GipsyX/RTGx, A New Tool Set for Space Geodetic Operations and Research
Willy Bertiger, Yoaz Bar-Sever, Angie Dorsey, Bruce Haines, Nate Harvey, Dan Hemberger, Michael Heflin, Wenwen Lu, Mark Miller, Angelyn W. Moore, Dave Murphy, Paul Ries, Larry Romans, Aurore Sibois, Ant Sibthorpe, Bela Szilagyi, Michele Vallisneri, Pascal Willis
CContents1 Introduction 42 Software Design, Overview 83 User interface - the input tree 124 Main C++ Software Modules/Classes 12 a r X i v : . [ phy s i c s . g e o - ph ] A p r .6 Building Terrestrial Reference Frames and Fitting Ground SiteTime Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 ipsyX/RTGx, A New Tool Set for Space GeodeticOperations and Research Willy Bertiger a, ∗ , Yoaz Bar-Sever a , Angie Dorsey a , Bruce Haines a , NateHarvey a , Dan Hemberger a , Michael Heflin a , Wenwen Lu a , Mark Miller a ,Angelyn W. Moore a , Dave Murphy a , Paul Ries a , Larry Romans a , AuroreSibois a , Ant Sibthorpe a , Bela Szilagyi a , Michele Vallisneri a , Pascal Willis b,c a Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,Pasadena CA 91109 b Universit´e de Paris, Institut de physique du globe de Paris, CNRS, IGN, F-75005 Paris,France c ENSG-G´eomatique, IGN, F-77455 Marne-la-Vall´ee, France
Abstract
GipsyX/RTGx is the Jet Propulsion Laboratory’s (JPL) next generationsoftware package for positioning, navigation, timing, and Earth science usingmeasurements from three geodetic techniques: Global Navigation Satellite Sys-tems (GNSS), Satellite Laser Ranging (SLR), and Doppler Orbitography andRadiopositioning Integrated by Satellite (DORIS); with Very Long BaselineInterferometry (VLBI) under development. The software facilitates combinedestimation of geodetic and geophysical parameters using a Kalman filter ap-proach on real or simulated data in both post-processing and in real-time. Theestimated parameters include station coordinates and velocities, satellite orbitsand clocks, Earth orientation, ionospheric and tropospheric delays. The soft-ware is also capable of full realization of a dynamic terrestrial reference throughanalysis and combination of time series of ground station coordinates.Applying lessons learned from its predecessors, GIPSY-OASIS and RealTime GIPSY (RTG), GipsyX/RTGx was re-designed from the ground up tooffer improved precision, accuracy, usability, and operational flexibility. We ∗ Corresponding author
Email address: [email protected] (Willy Bertiger)c (cid:13)
Preprint submitted to Advances in Space Research 2020-04-29 resent some key aspects of its new architecture, and describe some of its ma-jor applications, including Real-time orbit determination and ephemeris predic-tions in the U.S. Air Force Next Generation GPS Operational Control Segment(OCX), as well as in JPL’s Global Differential GPS (GDGPS) System, sup-porting User Range Error (URE) of < Keywords:
Multi-technique space geodesy , orbit determination andsatellite clocks, Precise Point Positioning (PPP), GNSS, SLR, DORIS
1. Introduction
Over the past thirty years, Global Navigation Satellite Systems (GNSS),starting with GPS, have become ubiquitous in our daily lives. A growing num-ber of scientific, industrial, and public safety applications, spanning geodesy,geophysics, seismology, atmospheric sciences, weather forecast and climatology,time and frequency transfer, have come to depend on precision modeling of allaspects of GNSS at the cm and mm accuracy. Very few software packages existwith the capabilities to obtain these highest accuracy results, keeping up withthe latest GNSS models and data processing techniques. Fewer still are capa-4le of also modeling and processing data from other space geodetic techniquessuch as SLR (Satellite laser ranging), DORIS (Doppler orbit determination andradio-positioning integrated by satellite), or VLBI (Very long baseline interfer-ometry). Recently, JPL has embarked upon a major overhaul of its widely-usedspace geodetic data analysis software packages, GIPSY-OASIS and RTG, to de-rive GipsyX/RTGx, with many advanced new capabilities and quality features.This paper is intended for the users and developers of space geodesy tools.We present the design and some implementation notes for a new, but alreadywidely used software set, and describe its performance in a broad range ofapplications spanning orbit determination and positioning operations, geodesy,and remote sensing. We first give some historical context, which influences anylarge software and research project design. We then present the overall designof the software, and sample use cases with tests of accuracy and precision.The Jet Propulsion Laboratory (JPL) has a long history in space geodesyand precision orbit determination (POD) for Earth orbiting satellites, and Gip-syX/RTGx is the 4th major redesign of JPL’s GNSS data analysis software.For an overview of POD and measurement processing see the books [Tapleyet al., 2004b] and [Bierman, 1977]. Born from Very Long Baseline Interferome-try (VLBI) data analysis expertise and software [Sovers and Fanselow, 1987], thefirst JPL GPS data models were coded during 1984-1985 in the GPSOMC FOR-TRAN software [Sovers and Border, 1990]. Immediately thereafter we begandevelopment of a more comprehensive software set, the GPS Inferred Position-ing System and Orbit Analysis Simulation Software package (GIPSY-OASIS,forever nicknamed GIPSY) [Wu et al., 1986], also coded in FORTRAN, to sup-port the early campaign-style GPS orbit determination (GiG’91 for example[Melbourne et al., 1993]) and positioning experiments [Blewitt, 1989a]. Thatvery early version of GIPSY should be considered a prototype for the more for-mally designed, enhanced, and documented version [Wu et al., 1990], writtento support the first precision GPS flight experiment on the TOPEX/Poseidonaltimetry mission [Bertiger et al., 1994] as well as the continuous GPS orbit de-termination operations at JPL that are the cornerstone for all precision GIPSY5pplications.With the maturation of the GPS constellation, which became fully opera-tional in 1994, real-time operational applications, such as differential position-ing, started to emerge. The state-space formulation of real-time differentialsystems, today a universally accepted practice also known as wide area differen-tial GPS (WADGPS) or global differential GPS (GDGPS), was conceived andpatented at JPL [Yunck et al., 1989], and led to the creation of the Real TimeGIPSY (RTG) software. RTG ported most of GIPSY’s precise satellite andsignal models from FORTRAN into C, but redesigned the software architec-ture, and in particular the estimation filter, for efficient real-time operations.Successful early demonstration of RTG [Whitehead et al., 1998] has led theUnited States Federal Aviation Authority’s (FAA) to adopt JPL’s state-spacealgorithms for its Wide Area Augmentation System (WAAS), with RTG as theprototype software for this critical aviation infrastructure, which has since beenadopted by several other countries as well [Bertiger et al., 1997]. In 2000, RTGbecame core software for JPL’s GDGPS system, as well as for other commercialsystems.As with any JPL-developed software, GIPSY and RTG are owned by the Cal-ifornia Institute of Technology (Caltech). Licensing requests are available from[https:// gipsy-oasis.jpl.nasa.gov]. With hundreds of issued licenses to academia(which are free of license fees), industry, and government, GIPSY and RTG areamong JPL and NASA’s most licensed software, and the recipient of multiple in-dustry and NASA awards, including the 2000 NASA Software of the Year Awardfor RTG, and 2004 Space Technology Hall of Fame induction for GIPSY andRTG (as “Precision GPS Software System” ) [https://spinoff.nasa.gov/Spinoff2008/award winners.html].In 2005 Raytheon (as lead), ITT (now L3Harris Corporation), and JPLteamed up to develop an innovative navigation concept of operation for theU.S. Air Force next generation GPS operational control segment, known asOCX. The OCX project is a complete overhaul of the GPS operational con-trol segment, including new architecture, infrastructure, hardware, and software6equired to comply with a set of demanding performance and quality specifi-cations. The team’s proposed navigation concept was patterned after JPL’sGDGPS System and built upon JPL’s proven GIPSY and RTG navigationsoftware technology. In 2010 the team was competitively awarded the $1B+project to develop and deploy OCX [http://insidegnss.com/raytheon-wins-1-5-billion-gps-ocx-contract/], [Bertiger et al., 2010a], and we set out to createJPL’s 4th generation GPS data processing software, entitled RTGx. Later, theNASA Space Geodesy Project (SGP) provided additional support to enhancepost-processing for space geodesy [Merkowitz et al., 2018]. All programs syner-gistically benefited.This was an opportunity to modernize the entire geodetic data processingsoftware set at JPL and unify the agile real-time processing of RTG with thepost-processing flexibility of GIPSY, all within a new architecture that cansupport all of JPL’s, NASA’s and the Air Force’s OCX current and anticipatedneeds. This unified multi-capability software set was named GipsyX/RTGx (orRTGx/GipsyX, depending on the main use case. The choice of capitalization isintentional).The development of GipsyX/RTGx was mostly completed by 2016. By 2014it had replaced RTG as the orbit determination engine for most GDGPS real-time GNSS operations, and by 2017 it had replaced GIPSY as the orbit de-termination engine of all post-processed GPS orbit determination operations atJPL, including the reprocessing of the entire record of GPS ground trackingdata back to the early 1990s (in order to establish a consistent long-term set oforbit and clock solutions in ITRF2014). However, with the ever-changing GNSSlandscape and the on-going quest to combine the various geodetic measurementtechniques, GipsyX/RTGx is constantly being updated and upgraded.GipsyX/RTGx, as was GIPSY-OASIS, is a member of a small ‘club’ of avail-able precision space geodetic data analysis packages, with diverse capabilities,and with a track record of contributing high quality GNSS data analysis prod-ucts. These include Bernese [Dach et al., 2015], EPOS.P8 [Uhlemann et al.,2015], GAMIT [Herring and Floyd, 2018], GEODYN [Pavlis et al., 2017], GINS7Marty et al., 2011], NAPEOS [Springer et al., 2011], and PANDA [Shi et al.,2010].Since 2018, GIPSY and RTG are no longer supported by JPL. The largeGIPSY licensee community is transitioning to GipsyX/RTGx with the help ofJPL-provided classes, online documentation, tutorials and licensing informationon (https://gipsy-oasis.jpl.nasa.gov) with over 230 licenses of which 80% are freeacademic licenses.
2. Software Design, Overview
GIPSY’s core computational engines were written in FORTRAN with gluecode and automation in C-shell, Bourne-Shell, and Perl. RTG was written inC. Both GIPSY and RTG implemented precise sets of models consistent withthe 2010 Conventions of the International Earth Rotation Services (IERS) [Pe-tit and Luzum, 2010]. RTG was designed for lean real-time processing, anddid not have post-processing capabilities required by many of NASA’s scienceapplications and by the geodetic user community. While FORTRAN has beenmodernized since our original GIPSY writing, it is not currently as widely usedas C or C++, and is hardly taught at universities. The U.S. Air Force con-tract for OCX forbade outright the use of FORTRAN. C does not supportobject-oriented programing, which we deemed necessary for ease of develop-ment and maintenance. We chose, therefore, to write the main computationalparts of the new software set in C++. We wanted to avoid the hodgepodge ofscripting languages used in GIPSY and chose Python3, which has a large userbase and community support in the sciences and engineering, as the sole script-ing language. For small problems and identical use cases (for instance precisepoint positioning with GPS or low Earth orbit determination with GPS) whichare implemented in GIPSY and GipsyX/RTG, run times are nearly identical.Larger problems, that can be handled by GIPSY and GipsyX/RTGx can befaster with the new software, due to optimization and use of parallel compu-tation. Table 1, shows almost a factor of three increase in performance for a8oderate size problem, the problem is too small for realizing large increases inspeed with multiple cores/CPUs. In addition to new use cases, which are notimplemented in GIPSY, there are very large problems that can only be handledin GipsyX/RTGx, simultaneous adjustment of a large gravity field, GNSS or-bits, GRACE orbits and additional low Earth orbiters. For use cases that arecommon to GIPSY and GipsyX/RTGx, we expect almost identical precisionand accuracy, but a much improved user interface. It is the preservation of theaccuracy and precision, along with the additional use cases that adds new valueto space geodesy.
Table 1: CPU Time comparison, GIPSY verses GipsyX/RTGx for a moderate size problem,45 stations, 32 GPS satellites with bias fixing. Unloaded Intel R (cid:13) Xeon R (cid:13) Gold 6130 CPU at2.1 GHz. GIPSY does not support multiple cores.
CPU Time(minutes)GIPSY 45GipsyX/RTGx 1-core 16GipsyX/RTGx 2-core 11Among the key new capabilities of GipsyX/RTGx are: • Complete support for most Linux distributions and Mac OS X; tailoredinstallation on embedded flight hardware • Full GNSS satellite and signal modeling, including GPS, GLONASS, Bei-Dou, Galileo, and QZSS • Seamless processing of data from shared memory or files supports bothreal-time and post-processing operations • High fidelity data simulator capable of simulating all the data types it canprocess • Efficient square root information filter (SRIF) formulation featuring multi-threading and parallelization with Message Passing Interface (MPI)9
Hot start capability with archived filter state and covariance • Integer GNSS phase ambiguity resolution in post-processing and in real-time • Inertial measurement modeling to optimally combine GNSS and inertialdata in real-time and in post-processing • Hyperlinked documentation using Doxygen and Sphinx • User input interface featuring inheritance • Reference frame determination and time series analysis of Earth stationpositionsTable 2 shows the size of the entire GipsyX/RTGx distribution in terms ofthe number of lines of code. Raw lines are just the total number of lines in allthe source files. Physical lines are lines that are not comments or blank. Themajority of the C++ code occurs in the single executable module, “rtgx”, whichmodels the GNSS data and other tracking data types, and estimates parameterssuch as station and satellite position. We describe the structure of “rtgx” below.There are approximately 140 individual executable programs in GipsyX/RTGx.Included are many small utilities, such as time format manipulation, time seriesand data manipulation, trend analysis, data archive access and plotting utilities.Most users will only use a small set of these. In addition to the tracking dataanalysis tools, there is a set of Python3 executables dedicated to time seriesanalysis of positions on the Earth and reference frame determination as well asmany other small utility tools (for example, to convert between file formats ortiming formats).We have attempted to apply in this development the many lessons learnedfrom the previous iterations of GIPSY and RTG. GIPSY was written by manypeople under a fairly loose set of coding rules. The main computational pieces ofGIPSY were divided into several independent FORTRAN modules (orbit inte-gration, signal/Earth model, filter, smoother...). There was considerable incon-sistency in the input to these pieces, which were mostly FORTRAN namelists.10 able 2: GispyX source lines, 1k=1,000
Language Physical Lines Raw Lines Comment LinesC++ 202.7k 353.7k 103.3kPython3 35.6k 60.4k 14.6kCommon information across these FORTRAN executables was not consistentlynamed or configured. To mitigate the complex configuration of the variousGIPSY modules, we wrote a Perl script (gd2p.pl) to hide the complexity andact as the interface for most of our external users who were doing precise pointpositioning (PPP) or precise orbit determination (POD) of low Earth Orbitersusing GPS [Bertiger et al., 2010c]. GipsyX/RTGx improves upon GIPSY in twoways here. One, there is a uniform input format, referred to as a ‘tree’ inputdefined in detail below, which has a general structure similar to YAML. We didnot use YAML because, at the time of our development, it did not have someobject-oriented inheritance properties or arbitrary script execution that wouldallow human readable, compact input for GNSS constellations where many ofthe satellites have identical properties. Second, instead of writing many indi-vidual executable modules as in GIPSY, the object-oriented C++ allowed us towrite a single main executable, rtgx.For version control, we are using svn, subversion [Pilato et al., 2008] chosenbefore distributed version control systems such as git [Chacon and Straub, 2014]were more popular. We believe that documentation is best maintained insidethe source code; thus, we chose to use Doxygen for C++ code, and Sphinx forPython. Doxygen and Sphinx both output html documentation and it is easy tolink the two sets of documentation. The mathematical description for the radio-metric signals, solid tides, Earth orbiting satellite forces, ordinary differentialequation integrator, etc., are best written in L A TEX. Our html documentationincludes a pdf containing the mathematical description, generated with L A TEX,with links to the source code documentation.11aving a single main executable, nearly all use cases can be constructed asa very thin wrapper around a single command line: rtgx myInput.tree
To automate the most common tasks carried out by our user community,namely precise static point positioning with single receiver ambiguity resolu-tion, we have provided a Python3 wrapper, where the only required input is aRINEX2 (Receiver Independent Exchange Format) or RINEX3 GNSS data file. gd2e.py -rnx my.rnx
This is the analog of GIPSY’s gd2p.pl automation script, and it contains manyenhancements over its predecessor in terms of ease of use and documentation.
3. User interface - the input tree
Several of our executables, especially those requiring more complicated andfinely controllable user inputs, are configured by a single interface called a tree.A tree is a text file with a hierarchical structure identified using Python-likeindentations that consist of roots (the highest level), branches, and leaves (thelowest level; the leaves of the tree are the parts of a tree with no branches andare generally the ones that contain specific data). See electronic supplement 1for details.
4. Main C++ Software Modules/Classes
The computationally intensive software breaks into several broad categories: • Data editing • Orbit Integration and force models • Signal Models • Earth Models 12
Filter, optimized fit to the linearized model forward in time • Smoother, optimized fit to the linearized model over all timeAll of these items are implemented as C++ classes or functions in a singleexecutable module, rtgx, except for data editing, which is provided by the “gde”module.
GNSS data must be edited for phase breaks and gross outliers before it isprocessed to fit model parameters. The GNSS Data Editor (gde), is a C++code that implements two distinct algorithms: turbo-edit [Blewitt, 1990], andsimple continuity checks of linear combinations of phase data based on low-degree polynominal fits. Turbo-edit looks at averages of pseudorange − phase measurements to detect jumps in the phase measurements. It is well suited tolow rate data, such as the large number of RINEX files typically recorded ata 30-sec rate. When data rates are high, for example sampled every second asoften seen in real-time applications, it is possible to detect phase breaks simplyby monitoring the change in time of differences in phase observations on twofrequencies. Such a difference cancels out receiver and transmitter clock jumps.Removing a low order time polynomial from these differences effectively removesthe slow-changing ionospheric signal in this difference. Single differences of dual-frequency combinations across two satellites are also available as an option. The basic signal model is the time of propagation from a transmitter to a re-ceiver. For GNSS range measurements recorded at receiver time, ˜ t r , determinedby the receiver’s clock and transmitted at time ˜ t t , we model the measured rangeas R = c ( ˜ t r − ˜ t t ) + d trop + d iono (1)where c is the speed of light, d trop is a delay due to troposphere and d iono isthe delay due to the ionosphere. For many GNSS measurements the first orderdelay of the ionosphere is removed by a dual-frequency combination of the data[Parkinson et al., 1996] and a model for higher order effects [Kedar et al., 2003].The troposphere is modeled as a delay at zenith plus gradient parameters ([Bar-Sever et al., 1998], [B¨ohm and Schuh, 2004], [B¨ohm et al., 2006], [B¨ohm et al.,2015]). The difference in the time of reception, ˜ t r , and the time of transmission,˜ t t , in equation 1 can be modeled as˜ t r − ˜ t t = ˜ t r − ¯ t r + ¯ t r − t r + t r − t t + t t − ¯ t t + ¯ t t − ˜ t t (2)where ˜ t r − ¯ t r is the difference between the time on the receiver clock and propertime(time clock would have read with no errors) and ¯ t r − t r is the difference15etween proper time and coordinate time (General Relativistic effects, [Moyer,1971], [Thomas, 1975], [Moyer, 1981]). The last two lines of eq. 2 contain similardifferences for the transmitter. The middle term, difference in coordinate time, t r − t t , is modeled as the geodesic distance (General Relativity with the onlymass being the Earth’s point mass) between the transmitter and receiver phasecenters. The fit to measurements of the range is optimized by linearizing aboutthe nominal parameter values in equations 1, 2, first analytically taking partialderivatives with respect to the parameters and then in the case of satellites usingthe numerically calculated partials in sec. 4.2.For multi-GNSS, eq. 1, must be modified due to different delays of rangingcodes through the receiver for different constellations. The code adds a biasparameter for each receiver by constellation [Odijk and Teunissen, 2013]. Oneconstellation must be held as reference to prevent singularity. Typically we holdGPS as reference, but it is arbitrary.The model for GNSS phase data is identical to range, except two terms mustbe added to eq. 1 φ = c ( ˜ t r − ˜ t t ) + d trop + d iono + ω ( t r ) + B tr (3)where φ is the modeled phase, B tr , is an arbitrary phase bias between the trans-mitter and receiver over time periods where the receiver has not lost lock, and ω ( t r ) is the phase windup [Wu et al., 1993]. The B tr may further be modeled asinteger number of wavelengths and fractional hardware delays in the given re-ceiver and transmitter; see [Blewitt, 1989b] for treatment of network ambiguityresolution and [Bertiger et al., 2010c] for treatment of the integer ambiguitieswith a single receiver. For receivers or transmitters that are not orbiting the Earth and are eitherattached to or associated with the Earth’s crust, we must model the deformationof the Earth’s crust and the orientation of the Earth in inertial space sincesatellite positions are integrated in inertial space. GipsyX/RTGx implements16he IERS standards [Petit and Luzum, 2010]. Adjustable parameters includethe Earth orientation parameters, polar motion and hour angle.
Except for single receiver use cases, most of the computation time is domi-nated by filtering, smoothing and ambiguity resolution functions. If we treatedall the parameters as constant in time, the filter and smoother parts of the codewould just be a standard least squares; but many of the parameters do vary intime, for instance the zenith troposphere delay or the receiver and transmitterclock errors. Many force parameters, including empirical accelerations affect-ing satellite dynamics, are also best treated as stochastic variables in a processcalled reduced-dynamic orbit determination [Yunck et al., 1990; Wu et al., 1991].We chose to handle these time variations as a first order Markov process with aforward-in-time filter implemented as a Square Root Information Filter (SRIF)detailed in Bierman [Bierman, 1977]. The square root implementation allowsfor better conditioned matrices, and the use of Householder (orthogonal trans-formation in multi-dimensional space) transformations in our implementation ofthe Bierman algorithms lends itself naturally to more efficient use of processorspecific pipelining [Jeong et al., 2012], when available, along with the MessagePassing Interface (MPI [Gropp et al., 1999]) for processing across multiple CPUcores and computer clusters (Beowulf [Sterling et al., 2002]).The forward filter is the best fit of all the past data up to the current epoch.In order to have the parameters fit the future as well as the past data opti-mally, one needs to smooth the information back in time. We again followBierman’s algorithm [Bierman, 1977] for a SRIF smoother, which uses a seriesof Givens (two-dimensional orthogonal rotation) and Householder transforma-tions. We again optimize efficiency using machine-specific-low-level routinesand MPI where appropriate. After editing for outliers in the smoother, integerambiguities may be constrained for GNSS data. For single receiver ambiguityresolution, we follow the procedure in [Bertiger et al., 2010c] extended to multi-GNSS, applying constraints to single differences. For multiple GNSS receivers,17e can resolve double difference integer ambiguities following [Blewitt, 1989a]extended to multi-GNSS to constrain the double-differenced phase ambiguities,as well as adding single-receiver constraints when appropriate external infor-mation is available. The single receiver methods are related but not identicalto methods developed in [Laurichesse et al., 2009; Laurichesse, 2011], [Loyeret al., 2012]. Our ambiguity resolution algorithms, do not currently extend toGLONASS Frequency Division Multiple Access (FDMA) signals.
5. Main executable, rtgx
A detailed description of the main loop of the primary executable is containedin electronic supplement 2, rtgx main loop.
6. Sample Use Cases, Accuracy, Precision
JPL delivers to the geodetic community, and for combination by the Inter-national GNSS Service (IGS) [Johnston et al., 2017], two sets of GPS productscharacterized by different latencies, precision and accuracy levels, but all basedon filtering and smoothing of ground tracking data in post-processing.“Rapid”products are generated and distributed daily. “Final” products are generatedweekly and typically have a 14-day latency. We also distribute “Ultra-rapid”products, generated every hour. While ultra-rapid and rapid products aretightly tied to the IGS realization of the ITRF by fixing the coordinates ofa subnetwork of stations in the POD process to their ITRF coordinates, Finalproducts come in three flavors. Fiducial-free products, identified by the suffix‘nf’ (non-fiducial) in their names, are not tied to any specific terrestrial frame;the positions of the stations constituting the network are left floating with a 1km a priori sigma, so that the frame of these solutions changes from day-to-day.No-net-rotation (‘nnr’ suffix) products are such that 3 no-net-rotation (relative18o the ITRF) constraints are enforced in their generation process. Final prod-ucts with no suffix are tied to the ITRF by means of 7 constraints (3 rotations,3 translations and 1 scale parameter) and are referred to as NNRTS (no-net-rotation, translation, or scale) or ’fiducial’ products, though their fiducializationdiffers from Rapid and Ultra-Rapid. Every set of products contain files withconsistent orbital state estimates, transmitter clock estimates, spacecraft at-titude information, Earth rotation parameter (ERP) estimates, and widelanephase biases information. In addition, the no-net-rotation and fiducial-free so-lutions are associated with coordinate transformation files referred to as x-files.These x-files contain the set of 7 Helmert parameters (3 small rotations, 3 trans-lations, and 1 scale parameter) needed to transform from the frame of the dayto the ITRF. The format of these different products is detailed in the GipsyXsoftware documentation. Following extensive testing and validation, the JPLGNSS analysis center transitioned seamlessly from products generated usingthe GIPSY software package to products created using GipsyX on January 29,2017. More recently, the entire span of 1994 through 2018 were reprocessedusing GipsyX, consistent with IGS repro2 standards. All products are availableat https://sideshow.jpl.nasa.gov/pub/JPL_GNSS_Products .Table 3 displays the characteristics of each type of post-processed product.Latencies are indicated as well as commonly used performance metrics. JPLorbit and clock products cover 30 hours centered at noon, so that each dailysolution overlaps with the next-day solution by 6 hours. After removing 30-minute tails at both ends of this overlap period, RMS statistics on orbit andclock differences are computed in the 5-hour overlap period as an internal mea-sure of the precision of the product. The long-term medians of the RMS clockand orbit differences in the overlap is shown as “Precision” in Table 3. We mea-sure accuracy in Table 3 by comparing JPL’s orbit and clock solutions with thecombined final IGS orbit and clock solutions for the same days. Although wehave listed this as “Accuracy” in Table 3, we note that the IGS Final productis a weighted average of all the contributing analysis centers including JPL.19 roduct Latency OrbitPrecision(cm) ClockPrecision(cm) OrbitAccuracy(cm) ClockAccuracy(cm)
Ultra < <
14 days 2.3 2.3 1.9 3.8
Table 3: JPL post-processed operational products. Units for all precision and accuracy metricsare centimeters. Statistics were computed from time of switch (Jan. 29, 2017) to Apr. 20,2019. Each clock metric is the median value of the daily root-mean- square values of theoverlaps/differences across the GPS satellites after removing a linear trend from the entireGPS constellation to account for reference clock differences. Each orbit metric is the medianvalue of the daily median of the 3D RSS of RMS positions across the GPS constellation.
As mentioned above, each set of products includes a file containing estimatesof the Earth rotation parameters. The ERPs consist of two biases and two ratesto describe the motion of the Earth’s pole with respect to the Earth’s crust:Xp, Yp and their respective rates. The excess length-of-day (LOD) is definedas the time derivative of UT1-UTC, where UT1 is the time scale associated tothe total rotational phase angle of the Earth and UTC is the Universal TimeCoordinated. All 6 parameters are directly observable by GNSS, with the ex-ception of UT1-UTC. As a result, the polar motion coordinates and rates alongwith LOD are freely estimated in the GNSS precise orbit determination processwhereas UT1-UTC is tightly constrained to a nominal value reported in theIERS combined ERP solution, the Bulletin A file [IERS, 2019]. Operationalprocesses at JPL rely on the predicted portion of Bulletin A for a priori val-ues for Earth orientation parameters, while reprocessing campaigns typicallyuse the Bulletin A final values of UT1-UTC. All JPL estimates are routinelycontributed to the IGS for their combined ERP products. The IGS, in turn,contribute these combined GNSS ERP products to the IERS for their finalmulti-technique combined products. Figures 1 through 3 show the differences20etween the JPL Final no-net-rotation solutions (contributed to the combinedIGS products) relative to the final combined IGS solution for Earth RotationParameters. The noise in the differences in the polar motion values amounts toabout 20 µ as for both coordinates, which corresponds to 0.6 mm at the surfaceof the Earth. The scatter in the differences of the LOD estimates is higher at 16 µ s/day, translating into 1.2 mm at the surface of the Earth over one day. Thesenumbers are consistent, even slightly better for the pole coordinates, than thestatistics reported by [Rebischung et al., 2016]: they found that the weightedRMS of the IGS analysis centers (AC) pole coordinate residual time series rangebetween 25 to 40 µ as, while the weighted RMS of the AC LOD residual timeseries range from 8 to 20 µ s/day. Over the timespan extending from Jan. 29,2017 to Apr. 20, 2019 (since the transition from JPL’s legacy software to Gip-syX), the scatter in the differences between the JPL Xp, Yp, and LOD solutionsrelative to 6 other IGS analysis centers using different software packages rangesfrom 27 to 49 µ as, 26 to 44 µ as, and 13 to 18 µ s/day, respectively. Again, thesestatistics are in full agreement with the numbers cited in [Rebischung et al.,2016]. Orbit modeling differences, e.g., in solar radiation pressure modeling, areknown to impact the accuracy of GNSS-based ERP determination. In partic-ular, they could explain the bias visible in Fig. 3. The JPL versus IGS ERPdifferences may be compared directly to the published uncertainties of the finalcombined ERP values from the IERS Bulletin A relative to the IGS combinedseries [Bizouard et al., 2017]. Table 4 of [Bizouard et al., 2017] shows Xp andYp scatter of IGS combined at 31 and 27 µ as respectively and 10 µ s for LODfor ITRF 2014 from 2010-2015. A greater number of satellites may provide significant benefits to users, in-cluding additional coverage in urban canyons, and perhaps better estimatesof parameters such as troposphere, Earth orientation, and geocenter. To thisend, many IGS Multi-GNSS Experiment (MGEX, [Montenbruck et al., 2017], http://mgex.igs.org/ ) analysis centers are now routinely processing multiple21 igure 1: Differences between the Earth’s pole coordinates (Xp, Yp) determined by JPL’sFinal no-net-rotation solutions and values from the IGS final combined solution. The startdate of the period covered corresponds to the date of the operational transition from GIPSYto GipsyX at the JPL IGS Analysis Center. The scatter for both coordinates, once convertedto equivalent linear distance, is of the order of 0.6 mm at the surface of the Earth. igure 2: Differences between the Earth’s pole coordinate (Xp, Yp) rates determined byJPL’s Final no-net-rotation solutions and the IGS final combined ERP product. The startdate of the period covered corresponds to the date of the operational transition from GIPSYto GipsyX at the JPL IGS Analysis Center. The scatter for both rates correspond to anequivalent linear distance of about 2.8 mm/day at the surface of the Earth. igure 3: Differences between Length-of-Day recovered by JPL’s Final no-net-rotation solu-tions and LOD final combined solution distributed by the IGS. The start date of the periodcovered corresponds to the date of the operational transition from GIPSY to GipsyX at theJPL IGS Analysis Center. The scatter around the mean is of the order of 16 µ s per day, equiv-alent to 1.2 mm at the surface of the Earth over a day. The visible -35 µ s/d bias, equivalentto 2.6 mm at the surface of the Earth over a day, is attributed to orbit modeling errors andin particular solar radiation pressure modeling errors in GNSS data processing, as discussedin [Sibthorpe et al., 2011] and [Ray, 1996] for instance. https://kb.igs.org/hc/en-us/articles/216104678-ANTEX-format-description ) which, for the first time,includes antenna corrections for all satellites from the four major constellations.With our most recent fully automated software, we have produced daily, Rapid-like 4-constellation products for the month of August, 2019, using 120 stationsfor GPS and 80 for the remaining constellations. Accuracy is more difficult tomeasure in this case owing to the lack of a provably more accurate multi-GNSSproduct with which to compare, whether from IGS MGEX or elsewhere, andtherefore we leave off such an assessment until a future date. Individual MGEXanalysis center contributions may continue to exhibit significant differences untilconsistent antenna information, only relatively recently available, begins to seewidespread use. Our four-constellation products contain an average of 102 satel-lites per day, approximately comprised of 31 GPS, 28 Beidou, 22 Galileo and21 GLONASS. While this dataset is limited, it gives a preliminary indicationof the sort of performance that might be expected from multi-GNSS productsprocessed with GipsyX/RTGx, which should also improve with time as modelsand procedures are further enhanced. 25able 4 displays the overlap precision statistics of each constellation/sub-constellation along with statistics for the JPL GPS Rapid products described insection 6.1.1 over the same time period for comparison. As with Table 3, eachdaily solution overlaps with the next-day solution by 6 hours. After removing30-minute tails at both ends of this overlap period to avoid edge effects, statisticson orbit and clock differences are computed in the 5-hour overlap period as aninternal measure of the precision of the product. The long-term medians of theclock and orbit differences in the overlap is shown as “Precision” in Table 4.26 roduct OrbitPrecision(cm) ClockPrecision(cm) GPS (JPLRapid) 1.9 1.9GPS (4-constellation) 2.0 1.5BeiDouGEO 67.9 15.3BeiDouIGSO 10.2 7.8BeiDouMEO 5.3 5.4Galileo 2.8 1.4GLONASS 5.5 1.1 ∗ Table 4: Daily overlaps of JPL four-constellation products (GPS, BeiDou, Galileo andGLONASS). GPS (JPL Rapid), provided for comparison, is computed using JPL’s stan-dard GPS-only Rapid products described in section 6.1.1. Units for all precision metrics arecentimeters. All statistics were computed from Aug. 1 to Aug. 31, 2019. Each clock metric isthe median value of the daily root-mean-square values of the overlaps/differences across theGNSS satellites after removing a linear trend from the entire GPS constellation to accountfor reference clock differences, a subsequent linear trend from each of Galileo and BeiDou toaccount for constellation bias reference differences, and a linear trend from each GLONASSsatellite due to the presence of range biases – ∗ likely making the GLONASS clock overlapsspuriously small. Each orbit metric is the median value of the daily median of the 3D RSS ofRMS positions across the GNSS constellations. The real-time configuration of GipsyX/RTGx is typically called just RTGx.RTGx has been driving real-time orbit determination processes in the GDGPSSystem since 2014 (RTG was the engine prior to that, with some overlap). Theseinclude GPS-only orbit determination filters as well as GPS plus various other27NSS constellations. A typical GNSS orbit determination filter may include1 Hz phase and pseudorange measurements from 150 ground sites tracking32 GPS satellites, 24 GLONASS satellites, 35 BDS satellites, and 24 Galileosatellites (as of June 2019). Such a filter produces orbital states every 60 secondsand clock solutions at 1 Hz, with a latency(difference in the time correctionsare available to a user − epoch of the data used for the clock correction) thatnever exceeds 6 seconds relative to the measurement epochs. GNSS accuracyis typically quoted in terms of User Range Error (URE), eq. 4, where h is theradial orbit error, c is the cross-track error, l is the along-track error, and clk isthe clock error: U RE = (cid:112) ( h − clk ) + ( l + c ) /
50 (4)For the full derivation, see the appendix in [Zumberge and Bertiger, 1996].Here we have used the standard approximations of the coefficients. The real-time URE relative to post-processed solutions is typically 5 cm RMS (Fig.4). The specialized requirements of real-time operations have driven the designof some unique and powerful RTGx features. One such feature is the ability toreconfigure a real-time running filter into partitions such that some parametersassociated with specific satellites or specific stations, are estimated but have noinfluence on any other parameters. At the GDGPS System these “decoupled”partitions are used to accommodate unhealthy satellites in order to keep mon-itoring them while protecting the rest of the estimated constellations from thepotential mismodeling of unhealthy satellites, for example due to maneuvers.Our decoupling algorithm is equivalent to infinitely de-weighting the data fromthe associated satellite or station following a white-noise re-set of the param-eters associated with the satellite or station. For earthquake monitoring theGDGPS System operates orbit determination filters with multiple decoupledpartitions where the position of hundreds of ground sites (a site per partition)are estimated kinematically at 1 Hz [Larson et al., 2007] , but these sites are28 number of stations in POD ti m e a v e r a g e d U R E ( c m ) non ambiguity fixed, rms-over-satsnon ambiguity fixed, max-over-satsambiguity fixed, rms-over-satsambiguity fixed, max-over-sats Forward Filter GPS-only 5-minute POD, May 1 - 13, 2018 (reference: JPL Rapid)
Figure 4: RMS URE (black curves) and worst URE (red curves) across all GPS satellitesas a function of tracking network size for real-time orbit determination by RTGx within theGDGPS System during May 1 - 13, 2018. Significant improvement due to integer phaseambiguity resolution (dashed curves) is evident relative to the solutions with float ambiguityresolution (solid curves). The reference solutions are provided by JPL’s daily post-processedsolutions (see Table 3 above for post-processing accuracy). The RMS URE approaches 5 cmwith ambiguity resolution and 90 or more real-time tracking sites.
25 50 75 100 125 station H o r z ( D ) PPP a vg hou r e rr o r ( c m ) ambiguity fixed orb/clknon ambiguity fixed orb/clk Horizontal (1D) PPP Error, September 2017 (average / standard deviation of 24-hour RMS error)0 25 50 75 100 125 station V e r t PPP a vg hou r e rr o r ( c m ) ambiguity fixed orb/clknon ambiguity fixed orb/clk Vertical PPP Error, September 2017 (average / standard deviation of 24-hour RMS error)
Figure 5: Horizontal (top) and vertical (bottom) real-time positioning accuracy of real-timekinematic 5-minute point-positioning of 125 GDGPS tracking sites with RTGx as decoupledpartition of the GDGPS GPS orbit determination filter during September 2017. Each pointrepresents a monthly average of daily RMS positioning error. The error bars depict thestandard deviation of the daily RMS values over the entire month. Integer phase ambiguityresolution was used to generate the black curves, and float phase ambiguity resolution wasused to generate the red curves. Stations are ordered according to their integer ambiguity-resolved positioning accuracy. The reference solutions are provided by long-term static point-positioning.
In [Bertiger et al., 2010c], it was demonstrated that the IGS implementationof the current ITRF frame at the time, ITRF05, could be realized with 24-hoursof GPS data to an accuracy of 2 mm in the horizontal and 6 mm in the verticalprocessing 6-months of data from a 106 reference frame sites. Here, we do asimilar experiment with 59 stations in ITRF2014. The stations selected areavailable on at least 90% of the days from 2002-2012, are part of IGS14 (IGSimplementation of ITRF2014) [Rebischung et al., 2016], and are selected to bewell-distributed geographically. Figure 6 shows the geographic distribution ofsites used for this test.
Figure 6: Geographic distribution of the 59 sites used for PPP testing.
First, each site was point positioned using a tree very similar to the defaulttree included with GipsyX-1.0. The only substantive difference with the defaulttree is the use of Ionosphere Exchange (IONEX) files [Schaer et al., 1998] for32PP type East (mm) North (mm) Vertical (mm)NF no-IONEX 1.90 1.98 6.47NF 1.89 2.07 6.49NNR 1.92 2.11 6.53NNRTS 1.96 2.11 6.45
Table 5: Median daily RMS repeatability relative to ITRF2014 solution second-order ionospheric corrections (except for one no-IONEX case). A GPT2-based [B¨ohm et al., 2015] nominal troposphere and mapping function was used.Each site was positioned using JPL’s repro3.0 IGS14 Final products, with sep-arate PPP runs for the non-fiducial (NF), no-net rotation (NNR), and no-nettranslation, rotation, or scale constraint (NNRTS also referred to as “fiducial”)products from 2008-06-01 through 2008-11-30. In the case of the NNR and NFproducts, a 7-parameter Helmert transformation is performed using the appro-priate product x-file to convert the resulting position into the reference frame.Positions are compared with those given in ITRF2014. For each station, a 5-sigma edit is performed on total position differences, then the root-mean-square(RMS) is calculated in east, north and vertical (E, N, V) components. We thenreport the median of each of these components in Table 5. Figure 7 shows ahistogram of the frame repeatability for all 59 stations including all outliers.All three methods (NF, NNR, NNRTS) produce nearly identical results. Whencompared to the GIPSY-OASIS results in [Bertiger et al., 2010c], E and N arealmost identical but the results here are a bit worse in V (6.5 vs. 6.0 mm).We attribute the difference in vertical to station selection differences (i.e. 59IGS14 stations vs. 106 IGS08), as vertical repeatability is highly site-dependent.While using IONEX files does not improve repeatability in this analysis, we stillrecommend its use to be consistent with the models used in the Final PODprocess, and because other analyses show that omitting it can introduce an off-set in the z-component [Ries et al., 2018]. In this test, the offset is an averageof 0.4 mm. The ENV frame repeatability of about 2, 2, and 6 mm in Table33 is significantly better than the 24-hr RMS repeatability of 3, 6, and 9 mmshown in [Soycan, 2011] using Bernese 5.0 software. We note that significantimprovements are seen in the east component with bias fixing [Bertiger et al.,2010c] with the GipsyX/RTGx bias fixing methods as well as the result withPANDA software [Ge et al., 2007] with bias fixing based on fractional satellitedelays. In [Ge et al., 2007], they compute repeatability relative to IGS weeklysolutions after removing a 7-parameter Helmert transformation and get meanRMS E, N, and V repeatability of 2.4, 2.7, and 5.3 mm with bias fixing. Theseare not exactly the same statistics as shown in Table 5. The weekly solutionswill take out some vertical signal from seasonal loading not contained in theITRF2014 frame.
Figure 7: Histogram: East, North, and Vertical ITRF repeatability for 59 sites used for staticPPP testing using NF products and IONEX corrections. Each count represents a single dayof processing for a single station.
Figure 8 shows the seasonality of PPP residuals relative to the ITRF so-lution for ALGO (Algonquin Park, Canada) using IONEX corrections and NFproducts for 16 years years. Most of the vertical residual can be explained by34tmospheric and hydrological loading [Tregoning and Watson, 2009], models ofwhich are also plotted. The horizontal displacements also show seasonality dueto other effects such as snow cover [Larson and Nievinski, 2013]. This exampleillustrates one complexity of repeatability calculations, and how results can bebiased by short time periods and/or inhomogenous distributions of stations.
Figure 8: Daily of PPP ALGO over 13 years vs ITRF frame solution compared with dis-placements from http://loading.u-strasbg.fr/displ all.php [Gegout et al., 2010] using the sumof atmospheric loading (ATMMO) and hydrological loading (GLDAS2, Rodell et al. [2004])models in E (upper-left), N (upper-right), and V (lower-left) components. A higher temporal-resolution plot of V is provided in the lower-right.
For many applications the receiver is moving, and it is the accuracy of thekinematic position of the GNSS receiver that matters. Applications, among35any, include synthetic aperture radar (SAR) from aircraft, ocean floatingbuoys used to determine sea surface height, co-seismic deformation, and icesheet movement, see [Hensley et al., 2008; Bonnefond et al., 2003; Born et al.,1994; Simons et al., 2011; Doake et al., 2002] for example. To give an idea ofthe expected performance from GipsyX, we kinematically positioned a set of 45ITRF2014 frame stations every 5 minutes for the month of June 2008 using GPSdata. Table 6 shows the RMS differences with the ITRF2014 frame positionswhere the position has been adjusted as a loose random walk, 1 m/ √ s , while thetroposphere is a bit more constrained than in the static point positioning. In-stead of adjusting the zenith delay and tropospheric gradient parameters, onlya more constrained zenith delay is adjusted to help break the correlation withthe random walk vertical position. Table 6: Kinematic positioning 45 ITRF2014 frame stations, adjusting troposphere zenithdelay. For each station RMS difference relative to the station frame position is computed forthe month of June 2008. The mean and median of the station RMS values are listed.
RMS(mm)East North VerticalMean 6.3 7.2 20.3Median 6.0 7.2 20.0Some kinematic applications may have better information about the tropo-spheric delay. For instance, high flying aircraft typically have a small wet delayand the dry zenith delay may be computed using a pressure sensor. To demon-strate the expected performance of kinematic positioning with better knowntroposphere, we repeated the experiment from Table 6, but fixed the zenithdelay and the gradient parameters to the values from static 24-hour positionsolutions. Comparing Table 6 with Table 7, one can see a significant and largerimprovement in the vertical. 36 able 7: Kinematic positioning 45 ITRF2014 frame stations, tropospheric delay from staticpositioning, statistics as in 6.
RMS(mm)East North VerticalMean 5.6 6.3 15.4Median 5.4 6.3 14.9
Both GIPSY and RTG supported POD of satellites in Low Earth Orbit(LEO), starting with the launch of TOPEX/Poseidon [Bertiger et al., 1994].As a superset of these two software, GipsyX/RTGx supports precise post-processing, reduced-dynamic orbit determination, as well as embedded real-timePOD. For post-processed LEO POD using GPS data, the GipsyX/RTGx pro-vides identical capability to GIPSY, but with a simpler user interface alongwith additional capability for the newer GNSS constellations, DORIS, andSLR. Tests were performed with GRACE [Tapley et al., 2004a], the follow-on GRACE mission (GRACE-FO), and Jason-2 [Lambin et al., 2010; Bertigeret al., 2010b; Cerri et al., 2010]. Since the GPS determined orbits for Jason-2 are sub-centimeter accurate [Bertiger et al., 2010b], we can use those orbitsto measure our accuracy for Jason-2 orbits determined with other data types.Mixing GNSS, SLR, and DORIS data is also possible in GipsyX/RTGx, but hasnot had extensive testing yet. In the subsections below, we detail the expectedaccuracy and software capabilities for LEO POD using GPS, SLR, and DORISdata.
GipsyX has many capabilities for SLR processing, including producing resid-uals to orbits determined from other techniques and independent orbit deter-mination. For one experiment, We used 30-hour arcs of SLR data from 15well-distributed, low-bias SLR sites, centered on noon of each day in 2015 to de-37ermine Jason 2’s orbit with a median radial RMS difference to GPS-determinedorbits of 1.9 cm. We also validated our SLR capabilities by performing orbitdetermination on the LAGEOS 1 and 2 satellites using 7-day arcs for all of2017. We then compared our orbits to the ILRSA combined orbits. Our LA-GEOS 1 and 2 orbits have an overall RMS difference of 5 mm in radial, 16 mmin cross-track and 18 mm in along-track to LAGEOS, which is comparable inmagnitude to the inter-center differences measured by the ILRSA combinationto other centers over the course of the year (averages of 5 mm, 24 mm, and 25mm in the weekly ilrsa weekly sum files across all centers for both LAGEOSsatellites).
GipsyX/RTGx is the operational software used for GRACE-FO to determinethe orbit and clock of the GRACE-FO spacecraft.GRACE and GRACE-FO are among the best low Earth orbiting satellites totest POD with GPS since they have a measurement of the inter-satellite range(up to a bias) that is good to the micron-level. This is the dual-one way rangemeasurement made at K and Ka band, K-Band Range (KBR) [Dunn et al.,2003; Thomas, 1999]. It is the KBR’s precision along with an accelerometermeasuring the non-gravitational forces that allows the precise recovery of theEarth’s time varying gravity field. Although GipsyX/RTGx, can process KBRrange data and use accelerometer data, neither is used in the operational PODfor GRACE or GRACE-FO discussed here. Figure 9 shows the daily standarddeviation of the difference of the range determined by GPS POD and the KBR(clocks aligned with the independent operational code). The processing usedGPS data sampled every 10-sec, antenna calibrations based on one month ofdata, August 2010, reduced dynamics selected to perform well over the full timeperiod, and bias fixing. The average daily baseline standard deviation was 1.6mm. This is significantly better than the 10 mm found in Table 8 of [Kanget al., 2006] using the Center for Space Research’s MSODP software which doesnot include bias fixing. It improves over the results in [Bertiger et al., 2010c]38ostly due to the use of higher rate data. [Kroes et al., 2005] and [Jggi et al.,2007] show improved baseline determination of a little under a mm if biases arefixed between the two spacecraft with a simultaneous POD of both spacecraft.In this processing, both spacecraft are processed independently.
Figure 9: GRACE KBR-GPS Range, Daily GPS POD Baseline Accuracy, Four 1-MonthSamples: Aug. 2008, Aug. 2010, June 2016, April 2017
Although the KBR measurement is not strongly dependent on the GPSPOD/Clock solution for GRACE at the 100 micron level, it is necessary to havethe error of the relative clocks between the two GRACE spacecraft less than160 ps, 1-sigma, after removing a bias (see [Thomas, 1999] eq. 3.19) to havethe errors in the KBR range due to the clock alignment less than 0.5 microns.Figure 10 shows a measure of the precision of the relative clock between thetwo GRACE spacecraft. Since we are solving for the GRACE clock as a whitenoise process, relative to a fixed GPS reference with 30-hours of data centeredon noon of each day, there is a six hour overlap from one day to the next. Ifour reference clock were the same, and our solution were perfect, the differenceof the clock solutions between these two days would be zero. In eq. 5, the first39erm is the difference of the two GRACEA clocks, the second GRACEB. Takingthe difference of the A and B differences removes any reference clock, thus theRMS of this quantity over the central 5 hours of the 6-hours is a good measureof the relative clock precision. Fig. 10 shows that we are significantly under the160 ps requirement with a median value of 20.3 ps. dd clk = ( A day clk − A day clk ) − ( B day clk − B day clk ) (5) Figure 10: RMS Double Difference GRACE Clock Overlaps, Four 1-Month Samples: Aug.2008, Aug. 2010, June 2016, April 2017
In addition to GNSS phase and range data, GipsyX/RTGx can process al-most any radio-metric phase and range data and is easily extended to datatypes that are linear combinations of radio-metric range/phase data; for in-stance, Satellite Laser Ranging or Doppler Orbitography and RadiopositioningIntegrated by Satellite (DORIS) [Willis et al., 2010]. Current DORIS data isgiven in a RINEX like format [Auriol and Tourain, 2010] with dual-frequency40hase measurements and range measurements similar to GNSS. Traditionallythis is processed as Doppler D = φ ( τ ) − φ ( τ ) τ − τ (6)where φ ( τ ) is the measured phase on an orbiter from a ground transmitter atit’s local time τ . Prior to June 20, 2008 the Doppler measurements were givendirectly with corrections for errors in the satellite clock and phase center offsets.The count time, τ − τ , is 10 seconds of local satellite time in eq. 6. Whenforming DORIS Doppler from the phase on the RINEX DORIS data, one mustmodel the satellite receiver clock errors for the computed Doppler model, C , C = ψ ( τ ) − ψ ( τ ) + c ( E ( τ ) − E ( τ )) t − t + E ( τ ) − E ( τ )= ψ ( τ ) − ψ ( τ ) t − t + c ( E ( τ ) − E ( τ )) t − t E ( τ ) − E ( τ ) t − t (7)The phase measurement, with units of length, is written as φ ( τ ) = ψ ( τ )+ cE ( τ ),where E ( τ ) is the difference between coordinate time ( t ) and the local time ofthe receiver in seconds and c is the speed of light. For the DORIS system, thereceiver is driven by a stable clock (Allan deviation on the order of 10 − at aday) and the rate of the clock errors including relativistic effects, E ( τ ) − E ( τ ) t − t issmall, typically on the order of 10 − s/s, we can expand eq. 7 C ≈ ψ ( τ ) − ψ ( τ ) t − t + c E ( τ ) − E ( τ ) t − t − E ( τ ) − E ( τ ) t − t ψ ( τ ) − ψ ( τ ) t − t − c (cid:18) E ( τ ) − E ( τ ) t − t (cid:19) (8)The computed measurement model in eq. 8 is very close to the difference ofphase measurements and fairly easy to code in terms of the basic phase measure-ment used for GNSS. This model also may be used for the legacy DORIS dopplerdata since the clock error terms are essentially zero, due to pre-calibration. On41he DORIS RINEX file, the nominal receiver clock values are given as a timeseries derived from the range data. A quadratic fit over time periods on theorder of a day maybe used for E ( τ ).We have tested this with data from the Jason-2 spacecraft [Couhert et al.,2015] using station coordinates from the latest DPOD (DORIS Precise OrbitDetermination) solution, DPOD2014, aligned on ITRF2014 [Moreaux et al.,2019]. To take into account the effect of the South Atlantic Anomaly (SAA) onthe onboard oscillator [Willis et al., 2016], we did not use any correction modelbut removed a few stations in the South America region. In Fig. 11, we comparethe Jason-2 radial orbit position determined with the DORIS RINEX data fromFeb. 14, 2014 through August 23, 2014 with a GPS-determined orbit whose ra-dial accuracy is about 5 mm [Desai et al., 2018] using ITRF2014 coordinates fortracking stations and typical RMS differences with the GipsyX/RTGx DORISdetermined orbit are at the 9.9 mm level. Errors in radial position go directlyinto the mission’s prime objective to measure sea surface height and are themost important metric for ocean altimetry missions.To better evaluate the SAA effect on Jason2, we will soon investigate whichstations are the most affected and use the new available correction model from[Belli and Exertier, 2018], based on T2L2 measurements. In the future, we planto analyze the Sentinel-3A DORIS RINEX data. The fact that satellite clockfor Sentinel-3A is the same for the GPS and the DORIS on-board instrumentsshould allow us to compare the GPS clock solution and the DORIS clock. TheGPS solution for the on-board clock could be used to properly correct the SAAeffects for this satellite, [Jalabert and Mercier, 2018]. As an example of multi-technique use, we processed GPS and SLR datasimultaneously using GPS and SLR data from low Earth orbiters to tie thesystems together. For the development of reference frames, the ties are tradi-tionally made through local ground surveys to measure the vector between theGPS and SLR instruments. With only three days of data, and no ground survey42 igure 11: RMS Radial DORIS Doppler radial orbit errors relative to GPS JPL RLSE18 ties, we show agreement at the cm level.Depicted in Figure 12 are summaries (by satellite) of tracking data residualsfrom a multi-day GipsyX/RTGx solution in which SLR and GPS are combinedat the observation level. Represented in the solution are 31 GPS satellites, 5dedicated SLR targets in space (LAGEOS 1 and 2, Starlette, Stella and Ajisai),and 3 low-Earth orbiters (LEO) with both GPS receivers and corner reflectors(Jason-2 and GRACE A and B). The latter three LEO missions provide a meansof accurately linking the SLR and GPS systems without the benefit of groundsurvey ties. The uniform and precise (cm-level) tracking residuals across bothdata types (SLR and GPS) testify to the coherence of these diverse space-geodetic observations (radiometric and optical) in this grand GipsyX/RTGxnetwork solution.The solution also features 45 and 18 GPS and SLR ground stations re-spectively. To compensate for know systematic SLR errors, range biases (persatellite) were estimated for a minority (40%) of the stations. Satellite-specificestimates of the optical range variations as a function of the line-of-sight could43 igure 12: GPS dual-freq. phase residuals and SLR residuals combining SLR and GPS Data;Jason-2, GRACE A, B = Sat. Number 32, 33, 34; LAGEOS 1, 2, Starlette, Stella, Ajisai =35, 36, 37, 38, 39. further improve the results, but were not applied in this case. The positions ofall satellites and stations were estimated simultaneously in the GipsyX/RTGxrun (ref.), along with Earth orientation. Using this ‘fiducial-free’ strategy (ref.),the network of satellites and stations will be subject to rotation, but the scale,origin, and relative positions will be well determined. Two of the SLR stationsin the run (Matera, Italy and Tahiti, French Polynesia) also have participatingGPS stations linked by ground survey ties. With only 3 days of tracking data,the GipsyX/RTGx solution reproduced these independent ground ties to 1 cm(3D). The tie between SLR and GPS in the GipsyX/RTGx solution comes solelyfrom the space ties on Jason-1 and the GRACE tandem, testifying not only tothe benefits of combining data at the observation level but also to the fidelityof the GipsyX/RTGx modeling.
GipsyX includes station coordinate processing software which can combinesolutions from several techniques to build reference frames, simulate future per-formance, compute transformation parameters between reference frames, andfit individual time series to estimate positions, velocities, seasonals, and possi-ble discontinuities in the linear and periodic fit, which we refer to as breaks.Each tool has command line help available. On-line training provides detailedinstructions and example data sets for the most common use cases.44 able 8: Comparison of GipsyX frame with ITRF2014 on January 1, 2005. Three translations,one scale, and three rotations are given in mm while the corresponding rates are given inmm/yr. Rotations and scale are multiplied by the Earth radius to get mm at the surface.
Parameter TX TY TZ S RX RY RZ Unit
Offset 0.508 -0.192 -0.144 2.903 0.543 -0.053 -0.354 mmOffset s.d. 0.102 0.095 0.200 0.521 0.117 0.141 0.204 mmRate -0.184 0.044 0.498 0.153 0.001 0.076 0.156 mm/yrRate s.d. 0.013 0.012 0.027 0.036 0.018 0.021 0.026 mm/yr
Table 9: Comparison of GipsyX frame with DTRF2014 on January 1, 2005. Three transla-tions, one scale, and three rotations are given in mm while the corresponding rates are givenin mm/yr. Rotations and scale are multiplied by the Earth radius to get mm at the surface.
Parameter TX TY TZ S RX RY RZ Unit
Offset 0.434 -0.032 -0.861 0.049 0.693 1.221 -1.023 mmOffset s.d. 0.078 0.077 0.174 0.079 0.048 0.067 0.079 mmRate -0.112 0.077 0.629 0.057 -0.098 -0.121 0.329 mm/yrRate s.d. 0.009 0.010 0.021 0.012 0.010 0.012 0.014 mm/yr45 terrestrial reference frame is typically defined by a set of reference positionswith a model of time evolution, the simplest example being a table of positionsand velocities. Reference frames are built by first combining daily or weeklysolutions for each individual technique and then combining all techniques withties into a single frame. A terrestrial reference frame built using GipsyX withinputs from all four geodetic techniques and ties is compared to ITRF2014[Altamimi et al., 2016] in Table 8 and DTRF2014 [Seitz et al., 2016] in Table 9.See electronic supplement 3 for details.GipsyX includes a network simulation tool which can generate output filesat a given frequency for a specified time span, for example daily files spanningone year. The user provides a model consisting of positions, velocities, breaks,and/or seasonal terms. Various forms of white noise can then be injected. Co-ordinate noise can be added which is independent from site to site. Geocenter,scale, and/or rotational noise can be injected which is correlated and impactsall sites. Simulated solutions can be processed just like real ones to test softwareor predict performance of future networks.The transformation between two reference frames at a particular time canbe described by three translations, three rotations, and one scale. Daily trans-formation parameters known as x-files are computed using an input referenceframe to predict coordinates at a particular epoch and then using those pre-dictions to estimate transformation parameters to GNSS positions observed atthat epoch. Daily x-files are publicly available as described in section 6.1.1. Aplot of x-file parameters between IGS14 and GipsyX free-network solutions isshown in Figure 13 . The TX parameter has a mean value of -0.5 mm and astandard deviation of 4.7 mm. The TY parameter has a mean value of -0.7 mmand a standard deviation of 5.6 mm. The TZ parameter has a mean value of-5.3 mm and a standard deviation of 6.8 mm. The Scale parameter has meanvalue of 0.0 mm and a standard deviation of 1.7 mm. These daily correctionsindicate how far GNSS only solutions are from a standard reference frame suchas IGS14. The GNSS only geocenter values have approached IGS14 more closelyover time as modeling and data quality have improved and recent research has46 igure 13: X-file geocenter and scale parameters relative to IGS14. https://sideshow.jpl.nasa.gov/post/series.html . Results for thesite ALGO are shown in Figure 14. The plot shows daily measurements witherror bars in black, the model fit in red, and break times in green. Velocityestimates with error bars are provided along with residual repeatability/WRMSvalues for each component. 48 igure 14: Time series and model fit for ALGO, Algonquin Park, Canada. . Summary The new GipsyX/RTGx software is a robust and powerful tool for geodeticdata analysis and simulations, incorporating decades of expertise and lessonslearned from the design and operations of previous software generations, andtheir applications to the most challenging positioning, navigation, timing, andscience applications. GipsyX/RTGx now underlie all GNSS orbit determinationoperations at JPL, and with hundreds of academic and research licenses, powersgeodetic analyses and science operations across the globe.
8. Acknowledgements
We are grateful to the following individuals for contributions to GipsyX/RTGx:Jason Gross, Miquel Garcia Fernandez, Jan Weiss.The research was carried out at the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, under a contract with the National Aeronautics andSpace Administration.We acknowledge support from the U.S Air Force GPS OCX program, fromthe JPL Global Differential GPS (GDGPS) System, and from NASAs SpaceGeodesy Program.Part of this work was performed supported by the
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