Precise point positioning using IGS orbit products

Abstract: The least-squares integer ambiguity decorrelation adjustment (LAMBDA) method is adapted for absolute positioning with satellite-satellite single difference measurements. The integer decorrelation transformation of LAMBDA takes only the covariance matrix of float ...

Carrier phase measurements are extremely accurate but ambiguous. The estimation of the integer ambiguities is in general split in two parts: A least-squares float solu-tion, which is obtained by disregarding the integer prop-erty, and the actual fixing. The latter one can be a simple ...

The maximum-marginal-a-posteriori success rate of statistical decision under multivariate Gaussian error distribution on an integer lattice is almost rigorously calculated by using union-bound approximation and Monte Carlo integration. These calculations are applied to the revelation of the various possible realizations of the reliable and short-period integer ambiguity resolution in precise carrier-phase relative positioning by GPS/GNSS. The theoretical foundation and efficient methodology are systematically developed, and two types of the enhancement of union-bound approximation are proposed and examined. The results revealed include an extremely high reliability under the condition of accurate carrier-phase measurements and a large number of visible satellites, its heavy degradation caused by the slight amount of differentiated ionospheric delays due to the nonvanishing baseline length between rover and reference receivers, and the advantages of the use of the multiple carrier frequencies. The succeeding initialization of the integer ambiguities is shown to overcome the disadvantageous condition of the nonvanishing baseline length effectively due to the reasonably assumed temporal and spatial constancy of differentiated ionospheric delays.

El objetivo de esta publicación es la de abordar el cálculo de una red GNSS y su posterior ajuste por medios sencillos y económicos.
El cálculo se va a hacer con el programa RTKPOST, que es un software libre; y el ajuste con una hoja de cálculo, en primera opción de forma generalizada; y después para unas condiciones muy particulares donde se va a desarrollar un algoritmo de ajuste que da excelentes resultados orientados a la topografía, y/o también como un preajuste para conocer de antemano el estado de los cálculos del postproceso y seleccionar o ponderar los datos antes de hacer un ajuste definitivo si se quiere alcanzar un mayor nivel.

I would like to thank Prof. Dr. sc. nat. Christoph Günther for the cordially incorporation to his team and for giving me the chance to fulfill my master thesis on this interesting research topic. I am greatly thankful to my supervisor, Patrick Henkel, for the allocation of this very interesting topic, for his always friendly and excellent provided support, and for his singular suggestions and ideas to improve this work. My sincere thanks to Kaspar Giger and Vladimir Kuryshev for their help and friendly discussions. Besides, I would like to thank the family of my girlfriend Linda, particularly her parents, for all their support in Germany. Especially, I want to thank my family, mainly my parents for all their support, trust and affection, as well as my sisters, Silvia and Perla, and my brothers, Goyo and Héctor, for all their help and advice. Finally, I want to express my special gratitude to mi lovely pequeñita Linda for her support in all respects and invaluable company.

The objective of this research was to develop new precise point positioning (PPP) processing models using triple-frequency GPS/Galileo observations. Different triple-frequency PPP models were developed including undifferenced, between-satellite single-difference (BSSD) and semi-decoupled PPP models. Additionally, a dual-frequency ionosphere-free undifferenced PPP model was developed. The performance of our developed PPP models was evaluated for both static and kinematic applications. To validate the proposed PPP models for static applications, triple-frequency GPS/Galileo observations spanning three successive days from eight globally distributed reference stations were acquired. Then, the observations were processed using the four static PPP solutions. It is found that the 3D positioning accuracy of the triple-frequency semi-decoupled, BSSD and undifferenced PPP models is enhanced after 10 min by about 50, 41 and 29%, respectively, compared with the dual-frequency undifferenced PPP...

In this work, the accuracy of using Single Point Positioning (SPP) and Precise Point Positioning (PPP) techniques is assessed in case of using long observational periods. Positioning using Differential Global Navigation Satellite System (DGNSS) technique is adopted to achieve reliable accurate results to be used as a reference in the evaluation process for both SPP and PPP positioning techniques. A number of neighboring International GNSS Service (IGS) stations were participated in this study for the differential positioning. GNSS data over one month for a continuous operating station at Faculty of Engineering, Ain Shams University were collected and processed on a daily basis in the SPP and PPP processing modes. In addition, DGNSS processing sessions using the IGS stations were carried out for each day of the month. The positional differences for both SPP and PPP solutions with respect to the DGNSS solutions were computed. The results showed that the SPP solutions had positional differences with mean value 23.4cm, while the PPP solutions had positional differences with mean value 12.7cm. In addition, by considering a unique monthly solution for each technique, the positional difference reaches to 15 cm in case of the SPP solution and 12.5 cm in case of the PPP solution. Thus, applications that do not require immediate positioning, such as wildlife management and insect infestation, can benefit from these results with low-cost hardware components. In addition, monitoring significant tectonic motions caused by earthquakes is another application in this context.

High-precision positioning from Global Navigation Satellite Systems (GNSS) has garnered increased interest due to growing demand in various applications, like autonomous car navigation and precision agriculture. Precise Point Positioning (PPP) offers a distinct advantage over differential techniques by enabling precise position determination of a GNSS rover receiver through the use of external corrections sourced from either the Internet or dedicated correction satellites. However, PPP’s implementation has been challenging due to the need to mitigate numerous GNSS error sources, many of which are eliminated in differential techniques such as Real-Time Kinematics (RTK) or overlooked in Standard Point Positioning (SPP). This paper extensively reviews PPP’s error sources, such as ionospheric delays, tropospheric delays, satellite orbit and clock errors, phase and code biases, and site displacement effects. Additionally, this article examines various PPP models and correction sources th...

This paper summarizes the main results obtained during the development of an Enhanced Precise Point Positioning (EPPP) Global Navigation Satellite Systems multifrequency user algorithm. The main innovations include the application of precise ionospheric corrections to facilitate the resolution of undifferenced carrier phase ambiguities, ambiguity validation, and integrity monitoring. The performance of the EPPP algorithm in terms of accuracy, convergence time, and integrity is demonstrated with actual GPS and simulated Galileo data. This can be achieved with very limited bandwidth requirements for EPPP users (less than 300 b/s for dual-frequency GPS data). Index Terms-Global Navigation Satellite Systems (GNSS), high precise positioning, integrity monitoring, Precise Point Positioning (PPP), real-time ionospheric corrections. I. INTRODUCTION P RECISE point Positioning is typically considered as the technique that allows a dual-frequency GPS user to determine a position at the decimeter error level (kinematic mode) and centimeter error level (static mode) with a single receiver. This is based on the real-time availability of satellite products (GPS orbits and clocks) that, by using data from a network of permanent GPS receivers and better modeling, are significantly more precise than those computed by the GPS control segment. Another important characteristic of the classical PPP user algorithm is the usage of the ionospheric-free combinations of observables to remove more than 99.9% of the slant ionospheric delay. These main observables, ionospheric-free carrier phases, and code observations for all of the satellites in view must be modeled by the user in a precise way by correcting the dependencies that are relevant at the centimeter level and estimating,

The present work investigates the positioning error of five Nigeria GNSS network stations during the geomagnetic storm of 24-27 October 2011, a sudden storm commencement (SSC) with disturbance storm time (Dst) minimum of -134 nT; and 7-10 October 2012, a gradual storm commencement (GSC) with Dst minimum -105 nT. Satellite data were obtained from Nigeria GNSS network stations and Dst values were obtained from World Data Center (WDC) for Geomagnetism Kyoto, Japan while the quiet period was selected with Ap index of zero (0) and one (1) for the two storms, respectively from the same World Data Center. RTKLIB (version 2.4.2), a GNSS analysis software, was used to determine the positioning of the stations during the selected storm period and quiet period and the results were analyzed using MATLAB. This investigation revealed that during the selected storm period, the positioning error of the stations increase; though the two storms do not show the same characteristics on GNSS positioning...

High-precision positioning from Global Navigation Satellite Systems (GNSS) has garnered increased interest due to growing demand in various applications, like autonomous car navigation and precision agriculture. Precise Point Positioning (PPP) offers a distinct advantage over differential techniques by enabling precise position determination of a GNSS rover receiver through the use of external corrections sourced from either the Internet or dedicated correction satellites. However, PPP’s implementation has been challenging due to the need to mitigate numerous GNSS error sources, many of which are eliminated in differential techniques such as Real-Time Kinematics (RTK) or overlooked in Standard Point Positioning (SPP). This paper extensively reviews PPP’s error sources, such as ionospheric delays, tropospheric delays, satellite orbit and clock errors, phase and code biases, and site displacement effects. Additionally, this article examines various PPP models and correction sources that can be employed to address these errors. A detailed discussion is provided on implementing the standard dual-frequency (DF)-PPP to achieve centimeter- or millimeter-level positioning accuracy. This paper includes experimental examples of PPP implementation results using static data from the International GNSS Service (IGS) station network and a kinematic road test based on the actual trajectory to showcase DF-PPP development for practical applications. By providing a fusion of theoretical insights with practical demonstrations, this comprehensive review offers readers a pragmatic perspective on the evolving field of Precise Point Positioning.

Original scientific paper Precise point positioning with satellite navigation signals requires knowledge of satellite code and phase biases. In this paper, a new multi-stage method is proposed for estimating of these biases using measurements from a geodetic network. The method first subtracts all available a priori knowledge on orbits, satellite clocks and multipath from the measurements to reduce their dynamics. Secondly, satellite phase biases, ionospheric delays, carrier phase integer ambiguities and the geometry combining all non-dispersive parameters are jointly estimated in a Kalman filter. Finally, the a posteriori geometry estimates are refined in a second Kalman filter for the computation of orbital errors, code biases and tropospheric delays. As the first Kalman filter introduces time correlation, a generalized Kalman filter for colored measurement noise is applied in the second stage. The proposed algorithm is applied to dual frequency GPS measurements from a local geodetic network in Germany. A remarkable bias stability with variations of less than 3 cm over 4 hours is observed.

He completed his master studies with highest distinction and a thesis on the"Estimation of GNSS satellite phase biases using a global network of reference stations". Currently, he is a PhD researcher at Fugro Intersite B.V. and TU Delft working on "Fast and reliable multi-GNSS PPP with integer ambiguity resolution", under the Horizon 2020 Marie Sklodowska-Curie TREASURE project. Christoph Günther studied theoretical physics at the Swiss Federal Institute of Technology in Zurich. He received his diploma in 1979 and completed his PhD in 1984. He worked on communication and information theory at Brown Boveri and Ascom Tech. From 1995, he led the development of mobile phones for GSM and later dual mode GSM/Satellite phones at Ascom. In 1999, he became head of the research department of Ericsson in Nuremberg. Since 2003, he is the director of the Institute of Communication and Navigation at the German Aerospace Center (DLR) and since December 2004, he additionally holds a Chair at the Technische Universität München (TUM). His research interests are in satellite navigation, communication and signal processing.

The application of precise point positioning with broadcast ephemerides (PPP-BCE) is discussed as an alternative to the established all-in-view technique for multi-GNSS time transfer. It combines the use of broadcast ephemerides with low-noise carrier-phase observations for accessing GNSS system time scales and Coordinated Universal Time (UTC) with improved precision, and can be employed on stationary as well as mobile receivers in offline or real-time analyses. Using calibrated timing receivers, the method is shown to provide estimates of the GNSS-to-GNSS time offsets (XYTOs) with an accuracy at the 2 ns level. In the absence of prior calibrations, 0.5 ns consistency across different stations is achieved for GPS, Galileo, and BeiDou-3 after adjustment of systematic biases in comparison with calibrated reference stations or broadcast XYTO values. Furthermore, access to GNSS-specific UTC realizations can be obtained through predictions of the UTC offset from GNSS system time as provided in the broadcast ephemerides of individual constellations. The overall quality of the PPP-BCE-derived receiver clock offsets from UTC is assessed using calibrated receivers at various timing laboratories along with BIPM-provided UTC-UTC(k) measurements. Over the 1.5 years covered in the study, an accuracy of 1.8 ns for GPS and 2.5 ns for Galileo is demonstrated. For BeiDou, a slightly worse accuracy of 3 ns is obtained for a single timing laboratory over 9 months.

The Nigerian Geodetic Reference Frame is defined by a number of Continuously Operating Reference Stations (CORS) that constitute the Nigerian GNSS Network (NIGNET). NIGNET is essential for planning and national development with the main goal of ensuring consistency in the geodetic framework both nationally and internationally. Currently, the strength of the network in terms of data reliability has not been adequately studied due to the fact that research into CORS in Nigeria is just evolving, which constitutes a limitation in its applications. Therefore, the aim of this research is to explore the reliability of the 3-dimensional coordinates of NIGNET to inform usability and adequacy for both scientific and practical applications. In particular, this study examines if the 3-dimensional coordinates of NIGNET are equally reliable in terms of positional accuracy. Accordingly, this study utilised GNSS data collected over a period of six years (2011 – 2016) from the network to compute the...

There are mainly two different orbital information, namely broadcast ephemerides and IGS final ephemerides (IGS rapid, ultra rapid, predicted and final ephemerides) used in the GPS positioning. The broadcast ephemerides used in practice and real time are obtained through assessments derived from the observations from the USA GPS reference stations. Broadcast ephemerides are formed (depending on GPS week) from satellite information and the accuracies they provide are adequate in many GPS applications. On the other hand, several parameters (for example, information about gravity area, improved satellite orbit information, etc.) need to be known in order to attain high accuracy in engineering and geodetic applications. Final ephemeris information can be downloaded from the related web sites via the internet. In this study, Keplerian motion and Keplerian orbital parameters will be explained briefly and extensive information about ephemerides and numerical applications will be given. Within this scope, for GPS satellites, ECEF coordinates of the satellites were computed using the broadcast ephemerides. The coordinates computed by using broadcast ephemerides were compared with the coordinates obtained from the IGS final orbits.

Since the establishment of the International GNSS Service (IGS) stations, they have been used as control stations for assigning the Precise point positioning (PPP) positions using one Global Navigation Satellite System (GNSS) receiver,
which has increased from day-to-day. There are some factors affecting the accuracy of PPP positioning. This research
aims to investigate the relation between the IGS distance and observed field points as well as to attempt to describe that
relation mathematically/statically. For the realization of that aim, two field points are fixed inside the Assiut University
campus and observed successively for a session of 24 hour observation. The position of each field point is assigned with
the help of each one of the available IGS station products. It must be known that these products are found after observations in three files (IGU, IGR, and final IGS), whereas IGU is used directly as real-time data (ultra-rapid), IGR (rapid) is
used through (17-41 hours) after observation, and (final IGS) used after 12 – 18 days. Coordinates and point errors of each
field points are computed and represented. It has been found that the errors have a positive relation with the available
IGS stations distances. The relation between these distances and point positioning errors have been represented and
described according to a model. The accuracy of the presented model is (R ≅ .98, x2 ≅ 2.5 × 10-3).

We develop new single-frequency PPP models, which combine the observations of the current GNSS constellations, including GPS, GLONASS, Galileo and BeiDou. Four single-frequency GNSS PPP models are developed, namely, the undifferenced single-frequency GNSS PPP model, the undifferenced ionosphere-free (IF) code and phase model known as quasi-phase model, the between-satellite-single-difference model (BSSD) and the between-satellite-singledifference ionosphere-free (BSSDIF) model. The IGS final precise products are used to account for the orbital and clock errors. For both undifferenced and BSSD models, the IGS final global ionospheric maps (GIM) model is used to correct the ionospheric delay. The GNSS inter-system biases are treated as additional unknowns in the estimation process for the undifferenced models, while a loosely coupled technique is used for the BSSD models. Various GNSS combinations are considered in the assessment for each PPP model, including GPS/GLONASS, GPS/Galileo, GPS/BeiDou and quad-constellation GNSS observations. It is shown that the multi-GNSS observations enhance the PPP solution accuracy in comparison with the GPS-only solution. Furthermore, the use of IF-PPP technique enhances the positioning accuracy by 25, 20, 24, 20 and 19% compared with the GIM-based PPP model for the GPS-only, GPS/GLONASS, GPS/Galileo, GPS/BeiDou and quad-GNSS combinations, respectively, for 1 h of GNSS data processing. In addition, an average of 15% positioning accuracy improvement can be obtained when the BSSD techniques are used compared with the undifferenced techniques. However, for 6 h of processing, comparable positioning accuracy can be obtained from all four singlefrequency models.

Denis Laurichesse is a member of the orbit determination service at CNES. He has been in charge of the DIOGENE GPS orbital navigation filter, and is now involved in navigation algorithms for GNSS systems. He is curre ntly in charge of the CNES IGS real time analysis center. H e was the co-recipient of the 2009 ION Burka award for hi s work on phase ambiguity resolution. Luca Cerri is a member of the orbit determination service at CNES, producing the operational precise orbits for several altimeter missions. He co-chairs the international Precise Orbit Determination science working team for the Ocean Surface Topography missions. Jean-Paul Berthias is a senior expert in Flight Dynamics and Orbit Determination at CNES. Flavien Mercier is a member of the orbit determination service at CNES. He participates also to the CNES/C LS IGS analysis center, for the formulation and improvemen ts of the 'GRG' solution. He is a senior expert in GPS proces sing for precise applications.

The on-board GNSS clock technology has evolved greatly in the last years, moving from the initial Caesium atomic clocks, to the latest Rubidium (Rb) and Passive Hydrogen-Maser (PHM) clocks. Both Rb and PHM technologies have proven to be highly predictable clocks, which opens the door to a series of improvements or modifications with respect to the “classical” Orbit Determination and Clock Synchronisation (ODTS) algorithms that would not only lead to the consequent and quite evident performance improvement, but it may also pave the way for the provision of advance services such as extended long-term predictions or an autonomous navigation service implemented on-board. The most common approach for any ODTS process is to estimate the satellite orbits and clock parameters by means of a Weighted Least-Square or a Kalman Filter processing, but whereas the satellite orbits are integrated by using a dynamical model with at most 15 parameters, the estimation of the satellite clock parameters...

In this manuscript, we introduce the Ionospheric Tomographic Common Clock (ITCC) model of undifferenced uncombined GNSS measurements. It is intended for improving the Wide Area precise positioning in a consistent and simple way in the multi-GNSS context, and without the need of external precise real-time products. This is the case, in particular, of the satellite clocks, which are estimated at the Wide Area GNSS network Central Processing Facility (CPF) referred to the reference receiver one; and the precise realtime ionospheric corrections, simultaneously computed under a voxel-based tomographic model with satellite clocks and other geodetic unknowns, from the uncombined and undifferenced pseudoranges and carrier phase measurements at the CPF from the Wide Area GNSS network area. The model, without fixing the carrier phase ambiguities for the time being (just constraining them by the simultaneous solution of both ionospheric and geometric components of the uncombined GNSS model), h...

The availability of signals on three or more frequencies from multiple GNSS constellations provides opportunities for improving precise point positioning (PPP) convergence time and accuracy, compared to when using dualfrequency observations from a single constellation. Although the multifrequency and multi-constellation (MFMC) data may be used with present day precise orbit and clock products, there are several biases that must be considered to get the best results. When using IGS products, the precise orbit and clock corrections are generated using dual-frequency ionosphere-free combinations of a ‘base’ pair of signals, and usage of other signals in the PPP model results in differential code biases (DCB). Other biases to consider include differential phase biases (DPB) for the satellites and receiver and satellite antenna offsets for individual frequencies. Integrating multiconstellation data introduces additional biases, such as inter-system hardware and time biases and inter-freq...

A set of Continuously Operating Reference Stations (CORS) distributed all over Nigeria constitutes the Nigerian GNSS Reference Network referred to  as NIGNET. Global Navigation Satellite System (GNSS) is a system tha  uses satellites for autonomous position determination, and is a critical  component of the modern-day geodetic infrastructure and services. Using CORS provide geodetic controls of comparable accuracy and a better alternative to the classical geodetic network. As the NIGNET infrastructure is utilised for different geodetic applications, it has become necessary to evaluate the suitability of the network data for the definition of a geodetic reference frame (GRF). This study utilised the technique of Precise Point Positioning (PPP) in position estimation, and time series analysis for temporal monitoring of the network. The sufficiency and adequacy of the NIGNET data archive was also evaluated against that of an International GNSS Service (IGS) Station. The temporal stabil...

This paper presents a URA/SISA analysis to support ARAIM based on a time-dependent statistical characterization of orbit and clock errors observations. For each individual GPS and Galileo satellites, by comparing precise orbits to broadcast ephemeris data, this work computes the Signal in Space Range Error (SISRE) which needs to be overbounded by the URA/SISA value included in the ISM. Over seven years of service history data for GPS and four months for Galielo are computed in this analysis, showing that range error is manly driven by satellite's clock performance. Satellites that historically have presented well behaved $\sigma_{SISRE}$ are equipped with stable clocks which display small error dispersion. A particular example is provided through GPS SVN65/PRN24 whose Cesium clock worsens satellite's performance as compared to the rest of the GPS block IIF equipped with Rubidium clocks. Time-dependent results show that orbit and clock error distributions are not zero mean on...

Navigation message designing with high accuracy guarantee is the key to efficient navigation message distribution in the global navigation satellite system (GNSS). Developing high accuracy-aware navigation message designing algorithms is an important topic. This paper investigates the high-accuracy navigation message designing problem with the message structure unchanged. The contributions made in this paper include a heuristic that employs the concept of the estimated range deviation (ERD) to improve the existing well-known navigation message on L1 frequency (NAV) of global positioning system (GPS) for good accuracy service; a numerical analysis approximation method (NAAM) to evaluate the range error due to truncation (RET) of different navigation messages; and a basic positioning parameters designing algorithm in the limited space allocation. Based on the predicted ultra-rapid data from the ultra-rapid data from the international GPS service for geodynamic (IGU), ERDs are generated in real time for error correction. Simulations show that the algorithms developed in this paper are general and flexible, and thus are applicable to NAV improvement and other navigation message designs. ª 2014 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

In this manuscript, we introduce the Ionospheric Tomographic Common Clock (ITCC) model of undifferenced uncombined GNSS measurements. It is intended for improving the Wide Area precise positioning in a consistent and simple way in the multi-GNSS context, and without the need of external precise real-time products. This is the case, in particular, of the satellite clocks, which are estimated at the Wide Area GNSS network Central Processing Facility (CPF) referred to the reference receiver one; and the precise realtime ionospheric corrections, simultaneously computed under a voxel-based tomographic model with satellite clocks and other geodetic unknowns, from the uncombined and undifferenced pseudoranges and carrier phase measurements at the CPF from the Wide Area GNSS network area. The model, without fixing the carrier phase ambiguities for the time being (just constraining them by the simultaneous solution of both ionospheric and geometric components of the uncombined GNSS model), h...

This paper describes a new model for precise point positioning (PPP), which overcomes the drawbacks of existing PPP models. This model is based on between-satellite single-difference (BSSD), which cancels out the receiver clock error, receiver initial phase bias, and receiver hardware delay. The decoupled clock (DC) corrections, which were provided by Natural Resources Canada (NRCan), were applied to account for code and carrier-phase satellite clock corrections, satellite hardware delay, and satellite initial phase bias. The results from three PPP models (namely, undifferenced-DC, BSSD, and BSSD-DC) were compared with the traditional (i.e., undifferenced) PPP solution. It is shown that the proposed BSSD models improves the PPP convergence time by up to 50% and improves the solution precision by more than 60% in comparison with the traditional PPP model.

The Federal Government of Nigeria through the Office of the Surveyor General of the Federation (OSGoF) set up surveying infrastructure throughout the country known as the NIGerian Reference GNSS NETwork (NIGNET). The NIGNET is a network of Global Navigation Satellite System (GNSS) Continuously Operating Reference Stations (CORS) set up at different locations in Nigeria for surveying and mapping. They are satellite tracking stations operating 24 hours a day providing positional solutions. As signals from the satellite pass through the different layers of the atmosphere (ionosphere and troposphere), they are refracted thus, causing delay on the arrival of the signal, which in-turns affect positioning in the horizontal and height component. The most dominant spatially correlated bias is the tropospheric effect on the GNSS satellite signals. Several global tropospheric delay models are in use by different countries to mitigate the biases cause by the troposphere. This study therefore ai...

By convention, IGS precise clock products are computed using the ionosphere-free linear combination. Due to the broad use of IGS products, this convention is exploited in PPP-RTK models not using such a linear combination. So, in different carrier phase combinations, the code hardware biases are contained in different combinations, thus making the problem of separating biases from integer ambiguities more complicated. In this paper, we proposed a novel clock parameterization which allows facilitating this problem. Based on the proposed parameterization, we derived a dual-frequency PPP-RTK model for the undifferenced measurements and assessed this model for the static positioning case in terms of positioning accuracy, convergence, and ambiguity resolution performance. The results showed that a cm-level accuracy level is achievable with the derived models with nearly instant convergence and almost 100% successfully resolved ambiguities. We demonstrated the use of this parameterization...

The Federal Government of Nigeria through the Office of the Surveyor General of the Federation (OSGoF) set up surveying infrastructure throughout the country known as the NIGerian Reference GNSS NETwork (NIGNET). The NIGNET is a network of Global Navigation Satellite System (GNSS) Continuously Operating Reference Stations (CORS) set up at different locations in Nigeria for surveying and mapping. They are satellite tracking stations operating 24 hours a day providing positional solutions. As signals from the satellite pass through the different layers of the atmosphere (ionosphere and troposphere), they are refracted thus, causing delay on the arrival of the signal, which in-turns affect positioning in the horizontal and height component. The most dominant spatially correlated bias is the tropospheric effect on the GNSS satellite signals. Several global tropospheric delay models are in use by different countries to mitigate the biases cause by the troposphere. This study therefore ai...

The quest for the use of GNSS in developing countries is on the rise following the realization of its numerous advantages over the conventional methods of positioning, navigation and timing. Africa's attempt to harness this technology has made it imperative to investigate the regional problems associated with its implementation by its member states, which constitute the AFREF. This study goes beyond the establishment of a GNSS reference network in Ghana by investigating and finding solutions to some of the regional problems associated with its implementation. The problem of turbulent atmospheric conditions which includes the severe ionospheric fluctuations and the erratic tropospheric conditions coupled with the sparsely populated base stations has led to the development of a new concept of correction, the Corridor Correction, which is able to correct the atmospheric effect comparable with the established concepts like the Virtual Reference Station, VRS, Flaechen-Korrektur-Param...

The Global Navigation Satellite System (GNSS) has been a very integral part of our modern-day communications and navigation. Initially it was limited for military systems only but now with involvement of both commercial and civilian access to the data the possibility of development for new applications is endless. So far only there has been a very limited number of Global Systems and a few regional systems which is likely to change in the coming days as more countries are looking to make their presence in Earth's orbit. The applications of GNSS are helping enormously for mapping, surveying, precise positioning, ionosphere research, earth data monitoring and more. But with the newly emerging trends and innovations in the commercial and research and development by so many private enterprises the need for GNSS will be greater than ever before. More devices will need the use of GNSS to integrate for various applications. The fast-paced innovation has led to the democratization of the system to a large extent. With more development and adoptions of next generation autonomous technology such as driverless cars, automatic traffic management system, more access to high-speed global network, GNSS will play and will have more impact on everyday life in the coming years. Thus, it is important to start finding use cases that can have a large-scale impact. This paper focuses specifically on the use case of GNSS for ground-based measurements that can be further developed for more niche applications. The GNSS receiver and the data used in the study is located at

Wide-lane (WL) uncalibrated phase delay (UPD) is usually derived from Melbourne–Wübbena (MW) linear combination and is a prerequisite in Global Navigation Satellite Systems (GNSS) precise point positioning (PPP) ambiguity resolution (AR). MW is a linear combination of pseudorange and phase, and the accuracy is limited by the larger pseudorange noise which is about one hundred times of the carrier phase noise. However, there exist inconsistent pseudorange biases which may have detrimental effect on the WL UPD estimation, and further degrade user-side ambiguity fixing. Currently, only the large part of pseudorange biases, e.g., the differential code bias (DCB), are available and corrected in PPP-AR, while the receiver-type-dependent biases have not yet been considered. Ignoring such kind of bias, which could be up to 20 cm, will cause the ambiguity fixing failure, or even worse, the incorrect ambiguity fixing. In this study, we demonstrate the receiver-type-dependent WL UPD biases and...

Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these parameters with a global network of reference stations is presented. The method processes uncombined and undifferenced measurements of an arbitrary number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense global networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm. Keywords Network solution • Satellite phase biases • Satellite position and clock corrections • Ambiguity fixing Kalman filter Kalman filter Ambiguity fixing Ambiguity fixing Kalman filter Ambiguity fixing Least−squares Estimation Ambiguity fixing Cluster 2 Cluster 1 reference cluster Combination of individual clusters Kalman filter Cluster C Ambiguity fixing Cluster optimization Coordinates of reference stations position, clock and phase bias corrections of satellites combined position, clock and phase bias corrections of all satellites

obtained a Master of Science in Aerospace Engineering from University of Sevilla (Spain) in 2013. In parallel, as a double degree student, he gained his Master in Mechanical and Aerospace Engineering from Illinois Institute of Technology (IIT) in 2013. Currently he is part of the staff at the Institute of Communications and Navigation at German Aerospace Center (DLR) and a PhD candidate at the Institute of Navigation at the RWTH Aachen University. His research focuses on new advanced algorithms for multiconstellation Residual Autonomous Integrity Monitoring (RAIM). Dr. Michael Meurer received the diploma in electrical engineering and the PhD degree from the University of Kaiserslautern, Germany. After graduation, he joined the Research Group for Radio Communications at the Technical University of Kaiserslautern, Germany, as a senior key researcher, where he was involved in various international and national projects in the field of communications and navigation both as project coordinator and as technical contributor. From 2003 till 2013, Dr. Meurer was active as a senior lecturer and Associate Professor (PD) at the same university. Since 2006 Dr. Meurer is with the German Aerospace Centre (DLR), Institute of Communications and Navigation, where he is the director of the Department of Navigation and of the center of excellence for satellite navigation. In addition, since 2013 he is a professor of electrical engineering and director of the Institute of Navigation at the RWTH Aachen University. His current research interests include GNSS signals, GNSS receivers, interference and spoofing mitigation and navigation for safety-critical applications. Dr. Ilaria Martini received the Master Degree in telecommunication engineering and the Ph.D. in information technology from the University of Florence, Italy. She was at the Galileo Project Office of ESA/ESTEC in 2003, working on the performance of the Galileo Integrity Processing Facility. She was research associate in 2004 at the University of Florence and in 2005 at the the Federal Armed Forces Germany in Munich. In 2006 she joined the navigation department of Ifen GmbH in Munich. Since 2012 she works as research associate in the Institute of Communication and Navigation at the German Aerospace Center (DLR), Oberpfaffenhofen. Her main area of interest is GNSS Integrity Monitoring.

Precise point positioning (PPP), considered an alternative to differential positioning, is used in a significantly increased number of applications. Its integration into many practical areas is, however, slowed down by the long convergence time required in order to obtain cm-level accuracy. This drawback is caused by the difficulty in fixing carrier-phase ambiguities to integers. As opposed to the differential mode, where many error sources are eliminated or greatly reduced, PPP has to properly account for all of them. Some of these error sources, such as code and phase biases, are complex to model as they tend to merge with the ambiguity parameters during the estimation process, leading to unsuccessful ambiguity resolution. This paper focuses on the receiver and satellite phase bias calibration required to recover the integer nature of carrier-phase ambiguities. A proper estimation of these biases would allow correcting the measurements and using the ambiguity resolution techniques...

Integer ambiguity resolution at a single station can be achieved by introducing predetermined uncalibrated phase delays (UPDs) into the float ambiguity estimates of precise point positioning (PPP). This integer resolution technique has the potential of leading to a PPP-RTK (Real-Time Kinematic) model where PPP provides rapid convergence to a reliable centimeter-level positioning accuracy based on an RTK reference network. Nonetheless, implementing this model is technically subject to how rapidly we can fix wide-lane ambiguities, stabilize narrow-lane UPD estimates, and achieve the first ambiguity-fixed solution. To investigate these issues, we used seven days of 1-Hz sampling GPS data at 91 stations across Europe. We find that at least 10 minutes of observations are required for most receiver types to reliably fix about 90% of wide-lane ambiguities corresponding to high elevations, and over 20 minutes to fix about 90% of those corresponding to low elevations. Moreover, several tens of minutes are usually required for a regional network before a narrow-lane UPD estimate stabilizes to an accuracy of far better than 0.1 cycles. Finally, for hourly data, ambiguity resolution can significantly improve the accuracy of epoch-wise position estimates from 13.7, 7.1 and 11.4 cm to 0.8, 0.9 and 2.5 cm for the East, North and Up components, respectively, but a few tens of minutes is required to achieve the first ambiguity-fixed solution. Therefore, from the timeliness aspect, our PPP-RTK model currently cannot satisfy the critical requirement of instantaneous precise positioning where ambiguity-fixed solutions have to be achieved within at most a few seconds. However, this model can still be potentially applied to some nearreal-time remote sensing applications, such as the GPS meteorology.

Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests OPEN ACCESS are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF.

The GPS observables (code and phase) can be used to compute the orbits of low earth orbiting (LEO) satellites employing kinematic approach of orbit determination, which is based on GPS satellite to satellite tracking. A precise GPS receiver is installed onboard the LEO satellite, while ensuring the continuous link between GPS and navigated satellites, code and phase observables for L1 and L2 frequencies (L1 and L2 are carrier frequencies for GPS signal at 1575.42 and 1227.60 MHz respectively) are recorded to compute the orbit. In this master's thesis work, GPS data from Challenging Mini-satellite Payload (CHAMP) is used for its orbit determination for the epoch day of January 1st 2002. The orbit of CHAMP is computed from the GPS data and ionospheric effects are removed by frequency combination. Earth centered Earth fixed (ECEF) positions are transformed to satellite ground tracks, latitude, longitude and altitude for visualization and analysis. Further, the orbits of CHAMP for the same epoch day are computed using the satellite tool kit (STK) employing simplified general perturbations (SGP4) and a high precision orbit propagator (HPOP). Results from both techniques (GPS computed orbit and STK computed orbit) are compared. Computed ECEF X, Y and Z coordinates using our algorithm have standard deviations of about 4 metres. Also the P1 and P2 (P1 and P2 are pseudorange observations on L1 and L2 GPS signals respectively) observation residuals are within range of few metres (below ±10 metres) having some spikes up to ±50m. Since the SGP4 propagator of the satellite tool kit inherits two line element (TLE) errors which can be up to 600 metres itself according to Mason (2009), therefore this propagator is utilized only for initial computation. After this initial computation, only the HPOP is used for orbit prediction and comparison. The STK/HPOP is accurate enough if proper model of spacecraft is provided for orbit propagation. Chao et al. (2000) have found that HPOP can be accurate up to millimeter level. Therefore we have compared our results with HPOP and it is observed that orbits computed using GPS data are agreeing to the HPOP predicted results. The maximum observed difference

The availability in real time of GNSS satellites orbits, clock corrections and code and phase biases provided the possibility of application of Real Time Precise Point Positioning (RTPPP). This paper presents the methodology concerning RTPPP and application to kinematic trajectories of airplane flight tests, but without using the carrier phase bias. So, it is PPP float solution. It requires RT positioning estimation, task that most of time presents certain difficulties due to loss of communication or of satellites during maneuvers of the airplane. However, if the corrections become unavailable for a certain period of time, the system starts using the ultra-rapid IGS orbits. The experiments were accomplished taking into account a case simulating RT and another in fact RT, but storing data and corrections for post processing. The PPP solutions obtained either simulating RT or in RT were compared against the PPP post processed solution that uses the final clock and orbit corrections. Then, statistics were generated to analyze the quality of both results.

Utilization of IGS Information for Improved Real-time GPS Positioning by Francis James Barchesky The estimation of a precise user's position is a difficult and complex problem. In addition, the use of geodetic grade position instruments is often not possible for Small Unmanned Aerial Vehicle (SUAV) systems. However, the availability of the global navigation satellite system (GNSS) and International GNSS Service (IGS) predicted product data allows an attempt to increase the precision of a navigation algorithm, which is the aim in this thesis. The utilization of this information within an algorithm work environment is a complex problem, requiring the development of multiple tools in order to use and access the IGS raw and product data. Therefore, the overall goal of this research project was the development of these tools using MATLAB®. The IGS information provided by these tools allows access to a particular set of product and raw data files. The available predicted product data is used to increase the precision of the position estimate for a real-time application. Within this, the conversion from a long time interval to a fast update rate was determined. The use of this information requires these tools to also include important orbit determinations of the GPS satellites. The use of only precise satellite position information from the developed M ATLAB tools is evaluated by a comparison of a position estimation algorithm using recorded satellite position information and the developed satellite position information from the IGS predicted data. The results show an increase in performance of position estimation with the use of the created MATLAB tools. A discussion in how the use of the created tools could further be expanded to increase the accuracy and precision of a position estimation algorithm is presented. iii Acknowledgements I would like to thank Dr. Marcello Napolitano, my research advisor, for your support, guidance and teachings throughout my education. I greatly appreciate all that you have done for me personally and my education. Dr. Gu, throughout this process our discussions about this graduate project have been invaluable and greatly appreciated. I feel from these a significant improvement has been made within this project. I would like to also thank my other committee member, Dr. Powsiri Klinkhachorn for providing me with helpful feedback. Dr. Srikanth Gururajan and Dr. Brad Seanor your support and encouragement throughout my graduate studies and within the WVU flight testing activities have been greatly appreciated. Thank you so much Steve Raque for your support, advice, and help throughout my undergraduate and graduate studies. To my fellow graduate student in the group: Jason Gross your advisement, discussions, and constant help were all appreciated, Matt Rhudy, your constant help and insight about problems and writing was valued, Matteo Guerra our conversions and help with concepts of GPS was very useful. Zach Merceruio, and Marc Gramlich your construction and development of the PAC aircraft was an immeasurable task, I appreciate you and your work. Thank you Haiyang Chao for your development and help with avionics, it has been appreciated. Kerri Phillips, thank you for all your work in PID and advice. I want to thank Daniele Tancredi, your help and presence was cherished. Giovanni De Nunzio, thank you for your advice and help. Matteo Dariol your insight with respect to many issues was useful and appreciated. Thank you Amanda McGrail, your work and helpfulness was valued. My girlfriend, Whitney Swesey, words cannot describe how appreciative I am for your love and support. To my family your love, consideration, enthusiasm and advisement has been inspirational to me.

We introduce a simple single-band receiver clock jump and cycle slip (CJCS) detection and correction algorithm suitable for a standalone single-frequency Global Navigation Satellite System (GNSS) receiver. The real-time algorithm involves using an adaptive time differencing technique for the generation of adaptive differenced sequences of single-frequency code and phase observations. The sequences are used for determining thresholds and for the detection and determination of a receiver clock jump and cycle slips. The cycle slip values are fixed by rounding-up float values obtained via weighted least squares adjustment, following the elimination of the receiver's high-order clock drift at every epoch. The performance of this new technique was investigated with simulated cycle slip values and with different types of receiver clock jumps at millisecond and microsecond levels. It achieved 100% detection and correction of all types of receiver clock jumps; between 97 to 100% cycle slip detection; and between 96.9 to 100% cycle slip correction including cycle slips of ±1 cycle, for different rates of observations acquired by different fixed and mobile GNSS receivers. The algorithm thus facilitates precise timing and positioning on standalone low-cost single-frequency GNSS devices.

The "Innovation" column and GPS World are celebrating a birthday. With this issue, we have started the 25th year of publication of the magazine and the column, which appeared in the very first issue and has been a regular feature ever since. Over the years, we have seen many developments in GPS positioning, navigation, and timing with a fair number documented in the pages of this column. In January 1990, GPS and GLONASS receivers were still in their infancy. Or perhaps their toddler years. But significant advances in receiver design had already been made since the introduction around 1980 of the first commercially available GPS receiver, the STI-5010, built by Stanford Telecommunications, Inc. It was a dual-frequency, C/A-and P-code, slowsequencing receiver. Cycling through four satellites took about five minutes, and the receiver unit alone required about 30 centimeters of rack space. By 1990, a number of manufacturers were offering single or dual frequency receivers for positioning, navigation, and timing applications. Already, the first handheld receiver was on the market, the Magellan NAV 1000. Its single sequencing channel could track four satellites. Receiver development has advanced significantly over the intervening 25 years with high-grade multiple frequency, multiple signal, multiple constellation GNSS receivers available from a number of manufacturers, which can record or stream measurements at data rates up to 100 Hz. Consumer-grade receivers have proliferated thanks, in part, to miniaturization of receiver chips and modules. With virtually every cell phone now equipped with GPS, there are over a billion GPS users worldwide. And the chips keep getting smaller. Complete receivers on a chip with an area of less than one centimeter squared are common place. Will the "GPS dot" be in our near future? The algorithms and methods used to obtain GPS-based positions have evolved over the years, too. By 1990, we already had double-difference carrier-phase processing for precise positioning. But the technique was typically applied in postprocessing of collected data. It is still often done that way today. But now, we also have the real-time kinematic (or RTK) technique to achieve similar positioning accuracies in real time and the non-differenced precise point positioning technique, which does not need base stations and which is also being developed for real-time operation. But in all this time, we have always had a "fly in the ointment" when using carrier-phase observations: cycle slips. These are discontinuities in the time series of carrier-phase measurements due to the receiver temporarily losing lock on the carrier of a GPS signal caused by signal blockage, for example. Unless cycle slips are repaired or otherwise dealt with, reduction in positioning accuracy ensues. Scientists and engineers have developed several ways of handling cycle slips not all of which are capable of working in real time. But now, a team of university researchers has developed a technique combining GPS receivers with an inexpensive inertial measuring unit to detect and repair cycle slips with the potential to operate in real time. They describe their system in this month's column.

The development of a global navigation satellite system (GNSS) brings the benefit of positioning, navigation and timing (PNT) services with three or even more available frequency signals. This paper developed five-system multi-frequency precise point positioning (PPP) models based on mathematical and stochastic models. Static positioning performances were evaluated and analyzed with multi-GNSS experiment (MGEX) network datasets and a vehicle-borne kinematic experiment was conducted to verify the kinematic PPP performances. In addition, the receiver clock, zenith tropospheric delay (ZTD), inter-frequency bias (IFB) and differential code bias (DCB) estimates were discussed. Results show that the triple-frequency PPP performances perform slightly better than the dual-frequency solutions, apart from the GPS-related PPP models based on a single ionosphere-free (IF) combined measurement. By introducing the external ionospheric products, the mean convergence time is reduced. For instance, the mean convergence time of ionosphere-constrained (IC) multi-frequency PPP is reduced by 7.4% from 35.7 to 33.1 min and by 19.0% from 7.8 to 6.3 min, for Galileo-only and five-constellation solutions, respectively, compared with dual-frequency IF PPP models. Similarly, the kinematic PPP can also achieve improved performances with more frequency signals and multi-GNSS observations.

With the development of the International GNSS Service, whose primary object is to provide highest quality data and products for research, education and multidisciplinary application, the concept of Precise Point Positioning began to receive more and more interest on the problem called “positioning”. Nowadays because of this development, the PPP technique it started to grow on the detriment of the relative GNSS positioning. PPP, it is able to offer point determination by processing undifferenced dual frequency receiver, combine with precise orbit and clock corrections offered by IGS to obtain centimeter accuracy. The aim of this paper is to make a comparative study between Precise Point Positioning (PPP) versus relative positioning under different conditions. The conditions or constrains used in this study are observation period and base line length. We apply base line technique in relative solution to spot the errors without adjustment that applied in network technique.