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Comparison of Clock Models in View of Clock Composition, Clock Steering and Measurement Fitting

Trainotti, Christian and Schmidt, Tobias and Furthner, Johann (2019) Comparison of Clock Models in View of Clock Composition, Clock Steering and Measurement Fitting. 50th Annual Precise Time and Time Interval Systems and Applications Meeting, 28 - 31 Jan 2019, Reston, USA. DOI: 10.33012/2019.16756 ISSN 2333-2069

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Official URL: http://dx.doi.org/10.33012/2019.16756

Abstract

Global navigation satellite systems need a stable and robust system time in order to provide services with high precision. A common approach for its generation is the composite clock method, where an ensemble of clocks contributes to the definition of the system time as a weighted average of the single clocks. In this way the robustness of the so generated time scale is enhanced, since a failure in one clock can be compensated by the others. The core part of the composite clock method is a Kalman filter, which estimates the future states of each clock depending on the relative measurements between all clocks. The Kalman filter implicitly provides the system time of the ensemble, in terms of the implicit ensemble mean (IEM), a so called paper clock. However, this quantity is not directly available, since it requires knowing the exact state of each clock at each time step which is not directly measurable. A solution consists in realizing the IEM by steering a clock signal towards the IEM. Different steering techniques can be used, for instance the pole placement method and the linear quadratic Gaussian regulator. Both the Kalman filter and the regulator are based on a clock model, which describes the clock as a linear dynamic system. Hence, the performance of the used clock has implications in every step of the ensembling and realization algorithms. This paper discusses the advantage and disadvantages of different clock models and gives a recommendation on which one is most promising for future investigations. The 3-state clock model and the 2-state clock model with and without drift are described and expanded with additional Gauss-Markov processes, to account for floors of flicker noise. These models are then compared by considering four properties, namely their precision, the number of states, their theoretical formulation and controllability. The precision refers to which noise characteristics a model is able to describe and how well each model is suited to fit a given clock behavior. The theoretical formulation is studied by means of the theoretical expression of the overlapping Allan deviation (OADEV), which is used to fit a model to real measurements. Finally, the controllability of the dynamic model is needed in order to use the aforementioned control techniques. In light of these criteria, the 2-state clock model with drift and Gauss-Markov processes has been chosen, since it is the one providing a good modeling precision and controllability while being simple and flexible. Furthermore, in order to more easily determine the model parameters, a semi-automatic fitting procedure has been developed. Previously, once a clock measurement was given in terms of OADEV, the parameters were found by trial and error, meaning that the model's dynamics was simulated, its OADEV computed and compared with the measured one. This procedure was repeated until the simulation described the measurement in a reasonable way. However, it is possible to describe the OADEV with a function which can be directly used to fit the measurement data. Several techniques are here described and have been implemented into a graphical interface which eases the fitting procedure.

Item URL in elib:https://elib.dlr.de/126871/
Document Type:Conference or Workshop Item (Speech)
Title:Comparison of Clock Models in View of Clock Composition, Clock Steering and Measurement Fitting
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Trainotti, ChristianChristian.Trainotti (at) dlr.deUNSPECIFIED
Schmidt, TobiasTobias.Schmidt (at) dlr.deUNSPECIFIED
Furthner, JohannJohann.Furthner (at) dlr.deUNSPECIFIED
Date:January 2019
Refereed publication:No
Open Access:No
In SCOPUS:No
In ISI Web of Science:No
DOI :10.33012/2019.16756
Page Range:pp. 265-283
ISSN:2333-2069
Status:Published
Keywords:clock model, Gauss Markov process, IEM, Implicit Ensemble Mean, Clock fitting, clock steering
Event Title:50th Annual Precise Time and Time Interval Systems and Applications Meeting
Event Location:Reston, USA
Event Type:international Conference
Event Dates:28 - 31 Jan 2019
Organizer:Institute of Navigation
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication and Navigation
DLR - Research area:Raumfahrt
DLR - Program:R KN - Kommunikation und Navigation
DLR - Research theme (Project):R - Vorhaben GNSS2/Neue Dienste und Produkte
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Navigation
Deposited By: Trainotti, Christian
Deposited On:26 Mar 2019 09:52
Last Modified:26 Mar 2019 09:52

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