Improving Reliability and Assessing Performance of Global Navigation Satellite System Precise Point Positioning Ambiguity Resolution

Conventional Precise Point Positioning (PPP) has always required a relatively long initialization period (few tens of minutes at least) for the carrier-phase ambiguities to converge to constant values and for the solution to reach its optimal precision. The classical PPP convergence period is primarily caused by the estimation of the carrier-phase ambiguity from the relatively noisy pseudoranges and the estimation of atmospheric delay. If the underlying integer nature of the ambiguity is known, it can be resolved, thereby reducing the convergence time of conventional PPP. To recover the underlying integer nature of the carrier-phase ambiguities, different strategies for mitigating the satellite and receiver dependent equipment delays have been developed, and products made publicly available to enable ambiguity resolution without any baseline restrictions. There has been limited research within the scope of interoperability of the products, combining the products to improve reliability and assessment of ambiguity resolution within the scope of being an integrity indicator. This study seeks to develop strategies to enable each of these and examine their feasibility. The advantage of interoperability of the different PPP ambiguity resolution (PPP-AR) products would be to permit the PPP user to transform independently generated PPP-AR products to obtain multiple fixed solutions of comparable precision and accuracy. The ability to provide multiple solutions would increase the reliability of the solution for, e.g., real-time processing: if there were an outage in the generation of the PPP-AR products, the user could instantly switch streams to a different provider. The satellite clock combinations routinely produced within the International GNSS Service (IGS) currently disregard that analysis centers (ACs) provide products which enable ambiguity resolution. Users have been expected to choose either an IGS product which is a combined product from multiple ACs or select an individual AC solution which provides products that enable PPP-AR. The goal of the novel research presented was to develop and test a robust satellite clock combination preserving the integer nature of the carrier-phase ambiguities at the user end. mm-level differences were noted, which was expected as the strength lies mainly in its reliability and stable median performance and the combined product is better than or equivalent to any single ACs product in the combination process. As have been shown in relative positioning and PPP-AR, ambiguity resolution is critical for enabling cm-level positioning. However, what if specifications where at the few dm-level, such as 10 cm and 20 cm horizontal what role does ambiguity resolution play? The role of ambiguity resolution relies primarily on what are the user specifications. If the user specifications are at the few cm-level, ambiguity resolution is an asset as it improves convergence and solution stability. Whereas, if the users specification is at the few dm-level, ambiguity resolution offers limited improvement over the float solution. If the user has the resources to perform ambiguity resolution, even when the specifications are at the few dm-level, it should be utilized

Testing gravity with cold atom interferometry: Results and prospects

Atom interferometers have been developed in the last three decades as new powerful tools to investigate gravity. They were used for measuring the gravity acceleration, the gravity gradient, and the gravity-field curvature, for the determination of the gravitational constant, for the investigation of gravity at microscopic distances, to test the equivalence principle of general relativity and the theories of modified gravity, to probe the interplay between gravitational and quantum physics and to test quantum gravity models, to search for dark matter and dark energy, and they were proposed as new detectors for the observation of gravitational waves. Here I describe past and ongoing experiments with an outlook on what I think are the main prospects in this field and the potential to search for new physics

Precise Point Positioning Augmentation for Various Grades of Global Navigation Satellite System Hardware

The next generation of low-cost, dual-frequency, multi-constellation GNSS receivers, boards, chips and antennas are now quickly entering the market, offering to disrupt portions of the precise GNSS positioning industry with much lower cost hardware and promising to provide precise positioning to a wide range of consumers. The presented work provides a timely, novel and thorough investigation into the positioning performance promise. A systematic and rigorous set of experiments has been carried-out, collecting measurements from a wide array of low-cost, dual-frequency, multi-constellation GNSS boards, chips and antennas introduced in late 2018 and early 2019. These sensors range from dual-frequency, multi-constellation chips in smartphones to stand-alone chips and boards. In order to be comprehensive and realistic, these experiments were conducted in a number of static and kinematic benign, typical, suburban and urban environments. In terms of processing raw measurements from these sensors, the Precise Point Positioning (PPP) GNSS measurement processing mode was used. PPP has become the defacto GNSS positioning and navigation technique for scientific and engineering applications that require dm- to cm-level positioning in remote areas with few obstructions and provides for very efficient worldwide, wide-array augmentation corrections. To enhance solution accuracy, novel contributions were made through atmospheric constraints and the use of dual- and triple-frequency measurements to significantly reduce PPP convergence period. Applying PPP correction augmentations to smartphones and recently released low-cost equipment, novel analyses were made with significantly improved solution accuracy. Significant customization to the York-PPP GNSS measurement processing engine was necessary, especially in the quality control and residual analysis functions, in order to successfully process these datasets. Results for new smartphone sensors show positioning performance is typically at the few dm-level with a convergence period of approximately 40 minutes, which is 1 to 2 orders of magnitude better than standard point positioning. The GNSS chips and boards combined with higher-quality antennas produce positioning performance approaching geodetic quality. Under ideal conditions, carrier-phase ambiguities are resolvable. The results presented show a novel perspective and are very promising for the use of PPP (as well as RTK) in next-generation GNSS sensors for various application in smartphones, autonomous vehicles, Internet of things (IoT), etc

Riemannian Optimization for Convex and Non-Convex Signal Processing and Machine Learning Applications

The performance of most algorithms for signal processing and machine learning applications highly depends on the underlying optimization algorithms. Multiple techniques have been proposed for solving convex and non-convex problems such as interior-point methods and semidefinite programming. However, it is well known that these algorithms are not ideally suited for large-scale optimization with a high number of variables and/or constraints. This thesis exploits a novel optimization method, known as Riemannian optimization, for efficiently solving convex and non-convex problems with signal processing and machine learning applications. Unlike most optimization techniques whose complexities increase with the number of constraints, Riemannian methods smartly exploit the structure of the search space, a.k.a., the set of feasible solutions, to reduce the embedded dimension and efficiently solve optimization problems in a reasonable time. However, such efficiency comes at the expense of universality as the geometry of each manifold needs to be investigated individually. This thesis explains the steps of designing first and second-order Riemannian optimization methods for smooth matrix manifolds through the study and design of optimization algorithms for various applications. In particular, the paper is interested in contemporary applications in signal processing and machine learning, such as community detection, graph-based clustering, phase retrieval, and indoor and outdoor location determination. Simulation results are provided to attest to the efficiency of the proposed methods against popular generic and specialized solvers for each of the above applications

Drag-free and attitude control for the GOCE satellite

The paper concerns Drag-Free and Attitude Control of the European satellite Gravity field and steady-state Ocean Circulation Explorer (GOCE) during the science phase. Design has followed Embedded Model Control, where a spacecraft/environment discrete-time model becomes the realtime control core and is interfaced to actuators and sensors via tuneable feedback laws. Drag-free control implies cancelling non-gravitational forces and all torques, leaving the satellite to free fall subject only to gravity. In addition, for reasons of science, the spacecraft must be carefully aligned to the local orbital frame, retrieved from range and rate of a Global Positioning System receiver. Accurate drag-free and attitude control requires proportional and low-noise thrusting, which in turn raises the problem of propellant saving. Six-axis drag-free control is driven by accurate acceleration measurements provided by the mission payload. Their angular components must be combined with the star-tracker attitude so as to compensate accelerometer drift. Simulated results are presented and discusse

ARAIM for Vertical Guidance Using GPS and BeiDou

An advanced Receiver Autonomous Integrity Monitoring (ARAIM) approach is investigated when augmenting GPS satellites with the current regional BeiDou constellation. A procedure for integrity monitoring, including checking its availability, fault detection and exclusion, and integrity testing is presented. Fault modes and their probabilities using GPS and GPS+BeiDou are discussed. Testing of ARAIM for vertical guidance using real data in eight sites distributed globally (Australia, China, Netherlands, eastern Canada and Peru) show that the addition of the BeiDou constellation, despite the decreased preliminary confidence placed in its performance compared with GPS, results in a substantial improvement to ARAIM availability performance and a higher level of integrity, in particular at sites observing all of its current constellation (Australia and China). The improvement was less in sites that can only observe some or no GEO and IGSO satellites (Netherlands, Canada and Peru). However, the benefit of adding BeiDou to GPS at these sites is expected to substantially improve with full deployment of MEO satellites

Enhancing Precise Point Positioning with global and regional ionospheric models

In the last two decades Precise Point Positioning (PPP) has become a well-established stand-alone positioning method by means of Global Navigation Satellite Systems (GNSSs) for a wide range of applications. By using code and phase measurements from a single GNSS receiver and precise orbit and clock information derived from global or regional GNSS networks, highly precise positions can be obtained. One critical problem of the PPP technique is that a typical period of about 30 minutes is required to reach decimeter-level under normal conditions. In order to shorten the convergence time and improve the positioning accuracy, several PPP integer ambiguity resolution methods have been developed in the last decades. The common approach is to provide additional corrections on the existing PPP (clock) products. Although improvement in positioning accuracy is achieved by fixing ambiguities, the initialization time of PPP is not significantly reduced. Rapid convergence and ambiguity resolution in PPP is still a challenge. The key to instantaneous ambiguity resolution in relative positioning for short baselines lies in the a priori knowledge of the ionosphere. Therefore, the primary objective of this thesis is to investigate the introduction of global and regional ionospheric models as external constraints for enhancing PPP ambiguity resolution. The main work and contributions of this thesis are specified as follows: a. Mathematical modeling aspects for PPP are investigated. The procedures of estimating FCBs for integer ambiguity resolution in PPP based on standard ionosphere-free model and uncombined model are derived. The compatibility of FCBs estimated from both models are validated by comparing their wide-lane and narrow-lane float ambiguities as well as estimated FCBs using real data sets. b. The equivalence of three extended PPP integer ambiguity resolution models with capabilities of constraining external ionosphere information is derived. The method equivalence is demonstrated in three aspects: the ionospheric parameter, integer property recovery and the system redundancies. It is shown that all three models permit strengthening solutions by constraining ionospheric parameter from global and regional ionospheric models. The positioning results indicate that PPP can be further improved if external ionospheric information is available. c. Accuracies of regional atmospheric corrections for PPP ambiguity resolution are assessed. The focus is on the achievable accuracies of interpolated tropospheric and ionospheric delays derived from a typical regional network from ambiguity-fixed PPP solutions. The results indicate that centimeter level accuracies can be obtained for both tropospheric and ionospheric corrections and fast ambiguity resolution can be achieved after applying the regional atmospheric corrections. d. Ambiguity-fixing approaches based on uncombined PPP model are investigated, the one-step approach, in which L1 and L2 ambiguities are simultaneously fixed, and the two-step approach which involves sequentially fixing wide-lane and N1 ambiguities such that the fixed wide-lane ambiguities are applied as constraints to update remaining unknown parameters. Experiment results demonstrate that ambiguity-fixing time can be reduced using the two-step approach as compared to the one-step approach. e. Software system is developed to estimate satellite FCBs from global and regional GNSS network using both ionosphere-free and uncombined model. A PPP software package is developed to validate the contribution of global and regional ionospheric information on PPP ambiguity resolution

Cold atoms in space: community workshop summary and proposed road-map

We summarise the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with the European Space Agency (ESA) and national space and research funding agencies