focus on the comparison of parental warmth and control variables as moderators for the relationship between peer influence and adolescent sexual risk-taking

Precise Point Positioning in the Airborne Mode

The Global Positioning System (GPS) is widely used for positioning in the airborne mode such as in navigation as a supplementary system and for geo-referencing of cameras in mapping and surveillance by aircrafts and Unmanned Aerial Vehicles (UAV). The Precise Point Positioning (PPP) approach is an attractive positioning approach based on processing of un-differenced observations from a single GPS receiver. It employs precise satellite orbits and satellite clock corrections. These data can be obtained via the internet from several sources, e.g. the International GNSS Service (IGS). The data can also broadcast from satellites, such as via the LEX signal of the new Japanese satellite system QZSS. The PPP can achieve positioning precision and accuracy at the sub-decimetre level. In this paper, the functional and stochastic mathematical modelling used in PPP is discussed. Results of applying the PPP method in an airborne test using a small fixed-wing aircraft are presented. To evaluate the performance of the PPP approach, a reference trajectory was established by differential positioning of the same GPS observations with data from a ground reference station. The coordinate results from the two approaches, PPP and differential positioning, were compared and statistically evaluated. For the test at hand, positioning accuracy at the cm-to-decimetre was achieved for latitude and longitude coordinates and doubles that value for height estimation

Precise Point Positioning Inertial Navigation Integration for Kinematic Airborne Applications

UAVs have the potential for autonomous airborne remote sensing applications that require rapid response to natural hazards (e.g. volcano eruptions, earthquakes). As these applications require very accurate positioning, tightly coupled Global Positioning System (GPS) Precise Point Positioning (PPP) Inertial Navigation Systems (INS) are an attractive method to perform real-time aircraft positioning. In particular, PPP can achieve a level of positioning accuracy that is similar to Real-Time Kinematic (RTK) GPS, without the need of a relatively close GPS reference station. However, the PPP method is known to converge to accurate positioning estimate more slowly when compared to RTK, a drawback of PPP that is amplified whenever the receiver platform is faced with GPS challenged environments, such as poor satellite visibility and frequent phase breaks.;This thesis presents the use of a simulation environment that characterizes the position estimation performance sensitivity of PPP/INS through a Monte Carlo analysis that is considered under various conditions: such as, the intensity of multipath errors, the number of phase breaks, the satellite geometry, the atmospheric conditions, the noise characteristics of the inertial sensor, and the accuracy of GPS orbit products. After the PPP/INS formulation was verified in a simulation environment, the INS formulation was incorporated into NASA JPL\u27s Real-Time GIPSY-x. This software was then verified using eight recorded flight data sets provided by the National Geodetic Survey (NGS), National Oceanic and Atmospheric Administration (NOAA) program called Gravity for the Redefinition of the American Vertical Datum (GRAV-D)

Consolidation and assessment of a technique to provide fast and precise point positioning (Fast-PPP)

Tesi per compendi de publicacions. La consulta íntegra de la tesi, inclosos els articles no comunicats públicament per drets d'autor, es pot realitzar prèvia petició a l'Arxiu de la UPCPremi extraordinari doctorat UPC curs 2015-2016, àmbit de CiènciesThe research of this paper-based dissertation is focused on the Fast Precise Point Positioning (Fast-PPP) technique. The novelty relies on using an accurate ionosphere model, in combination with the standard precise satellite clock and orbit products, to reduce the convergence time of state-of-the-art high-accuracy navigation techniques from approximately one hour to few minutes. My first contribution to the Fast-PPP technique as a Ph.D. student has been the design and implementation of a novel user navigation filter, based on the raw treatment of undifferenced multi-frequency code and carrier-phase Global Navigation Satellite System (GNSS) measurements. The innovative strategy of the filter avoids applying the usual ionospheric-free combination to the GNSS observables, exploiting the full capacity of new multi-frequency signals and increasing the robustness of Fast-PPP in challenging environments where the sky visibility is reduced. It has been optimised to take advantage of the corrections required to compensate the delays (i.e., errors) affecting the GNSS signals. The Fast-PPP corrections, and most important, their corrections uncertainties (i.e., the confidence bounds) are added as additional equations in the navigation filter to obtain Precise Point Positioning (PPP) in few minutes. A second contribution performed with the new user filter, has been the consolidation of the precise ionospheric modelling of Fast-PPP and its extension from a regional to a global scale. The correct use of the confidence bounds has been found of great importance when navigating in the low-latitude areas of the equator, where the ionosphere is difficult to be accurately modelled. Even in such scenario, a great consistency has been achieved between the actual positioning errors with respect to the formal errors, as demonstrated using similar figures of merit used in civil aviation, as the Stanford plot. A third contribution within this dissertation has been the characterisation of the accuracy of different ionospheric models currently used in GNSS. The assessment uses actual, unambiguous and undifferenced carrier-phase measurements, thanks to the centimetre-level modelling capability within the Fast-PPP technique. Not only the errors of the ionosphere models have been quantified in absolute and relative terms, but also, their effect on navigation.La investigació d'aquesta Tesi Doctoral per compendi d'articles es centra en la tècnica de ràpid Posicionament de Punt Precís (Fast-PPP). La novetat radica en l'ús d'un model ionosfèric precís que, combinat amb productes estàndard de rellotge i de l'òrbita de satèl·lit, redueix el temps de convergència de les actuals tècniques de navegació precisa d'aproximadament una hora a pocs minuts. La meva primera contribució a la tècnica Fast-PPP com a estudiant de Doctorat ha estat el disseny i la implementació d'un filtre de navegació d'usuari innovador, basat en el tractament de múltiples freqüències de mesures de codi i fase sense diferenciar (absolutes). La estratègia del filltre de navegació evita l'aplicació de l'habitual combinació lineal lliure de ionosfera per a aquests observables. Així, s'explota la capacitat completa dels senyals multi-freqüència en el nous Sistemes Globals de Navegació per Satèl·lit (GNSS) i s'augmenta la robustesa del Fast-PPP en entorns difícils, on es redueix la visibilitat del cel. S'ha optimitzat per tal de prendre avantatge de les correccions necessàries per a compensar els retards (és a dir, els errors) que afecten els senyals GNSS. Les correccions de Fast-PPP i més important, les seves incerteses (és a dir, els intervals de confiança) s'afegeixen com a equacions addicionals al filltre per aconseguir Posicionat de Punt Precís (PPP) en pocs minuts. La segona contribució ha estat la consolidació del modelat ionosfèric precís de Fast-PPP i la seva extensió d'un abast regional a una escala global. La correcta determinació i ús dels intervals de confiança de les correccions Fast-PPP ha esdevingut de gran importància a l'hora de navegar en zones de baixa latitud a l'equador, on la ionosfera és més difícil de modelar amb precisió. Fins i tot en aquest escenari, s'ha aconseguit una gran consistència entre els errors de posicionament reals i els nivells de protecció dels usuaris de Fast-PPP, tal com s'ha demostrat amb figures de mèrit similars a les utilitzades en l'aviació civil (els diagrames de Stanford). La tercera contribució d'aquesta Tesi Doctoral ha estat la caracterització de l'exactitud dels models ionosfèrics utilitzats actualment en GNSS. L'avaluació utilitza mesures de fase, sense ambigüitats i sense diferenciar, gràcies a la capacitat de modelatge centimètric emprat a la tècnica de Fast-PPP. No només els errors dels models de la ionosfera han estat quantificats en termes absoluts i relatius, sinó també, el seu efecte sobre la navegacióLa investigación de esta Tesis Doctoral, por compendio de artículos, se centra en la técnica de rápido Posicionamiento de Punto Preciso (Fast-PPP). La novedad, radica en el uso de un modelo ionosférico preciso que, combinado con productos estándard de reloj y órbita de satélite, reduce el tiempo de convergencia de las actuales técnicas de navegación precisa de una hora a pocos minutos.Mi primera contribución a la técnica Fast-PPP como estudiante de Doctorado ha sido el diseño y la implementación de un filtro de navegación de usuario innovador, basado en el tratamiento de múltiples frecuencias de medidas de código y fase sin diferenciar (absolutas). La estrategia del filtro de navegación evita la aplicación de la habitual combinación lineal libre de ionosfera para dichos observables. Así, se explota la capacidad de la señal multi-frecuencia en los nuevos Sistemas Globales de Navegación por Satélite (GNSS) y se aumenta la robustez del Fast-PPP en entornos difíciles, donde se reduce la visibilidad del cielo. Se ha optimizado para tomar ventaja de las correcciones necesarias para compensar los retardos (es decir, los errores) que afectan las señales GNSS. Las correcciones de Fast-PPP y más importante, sus incertidumbres (es decir, los intervalos de confianza) se añaden como ecuaciones adicionales al filtro para conseguir Posicionamiento de Punto Preciso (PPP) en pocos minutos. La segunda contribución ha estado la consolidación del modelado ionosférico preciso de Fast-PPP y la extensión de su cobertura regional a una escala global. La correcta determinación y uso de los intervalos de confianza de las correcciones Fast-PPP ha sido de gran importancia a la hora de navegar en zonas de latitudes ecuatoriales, donde la ionosfera es más difícil de modelar con precisión. Incluso en dicho escenario, se ha conseguido una gran consistencia entre los errores de posicionamiento reales y los niveles de protección de los usuarios de Fast-PPP, tal como se ha demostrado con figuras de mérito similares a las utilizadas en la aviación civil (los diagramas de Stanford).La tercera contribución de esta Tesis Doctoral ha sido la caracterización de la exactitud de los modelos ionosféricos utilizados actualmente en GNSS. El método usa medidas de fase, sin ambigüedad y sin diferenciar, gracias a la capacidad de modelado centimétrico empleado en la técnica de Fast-PPP. No solo los errores de los modelos de la ionosfera han sido cuantificados en términos absolutos y relativos, sino también, su efecto sobre la navegación.Award-winningPostprint (published version

The potential of LEO mega-constellations in aiding GNSS to enable positioning in challenging environments

Signals from the emerging Low Earth Orbit (LEO) satellites from mega-constellations that broadcast internet, such as Starlink (Space X), OneWeb, Iridium etc., also known as “signals of opportunity” (SOP), can potentially aid positioning. These LEO satellites are approximately 20 times closer to Earth compared to the GNSS medium-earth orbit (MEO) satellites – with 300-1500km altitudes, and 90-120 minutes orbital periods. Hence, LEO satellites provide a new navigation space infrastructure with much stronger signal power than GNSS signals. This makes these LEO signals more resilient to interference and available in deep attenuation settings. In challenging environments, with limited GNSS observations that may not allow positioning, such as in urban canyons, bushland, or bottom of mining pits, integrating LEO signals with the available GNSS observations can enable positioning. Moreover, the corresponding high speed of LEO satellites enables faster satellite geometry change, and hereby significantly shortens the convergence time for precise point positioning (PPP). In this contribution, the positioning from LEO Doppler shift time variation integrated with GNSS and two challenges in positioning using LEO will be briefly discussed. For positioning, the orbits of LEO satellites and their clock behaviour must be known. In addition, unlike GNSS satellites, LEO satellites are not equipped with atomic clocks, and typically use ultra-stable oscillators (USOs) or oven-controlled crystal oscillators (OCXOs), nor are they tightly time-synchronised with each other. The estimation and prediction of these orbits and clock errors and drift are discussed

Implementation of PPP as new GNSS Observation Type in the Geomonitoring System GOCA

[EN] Early detection of significant movements in both natural and artificial structures is crucial to prevent human, environmental and economic losses. For this reason, Geomonitoring in an active field. GNSS technics are also a filed in which lot of research and improvement have been made in recent years. Some studies have indicated the potential of GNSS technics in the field of Geomonitoring. The aim of this master thesis is developing a software that allows processing GNSS data with Precise Point Positioning technic in the context of the geomonitoring project GOCA. With this implementation, potential of PPP with low cost receiver (U-Blox ZED-F9P) using different products and settings is evaluated in this document. Based on a literature review, that includes the study of GOCA project and a summary of main PPP approaches, a C++ dialog-based software was design and developed, using RTKLIB and WaPPP as software engines. Besides that, two different observations were made (one 12 hours to post-processing and one real time) in order to test the developed software and evaluate the obtained results using different parameters or products. The obtained results reaffirm the potential of the PPP technique, even using low cost receiver. Even some differences between different software engines or IGS products were found, the results allow us to conclude that PPP is a technique with many advantages in the field of geomonitoring, since it avoids the use of several receivers and good accuracies are obtained. However, some aspects need further research in this context, as there is no common criterion for establishing convergence time and new methodologies and algorithms are being developed in the field of PPP processing.[ES] La detección temprana de movimientos significativos en estructuras naturales y artificiales es crucial para prevenir pérdidas humanas, ambientales y económicas. Por esta razón, Geomonitorización es un campo activo. Las técnicas de GNSS son también un campo en el que se han realizado muchas investigaciones y mejoras en los últimos años. Algunos estudios han indicado el potencial de las técnicas GNSS en el campo de la geomonitorización. El objetivo de esta tesis de máster es desarrollar un software que permita el procesamiento de datos GNSS con la técnica de posicionamiento de punto preciso en el contexto del proyecto de geomonitorización GOCA. Con esta implementación, el potencial del PPP con el receptor de bajo coste (U-Blox ZED-F9P) usando diversos productos y configuraciones se va a evalúar en este documento. Basado en una revisión de la literatura, que incluye el estudio del proyecto GOCA y un resumen de los principales enfoques PPP, se diseñó y desarrolló un software basado en diálogos C++, utilizando RTKLIB y WaPPP como motores de software. Además, se realizaron dos observaciones diferentes (una de 12 horas para el post-procesamiento y otra en tiempo real) con el fin de probar el software desarrollado y evaluar los resultados obtenidos utilizando diferentes parámetros o productos. Los resultados obtenidos reafirman el potencial de la técnica PPP, incluso utilizando un receptor de bajo coste. Incluso habiendo encontrado algunas diferencias entre diferentes motores de software o productos IGS, los resultados nos permiten concluir que PPP es una técnica con muchas ventajas en el campo de la geomonitorización, ya que evita el uso de varios receptores y se obtienen buenas precisiones. Sin embargo, algunos aspectos necesitan más investigación en este contexto, ya que no existe un criterio común para establecer el tiempo de convergencia y se están desarrollando nuevas metodologías y algoritmos en el campo del procesamiento PPP.Luján García Muñoz, R. (2020). Implementation of PPP as new GNSS Observation Type in the Geomonitoring System GOCA. http://hdl.handle.net/10251/139668TFG