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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Statistical Analysis of daily mean temperatures

Data of daily mean temperatures recorded at the Kennedy Center during the period of 1957-1977 were analyzed to forecast daily mean temperatures and their thirty-day moving averages for a period of ten to fifteen days in a given month. Since it is found that the standard deviation is linear in the mean, a logarithmic transformation of the data is used for finding an integrated moving average process IMA by the Box-Jenkins aproach. The first differences of the transformed data seem to fit a moving average model with parameter value 2, MA(2). The consideration of seasonality factor makes the fit worse.

Ross, D. C.↗
NASA NTRS1999

MOD Tool (Microwave Optics Design Tool)

The Jet Propulsion Laboratory (JPL) is currently designing and building a number of instruments that operate in the microwave and millimeter-wave bands. These include MIRO (Microwave Instrument for the Rosetta Orbiter), MLS (Microwave Limb Sounder), and IMAS (Integrated Multispectral Atmospheric Sounder). These instruments must be designed and built to meet key design criteria (e.g., beamwidth, gain, pointing) obtained from the scientific goals for the instrument. These criteria are frequently functions of the operating environment (both thermal and mechanical). To design and build instruments which meet these criteria, it is essential to be able to model the instrument in its environments. Currently, a number of modeling tools exist. Commonly used tools at JPL include: FEMAP (meshing), NASTRAN (structural modeling), TRASYS and SINDA (thermal modeling), MACOS/IMOS (optical modeling), and POPO (physical optics modeling). Each of these tools is used by an analyst, who models the instrument in one discipline. The analyst then provides the results of this modeling to another analyst, who continues the overall modeling in another discipline. There is a large reengineering task in place at JPL to automate and speed-up the structural and thermal modeling disciplines, which does not include MOD Tool. The focus of MOD Tool (and of this paper) is in the fields unique to microwave and millimeter-wave instrument design. These include initial design and analysis of the instrument without thermal or structural loads, the automation of the transfer of this design to a high-end CAD tool, and the analysis of the structurally deformed instrument (due to structural and/or thermal loads). MOD Tool is a distributed tool, with a database of design information residing on a server, physical optics analysis being performed on a variety of supercomputer platforms, and a graphical user interface (GUI) residing on the user's desktop computer. The MOD Tool client is being developed using Tcl/Tk, which allows the user to work on a choice of platforms (PC, Mac, or Unix) after downloading the Tcl/Tk binary, which is readily available on the web. The MOD Tool server is written using Expect, and it resides on a Sun workstation. Client/server communications are performed over a socket, where upon a connection from a client to the server, the server spawns a child which is be dedicated to communicating with that client. The server communicates with other machines, such as supercomputers using Expect with the username and password being provided by the user on the client.

Katz, Daniel S.↗
NASA NTRS2001

AIRS-Light Instrument Concept and Critical Technology Development

Understanding Earth's climate, atmospheric transport mechanisms, and the hydrologic cycle requires a precise knowledge of global atmospheric circulation, temperature profiles, and water vapor distribution. The accuracy of advanced sounders such as AIRS/AMSU/HSB on NASA's Aqua spacecraft can match radiosonde accuracy. It is essential to fold those capabilities fully into the NPOESS, enabling soundings of radiosonde accuracy, every 6 hours around the globe on an operational basis. However, the size, mass, power demands, and thermal characteristics of the Aqua sounding instrument suite cannot be accommodated on the NPOESS spacecraft. AIRS-Light is an instrument concept, developed under the Instrument Incubator Program, which provides IR sounding performance identical to the AIRS instrument, but uses advances in HgCdTe FPA technology and pulse tube cooler technology, as well as design changes to dramatically reduce the size, mass, and power demand, allowing AIRS-Light to meet all NPOESS spacecraft interface requirements. The instrument concept includes substantial re-use of AIRS component designs, including the complex AIRS FPA, to reduce development risk and cost. The AIRS-Light Instrument Incubator program fostered the development of photovoltaic-mode HgCdTe detector array technology for the 13.5-15.4 micron band covered by photoconductive-mode HgCdTe arrays in AIRS, achieved state of the art results in this band, and substantially reduced the development risk for this last new technology needed for AIRS-Light implementation, A demonstration of a prototype 14.5-15.4 micron band IRFPA in a reduced heat-load dewar together with the IMAS pulse tube cryocooler is in progress.

Maschhoff, Kevin↗
NASA NTRS2009

Avionics System Architecture for the NASA Orion Vehicle

It has been 30 years since the National Aeronautics and Space Administration (NASA) last developed a crewed spacecraft capable of launch, on-orbit operations, and landing. During that time, aerospace avionics technologies have greatly advanced in capability, and these technologies have enabled integrated avionics architectures for aerospace applications. The inception of NASA s Orion Crew Exploration Vehicle (CEV) spacecraft offers the opportunity to leverage the latest integrated avionics technologies into crewed space vehicle architecture. The outstanding question is to what extent to implement these advances in avionics while still meeting the unique crewed spaceflight requirements for safety, reliability and maintainability. Historically, aircraft and spacecraft have very similar avionics requirements. Both aircraft and spacecraft must have high reliability. They also must have as much computing power as possible and provide low latency between user control and effecter response while minimizing weight, volume, and power. However, there are several key differences between aircraft and spacecraft avionics. Typically, the overall spacecraft operational time is much shorter than aircraft operation time, but the typical mission time (and hence, the time between preventive maintenance) is longer for a spacecraft than an aircraft. Also, the radiation environment is typically more severe for spacecraft than aircraft. A "loss of mission" scenario (i.e. - the mission is not a success, but there are no casualties) arguably has a greater impact on a multi-million dollar spaceflight mission than a typical commercial flight. Such differences need to be weighted when determining if an aircraft-like integrated modular avionics (IMA) system is suitable for a crewed spacecraft. This paper will explore the preliminary design process of the Orion vehicle avionics system by first identifying the Orion driving requirements and the difference between Orion requirements and those of other previous crewed spacecraft avionics systems. Common systems engineering methods will be used to evaluate the value propositions, or the factors that weight most heavily in design consideration, of Orion and other aerospace systems. Then, the current Orion avionics architecture will be presented and evaluated.

Baggerman, Clint↗
NASA NTRS2010

Verification and Validation of Flight-Critical Systems

For the first time in many years, the NASA budget presented to congress calls for a focused effort on the verification and validation (V&V) of complex systems. This is mostly motivated by the results of the VVFCS (V&V of Flight-Critical Systems) study, which should materialize as a a concrete effort under the Aviation Safety program. This talk will present the results of the study, from requirements coming out of discussions with the FAA and the Joint Planning and Development Office (JPDO) to technical plan addressing the issue, and its proposed current and future V&V research agenda, which will be addressed by NASA Ames, Langley, and Dryden as well as external partners through NASA Research Announcements (NRA) calls. This agenda calls for pushing V&V earlier in the life cycle and take advantage of formal methods to increase safety and reduce cost of V&V. I will present the on-going research work (especially the four main technical areas: Safety Assurance, Distributed Systems, Authority and Autonomy, and Software-Intensive Systems), possible extensions, and how VVFCS plans on grounding the research in realistic examples, including an intended V&V test-bench based on an Integrated Modular Avionics (IMA) architecture and hosted by Dryden.

Brat, Guillaume↗
NASA NTRS2010

Software Model Checking of ARINC-653 Flight Code with MCP

The ARINC-653 standard defines a common interface for Integrated Modular Avionics (IMA) code. In particular, ARINC-653 Part 1 specifies a process- and partition-management API that is analogous to POSIX threads, but with certain extensions and restrictions intended to support the implementation of high reliability flight code. MCP is a software model checker, developed at NASA Ames, that provides capabilities for model checking C and C++ source code. In this paper, we present recent work aimed at implementing extensions to MCP that support ARINC-653, and we discuss the challenges and opportunities that consequentially arise. Providing support for ARINC-653 s time and space partitioning is nontrivial, though there are implicit benefits for partial order reduction possible as a consequence of the API s strict interprocess communication policy.

Thompson, Sarah J.↗
NASA NTRS2011

Discovery of Brownleeite: a New Manganese Silicide Mineral in an Interplanetary Dust Particle

The Earth accretes approximately 40,000 tons of cosmic dust annually, originating mainly from the disintegration of comets and collisions among asteroids. This cosmic dust, also known as interplanetary dust particles (IDPs), is a subject of intense interest since it is made of the original building blocks of our Solar System. Although the specific parent bodies of IDPs are unknown, the anhydrous chondritic-porous IDPs (CP-IDPs) subset has been potentially linked to a cometary source. The CP-IDPs are extremely primitive materials based on their unequilibrated mineralogy, C-rich chemistry, and anomalous isotopic signatures. In particular, some CP-IDPs escaped the thermal, aqueous and impact shock processing that has modified or destroyed the original mineralogy of meteorites. Thus, the CP-IDPs represent some of the most primitive solar system materials available for laboratory study. Most CP-IDPs are comprised of minerals that are common on Earth. However, in the course of an examination of one of the CP-IDPs, we encountered three sub-micrometer sized grains of manganese silicide (MnSi), a phase that has heretofore not been found in nature. In the seminar, we would like to focus on IDP studies and this manganese silicide phase that has been approved as the first new mineral identified from a comet by the International Mineralogical Association (IMA) in 2008. The mineral is named in honour of Donald E. Brownlee, an American astronomer and a founder of the field of cosmic dust research who is the principal investigator of the NASA Stardust Mission that collected dust samples from Comet 81P/Wild-2 and returned them to Earth. Much of our current view and understanding of the early solar system would not exist without the pioneering work of professor Don Brownlee in the study of IDPs.

Keller, Lindsay P.↗
NASA NTRS2012

Flux Estimates of Ions from the Lunar Exosphere

We compare estimates for the ion fluxes of twelve expected constituents of the lunar exosphere with estimates for the ion fluxes ejected from the lunar surface by solar wind ions and electrons. Our estimates demonstrate that measurements of lunar ions will help constrain the abundances of many undetected species in the lunar exosphere, particularly AI and Si, because the expected ion flux levels from the exosphere exceed those from the surface. To correctly infer the relative abundances of exospheric ions and neutrals from Kaguya Ion Mass Analyzer (IMA) measurements, we must take into account the velocity distributions of local ions. The predicted spectrum underestimates the measured levels of 0+ relative to other lunar ion species, a result that may suggest contributions by molecular ions to the measured 0+ rates.

Sarantos, M.↗
NASA NTRS2013

Assessment Environment for Complex Systems Software Guide

This Software Guide (SG) describes the software developed to test the Assessment Environment for Complex Systems (AECS) by the West Virginia High Technology Consortium (WVHTC) Foundation's Mission Systems Group (MSG) for the National Aeronautics and Space Administration (NASA) Aeronautics Research Mission Directorate (ARMD). This software is referred to as the AECS Test Project throughout the remainder of this document. AECS provides a framework for developing, simulating, testing, and analyzing modern avionics systems within an Integrated Modular Avionics (IMA) architecture. The purpose of the AECS Test Project is twofold. First, it provides a means to test the AECS hardware and system developed by MSG. Second, it provides an example project upon which future AECS research may be based. This Software Guide fully describes building, installing, and executing the AECS Test Project as well as its architecture and design. The design of the AECS hardware is described in the AECS Hardware Guide. Instructions on how to configure, build and use the AECS are described in the User's Guide. Sample AECS software, developed by the WVHTC Foundation, is presented in the AECS Software Guide. The AECS Hardware Guide, AECS User's Guide, and AECS Software Guide are authored by MSG. The requirements set forth for AECS are presented in the Statement of Work for the Assessment Environment for Complex Systems authored by NASA Dryden Flight Research Center (DFRC). The intended audience for this document includes software engineers, hardware engineers, project managers, and quality assurance personnel from WVHTC Foundation (the suppliers of the software), NASA (the customer), and future researchers (users of the software). Readers are assumed to have general knowledge in the field of real-time, embedded computer software development.

tests↗
NASA NTRS2018

Discreditation of Bobdownsite and the Establishment of Criteria for the Identification of Minerals with Essential Monofluorophosphate (PO3F2-)

Bobdownsite, IMA number 2008-037, was approved as a new mineral by the Commission on New Minerals, Nomenclature and Classification (CNMNC) as the fluorine endmember of the mineral whitlockite. The type locality of bobdownsite is in Big Fish River, Yukon Canada, and bobdownsite was reported to be the first naturally occurring mineral with essential monofluorophosphate (PO3F2-). The type specimen of bobdownsite has been reinvestigated by electron probe microanalysis (EPMA), and our data indicate that fluorine abundances are below detection in the mineral. In addition, we conducted detailed analysis of bobdownsite from the type locality by gas chromatography isotope ratio mass spectrometry, Raman spectroscopy, EPMA, and NMR spectroscopy. These data were compared with previously published data on synthetic monofluorophosphate salts. Collectively, these data indicate that bobdownsite is indistinguishable from whitlockite with a composition along the whitlockite-merrillite solid solution. Bobdownsite is therefore discredited as a valid mineral species. An additional mineral, krásnoite, has been purported to have monofluorophosphate components in its structure, but reexamination of those data indicate that F- in krásnoite forms bonds with Al, similar to OH- bonded to Al in perhamite. Consequently, krásnoite also lacks monofluorophosphate groups, and there are currently no valid mineral species with monofluorophosphate in their structure. We recommend that any future reports of new minerals that contain essential monofluorophosphate anions be vetted by abundance measurements of fluorine, vibrational spectroscopy (both Raman and FTIR), and where paramagnetic components are permissibly low, NMR spectroscopy. Furthermore, we emphasize the importance of using synthetic compounds containing monofluorophosphate anions as a point of comparison in the identification of minerals with essential monofluorophosphate. Structural data that yield satisfactory P-F bond lengths determined by X-ray crystallography, coupled with direct chemical analyses of fluorine in a material do not constitute sufficient evidence alone to identify a new mineral with essential monofluorophosphate anions.

McCubbin, Francis M.↗
NASA NTRS2020

Machiite, Al2Ti3O9, A New Oxide Mineral from the Murchison Carbonaceous Chondrite: A New Ultra-refractory Phase From the Solar Nebula

Machiite (IMA 2016-067), Al2Ti3O9, is a new mineral that occurs as a single euhedral crystal, 4.4 mm in size, in contact with an euhedral corundum grain, 12 mm in size, in a matrix of the Murchison CM2 carbonaceous chondrite. The mean chemical composition of holotype machiite by electron probe microanalysis is (wt%) TiO2 59.75, Al2O3 15.97, Sc2O3 10.29, ZrO2 9.18, Y2O3 2.86, FeO 1.09, CaO 0.44, SiO2 0.20, MgO 0.10, total 99.87, giving rise to an empirical formula (based on 9 oxygen atoms pfu) of (Al1.17Sc0.56Y0.10Ti4+0.08Fe0.06Ca0.03Mg0.01)(Ti4+2.71Zr0.28Si0.01)O9. The general formula is (Al,Sc)2(Ti4+,Zr)3O9. The end-member formula is Al2Ti3O9. Machiite has the C2/c schreyerite-type structure with a = 17.10 Å, b = 5.03 Å, c = 7.06 Å, b = 107°, V = 581 Å3, and Z = 4, as revealed by electron backscatter diffraction. The calculated density using the measured composition is 4.27 g/cm3. The machiite crystal is highly 16O-depleted relative to the coexisting corundum grain (D17O = –0.2 ± 2.4‰ and –24.1 ± 2.6‰, respectively; where D17O = d17O – 0.52 × d18O). Machiite is a new member of the schreyerite (V2Ti3O9) group and a new Sc,Zr-rich ultrarefractory phase formed in the solar nebula, either by gas-solid condensation or as a result of crystallization from a Ca,Al-rich melt having solar-like oxygen isotopic composition (D17O ~ –25‰) under high-temperature (~1400–1500 °C) and low-pressure (~10-4–10-5 bar) conditions in the CAI-forming region near the protosun. The currently observed disequilibrium oxygen isotopic composition between machiite and corundum may indicate that machiite subsequently experienced oxygen isotopic exchange with a planetary-like 16O-poor gaseous reservoir either in the solar nebula or on the CM chondrite parent body. The name machiite is in honor of Chi Ma, mineralogist at California Institute of Technology, for his contributions to meteorite mineralogy and discovery of many new minerals representing extreme conditions of formation.

Alexander N Krot↗
NASA NTRS2018

Adrianite, Ca12(Al4Mg3Si7)O32Cl6, a New Cl-rich Silicate Mineral From the Allende Meteorite: An Alteration Phase in a Ca-Al-rich Inclusion

Adrianite (IMA 2014-028), Ca12(Al4Mg3Si7)O32Cl6, is a new Cl-rich silicate mineral and the Si,Mg analog of wadalite. It occurs with monticellite, grossular, wadalite, and hutcheonite in altered areas along some veins between primary melilite, spinel, and Ti,Al-diopside in a Type B1 FUN (Fractionation and Unidentified Nuclear effects) Ca-Al-rich inclusion (CAI), Egg-3, from the Allende CV3 carbona-ceous chondrite. The mean chemical composition of type adrianite by electron probe microanalysis is (wt%) CaO 41.5, SiO2 27.5, Al2O3 12.4, MgO 7.3, Na2O 0.41, Cl 13.0, O=Cl –2.94, total 99.2, giving rise to an empirical formula of (Ca11.69Na0.21)(Al3.85Mg2.88Si7.23)O32Cl5.80. The end-member formula is Ca12(Mg5Si9)O32Cl6. Adrianite has the I43d wadalite structure with a = 11.981 Å, V = 1719.8 Å3, and Z = 2, as revealed by electron backscatter diffraction. The calculated density using the measured composition is 3.03 g/cm3. Adrianite is a new secondary mineral in Allende, apparently formed by alkali-halogen metasomatic alteration of primary CAI minerals such as melilite, anorthite, perovskite, and Ti,Al-diopside on the CV chondrite parent asteroid. Formation of secondary Cl-rich minerals sodalite, adrianite, and wadalite during metasomatic alteration of the Allende CAIs suggests that the metasomatic fluids had Cl-rich compositions. The mineral name is in honor of Adrian J. Brearley, mineralogist at the University of New Mexico, U.S.A., in recognition of his many contributions to the understanding of secondary mineralization in chondritic meteorites.

Chi Ma↗
NASA NTRS2020

Machiite, Al2Ti3O9, a New Oxide Mineral from the Murchison Carbonaceous Chondrite: A New Ultra-refractory Phase from the Solar Nebula

Machiite (IMA 2016-067), Al2Ti3O9, is a new mineral that occurs as a single euhedral crystal, 4.4 mm in size, in contact with an euhedral corundum grain, 12 mm in size, in a matrix of the Murchison CM2 carbonaceous chondrite. The mean chemical composition of holotype machiite by electron probe microanalysis is (wt%) TiO2 59.75, Al2O3 15.97, Sc2O3 10.29, ZrO2 9.18, Y2O3 2.86, FeO 1.09, CaO 0.44, SiO2 0.20, MgO 0.10, total 99.87, giving rise to an empirical formula (based on 9 oxygen atoms pfu) of (Al1.17Sc0.56Y0.10Ti4+0.08Fe0.06Ca0.03Mg0.01)(Ti4+2.71Zr0.28Si0.01)O9. The general formula is (Al,Sc)2(Ti4+,Zr)3O9. The end-member formula is Al2Ti3O9. Machiite has the C2/c schreyerite-type structure with a = 17.10 Å, b = 5.03 Å, c = 7.06 Å, b = 107°, V = 581 Å3, and Z = 4, as revealed by electron backscatter diffraction. The calculated density using the measured composition is 4.27 g/cm3. The machiite crystal is highly 16O-depleted relative to the coexisting corundum grain (D17O = –0.2 ±2.4‰ and –24.1 ± 2.6‰, respectively; where D17O = d17O – 0.52 ×d18O). Machiite is a new member of the schreyerite (V2Ti3O9) group and a new Sc,Zr-rich ultrarefractory phase formed in the solar nebula, either by gas-solid condensation or as a result of crystallization from a Ca, Al-rich melt having solar-like oxygen isotopic composition (D17O ~ –25‰) under high-temperature (~1400–1500 °C) and low-pressure (~10-4–10-5 bar) conditions in the CAI-forming region near the protosun. The currently observed disequilibrium oxygen isotopic composition between machiite and corundum may indicate that machiite subsequently experienced oxygen isotopic exchange with a planetary-like 16O-poor gaseous reservoir either in the solar nebula or on the CM chondrite parent body. The name machiite is in honor of Chi Ma, mineralogist at California Institute of Technology, for his contributions to meteorite mineralogy and discovery of many new minerals representing extreme conditions of formation.

Machiite↗
NASA NTRS2018

Adrianite, Ca12(Al4Mg3Si7)O32Cl6, a New Cl-rich Silicate Mineral from the Allende Meteorite: An Alteration Phase in a Ca-Al-rich Inclusion

Adrianite (IMA 2014-028), Ca12 (Al4Mg3Si7)O32Cl6, is a new Cl-rich silicate mineral and the Si, Mg analog of wadalite. It occurs with monticellite, grossular, wadalite, and hutcheonite in altered areas along some veins between primary melilite, spinel, and Ti, Al-diopside in a Type B1 FUN (Fractionation and Unidentified Nuclear effects) Ca-Al-rich inclusion (CAI), Egg-3, from the Allende CV3 carbonaceous chondrite. The mean chemical composition of type adrianite by electron probe microanalysis is (wt%) CaO 41.5, SiO2 27.5, Al2O3 12.4, MgO 7.3, Na2O 0.41, Cl 13.0, O=Cl –2.94, total 99.2, giving rise to an empirical formula of (Ca11.69Na0.21) (Al3.85Mg2.88Si7.23) O32Cl5.80. The end-member formula is Ca12 (Mg5Si9) O32Cl6. Adrianite has the I43d wadalite structure with a = 11.981 Å, V = 1719.8 Å3, and Z = 2, as revealed by electron backscatter diffraction. The calculated density using the measured composition is 3.03 g/cm3. Adrianite is a new secondary mineral in Allende, apparently formed by alkali-halogen metasomatic alteration of primary CAI minerals such as melilite, anorthite, perovskite, and Ti,Al-diopside on the CV chondrite parent asteroid. Formation of secondary Cl-rich minerals sodalite, adrianite, and wadalite during metasomatic alteration of the Allende CAIs suggests that the metasomatic fluids had Cl-rich compositions. The mineral name is in honor of Adrian J. Brearley, mineralogist at the University of New Mexico, U.S.A., in recognition of his many contributions to the understanding of secondary mineralization in chondritic meteorites.

Adrianite↗
DOE OSTI2025

Analyzing the Quantum Approximate Optimization Algorithm: Ansätze, Symmetries, and Lie Algebras

The quantum approximate optimization algorithm (QAOA) has been proposed as a method to obtain approximate solutions for combinatorial optimization tasks. In this work, we study the underlying algebraic properties of three QAOA ansätze for the maximum-cut problem on connected graphs, while focusing on the generated Lie algebras as well as their invariant subspaces. Specifically, we analyze the standard QAOA ansatz as well as the orbit and multiangle ansätze. We are able to fully characterize the Lie algebras of the multiangle ansatz across arbitrary connected graphs, finding that they only fall into one of just six families. Aside from the cycle and path graphs, the Lie dimensions for every graph are exponentially large in the system size, meaning that multiangle ansätze are extremely prone to exhibiting barren plateaus. Then, a similar quasi-graph-independent Lie-algebraic characterization beyond the multiangle ansatz is impeded as the circuit exhibits additional “hidden” symmetries besides those naturally arising from a certain parity-superselection operator and all automorphisms of the considered graph. Disregarding the “hidden” symmetries, we can upper bound the dimensions of the orbit and the standard Lie algebras, and the dimensions of the associated invariant subspaces are determined via explicit character formulas. To finish, we conjecture that (for most graphs) the standard Lie algebras have only components that are either exponential or that grow, at most, polynomially with the system size. This would imply that the QAOA is either prone to barren plateaus or classically simulable. More generally, our work provides a symmetry framework and tools to analyze any desired variational quantum algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

Precise measurement method for ionospheric total electron content using signals from GPS satellites

A GPS codeless receiver called GTR-2 was for measuring total electron content (TEC) along the line of sight to the GPS satellite by using the cross correlation amplitude of the received P-code signals carried by L1(1575.42 MHz) and L2(1227.6 MHz). This equipment has the performance of uncertainty in the measurement of TEC of about 2 X 10(exp 16) electrons/sq m when a 10 dBi gain antenna was used. To increase the measurement performance, an upper version of GTR-2 called GTR-3 is planned which uses the phase information of the continuous signals obtained by making a cross correlation or multiplication of the received L1 and L2 P-code signals. By using the difference of these measured phases values, the ionospheric delay with the ambiguities of the periods of L1+L2 and L1-L2 signals can be estimated.

Imae, Michito↗