Hypothesis Testing for Resolving Integer Ambiguity in GPS

Wolfe, Jonathan D.; Williamson, Walton R.; Speyer, Jason L.

doi:10.1002/j.2161-4296.2003.tb00317.x

Cited by 18 publications

(10 citation statements)

References 15 publications

(20 reference statements)

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“…Estimating the GNSS ambiguities in the multiple model approach for fixed models leads recursively to the same results as the Bayesian approach, see (Betti et al 1993) and (Gundlich, Koch 2002), that introduces the ambiguities as discrete integer random variables. In the context with ambiguity resolution the multiple model approach for switching models is used to model cycle slips, see Chen and Harigae (2001) and Wolfe et al (2001). In the following an overview of the multiple model approaches is given in the context of ambiguity resolution.…”

Section: Introductionmentioning

confidence: 99%

“…The technique of fixed multiple models was applied for ambiguity resolution already by Brown and Hwang (1983) as multiple model adaptive estimation or Magill adaptive filter and modified in Henderson (2001). Wolfe et al (2001) refer to the multiple model approach for fixed models as multiple hypothesis Wald sequential probability ratio test. Estimating the GNSS ambiguities in the multiple model approach for fixed models leads recursively to the same results as the Bayesian approach, see (Betti et al 1993) and (Gundlich, Koch 2002), that introduces the ambiguities as discrete integer random variables.…”

Section: Introductionmentioning

confidence: 99%

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Multiple Models — Fixed, Switching, Interacting

Gundlich

Teunissen

2004

International Association of Geodesy Symposia

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Abstract. In dynamic models the dynamic and the observation equations are based on a known system model. The multiple model approach introduces uncertainties about the system model by a set of possible system models. In the multiple model approach for fixed models the true system does not change during the whole observation process, wheareas in the approach for switching models a jump from one model to another is allowed. In the later case the state estimation usually has to be approximated, e.g. by so-called interacting multiple models. The multiple model approach for fixed, switching and interacting models are presented and their application for GNSS ambiguity resolution is discussed, but open questions still remain.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiple Models — Fixed, Switching, Interacting

Gundlich

Teunissen

2004

International Association of Geodesy Symposia

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“…(25) is introduced into Eqs. (18)(19)(20), then the controllable state space is [E A9 E q ,E qi ,e 1 ,e 2 ,e 3 ,f 1 J 29 f 3 ].…”

Section: B Linear Quadratic Regulator Synthesis Proceduresmentioning

confidence: 99%

Guidance, Control and Navigation for Aerospace Systems: Charles Stark Draper's influence on a Personal Perspective

Speyer

2013

AIAA Guidance, Navigation, and Control (GNC) Conference

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From a personal historical perspective, guidance, control, and navigation algorithms and their implementation into various classes of aerospace vehicles are described within the context of the prevalent system theoretic issues. This personal history is shown to be highly influenced by Charles Stark Draper, through his activities as Head of the Aeronautics and Astronautics Department and his Instrumentation Laboratory. The focus will be on the development of theory which led to actual flight tests or fielded systems. These developments include matrix optimization methods applied to the autonomous navigation system for Apollo, the evolution of modern control methods for guidance of the Patriot missile and of the synthesis of a multi-input/multi-output flight control compensator for the AFTI-F16, the development of model based fault detection, isolation, and identification schemes with application to the California PATH (Partners for Advanced Transportation TecHnology), and the development of relative navigation system based on differential carrier phase GPS, tested on F-18s at NASA Dryden. I. In the BeginningWhen I was an undergraduate student in the Department of Aeronautics and Astronautics at MIT, Doc Draper was the Department Head. Doc Draper instituted into the curriculum a course in classical control that I took in the spring of 1959. I took this course from Professor Walter McKay in my junior year, never noting that he and Draper wrote an early book on classical control. 1 This book, possibly the first comprehensive text on classical control, organized this new technology for engineers to understand and apply such topics as transfer functions, root locus, Bode plots, the Nyquist criterion, Routh-Hurwitz stability criteria, and gain and phase margin for robust control design. Even more astounding was a three week period spent on stochastic processes based on power spectral density, given by Wally Van Dervelde. I was sufficiently inspired that I took a graduate course in applications of control to aeronautical system in my senior year and wrote my undergraduate thesis on the application of the Bushaw minimum time problem to the control of the lateral motion of an aircraft. This began my long career in system and control theory.After graduation from MIT, I went to work for the Boeing Company in Seattle, starting in August, 1960. Although my direct boss was not a controls specialist, my lead engineer, Raymond (Ray) Morth, was excited and grew knowledgeable about the control theories that were emerging in the late 50's and very early 60's. From Ray I learned about the work of Rudolf Kalman, especially his extension of the Wiener filter to linear time-varying systems; Richard Bellman, whose development of dynamic programming extended Hamilton-Jacobi theory to stochastic systems, L. S. Pontryagin, whose development of the maximum principle generalized the Weierstrass condition, Halcombe Laning and Richard Battin, who wrote about constructing Earth-Moon trajectories, and Arthur Bryson and Henry Kelley, who were inde...

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“…However, this unknown integer ambiguity cannot be computed directly in this form, because the term r ij 12 is not known either. Therefore, the hypothesis tests over the ambiguity candidates are usually employed [12].…”

Section: B Difference Operationmentioning

confidence: 99%

Collision Detection System Based on Differential Carrier-Phase Global Positioning System Broadcasts

Hwang

Speyer

2009

Journal of Aircraft

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The Global Positioning System has great potential for the development of new collision avoidance systems and is being considered for the next-generation traffic alert and collision avoidance system. The navigation states estimated by Global Positioning System code information can be broadcast to nearby airplanes via the current traffic alert and collision avoidance system equipment. In this paper, the problem of aircraft collision detection system using Global Positioning System carrier-phase information is addressed. A new approach to the carrier-phase-based relative position estimation problem is proposed that uses particle filters in which the samples are drawn from Cartesian position space coordinates. The particle filters with position samples makes the Global Positioning System carrierphase-based position estimation algorithm robust and practical in that the algorithm is not sensitive to changes of Global Positioning System satellites and cycle slips. The same algorithm can be used to estimate the vehicle attitude if multiple Global Positioning System antennas are used. For a reliable and enhanced collision avoidance system, threedimensional trajectories are projected using relative position, velocity, and attitude estimates. It is shown that the performance of the Global Positioning System carrier-phase-based collision-detecting algorithm meets the accuracy requirements for a precise approach of flight with significantly less collision false alarms and no miss alarms.

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Hypothesis Testing for Resolving Integer Ambiguity in GPS

Cited by 18 publications

References 15 publications

Multiple Models — Fixed, Switching, Interacting

Multiple Models — Fixed, Switching, Interacting

Guidance, Control and Navigation for Aerospace Systems: Charles Stark Draper's influence on a Personal Perspective

Collision Detection System Based on Differential Carrier-Phase Global Positioning System Broadcasts

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