14 I, Santosh Bhattarai Confirm That the Work Presented in This Thesis Is My Own
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Satellite clock time offset prediction in global navigation satellite systems Santosh Bhattarai Department of Civil, Environmental and Geomatic Engineering University College London A thesis submitted for the degree of Doctor of Philosophy July 2014 I, Santosh Bhattarai confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. ............................................. Abstract In an operational sense, satellite clock time offset prediction (SCTOP) is a fundamental requirement in global navigation satellite systems (GNSS) tech- nology. SCTOP uncertainty is a significant component of the uncertainty budget of the basic GNSS pseudorange measurements used in standard (i.e not high-precision), single-receiver applications. In real-time, this prediction uncertainty contributes directly to GNSS-based positioning, navigation and timing (PNT) uncertainty. In short, GNSS performance in intrinsically linked to satellite clock predictability. Now, satellite clock predictability is affected by two factors: (i) the clock itself (i.e. the oscillator, the frequency standard etc.) and (ii) the prediction algorithm. This research focuses on aspects of the latter. Using satellite clock data—spanning across several years, corresponding to multiple systems (GPS and GLONASS) and derived from real measurements— this thesis first presents the results of a detailed study into the characteristics of GNSS satellite clocks. This leads onto the development of strategies for modelling and estimating the time-offset of those clocks from system time better, with the final aim of predicting those offsets better. The satellite clock prediction scheme of the International GNSS Service (IGS) is analysed, and the results of this prediction scheme are used to evaluate the performance of new methods developed herein. The research presented in this thesis makes a contribution to knowledge in each of the areas of characterisation, modelling and prediction of GNSS satellite clocks. Regarding characterisation of GNSS satellite clocks, the space-borne clocks of GPS and GLONASS are studied. In terms of frequency stability—and thus predictability—it is generally the case that the GPS clocks out-perform GLONASS clocks at prediction lengths ranging from several minutes up to one day ahead. There are three features in the GPS clocks—linear frequency drift, periodic signals and and complex underlying noise processes—that are not observable in the GLONASS clocks. The standard clock model does not capture these features. This study shows that better prediction accuracy can be obtained by an extension to the standard clock model. The results of the characterisation and modelling study are combined in a Kalman filter framework, set up to output satellite clock predictions at a range of prediction intervals. In this part of the study, only GPS satellite clocks are considered. In most, but not all cases, the developed prediction method out- performs the IGS prediction scheme, by between 10% to 30%. The magnitude of the improvement is mainly dependent upon clock type. Acknowledgements I would like to thank my supervisors, Professor Marek Ziebart and Dr Paul Groves, for their support and guidance over the course of my research and for their careful review and comments on earlier versions of this thesis. I would also like to thank Dr John Davis of the National Physical Laboratory for working with me on developing the satellite clock prediction algorithm, and for sharing his knowledge and experience of time and frequency analysis methods. I thank my colleagues in the Space Geodesy and Navigation Laboratory, past and present. I shared my journey with them. This work was funded through an EPSRC studentship as part of the Insight project, which was a large UK collaboration between industry and academia aiming to address technical challenges relating to multi–constellation GNSS interoperability. Contents 1 Introduction 17 1.1 Background . 17 1.1.1 Satellite clock time offset (SCTO) as a problem in GNSS . 17 1.1.2 Satellite clock time offset predictions . 20 1.2 Objectives and methodology . 21 1.2.1 Statement of general objective . 21 1.2.2 Prediction method . 22 1.2.3 Statement of detailed objectives . 22 1.2.4 Motivation . 23 1.3 Thesis outline . 25 2 GNSS theory 27 2.1 An overview of the relevant aspects of GNSS theory . 27 2.1.1 Spatial reference frames and timescales . 28 2.1.2 Satellite orbit and satellite clock time determination . 33 2.1.3 The pseudorange measurement . 34 2.2 Satellite clock time offset in GNSS . 36 2.2.1 The apparent clock . 36 2.2.2 The satellite clock time offset parameter, the δts(t − τ) term. 37 2.2.3 Satellite clock models in GNSS . 37 2.2.4 Modelling the relativistic time transformation (RTT) . 39 2.2.5 Satellite clock time offset predictions . 43 2.3 The status of the GNSS’s (GPS and GLONASS)—2013 . 46 2.3.1 NAVSTAR Global Positioning System . 46 2.3.2 The GPS satellite clocks (2012) . 47 2.3.3 GLONASS . 48 2.3.4 The GLONASS space segment . 49 3 Methods from precise time and frequency metrology 50 3.1 What is a clock model? . 51 3.1.1 Two ways of thinking about clock models . 51 3.1.2 Introducing the normalised (or fractional) frequency offset . 52 3.1.3 Clock modelling in practice . 53 3.2 Clock modelling in the GNSS context . 53 5 CONTENTS 3.2.1 Revisiting the matter of reference timescales . 53 3.2.2 Terminology and notation . 54 3.3 The standard clock model . 54 3.3.1 The basic clock model . 55 3.3.2 The oscillator noise model . 55 3.3.3 The standard clock model as a stochastic differential equation . 57 3.4 Stability analysis . 58 3.4.1 Allan variance . 58 3.4.2 Hadamard variance . 60 3.4.3 Modified Allan variance . 60 3.4.4 Time–domain stability analysis based on sigma-tau curves . 61 3.4.5 Dynamic (time–domain) frequency stability analysis . 62 3.5 The Kalman filter for clock estimation and prediction . 63 3.5.1 The Kalman filter as estimator of choice . 63 3.5.2 A Kalman filter implementation of the standard clock model . 64 3.6 Clock predictability analysis . 66 3.6.1 Prediction error deviation . 66 3.6.2 Clock difference prediction error . 67 4 Review and data sources 68 4.1 Review . 68 4.1.1 The in–orbit characteristics of GNSS satellite clocks . 69 4.1.2 The state–of–the–art in SCTO estimation in GNSS . 70 4.1.3 Relativistic time transformation modelling in GNSS . 72 4.1.4 Navigation message style, high latency satellite clock predictions . 73 4.2 The data . 75 4.2.1 The CDDIS archive . 75 4.2.2 Key properties of the IGS satellite clock data . 75 4.2.3 The clock data formats . 78 4.3 Software tools . 79 4.3.1 Data management . 79 4.3.2 Code for the clock characterisation, RTT modelling and SCTO pre- diction algorithm studies . 80 4.3.3 Code verification . 80 5 The characteristics of GNSS satellite clocks 81 5.1 The scope of the characterisation study . 82 5.2 Method . 82 5.2.1 GPS . 83 5.2.2 GLONASS . 84 5.3 Results . 84 5.3.1 GPS . 85 5.3.2 GLONASS . 97 6 CONTENTS 5.4 Findings . 101 6 Satellite clock prediction schemes 104 6.1 Satellite clock time offset (SCTO) prediction error in GNSS . 104 6.1.1 Defining clock prediction error (CPE) . 104 6.1.2 Defining clock difference prediction error (CDPE) . 105 6.1.3 Clock difference prediction error and positioning . 105 6.1.4 Satellite clock predictions and the IGS . 107 6.2 The scope of the prediction scheme performance study . 107 6.3 Method . 109 6.4 Results . 110 6.4.1 Time–series: IGS GPS CPE . 110 6.4.2 The contribution of Tigr − Tigu to Eigr,i,p,n ............... 110 6.4.3 Discontinuities at the boundary between consecutive prediction sets 114 6.4.4 Choosing a reference clock for CDPE computation . 115 6.4.5 Prediction length analysis: GPS CDPE Biases . 117 6.4.6 Summary statistics: GPS CDPE Biases . 118 6.4.7 Prediction length analysis: GPS RMS CDPE . 119 6.4.8 Summary statistics: IGS GPS RMS CDPE . 120 6.5 Findings . 121 6.6 Discussion . 122 7 Enhanced modelling of relativistic time transformations in GNSS 124 7.1 Relativistic time transformations in GNSS . 125 7.1.1 The conventional GPS RTT as a correction term . 125 7.1.2 The precise GPS RTT as a correction term . 125 7.1.3 Earth Gravity Model . 126 7.2 The scope of the GNSS RTT modelling study . 127 7.3 Method . 127 7.4 Results . 128 7.4.1 Earth Gravity Modelling . 128 7.4.2 RTT modelling over a variety of integration arc–lengths . 130 7.5 Discussion . 130 8 A new GPS satellite clock prediction system 132 8.1 A system developed around the IGS operational scheme . 133 8.2 Critical factors affecting SCTO prediction performance . 133 8.3 Elements of the new prediction system . 135 8.3.1 A broad overview of the EMP system . 136 8.3.2 An extension to the standard clock model . 137 8.3.3 A KF implementation of the extended clock model . 139 8.3.4 Introducing new information into the EMP system . 143 8.4 Scope of the prediction system development study . 145 7 CONTENTS 8.5 Method . 145 8.6 Results . ..