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NASA NTRS2010

Proceedings of the Second NASA Formal Methods Symposium

This publication contains the proceedings of the Second NASA Formal Methods Symposium sponsored by the National Aeronautics and Space Administration and held in Washington D.C. April 13-15, 2010. Topics covered include: Decision Engines for Software Analysis using Satisfiability Modulo Theories Solvers; Verification and Validation of Flight-Critical Systems; Formal Methods at Intel -- An Overview; Automatic Review of Abstract State Machines by Meta Property Verification; Hardware-independent Proofs of Numerical Programs; Slice-based Formal Specification Measures -- Mapping Coupling and Cohesion Measures to Formal Z; How Formal Methods Impels Discovery: A Short History of an Air Traffic Management Project; A Machine-Checked Proof of A State-Space Construction Algorithm; Automated Assume-Guarantee Reasoning for Omega-Regular Systems and Specifications; Modeling Regular Replacement for String Constraint Solving; Using Integer Clocks to Verify the Timing-Sync Sensor Network Protocol; Can Regulatory Bodies Expect Efficient Help from Formal Methods?; Synthesis of Greedy Algorithms Using Dominance Relations; A New Method for Incremental Testing of Finite State Machines; Verification of Faulty Message Passing Systems with Continuous State Space in PVS; Phase Two Feasibility Study for Software Safety Requirements Analysis Using Model Checking; A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover; SimCheck: An Expressive Type System for Simulink; Coverage Metrics for Requirements-Based Testing: Evaluation of Effectiveness; Software Model Checking of ARINC-653 Flight Code with MCP; Evaluation of a Guideline by Formal Modelling of Cruise Control System in Event-B; Formal Verification of Large Software Systems; Symbolic Computation of Strongly Connected Components Using Saturation; Towards the Formal Verification of a Distributed Real-Time Automotive System; Slicing AADL Specifications for Model Checking; Model Checking with Edge-valued Decision Diagrams; and Data-flow based Model Analysis.

Munoz, Cesar↗
NASA NTRS2009

Icy Satellites of Saturn: Impact Cratering and Age Determination

Saturn is the first giant planet to be visited by an orbiting spacecraft that can transmit large amounts of data to Earth. Crater counts on satellites from Phoebe inward to the regular satellites and ring moons are providing unprecedented insights into the origin and time histories of the impacting populations. Many Voyager-era scientists concluded that the satellites had been struck by at least two populations of impactors. In this view, the Population I impactors, which were generally judged to be comets orbiting the Sun, formed most of the larger and older craters, while Population II impactors, interpreted as Saturn-orbiting ejecta from impacts on satellites, produced most of the smaller and younger craters. Voyager data also implied that all of the ring moons, and probably some of the midsized classical moons, had been catastrophically disrupted and reaccreted since they formed. We examine models of the primary impactor populations in the Saturn system. At the present time, ecliptic comets, which likely originate in the Kuiper belt/scattered disk, are predicted to dominate impacts on the regular satellites and ring moons, but the models require extrapolations in size (from the observed Kuiper belt objects to the much smaller bodies that produce the craters) or in distance (from the known active Jupiter family comets to 9.5 AU). Phoebe, Iapetus, and perhaps even moons closer to Saturn have been struck by irregular satellites as well. We describe the Nice model, which provides a plausible mechanism by which the entire Solar System might have experienced an era of heavy bombardment long after the planets formed. We then discuss the three cratering chronologies, including one based upon the Nice model, that have been used to infer surface ages from crater densities on the saturnian satellites. After reviewing scaling relations between the properties of impactors and the craters they produce, we provide model estimates of the present-day rate at which comets impact, and catastrophically disrupt, the saturnian moons. Finally, we present crater counts on the satellites from two different groups. Many of the heavily cratered terrains appear to be nearly saturated, so it is difficult to infer the provenance of the impactors from crater counts alone. More large craters have been found on Iapetus than on any other satellite. Enceladus displays an enormous range of surface ages, ranging from the old mid-latitude plains to the extremely young South Polar Terrain. Cassini images provide some evidence for the reality of Population II. Most of the observed craters may have formed in one or more cataclysms, but more work is needed to determine the roles of heliocentric and planetocentric bodies in creating the craters.

Dones, L.↗
NASA NTRS2010

Focusing Diffraction Grating Element with Aberration Control

Diffraction gratings are optical components with regular patterns of grooves, which angularly disperse incoming light by wavelength in a single plane, called dispersion plane. Traditional gratings on flat substrates do not perform wavefront transformation in the plane perpendicular to the dispersion plane. The device proposed here exhibits regular diffraction grating behavior, dispersing light. In addition, it performs wavelength transformation (focusing or defocusing) of diffracted light in a direction perpendicular to the dispersion plane (called sagittal plane). The device is composed of a diffraction grating with the grooves in the form of equidistant arcs. It may be formed by defining a single arc or an arc approximation, then translating it along a certain direction by a distance equal to a multiple of a fixed distance ("grating period") to obtain other groove positions. Such groove layout is nearly impossible to obtain using traditional ruling methods, such as mechanical ruling or holographic scribing, but is trivial for lithographically scribed gratings. Lithographic scribing is the newly developed method first commercially introduced by LightSmyth Technologies, which produces gratings with the highest performance and arbitrary groove shape/spacing for advanced aberration control. Unlike other types of focusing gratings, the grating is formed on a flat substrate. In a plane perpendicular to the substrate and parallel to the translation direction, the period of the grating and, therefore, the projection of its k-vector onto the plane is the same for any location on the grating surface. In that plane, no waveform transformation by the grating k-vector occurs, except of simple redirection.

Iazikov, Dmitri↗
NASA NTRS2010

Seasonal to Decadal Variations of Water Vapor in the Tropical Lower Stratosphere Observed with Balloon-Borne Cryogenic Frost Point Hygrometers

We investigated water vapor variations in the tropical lower stratosphere on seasonal, quasi-biennial oscillation (QBO), and decadal time scales using balloon-borne cryogenic frost point hygrometer data taken between 1993 and 2009 during various campaigns including the Central Equatorial Pacific Experiment (March 1993), campaigns once or twice annually during the Soundings of Ozone and Water in the Equatorial Region (SOWER) project in the eastern Pacific (1998-2003) and in the western Pacific and Southeast Asia (2001-2009), and the Ticosonde campaigns and regular sounding at Costa Rica (2005-2009). Quasi-regular sounding data taken at Costa Rica clearly show the tape recorder signal. The observed ascent rates agree well with the ones from the Halogen Occultation Experiment (HALOE) satellite sensor. Average profiles from the recent five SOWER campaigns in the equatorial western, Pacific in northern winter and from the three Ticosonde campaigns at Costa Rica (10degN) in northern summer clearly show two effects of the QBO. One is the vertical displacement of water vapor profiles associated with the QBO meridional circulation anomalies, and the other is the concentration variations associated with the QBO tropopause temperature variations. Time series of cryogenic frost point hygrometer data averaged in a lower stratospheric layer together with HALOE and Aura Microwave Limb Sounder data show the existence of decadal variations: The mixing ratios were higher and increasing in the 1990s, lower in the early 2000s, and probably slightly higher again or recovering after 2004. Thus linear trend analysis is not appropriate to investigate the behavior of the tropical lower stratospheric water vapor.

Fujiwara, M.↗
NASA NTRS2011

Assessing the Impact of Advanced Satellite Observations in the NASA GEOS-5 Forecast System Using the Adjoint Method

The adjoint of a data assimilation system provides a flexible and efficient tool for estimating observation impacts on short-range weather forecasts. The impacts of any or all observations can be estimated simultaneously based on a single execution of the adjoint system. The results can be easily aggregated according to data type, location, channel, etc., making this technique especially attractive for examining the impacts of new hyper-spectral satellite instruments and for conducting regular, even near-real time, monitoring of the entire observing system. In this talk, we present results from the adjoint-based observation impact monitoring tool in NASA's GEOS-5 global atmospheric data assimilation and forecast system. The tool has been running in various off-line configurations for some time, and is scheduled to run as a regular part of the real-time forecast suite beginning in autumn 20 I O. We focus on the impacts of the newest components of the satellite observing system, including AIRS, IASI and GPS. For AIRS and IASI, it is shown that the vast majority of the channels assimilated have systematic positive impacts (of varying magnitudes), although some channels degrade the forecast. Of the latter, most are moisture-sensitive or near-surface channels. The impact of GPS observations in the southern hemisphere is found to be a considerable overall benefit to the system. In addition, the spatial variability of observation impacts reveals coherent patterns of positive and negative impacts that may point to deficiencies in the use of certain observations over, for example, specific surface types. When performed in conjunction with selected observing system experiments (OSEs), the adjoint results reveal both redundancies and dependencies between observing system impacts as observations are added or removed from the assimilation system. Understanding these dependencies appears to pose a major challenge for optimizing the use of the current observational network and defining requirements for future observing systems.

Gelaro, Ron↗
NASA NTRS2009

Integration of the Radiation Belt Environment Model Into the Space Weather Modeling Framework

We have integrated the Fok radiation belt environment (RBE) model into the space weather modeling framework (SWMF). RBE is coupled to the global magnetohydrodynamics component (represented by the Block-Adaptive-Tree Solar-wind Roe-type Upwind Scheme, BATS-R-US, code) and the Ionosphere Electrodynamics component of the SWMF, following initial results using the Weimer empirical model for the ionospheric potential. The radiation belt (RB) model solves the convection-diffusion equation of the plasma in the energy range of 10 keV to a few MeV. In stand-alone mode RBE uses Tsyganenko's empirical models for the magnetic field, and Weimer's empirical model for the ionospheric potential. In the SWMF the BATS-R-US model provides the time dependent magnetic field by efficiently tracing the closed magnetic field-lines and passing the geometrical and field strength information to RBE at a regular cadence. The ionosphere electrodynamics component uses a two-dimensional vertical potential solver to provide new potential maps to the RBE model at regular intervals. We discuss the coupling algorithm and show some preliminary results with the coupled code. We run our newly coupled model for periods of steady solar wind conditions and compare our results to the RB model using an empirical magnetic field and potential model. We also simulate the RB for an active time period and find that there are substantial differences in the RB model results when changing either the magnetic field or the electric field, including the creation of an outer belt enhancement via rapid inward transport on the time scale of tens of minutes.

Glocer, A.↗
NASA NTRS2011

Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids

Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.

Diskin, Boris↗
NASA NTRS2006

Implementing Access to Data Distributed on Many Processors

A reference architecture is defined for an object-oriented implementation of domains, arrays, and distributions written in the programming language Chapel. This technology primarily addresses domains that contain arrays that have regular index sets with the low-level implementation details being beyond the scope of this discussion. What is defined is a complete set of object-oriented operators that allows one to perform data distributions for domain arrays involving regular arithmetic index sets. What is unique is that these operators allow for the arbitrary regions of the arrays to be fragmented and distributed across multiple processors with a single point of access giving the programmer the illusion that all the elements are collocated on a single processor. Today's massively parallel High Productivity Computing Systems (HPCS) are characterized by a modular structure, with a large number of processing and memory units connected by a high-speed network. Locality of access as well as load balancing are primary concerns in these systems that are typically used for high-performance scientific computation. Data distributions address these issues by providing a range of methods for spreading large data sets across the components of a system. Over the past two decades, many languages, systems, tools, and libraries have been developed for the support of distributions. Since the performance of data parallel applications is directly influenced by the distribution strategy, users often resort to low-level programming models that allow fine-tuning of the distribution aspects affecting performance, but, at the same time, are tedious and error-prone. This technology presents a reusable design of a data-distribution framework for data parallel high-performance applications. Distributions are a means to express locality in systems composed of large numbers of processor and memory components connected by a network. Since distributions have a great effect on the performance of applications, it is important that the distribution strategy is flexible, so its behavior can change depending on the needs of the application. At the same time, high productivity concerns require that the user be shielded from error-prone, tedious details such as communication and synchronization.

James, Mark↗
NASA NTRS2004

Hexagonal Pixels and Indexing Scheme for Binary Images

A scheme for resampling binaryimage data from a rectangular grid to a regular hexagonal grid and an associated tree-structured pixel-indexing scheme keyed to the level of resolution have been devised. This scheme could be utilized in conjunction with appropriate image-data-processing algorithms to enable automated retrieval and/or recognition of images. For some purposes, this scheme is superior to a prior scheme that relies on rectangular pixels: one example of such a purpose is recognition of fingerprints, which can be approximated more closely by use of line segments along hexagonal axes than by line segments along rectangular axes. This scheme could also be combined with algorithms for query-image-based retrieval of images via the Internet. A binary image on a rectangular grid is generated by raster scanning or by sampling on a stationary grid of rectangular pixels. In either case, each pixel (each cell in the rectangular grid) is denoted as either bright or dark, depending on whether the light level in the pixel is above or below a prescribed threshold. The binary data on such an image are stored in a matrix form that lends itself readily to searches of line segments aligned with either or both of the perpendicular coordinate axes. The first step in resampling onto a regular hexagonal grid is to make the resolution of the hexagonal grid fine enough to capture all the binaryimage detail from the rectangular grid. In practice, this amounts to choosing a hexagonal-cell width equal to or less than a third of the rectangular- cell width. Once the data have been resampled onto the hexagonal grid, the image can readily be checked for line segments aligned with the hexagonal coordinate axes, which typically lie at angles of 30deg, 90deg, and 150deg with respect to say, the horizontal rectangular coordinate axis. Optionally, one can then rotate the rectangular image by 90deg, then again sample onto the hexagonal grid and check for line segments at angles of 0deg, 60deg, and 120deg to the original horizontal coordinate axis. The net result is that one has checked for line segments at angular intervals of 30deg. For even finer angular resolution, one could, for example, then rotate the rectangular-grid image +/-45deg before sampling to perform checking for line segments at angular intervals of 15deg.

Johnson, Gordon G.↗
NASA NTRS2004

Format for Interchange and Display of 3D Terrain Data

Visible Scalable Terrain (ViSTa) is a software format for production, interchange, and display of three-dimensional (3D) terrain data acquired by stereoscopic cameras of robotic vision systems. ViSTa is designed to support scalability of data, accuracy of displayed terrain images, and optimal utilization of computational resources. In a ViSTa file, an area of terrain is represented, at one or more levels of detail, by coordinates of isolated points and/or vertices of triangles derived from a texture map that, in turn, is derived from original terrain images. Unlike prior terrain-image software formats, ViSTa includes provisions to ensure accuracy of texture coordinates. Whereas many such formats are based on 2.5-dimensional terrain models and impose additional regularity constraints on data, ViSTa is based on a 3D model without regularity constraints. Whereas many prior formats require external data for specifying image-data coordinate systems, ViSTa provides for the inclusion of coordinate-system data within data files. ViSTa admits highspeed loading and display within a Java program. ViSTa is designed to minimize file sizes and maximize compressibility and to support straightforward reduction of resolution to reduce file size for Internet-based distribution.

Backes, Paul↗
NASA NTRS2012

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

Xu, Feng↗
NASA NTRS2014

Dielectric Performance of a High Purity HTCC Alumina at High Temperatures - a Comparison Study with Other Polycrystalline Alumina

A very high purity (99.99+%) high temperature co-fired ceramic (HTCC) alumina has recently become commercially available. The raw material of this HTCC alumina is very different from conventional HTCC alumina, and more importantly there is no glass additive in this alumina material for co-firing processing. Previously, selected HTCC and LTCC (low temperature co-fired ceramic) alumina materials were evaluated at high temperatures as dielectric and compared to a regularly sintered 96% polycrystalline alumina (96% Al2O3), where 96% alumina was used as the benchmark. A prototype packaging system based on regular 96% alumina with Au thickfilm metallization successfully facilitated long term testing of high temperature silicon carbide (SiC) electronic devices for over 10,000 hours at 500 C. In order to evaluate this new high purity HTCC alumina for possible high temperature packaging applications, the dielectric properties of this HTCC alumina substrate were measured and compared with those of 96% alumina and a previously tested LTCC alumina from room temperature to 550 C at frequencies of 120 Hz, 1 KHz, 10 KHz, 100 KHz, and 1 MHz. A parallel-plate capacitive device with dielectric of the HTCC alumina and precious metal electrodes were used for measurements of the dielectric constant and dielectric loss of the co-fired alumina material in the temperature and frequency ranges. The capacitance and AC parallel conductance of the capacitive device were directly measured by an AC impedance meter, and the dielectric constant and parallel AC conductivity of the dielectric were calculated from the capacitance and conductance measurement results. The temperature and frequency dependent dielectric constant, AC conductivity, and dissipation factor of the HTCC alumina substrate are presented and compared to those of 96% alumina and a selected LTCC alumina. Other technical advantages of this new co-fired material for possible high packaging applications are also discussed.

Electronic packaging↗
NASA NTRS2012

Linear Estimation of Particle Bulk Parameters from Multi-Wavelength Lidar Measurements

An algorithm for linear estimation of aerosol bulk properties such as particle volume, effective radius and complex refractive index from multiwavelength lidar measurements is presented. The approach uses the fact that the total aerosol concentration can well be approximated as a linear combination of aerosol characteristics measured by multiwavelength lidar. Therefore, the aerosol concentration can be estimated from lidar measurements without the need to derive the size distribution, which entails more sophisticated procedures. The definition of the coefficients required for the linear estimates is based on an expansion of the particle size distribution in terms of the measurement kernels. Once the coefficients are established, the approach permits fast retrieval of aerosol bulk properties when compared with the full regularization technique. In addition, the straightforward estimation of bulk properties stabilizes the inversion making it more resistant to noise in the optical data. Numerical tests demonstrate that for data sets containing three aerosol backscattering and two extinction coefficients (so called 3 + 2 ) the uncertainties in the retrieval of particle volume and surface area are below 45% when input data random uncertainties are below 20 %. Moreover, using linear estimates allows reliable retrievals even when the number of input data is reduced. To evaluate the approach, the results obtained using this technique are compared with those based on the previously developed full inversion scheme that relies on the regularization procedure. Both techniques were applied to the data measured by multiwavelength lidar at NASA/GSFC. The results obtained with both methods using the same observations are in good agreement. At the same time, the high speed of the retrieval using linear estimates makes the method preferable for generating aerosol information from extended lidar observations. To demonstrate the efficiency of the method, an extended time series of observations acquired in Turkey in May 2010 was processed using the linear estimates technique permitting, for what we believe to be the first time, temporal-height distributions of particle parameters.

linear estimation↗
NASA NTRS2014

APC: A New Code for Atmospheric Polarization Computations

A new polarized radiative transfer code Atmospheric Polarization Computations (APC) is described. The code is based on separation of the diffuse light field into anisotropic and smooth (regular) parts. The anisotropic part is computed analytically. The smooth regular part is computed numerically using the discrete ordinates method. Vertical stratification of the atmosphere, common types of bidirectional surface reflection and scattering by spherical particles or spheroids are included. A particular consideration is given to computation of the bidirectional polarization distribution function (BPDF) of the waved ocean surface.

surface reflection↗
NASA NTRS2012

Dielectric Performance of High Purity HTCC Alumina at High Temperatures - A Comparison Study with Other Polycrystalline Alumina

A very high purity (99.99+) high temperature co-fired ceramic (HTCC) alumina has recently become commercially available. The raw material of this HTCC alumina is very different from conventional HTCC alumina, and more importantly there is no glass additive in this co-fired material. Previously, selected HTCC and LTCC (low temperature co-fired ceramic) alumina materials were evaluated at high temperatures as dielectric and compared to a regularly sintered 96 polycrystalline alumina (96 Al2O3), where 96 alumina was used as the benchmark. A prototype packaging system based on regular 96 alumina with Au thick-film metallization successfully facilitated long term testing of high temperature silicon carbide (SiC) electronic devices for over 10,000 hours at 500C. In order to evaluate this new HTCC alumina for possible high temperature packaging applications, the dielectric properties of this HTCC alumina substrate were measured and compared with those of 96 alumina and a LTCC alumina from room temperature to 550C at frequencies of 120 Hz, 1 KHz, 10 KHz, 100 KHz, and 1 MHz. A parallel-plate capacitive device with dielectric of the HTCC alumina and precious metal electrodes were used for measurements of the dielectric constant and dielectric loss of the co-fired alumina material in the temperature and frequency ranges. The capacitance and AC parallel conductance of the capacitive device were directly measured by an AC impedance meter, and the dielectric constant and parallel AC conductivity of the dielectric were calculated from the capacitance and conductance measurement results. The temperature and frequency dependent dielectric constant, AC conductivity, and dissipation factor of the HTCC alumina substrate are presented and compared to those of 96 alumina. Other technical advantages of this new co-fired material for possible high packaging applications are also discussed.

High temperature↗
NASA NTRS2014

Monitoring of the Crab Nebula with Chandra and Other Observatories Including HST

Subsequent to the detections AGILE and Fermi/LAT of the gamma‐ray flares from the Crab Nebula in the fall of 2010, this team has been monitoring the X‐Ray emission from the Crab on a regular basis. X‐Ray observations have taken place typically once per month when viewing constraints allow and more recently four times per year. There have been notable exceptions, e.g. in April of 2011 and March 2013 when we initiated a set of Chandra Target of opportunity observations in conjunction with bright gamma‐ray flares. For much of the time regular HST observations were made in conjunction with the Chandra observations. The aim of this program to further characterize, in depth, the X‐Ray and optical variations that take place in the nebula, and by so doing determine the regions which contribute to the harder X‐ray variations and, if possible, determine the precise location within the Nebula of the origin of the gamma‐ray flares. As part of this project members of the team have developed Singular Value Decomposition techniques to sequences of images in order to more accurately characterize features. The current status of the project will be presented highlighting studies of the inner knot and possible correlations with the flares.

Weisskopf, Martin C.↗
NASA NTRS2013

VERA Geodetic Activities

This report briefly describes the geodetic activities of VERA in the year 2012. The regular geodetic observations are carried out both in K- and S/X-bands. The frequency of regular observations is three times a month-twice for the VERA internal observations in K-band. The networks of the S/X sessions are JADE of GSI and IVS-T2. The raw data of the T2 and JADE sessions are electronically transferred to the Bonn, Haystack, and GSI correlators via Internet. Gravimetric observations are carried out at the VERA stations. An SG was installed at Mizusawa and placed in the vicinity of the VERA antenna in order to monitor vertical displacement at the end of 2008, and the observations continued throughout the year. Also at the VERA-Ishigakijima station, continuous operation of the SG started in 2012. The crustal movements generated by the 2011 earthquake off the Pacific coast of Tohoku continued during 2012, and displacement of the VERA-Mizusawa position by post-seismic creeping continued.

Jike, Takaaki↗
NASA NTRS2013

Data Center at NICT

The Data Center at the National Institute of Information and Communications Technology (NICT) archives and releases the databases and analysis results processed at the Correlator and the Analysis Center at NICT. Regular VLBI sessions of the Key Stone Project VLBI Network were the primary objective of the Data Center. These regular sessions continued until the end of November 2001. In addition to the Key Stone Project VLBI sessions, NICT has been conducting geodetic VLBI sessions for various purposes, and these data are also archived and released by the Data Center.

Ichikawa, Ryuichi↗