Contributions to ionospheric modeling with GNSS in mapping function, tomography and polar electron

This dissertation focuses on determining the vertical electron content distribution in low and high vertical resolution from ground-based and LEO on board GNSS data and improving the knowledge of ionosphere climatology in northern mid-latitude and polar regions. The novelty is summarized in the following four aspects: The first contribution is to propose a new ionospheric mapping function concept - Barcelona Ionospheric Mapping Function (BIMF), in order to improve STEC (Slant Total Electron Content) conversion accuracy from any given VTEC (Vertical Total Electron Content) model. BIMF is based on the climatic modeling of the VTEC fraction in the second layer - µ2, which is the byproduct of UQRG generated by UPC. The first implementation of BIMF is BIMF-nml for the northern mid-latitudes, where the latitudinal variation of µ2 is neglected. µ2 is modeled as function of date and local time. From the user’s perspective, BIMF is the linear combination of µ2 and the standard ionospheric mapping function, and only needs 41 constant coefficients, making BIMF achieve the simplicity for application. The good performance has been demonstrated in the dSTEC assessment for different IGSGIMs: UQRG, CODG and JPLG. The second contribution is to confirm the capability of UQRG GIMs to detect representative ionospheric features in polar regions through six case studies, including TOI (Tongue of Ionization), trough, flux transfer event, theta-aurora, ionospheric convection patterns and storm enhanced density. The long-term VTEC and µ2 data provide valuable databases for studying the morphology and climatology of polar ionospheric phenomena. The unsupervised clustering results of normalized VTEC distribution show that TOI and polar cap patches exhibit an annual dependence, i.e. most TOI and patches occurring in the North Hemisphere winter and the South Hemisphere summer. The third contribution is to propose a hybrid method - AVHIRO (the Abel-VaryChap Hybrid modeling from topside Incomplete RO data), to solve an ill-posed rank-deficient problem in the Abel electron density retrieval. This work is driven by the future EUMETSAT Polar System 2nd Generation, which provides truncated ionospheric RO data, only below impact heights of 500 km, in order to guarantee a full data gathering of the neutral part. AVHIRO takes advantage of one Linear Vary-Chap model, where the scale height increases linearly with altitude above the F2 layer peak, and uses Powell search to solve the full electron densities, ambiguity term, and four parameters of the Vary-Chap model simultaneously, taking into account the nonlinear interactions between the unknown parameters. The fourth contribution is to take advantage of the geometry brought by combining DORIS, ground-based Galileo, ground-based, LEO-POD and vessel-based GPS data and ingest the multi-source dual-frequency carrier phase measurements into the tomographic model to improve the GIM VTEC estimation precision. The impact of adding each type of measurements, which are Galileo data, vessel-based GPS data, DORIS and LEO-POD GPS data, to ground-based GPS data on GIM product is examined according to two complementing evaluation criteria, JASON-3 VTEC comparison and GPS dSTEC test. This study proves the expected better GIM performance by new data ingestion into tomographic model, which is a successful step forward from conception to initial experimental validation.electrones en resolución vertical baja y alta a partir de medidas GNSS terrestres y a bordo de satélites de órbita baja (LEO), además de utilizar medidas GNSS desde buques y medidas DORIS, además de mejorar el conocimiento de la climatología de la ionosfera en las regiones polares y en latitudes medias del hemisferio norte. Las contribuciones se pueden resumir en los siguientes cuatro aspectos: La primera contribución consiste en proponer un nuevo concepto de función de mapeo ionosférico: la función de mapeo ionosférico de Barcelona (BIMF), con el fin de mejorar la precisión de conversión de STEC (contenido total de electrones inclinado) a partir de cualquier modelo de VTEC (contenido total de electrones vertical). BIMF se basa en el modelado climático de la fracción VTEC en la segunda capa - μ2, que es el subproducto de UQRG generado por UPC. La primera implementación de BIMF es BIMF-nml para las latitudes medias del hemisferio norte. μ2 se modela en función del dia y la hora local. Desde la perspectiva del usuario, BIMF es la combinación lineal de μ2 y la función de mapeo ionosférico estándar, y solo necesita 41 coeficientes constantes, lo que hace que BIMF sea facilmente aplicable. Su buen comportamiento se demostró en la evaluación dSTEC para diferentes IGS GIM: UQRG, CODG y JPLG. La segunda contribución se centró en confirmar la capacidad de los GIM UQRG para detectar características ionosféricas representativas en regiones polares a través de seis estudios de casos, que incluyen lenguas de ionización (TOI), depresión de ionización en forma de canal, sucesos de transferencia de flujo, theta-aurora, patrones de convección ionosférica y densidad aumentada durante tormentas geomagnéticas. Los datos a largo plazo de VTEC y μ2 proporcionan valiosas bases de datos para estudiar la morfología y climatología de los fenómenos ionosféricos polares. Los resultados de agrupamiento no supervisados de la distribución normalizada de VTEC muestran que los TOI y los parches en los casquetes polares exhiben una dependencia anual, es decir, la mayoría de los TOI y parches ocurren en el invierno del Hemisferio Norte y el verano del Hemisferio Sur. La tercera contribución ha consistido en proponer un método híbrido: AVHIRO (el modelo híbrido Abel-VaryChap a partir de datos de RO incompletos en la parte superior), para resolver un problema de rango deficiente en la recuperación de la densidad electrónica con el modelo de Abel. Este trabajo está motivado por el futuro sistema polar EUMETSAT de segunda generación, que proporciona datos truncados de RO ionosférica, sólo por debajo de las alturas de impacto de 500 km, con el fin de garantizar una recopilación completa de medidas de la parte neutra. AVHIRO aprovecha un modelo Linear Vary-Chap, donde la altura de la escala aumenta linealmente con la altitud por encima del pico de la capa F2, y utiliza la búsqueda Powell para resolver las densidades completas de electrones, el término de ambig ¨ uedad y cuatro parámetros del modelo Vary-Chap simultáneamente, teniendo en cuenta las interacciones no lineales entre los parámetros desconocidos. La cuarta contribución es aprovechar la geometría aportada por la combinación de datos GPS DORIS, Galileo en tierra, LEO-POD y en barco, e incorporar las mediciones de la fase de la portadora de doble frecuencia de múltiples fuentes en el modelo tomográfico para mejorar la precisión de estimación de GIM VTEC. El impacto de agregar cada tipo de mediciones, que son datos de Galileo, datos de GPS basados en embarcaciones, datos de GPS DORIS y LEO-POD, a datos de GPS terrestres en productos GIM se examina de acuerdo con dos criterios de evaluación complementarios, comparación con VTEC[JASON-3] y con dSTEC[GPS]. Este estudio demuestra el mejor rendimiento esperado de GIM por la nueva ingesta de datos en el modelo tomográfico, que es un exitoso paso adelante desde la concepción hasta la validación experimental inicial

Undifferenced and Uncombined GNSS Time Transfer and its Space Applications

This thesis presents a framework for developing a state-of-the-art undifferenced and uncombined (UDUC) time transfer technique for space applications. It addresses challenges in GNSS time transfer, such as multi-frequency signal modelling, satellite clock estimation, and hardware delay variations. The thesis introduces the UDUC POD method for GNSS time transfer in space and explores the feasibility of constructing a LEO-based space-time reference. This PhD dissertation is among the first to investigate the UDUC GNSS time transfer

Bayesian approach to ionospheric imaging with Gaussian Markov random field priors

Ionosfääri on noin 60–1000 kilometrin korkeudella sijaitseva ilmakehän kerros, jossa kaasuatomien ja -molekyylien elektroneja on päässyt irtoamaan auringon säteilyn ja auringosta peräisin olevien nopeiden hiukkasten vaikutuksesta. Näin syntyneillä ioneilla ja vapailla elektroneilla on sähkö- ja magneettikenttien kanssa vuorovaikuttava sähkövaraus. Ionosfäärillä on siksi merkittävä rooli radioliikenteessä. Se voi mahdollistaa horisontin yli tapahtuvat pitkät radiolähetykset heijastamalla lähetetyn sähkömagneettisen signaalin takaisin maata kohti. Toisaalta ionosfääri vaikuttaa myös sen läpäiseviin korkeampitaajuuksisiin signaaleihin. Esimerkiksi satelliittipaikannuksessa ionosfäärin vaikutus on parhaassakin tapauksessa otettava huomioon, mutta huonoimmassa se voi estää paikannuksen täysin. Näkyvin ja tunnetuin ionosfääriin liittyvä ilmiö lienee revontulet. Yksi keskeisistä suureista ionosfäärin tutkimuksessa on vapaiden elektronien määrä kuutiometrin tilavuudessa. Käytännössä elektronitiheyden mittaaminen on mahdollista mm. tutkilla, kuten Norjan, Suomen ja Ruotsin alueilla sijaitsevalla EISCAT-tutkajärjestelmällä, sekä raketti- tai satelliittimittauksilla. Mittaukset voivat olla hyvinkin tarkkoja, mutta tietoa saadaan ainoastaan tutkakeilan suunnassa tai mittalaitteen läheisyydestä. Näillä menetelmillä ionosfäärin tutkiminen laajemmalla alueella on siten vaikeaa ja kallista. Olemassa olevat paikannussatelliitit ja vastaanotinverkot mahdollistavat ionosfäärin elektronitiheyden mittaamisen alueellisessa, ja jopa globaalissa mittakaavassa, ensisijaisen käyttötarkoituksensa sivutuotteena. Satelliittimittausten ajallinen ja paikallinen kattavuus on hyvä, ja kaiken aikaa kasvava, mutta esimerkiksi tarkkoihin tutkamittauksiin verrattuna yksittäisten mittausten tuottama informaatio on huomattavasti vähäisempää. Tässä väitöstyössä kehitettiin tietokoneohjelmisto ionosfäärin elektronitiheyden kolmiulotteiseen kuvantamiseen. Menetelmä perustuu matemaattisten käänteisongelmien teoriaan ja muistuttaa lääketieteessä käytettyjä viipalekuvausmenetelmiä. Satelliittimittausten puutteellisesta informaatiosta johtuen työssä on keskitytty etenkin siihen, miten ratkaisun löytymistä voidaan auttaa tilastollisesti esitetyllä fysikaalisella ennakkotiedolla. Erityisesti työssä sovellettiin gaussisiin Markovin satunnaiskenttiin perustuvaa uutta korrelaatiopriori-menetelmää. Menetelmä vähentää merkittävästi tietokonelaskennassa käytettävän muistin tarvetta, mikä lyhentää laskenta-aikaa ja mahdollistaa korkeamman kuvantamisresoluution.Ionosphere is the partly ionised layer of Earth's atmosphere caused by solar radiation and particle precipitation. The ionisation can start from 60 km and extend up to 1000 km altitude. Often the interest in ionosphere is in the quantity and distribution of the free electrons. The electron density is related to the ionospheric refractive index and thus sufficiently high densities affect the electromagnetic waves propagating in the ionised medium. This is the reason for HF radio signals being able to reflect from the ionosphere allowing broadcast over the horizon, but also an error source in satellite positioning systems. The ionospheric electron density can be studied e.g. with specific radars and satellite in situ measurements. These instruments can provide very precise observations, however, typically only in the vicinity of the instrument. To make observations in regional and global scales, due to the volume of the domain and price of the aforementioned instruments, indirect satellite measurements and imaging methods are required. Mathematically ionospheric imaging suffers from two main complications. First, due to very sparse and limited measurement geometry between satellites and receivers, it is an ill-posed inverse problem. The measurements do not have enough information to reconstruct the electron density and thus additional information is required in some form. Second, to obtain sufficient resolution, the resulting numerical model can become computationally infeasible. In this thesis, the Bayesian statistical background for the ionospheric imaging is presented. The Bayesian approach provides a natural way to account for different sources of information with corresponding uncertainties and to update the estimated ionospheric state as new information becomes available. Most importantly, the Gaussian Markov Random Field (GMRF) priors are introduced for the application of ionospheric imaging. The GMRF approach makes the Bayesian approach computationally feasible by sparse prior precision matrices. The Bayesian method is indeed practicable and many of the widely used methods in ionospheric imaging revert back to the Bayesian approach. Unfortunately, the approach cannot escape the inherent lack of information provided by the measurement set-up, and similarly to other approaches, it is highly dependent on the additional subjective information required to solve the problem. It is here shown that the use of GMRF provides a genuine improvement for the task as this subjective information can be understood and described probabilistically in a meaningful and physically interpretative way while keeping the computational costs low

Ionospheric path delay models for spaceborne GPS receivers flying in formation with large baselines

GPS relative navigation filters could benefit notably from an accurate modeling of the ionospheric delays, especially over large baselines (>100 km) where double difference delays can be higher than several carrier wavelengths. This paper analyzes the capability of ionospheric path delay models proposed for spaceborne GPS receivers in predicting both zero-difference and double difference ionospheric delays. We specifically refer to relatively simple ionospheric models, which are suitable for real-time filtering schemes. Specifically, two ionospheric delay models are evaluated, one assuming an isotropic electron density and the other considering the effect on the electron density of the Sun aspect angle. The prediction capability of these models is investigated by comparing predicted ionospheric delays with measured ones on real flight data from the Gravity Recovery and Climate Experiment mission, in which two satellites fly separated of more than 200 km. Results demonstrate that both models exhibit a correlation in the excess of 80% between predicted and measured double-difference ionospheric delays. Despite its higher simplicity, the isotropic model performs better than the model including the Sun effect, being able to predict double differenced delays with accuracy smaller than the carrier wavelength in most cases. The model is thus fit for supporting integer ambiguity fixing in real-time filters for relative navigation over large baselines. Concerning zero-difference ionospheric delays, results demonstrate that delays predicted by the isotropic model are highly correlated (around 90%) with those estimated using GPS measurements. However, the difference between predicted and measured delays has a root mean square error in the excess of 30 cm. Thus, the zero-difference ionospheric delays model is not likely to be an alternative to methods exploiting carrier-phase observables for cancelling out the ionosphere contribution in single-frequency absolute navigation filters

Integer Ambiguity Resolution for Multi-GNSS and Multi-Signal Raw Phase Observations

The continuous modernisation of existing Global Navigation Satellite Systems (GNSS) and the development of new systems with a multitude of different carrier frequencies and a variety of signal modulations creates a true multi-GNSS and multi-signal environment available today. Still most precise GNSS processing strategies rely on dual-frequency measurements only by applying the Ionosphere-Free (IF) Linear Combination (LC) of GNSS observables and therefore do not benefit from the available multi-signal environment. While in this processing approach the first order effect of the ionospheric delay can be eliminated almost completely, the formation of linear combinations of GNSS observables leads to a noise increase for the resulting observations and a loss of some of the physical characteristics of the original signals, like the integer nature of the carrier phase ambiguity. In order to benefit from the multi-GNSS and multi-signal environment available today, the scientific analyses and precise applications presented in this work are based on the raw observation processing approach, which makes use of the original (raw) observations without forming any linear combinations or differences of GNSS observables. This processing strategy provides the flexibility to make use of all or a selection of available multi-GNSS and multi-signal raw observations, which are jointly processed in a single adjustment as there is no inherent limitation on the number of usable signals. The renunciation of linear combinations and observation differences preserves the physical characteristics of individual signals and implies that multi-signal biases and ionospheric delays need to be properly determined or corrected in the parameter estimation process. The raw observation processing approach is used in this work to jointly process measurements from up to three different GNSS, including eleven signals tracked on up to eight different carrier frequencies in one single adjustment. The bias handling for multi-GNSS and multi-signal applications is analysed with a focus on physically meaningful parameter estimates to demonstrate the benefits of handling clock offset parameters, multi-signal code biases and ionospheric delay estimates in a physically meaningful and consistent way. In this context, receiver-specific multi-GNSS and multisignal biases are analysed and calibrated by the use of a GNSS signal simulator. The disadvantages of eliminating physical characteristics due to the formation of linear combinations of observations or commonly used parameter estimation strategies are demonstrated and discussed. The carrier phase Integer Ambiguity Resolution (IAR) approach developed and implemented in the course of this work is based on the joint processing of multi-GNSS and multi-signal raw observations without forming any linear combinations or observation differences. Details of the implemented IAR approach are described and the performance is analysed for available carrier signal frequencies of different GNSS. Achieved results are compared to the conventional IAR approach based on IF linear combinations and the so called Widelane (WL) and Narrowlane (NL) ambiguities. In addition, the resolution of inter-system integer ambiguities is analysed for common GNSS signal frequencies. The performance of the implemented IAR approach is demonstrated and analysed by the joint Precise Orbit Determination (POD) of multi-GNSS satellites based on fixed multi-frequency carrier phase ambiguities. The improvement of the satellite orbit and clock quality by fixing raw observation ambiguities confirms the successful implementation of the IAR approach based on raw observation processing. Multi-GNSS satellite orbits and clock offsets determined with this approach are compared to results generated with the conventional IF linear combination processing approach and independent external products. This comparison demonstrates an at least equivalent performance of the implemented IAR approach based on raw observation processing. In addition, the fixed raw observation ambiguities are used to investigate and discuss characteristics of multi-GNSS and multi-frequency phase biases

BDS GNSS for Earth Observation

For millennia, human communities have wondered about the possibility of observing phenomena in their surroundings, and in particular those affecting the Earth on which they live. More generally, it can be conceptually defined as Earth observation (EO) and is the collection of information about the biological, chemical and physical systems of planet Earth. It can be undertaken through sensors in direct contact with the ground or airborne platforms (such as weather balloons and stations) or remote-sensing technologies. However, the definition of EO has only become significant in the last 50 years, since it has been possible to send artificial satellites out of Earth’s orbit. Referring strictly to civil applications, satellites of this type were initially designed to provide satellite images; later, their purpose expanded to include the study of information on land characteristics, growing vegetation, crops, and environmental pollution. The data collected are used for several purposes, including the identification of natural resources and the production of accurate cartography. Satellite observations can cover the land, the atmosphere, and the oceans. Remote-sensing satellites may be equipped with passive instrumentation such as infrared or cameras for imaging the visible or active instrumentation such as radar. Generally, such satellites are non-geostationary satellites, i.e., they move at a certain speed along orbits inclined with respect to the Earth’s equatorial plane, often in polar orbit, at low or medium altitude, Low Earth Orbit (LEO) and Medium Earth Orbit (MEO), thus covering the entire Earth’s surface in a certain scan time (properly called ’temporal resolution’), i.e., in a certain number of orbits around the Earth. The first remote-sensing satellites were the American NASA/USGS Landsat Program; subsequently, the European: ENVISAT (ENVironmental SATellite), ERS (European Remote-Sensing satellite), RapidEye, the French SPOT (Satellite Pour l’Observation de laTerre), and the Canadian RADARSAT satellites were launched. The IKONOS, QuickBird, and GeoEye-1 satellites were dedicated to cartography. The WorldView-1 and WorldView-2 satellites and the COSMO-SkyMed system are more recent. The latest generation are the low payloads called Small Satellites, e.g., the Chinese BuFeng-1 and Fengyun-3 series. Also, Global Navigation Satellite Systems (GNSSs) have captured the attention of researchers worldwide for a multitude of Earth monitoring and exploration applications. On the other hand, over the past 40 years, GNSSs have become an essential part of many human activities. As is widely noted, there are currently four fully operational GNSSs; two of these were developed for military purposes (American NAVstar GPS and Russian GLONASS), whilst two others were developed for civil purposes such as the Chinese BeiDou satellite navigation system (BDS) and the European Galileo. In addition, many other regional GNSSs, such as the South Korean Regional Positioning System (KPS), the Japanese quasi-zenital satellite system (QZSS), and the Indian Regional Navigation Satellite System (IRNSS/NavIC), will become available in the next few years, which will have enormous potential for scientific applications and geomatics professionals. In addition to their traditional role of providing global positioning, navigation, and timing (PNT) information, GNSS navigation signals are now being used in new and innovative ways. Across the globe, new fields of scientific study are opening up to examine how signals can provide information about the characteristics of the atmosphere and even the surfaces from which they are reflected before being collected by a receiver. EO researchers monitor global environmental systems using in situ and remote monitoring tools. Their findings provide tools to support decision makers in various areas of interest, from security to the natural environment. GNSS signals are considered an important new source of information because they are a free, real-time, and globally available resource for the EO community

On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements

Carrier phase measurements are primary observations for GPS attitude determination. Although the satellite-related errors can be virtually eliminated by forming single differences, the baseline-related errors such as line biases are still present in the single-differenced carrier phase measurements. It is, therefore, difficult to resolve the single-differenced integer ambiguities due to the line biases. By forming double differences, the line biases of the single-differenced carrier phase measurements can be effectively removed. However, the main disadvantages of this method lie in the fact that the double-differenced measurements are mathematically correlated and consequently the attitude obtained from the double differences is noisy. This paper presents a new algorithm through which both single and double differences are used simultaneously to resolve these problems in real-time. The solution of the integer ambiguities can be obtained by searching for the most likely grid point in the attitude domain that is independent of the correlation with the double differences. Next, the line biases and corresponding single difference integer ambiguities can be resolved on the fly by using the noisy attitude solution obtained from the previous double difference procedure. In addition, the relationship between the physical signal path difference and the line bias is formed. A new method is also applied to derive the attitude angles through finding the optimal solution of the attitude matrix element. The proposed new procedure is validated using ground and flight tests. Results have demonstrated that the new algorithm is effective and can satisfy the requirement of real-time applications

Real-time relative positioning of spacecraft over long baselines

This paper deals with the problem of real-time onboard relative positioning of low Earth orbit spacecraft over long baselines using the Global Positioning System. Large inter-satellite separations, up to hundreds of kilometers, are of interest to multistatic and bistatic Synthetic Aperture Radar applications, in which highly accurate relative positioning may be required in spite of the long baseline. To compute the baseline with high accuracy the integer nature of dual-frequency, double-difference carrier-phase ambiguities can be exploited. However, the large inter-satellite separation complicates the integer ambiguities determination task due to the presence of significant differential ionospheric delays and broadcast ephemeris errors. To overcome this problem, an original approach is proposed, combining an extended Kalman filter with an integer least square estimator in a closed-loop scheme, capable of fast on-the-fly integer ambiguities resolution. These integer solutions are then used to compute the relative positions with a single-epoch kinematic least square algorithm that processes ionospheric-free combinations of de-biased carrier-phase measurements. Approach performance and robustness are assessed by using the flight data of the Gravity Recovery and Climate Experiment mission. Results show that the baseline can be computed in real-time with decimeter-level accuracy in different operating conditions

Visionless TRAC

This final report documents the activities during a sabbatical. Leo Monford was the principal NASA contact for this work. The work supported a flight experiment planned by the Space Research Consortium which investigated the potential of using a Targeting Reflective Alignment Concept (TRAC) sensor to automatically rendezvous satellites. Other work supported the Explorer flight experiment by providing TRAC reflectors for future rendezvous experiments. The third project initiated was a visionless TRAC sensing concept called the PSD concept

Reduction of initial convergence period in GPS PPP data processing

Precise Point Positioning (PPP) has become a popular technique to process data from GPS receivers by applying precise satellite orbit and clock information, along with other minor corrections to produce cm to dm-level positioning. Although PPP presents definite advantages such as operational flexibility and cost effectiveness for users, it requires 15-25 minutes initialization period as carrier-phase ambiguities converge to constant values and the solution reaches its optimal precision. Pseudorange multipath and noise are the largest remaining unmanaged errors source in PPP. It is proposed that by reducing these effects carrier-phase ambiguities will reach the correct steady state at an earlier time, thus reducing the convergence period of PPP. Given this problem, this study seeks to improve management of these pseudorange errors. The well-known multipath linear combination was used in two distinct ways: 1) to directly correct the raw pseudorange observables, and 2) to stochastically de-weight the pseudorange observables. Corrections to the observables were made in real-time using data from the day before, and post-processed using data from the same day. Post-processing has shown 4 7% improvement in the rate of convergence, as the pseudorange multipath and noise were effectively mitigated. A 36% improvement in the rate of convergence was noted when the pseudorange measurements were stochastically de-weighting using the multipath observable. The strength of this model is that it allows for real-time compensation of the effects of the pseudorange multipath and noise in the stochastic model