Testing of a new single-frequency GNSS carrier phase attitude determination method: land, ship and aircraft experiments

Global navigation satellite system (GNSS) ambiguity resolution is the process of resolving the unknown cycle ambiguities of the carrier phase data as integers. The sole purpose of ambiguity resolution is to use the integer ambiguity constraints as a means of improving significantly on the precision of the remaining GNSS model parameters. In this contribution, we consider the problem of ambiguity resolution for GNSS attitude determination. We analyse the performance of a new ambiguity resolution method for GNSS attitude determination. As it will be shown, this method provides a numerically efficient, highly reliable and robust solution of the nonlinearly constrained integer least-squares GNSS compass estimators. The analyses have been done by means of a unique set of extensive experimental tests, using simulated as well as actual GNSS data and using receivers of different manufacturers and type as well as different platforms. The executed field tests cover two static land experiments, one in the Netherlands and one in Australia, and two dynamic experiments, a low-dynamics vessel experiment and high-dynamics aircraft experiment. In our analyses, we focus on stand-alone, unaided, single-frequency, single epoch attitude determination, as this is the most challenging case of GNSS compass processing

DIA-datasnooping and identifiability

In this contribution, we present and analyze datasnooping in the context of the DIA method. As the DIA method for the detection, identification and adaptation of mismodelling errors is concerned with estimation and testing, it is the combination of both that needs to be considered. This combination is rigorously captured by the DIA estimator. We discuss and analyze the DIA-datasnooping decision probabilities and the construction of the corresponding partitioning of misclosure space. We also investigate the circumstances under which two or more hypotheses are nonseparable in the identification step. By means of a theorem on the equivalence between the nonseparability of hypotheses and the inestimability of parameters, we demonstrate that one can forget about adapting the parameter vector for hypotheses that are nonseparable. However, as this concerns the complete vector and not necessarily functions of it, we also show that parameter functions may exist for which adaptation is still possible. It is shown how this adaptation looks like and how it changes the structure of the DIA estimator. To demonstrate the performance of the various elements of DIA-datasnooping, we apply the theory to some selected examples. We analyze how geometry changes in the measurement setup affect the testing procedure, by studying their partitioning of misclosure space, the decision probabilities and the minimal detectable and identifiable biases. The difference between these two minimal biases is highlighted by showing the difference between their corresponding contributing factors. We also show that if two alternative hypotheses, say (Formula presented.) and (Formula presented.), are nonseparable, the testing procedure may have different levels of sensitivity to (Formula presented.)-biases compared to the same (Formula presented.)-biases

Theory of carrier phase ambiguity resolution

Carrier phase ambiguity resolution is the key to high precision Global Navigation Satellite System (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. A proper handling of carrier phase ambiguity resolution requires a proper understanding of the underlying theory of integer inference. In this contribution a brief review is given of the probabilistic theory of integer ambiguity estimation. We describe the concept of ambiguity pull-in regions, introduce the class of admissible integer estimators, determine their probability mass functions and show how their variability affect the uncertainty in the so-called ‘fixed’ baseline solution. The theory is worked out in more detail for integer least-squares and integer bootstrapping. It is shown that the integer least-squares principle maximizes the probability of correct integer estimation. Sharp and easy-to-compute bounds are given for both the ambiguity success rate and the baseline’s probability of concentration. Finally the probability density function of the ambiguity residuals is determined. This allows one for the first time to formulate rigorous tests for the integerness of the parameters

A comparison of TCAR, CIR and LAMBDA GNSS ambiguity resolution

With the envisioned introduction of three-carrier GNSS's (modernized GPS, Galileo), new methods of ambiguity resolution have been developed. In this contribution we will compare two important candidate methods for triple-frequency ambiguity resolution with the already existing LAMBDA (Least-squares Ambiguity Decorrelation Adjustment) method; the TCAR (Three-Carrier Ambiguity Resolution) method; and the CIR (Cascading Integer Resolution) method. It will be shown that for their estimation principle, both TCAR and CIR rely on integer bootstrapping, whereas LAMBDA is based on integer least-squares, of which optimality has been proven, that is, highest probability of success. In TCAR and CIR pre-defined ambiguity transformation are used, whereas LAMBDA exploits the information content of the full ambiguity variance-covariance matrix, with statistical decorrelation the objective in constructing the ambiguity transformation. For the aspect of resolving the ambiguities, TCAR and CIR are designed for use with the geometry-free model. LAMBDA can intrinsically handle any GNSS model with integer ambiguities and thereby utilize satellite geometry to its benefit in geometry-based models

Fast Phase-Only Positioning with Triple-Frequency GPS

In this contribution, we study the phase-only ambiguity resolution and positioning performance of GPS for short baselines. It is well known that instantaneous (single-epoch) ambiguity resolution is possible when both phase and code (pseudorange) data are used. This requires, however, a benign multipath environment due to the severe effects multipath has on the code measurements. With phase-only processing, one would be free from such severe effects, be it that phase-only processing requires a change in receiver-satellite geometry, as a consequence of which it cannot be done instantaneously. It is thus of interest to know how much change in the relative receiver-satellite geometry is needed to achieve successful phase-only ambiguity resolution with correspondingly high precision baseline solutions. In this contribution, we study the two-epoch phase-only performance of single-, dual-, and triple-frequency GPS for varying time spans from 60 s down to 1 s. We demonstrate, empirically as well as formally, that fast phase-only very-precise positioning is indeed possible, and we explain the circumstances that make this possible. The formal analyses are also performed for a large area including Australia, a part of Asia, the Indian Ocean, and the Pacific Ocean. We remark that in this contribution "phase-only" refers to phase-only measurements in the observation model, while the code data are thus only used to compute the approximate values needed for linearizing the observation equations

Why impaired wellness may be inevitable in medicine, and why that may not be a bad thing

Context: A wellness crisis exists among physicians and medical trainees. High rates of burnout, depression, stress and other states of impaired wellness have driven a sense of urgency to create solutions, and the medical education community has mobilised impressively. However, we argue—and data suggest—that this rush to find solutions has outpaced our efforts to more fully understand the nature of impaired wellness in medicine. This, we believe, has led to the implementation of solutions informed by limited understanding of the problems we intend to solve. Methods: In this paper, we explore three contributors to this situation: (i) shaky definitions and conceptualisations of wellness, (ii) the predominance of deductive, quantitative research informing our understanding and current solutions, and (iii) the reliance on a ‘disease-focused’ approach to addressing impaired wellness in physicians and trainees. We discuss how these contributors have led to the current state of the science of wellness in medicine: one characterised by an expanding array of solutions built upon narrow conceptualisations of wellness and how it can be impaired. Discussion: Moving beyond the current state of the science on wellness in medicine will require three critical developments: (i) consistent use of clear definitions of wellness; (ii) expanding our methodologies to include those utilising direct interaction with participants; and (iii) moving beyond solutions informed by a disease-model approach. We propose a different way of thinking about wellness: one based on what we view as an inherent—and potentially unavoidable—risk of experiencing impairment during a career in medicine. We argue that efforts to extinguish and eliminate all states of impaired wellness may also eliminate opportunities to develop constructive coping mechanisms and future resilience, and that wellness may best be conceptualised as healthy and authentic engagement with the inevitable adversity of a career in medicine

Review and principles of PPP-RTK methods

PPP-RTK is integer ambiguity resolution-enabled precise point positioning. In this contribution, we present the principles of PPP-RTK, together with a review of different mechanizations that have been proposed in the literature. By application of S-system theory, the estimable parameters of the different methods are identified and compared. Their interpretation is essential for gaining a proper insight into PPP-RTK in general, and into the role of the PPP-RTK corrections in particular. We show that PPP-RTK is a relative technique for which the ‘single-receiver user’ integer ambiguities are in fact double-differenced ambiguities. We determine the transformational links between the different methods and their PPP-RTK corrections, thereby showing how different PPP-RTK methods can be mixed between network and users. We also present and discuss four different estimators of the PPP-RTK corrections. It is shown how they apply to the different PPP-RTK models, as well as why some of the proposed estimation methods cannot be accepted as PPP-RTK proper. We determine analytical expressions for the variance matrices of the ambiguity-fixed and ambiguity-float PPP-RTK corrections. This gives important insight into their precision, as well as allows us to discuss which parts of the PPP-RTK correction variance matrix are essential for the user and which are not

Integer Least-squares Theory for the GNSS Compass

Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to high-precision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable to models for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses non-quadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory presented is generally valid and it is not restricted to any particular GNSS or combination of GNSSs. Its general applicability also applies to the measurement scenarios (e.g. single-epoch vs. multi-epoch, or single-frequency vs. multi-frequency). In particular it is applicable to the most challenging case of unaided, single frequency, single epoch GNSS attitude determination. The success rate performance of the different methods is also illustrated