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NASA NTRS2000

Endpoint Security Using Biometric Authentication for Secure Remote Mission Operations

We propose a flexible security authentication solution for the spacecraft end-user, which will allow the user to interact over Internet with the spacecraft, its instruments, or with the ground segment from anywhere, anytime based on the user's pre-defined set of privileges. This package includes biometrics authentication products, such as face, voice or fingerprint recognition, authentication services and procedures, such as: user registration and verification over the Internet and user database maintenance, with a configurable schema of spacecraft users' privileges. This fast and reliable user authentication mechanism will become an integral part of end-to-end ground-to-space secure Internet communications and migration from current practice to the future. All modules and services of the proposed package are commercially available and built to the NIST BioAPI standard, which facilitates "pluggability" and interoperability.

Donohue, John T.↗
NASA NTRS2006

Results and Lessons from MODIS Reflective Solar Bands Calibration: Pre-launch to On-orbit

MODIS is a major instrument for the NASA EOS Terra (1aunched in December 1999) and Aqua (launched in May 2002) missions. It was designed and built to enhance and extend its heritage sensors' measurements and data records with applications covering a wide range of studies of the Earth's land, oceans, and atmosphere. MODIS has 36 spectral bands (0.41 - 14.4 micrometers) located on four focal plane assemblies (FPAs). It makes measurements at three nadir spatial resolutions: 250m (bands 1-2), 500m (bands 3-7), and lkm (bands 8-36). Because of instrument design complexity and stringent calibration requirements, extensive calibration and characterization activities were conducted pre-launch by the sensor vendor (Raytheon / Santa Barbara Remote Sensing) for both Tesa and Aqua MODIS. For the 20 reflective solar bands (RSB), these activities include measurements for the detectors noise characterization and radiometric performance, system level response versus scan-angle (RVS), polarization sensitivity, and relative spectral response (RSR). Key radiometric performance was evaluated using thermal vacuum observations. On-orbit MODIS RSB calibration is performed using a solar diffuser (SD) and solar diffuser stability monitor (SDSM) system. The SD bi-directional reflectance factor (BRF) was characterized pre-launch by the sensor vendor with reference samples traceable to NIST reflectance standards. This paper provides a summary of Terra and Aqua MODIS RSB pre-launch and on-orbit calibration and characterization activities and results with focus on the detectors' noise characterization and radiometric performance. Challenging and concerning issues and lessons learned from RSB pre-launch calibration and their impact on post launch performance are also presented. A similar summary for MODIS thermal emissive bands (TEB) is reported in a separate paper in these proceedings.

Xiong, X.↗
NASA NTRS2008

MODIS Solar Diffuser On-orbit Performance

MODIS is a key instrument for the NASA Earth Observing System (EOS), currently operated on both the Terra and Aqua missions. Each MODIS instrument has 20 reflective solar bands (RSBs) and 16 thermal emissive bands (TEBs). MODIS RSB on-orbit calibration is reflectance based using an on-board solar diffuser (SD). The SD bi-directional reflectance factors (BRFs) were characterized pre-launch using reference diffuser samples, which are traceable to NIST reflectance standards. The SD BRF on-orbit degradation (or change) is tracked by another onboard device, called the solar diffuser stability monitor (SDSM). The SDSM is operated during each scheduled SD calibration event, making alternate observations of direct sunlight and the diffusely reflected sunlight from the SD. The time series of the ratios of SDSM's SD view to its Sun view provide SD degradation information. This paper presents and compares the Terra and Aqua MODIS SD on-orbit performance. Results show that the SD on-orbit degradation depends on the amount of solar exposure of the SD plate. In addition, it is strongly wavelengthdependent, with a larger degradation rate at shorter wavelengths. For Terra MODIS, an SD door anomaly occurred in May 2003 that led to a decision to fix the door permanently at an "open" position. Since then, the SD degradation rate has significantly increased due to more frequent solar exposure. As expected, the SD on-orbit performance directly impacts the RSB calibration performance. The lessons learned from MODIS on-orbit calibration will provide useful insights into the development and operation of future SD calibration systems.

Xiong, Xiaoxiong↗
NASA NTRS2007

Characterization of MODIS Solar Diffuser On-orbit Degradation

MODIS reflective solar bands (RSB) are calibrated on-orbit by a solar diffuser (SD) and a solar diffuser stability monitor (SDSM). The SD bi-directional reflectance factor (BRF) was characterized pre-launch by the instrument vendor using reference samples traceable to NIST reflectance standards. Its on-orbit degradation is regularly monitored by the SDSM. It consists of a solar integration sphere (SIS) with 9 filtered detectors with wavelengths ranging from 0.41 to 0.94 micrometer, a rotating mirror assembly, and an electronics module. During each SD/SDSM calibration, the SDSM views the sunlight directly and the sunlight diffusely reflected from the SD panel. The time series of SDSM measurements (ratio of the SD view response to the Sun view response) is used to compute the SD BRF degradation at each SDSM detector wavelength. Since launch Terra MODIS has operated for more than seven years and Aqua for nearly five years. The SD panel on each MODIS instrument has experienced noticeable degradation with the largest changes observed in the VIS spectral region. Following a brief description of the MODIS RSB calibration methodology and SD/SDSM operational activities, this paper illustrates the SD on-orbit degradation results for both Terra and Aqua MODIS. It discusses the impacts on the SD RF degradation due to sensor operational conditions and SD solar exposure time. For Aqua MODIS, operated under the same conditions, the SD annual degradation rate is approximately 2.9% at 0.41 micrometers, 1.6% at 0.47 micrometers, and less than 1.1% at wavelengths above 0.53 micrometers. For Terra MODIS, however, an SD door (SDD) related anomaly in May 2003 had led to a decision to keep the SDD permanently at its open position. Since then its SD has experienced a much faster SD degradation rate.

Xiong, X.↗
NASA NTRS2009

Performance of MODIS Thermal Emissive Bands On-orbit Calibration Algorithms

Two nearly identical copies of the Moderate Resolution Imaging Spectroradiometer (MODIS) are currently operated on-board the Terra and Aqua spacecrafts, launched in December 1999 and May 2002, respectively. Together, they have produced an unprecedented amount of science data products, which are widely used for the studies of changes in the Earth's system of land, oceans, and atmosphere. MODIS is a cross-track scanning radiometer, which uses a two-sided scan mirror and collects data continuously over a wide scan angle range (+/-55 degree relative to the instrument nadir) each scan of 1.47 seconds. It has 36 spectral bands with wavelengths ranging from visible (VIS) to long-wave infrared (LWIR). MODIS bands 1-19 and 26 are the reflective solar bands (RSB) and bands 20-25 and 27-36 are the thermal emissive bands (TEB). MODIS was developed and designed with improvements made over its heritage sensors (such as AVHRR and Landsat) and, in particular, with more stringent calibration requirements. Because of this, MODIS was built with a set of state-of-art on-board calibrators (OBC), which include a solar diffuser (SD), a solar diffuser stability monitor (SDSM), a blackbody (BB), a spectroradiometric calibration assembly (SRCA), and a space view (SV) port. With the exception of view angle differences, MODIS OBC measurements and the Earth View (EV) observations are made via the same optical path. MODIS TEB have a total of 160 individual TEB detectors (10 per band), which are located on two cold focal plane assemblies (CFPA). For nominal on-orbit operation, the CFPA temperature is controlled at 83K via a passive radiative cooler. For the TEB, the calibration requirements at specified typical scene radiances are less than or equal to 1% with an exception for the fire detection (low gain) band. MODIS TEB on-orbit calibration is performed on a scan-by-scan basis using a quadratic calibration algorithm, and data collected from sensor responses to the onboard BB and SV. The BB serves as the thermal calibration source and the SV provides measurements for the sensor's background and offsets. MODIS on-board BB is a v-grooved plate with its temperature measured using 12 platinum resistive thermistors (PRT) uniformly embedded in the BB substrate. All the BB thermistors were characterized pre-launch with reference to the NIST temperature standards. Unlike typical BB operations in many heritage sensors, which have no temperature control capability, the MODIS on-board BB can be operated at any temperatures between instrument ambient (about 270K) and 315K and can also be varied continuously within this range. This feature has significantly enhanced the MODIS' capability of tracking and updating the TEB nonlinear calibration coefficients over its entire mission. Following a brief description of MODIS TEB on-orbit calibration methodologies and its onboard BB operational activities, this paper provides a comprehensive performance assessment of MODIS TEB quadratic calibration algorithm. It examines the scan-by-scan, orbit-by-orbit, daily, and seasonal variations of detector responses and associated impact due changes in the CFPA and instrument temperatures. Specifically, this paper will analyze the contribution by each individual thermal emissive source term (BB, scan cavity, and scan mirror), the impact on the Level 1 B data product quality due to pre-launch and on-orbit calibration uncertainties. A comparison of Terra and Aqua TEB on-orbit performance, lessons learned, and suggestions for future improvements will also be made.

Xiong, Xiaoxiong↗
NASA NTRS2009

MODIS On-Board Blackbody Function and Performance

Two MODIS instruments are currently in orbit, making continuous global observations in visible to long-wave infrared wavelengths. Compared to heritage sensors, MODIS was built with an advanced set of on-board calibrators, providing sensor radiometric, spectral, and spatial calibration and characterization during on-orbit operation. For the thermal emissive bands (TEB) with wavelengths from 3.7 m to 14.4 m, a v-grooved blackbody (BB) is used as the primary calibration source. The BB temperature is accurately measured each scan (1.47s) using a set of 12 temperature sensors traceable to NIST temperature standards. The onboard BB is nominally operated at a fixed temperature, 290K for Terra MODIS and 285K for Aqua MODIS, to compute the TEB linear calibration coefficients. Periodically, its temperature is varied from 270K (instrument ambient) to 315K in order to evaluate and update the nonlinear calibration coefficients. This paper describes MODIS on-board BB functions with emphasis on on-orbit operation and performance. It examines the BB temperature uncertainties under different operational conditions and their impact on TEB calibration and data product quality. The temperature uniformity of the BB is also evaluated using TEB detector responses at different operating temperatures. On-orbit results demonstrate excellent short-term and long-term stability for both the Terra and Aqua MODIS on-board BB. The on-orbit BB temperature uncertainty is estimated to be 10mK for Terra MODIS at 290K and 5mK for Aqua MODIS at 285K, thus meeting the TEB design specifications. In addition, there has been no measurable BB temperature drift over the entire mission of both Terra and Aqua MODIS.

Xiaoxiong, Xiong↗
NASA NTRS2009

Characterization of MODIS and SeaWiFS Solar Diffuser On-Orbit Degradation

MODIS has 20 reflective solar bands (RSB), covering the VIS, NIR, and SWIR spectral regions. They are calibrated on-orbit using a solar diffuser (SD) panel, made of space-grade Spectralon. The SD bi-directional reflectance factor (BRF) was characterized pre-launch by the instrument vendor reference to the NIST reflectance standard. Its on-orbit degradation is tracked by an on-board solar diffuser stability monitor (SDSM). The SeaWifS on-orbit calibration strategy uses monthly lunar observations to monitor the long-term radiometric stability of the instrument and applies daily observations of its solar diffuser (an aluminum plate coated with YB71 paint) to track the short-term changes in the instrument response. This paper provides an overview of MODIS and SeaWiFS SD observations, applications, and approaches used to track their on-orbit degradations. Results from sensors are presented with emphasis on the spectral dependence and temporal trends of the SD degradation. Lessons and challenges from the use of SD for sensor on-orbit calibration are also discussed.

Xiong, X.↗
NASA NTRS2009

On-Orbit Operation and Performance of MODIS Blackbody

MODIS collects data in 36 spectral bands, including 20 reflective solar bands (RSB) and 16 thermal emissive bands (TES). The TEB on-orbit calibration is performed on a scan-by-scan basis using a quadratic algorithm that relates the detector response with the calibration radiance from the sensor on-board blackbody (BB). The calibration radiance is accurately determined each scan from the BB temperature measured using a set of 12 thermistors. The BB thermistors were calibrated pre-launch with traceability to the NIST temperature standard. Unlike many heritage sensors, the MODIS BB can be operated at a constant temperature or with the temperature continuously varying between instrument ambient (about 270K) and 315K. In this paper, we provide an overview of both Terra and Aqua MODIS on-board BB operations, functions, and on-orbit performance. We also examine the impact of key calibration parameters, such as BB emissivity and temperature (stability and gradient) determined from its thermistors, on the TEB calibration and Level I (LIB) data product uncertainty.

Xiong, X.↗
NASA NTRS2011

Development and Performance of a Filter Radiometer Monitor System for Integrating Sphere Sources

The NASA Goddard Space Flight Center (GSFC) Radiometric Calibration Laboratory (RCL) maintains several large integrating sphere sources covering the visible to the shortwave infrared wavelength range. Two critical, functional requirements of an integrating sphere source are short and long-term operational stability and repeatability. Monitoring the source is essential in determining the origin of systemic errors, thus increasing confidence in source performance and quantifying repeatability. If monitor data falls outside the established parameters, this could be an indication that the source requires maintenance or re-calibration against the National Institute of Science and Technology (NIST) irradiance standard. The GSFC RCL has developed a Filter Radiometer Monitoring System (FRMS) to continuously monitor the performance of its integrating sphere calibration sources in the 400 to 2400nm region. Sphere output change mechanisms include lamp aging, coating (e.g. BaSO4) deterioration, and ambient water vapor level. The Filter Radiometer Monitor System (FRMS) wavelength bands are selected to quantify changes caused by these mechanisms. The FRMS design and operation are presented, as well as data from monitoring four of the RCL s integrating sphere sources.

Ding, Leibo↗
NASA NTRS2012

ACCESS: Design and Sub-System Performance

Establishing improved spectrophotometric standards is important for a broad range of missions and is relevant to many astrophysical problems. ACCESS, "Absolute Color Calibration Experiment for Standard Stars", is a series of rocket-borne sub-orbital missions and ground-based experiments designed to enable improvements in the precision of the astrophysical flux scale through the transfer of absolute laboratory detector standards from the National Institute of Standards and Technology (NIST) to a network of stellar standards with a calibration accuracy of 1% and a spectral resolving power of 500 across the 0.35 -1.7 micrometer bandpass.

Kaiser, Mary Elizabeth↗
NASA NTRS2012

Potassium Stable Isotopic Compositions Measured by High-Resolution MC-ICP-MS

Potassium isotopic (K-41/K-39) compositions are notoriously difficult to measure. TIMS measurements are hindered by variable fractionation patterns throughout individual runs and too few isotopes to apply an internal spike method for instrumental mass fractionation corrections. Internal fractionation corrections via the K-40/K-39 ratio can provide precise values but assume identical K-40/K-39 ratios (e.g. 0.05% (1sigma) in [1]); this is appropriate in some cases (e.g. identifying excess K-41) but not others (e.g., determining mass fractionation effects and metrologically traceable isotopic abundances). SIMS analyses have yielded measurements with 0.25% precisions (1sigma) [2]. ICP-MS analyses are significantly affected by interferences from molecular species such as Ar-38H(+) and Ar-40H(+) and instrument mass bias. Single collector ICP-MS instruments in "cold plasma" mode have yielded uncertainties as low as 2% (1sigma, e.g. [3]). Although these precisions may be acceptable for some concentration determinations, they do not resolve isotopic variation in terrestrial materials. Here we present data from a series of measurements made on the Thermo Scientific NEPTUNE Plus multi-collector ICP-MS that demonstrate the ability to make K-41/K-39 ratio measurements with 0.07% precisions (1sigma). These data, collected on NIST K standards, indicate the potential for MC-ICP-MS measurements to look for K isotopic variations at the sub-permil level. The NEPTUNE Plus can sufficiently resolve 39K and 41K from the interfering 38ArH+ and 40ArH+ peaks in wet cold plasma and high-resolution mode. Measurements were made on small but flat, interference-free, plateaus (ca. 50 ppm by mass width for K-41). Although ICP-MS does not yield accurate K-41/K-39 values due to significant instrumental mass fractionation (ca. 6%), this bias can be sufficiently stable over the time required for several measurements so that relative K-41/K-39 values can be precisely determined via sample-standard bracketing. As cold plasma conditions can amplify matrix effects, experiments were conducted to test the matrix tolerance of measurements; the use of clean, matrix-matched samples and standards is critical. Limitations of the cold-plasma high-resolution MC-ICP-MS methodology with respect to matrix tolerance are discussed and compared with the limitations of TIMS methodologies.

Morgan, Leah E.↗
NASA NTRS1994

Optical storage media data integrity studies

Optical disk-based information systems are being used in private industry and many Federal Government agencies for on-line and long-term storage of large quantities of data. The storage devices that are part of these systems are designed with powerful, but not unlimited, media error correction capacities. The integrity of data stored on optical disks does not only depend on the life expectancy specifications for the medium. Different factors, including handling and storage conditions, may result in an increase of medium errors in size and frequency. Monitoring the potential data degradation is crucial, especially for long term applications. Efforts are being made by the Association for Information and Image Management Technical Committee C21, Storage Devices and Applications, to specify methods for monitoring and reporting to the user medium errors detected by the storage device while writing, reading or verifying the data stored in that medium. The Computer Systems Laboratory (CSL) of the National Institute of Standard and Technology (NIST) has a leadership role in the development of these standard techniques. In addition, CSL is researching other data integrity issues, including the investigation of error-resilient compression algorithms. NIST has conducted care and handling experiments on optical disk media with the objective of identifying possible causes of degradation. NIST work in data integrity and related standards activities is described.

Podio, Fernando L.↗
NASA NTRS1996

SeaWiFs Technical Report Series. Volume 34: The Third SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-3), 19-30 September 1994

This report presents results of the third Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Intercalibration Round- Robin Experiment (SIRREX-3), which was held at the San Diego State University (SDSU) Center for Hydro-Optics and Remote Sensing (CHORS) on 19-30 September 1994. Spectral irradiances of FEL lamps belonging to each participant were intercompared by reference to the National Institute of Standards and Technology (NIST) scale of spectral irradiance using secondary standard lamps F268, F269, and F182, with a Type A uncertainty between 1.1-1.5%. This level of uncertainty was achieved despite difficulties with lamp F269. The average spectral irradiances of FEL lamps, compared in both SIRREX-2 and SIRREX-3, differed between the two experiments by 1.5%, which probably indicates that the values assigned to the secondary standard lamp at the time of SIRREX-2 were in error. With two exceptions, spectral radiance values of integrating sphere sources were measured during SIRREX-3 with uncertainties in temporal stability of less than 0.3% and absolute uncertainties of 1.5-2.0%. This is a significant improvement over similar intercomparisons in SIRREX- I and SIRREX-2. Plaque reflectances were intercompared with an uncertainty of about 1-2%, but the absolute uncertainty is undefined. Although this is an improvement over results of previous SIRREXS, the sources and magnitude of uncertainty associated with transfers of spectral radiance using plaques requires further evaluation in future experiments.

Hooker, Stanford B.↗
NASA NTRS2000

NIST Efforts to Quality-Assure Gunpowder Measurements

In the past few years, the National Institute for Standards and Technology (NIST) has been promoting the idea of quantitatively determining the additives in smokeless gunpowder using micellar capillary electrophoresis as a means of investigating the criminal use of hand guns and pipe bombs. As a part of this effort, we have evaluated both supercritical fluid and ultrasonic solvent extractions for the quantitative recovery of nitroglycerin (NG), diphenylamine (DPA), N-nitrosodiphenylamine (NnDPA), and ethyl centralite (EC) from gunpowder. Recoveries were evaluated by repeat extraction and matrix spiking experiments. The final extraction protocol provides greater than 95 percent recoveries. To help other researches validate their own analytical method for additive determinations, NIST is exploring the development of a standard reference material, Additives in Smokeless Gunpowder. The evaluated method is being applied to two double-base (NG-containing) powders, one stabilized with diphenylamine and the other with ethyl centralite. As part of this reference material development effort, we are conducting an interlaboratory comparison exercise among the forensic and military gunpowder measurement community.

MacCrehan, William A.↗
NASA NTRS2011

Calibrated Noise Measurements with Induced Receiver Gain Fluctuations

The lack of well-developed techniques for modeling changing statistical moments in our observations has stymied the application of stochastic process theory in science and engineering. These limitations were encountered when modeling the performance of radiometer calibration architectures and algorithms in the presence of non stationary receiver fluctuations. Analyses of measured signals have traditionally been limited to a single measurement series. Whereas in a radiometer that samples a set of noise references, the data collection can be treated as an ensemble set of measurements of the receiver state. Noise Assisted Data Analysis is a growing field of study with significant potential for aiding the understanding and modeling of non stationary processes. Typically, NADA entails adding noise to a signal to produce an ensemble set on which statistical analysis is performed. Alternatively as in radiometric measurements, mixing a signal with calibrated noise provides, through the calibration process, the means to detect deviations from the stationary assumption and thereby a measurement tool to characterize the signal's non stationary properties. Data sets comprised of calibrated noise measurements have been limited to those collected with naturally occurring fluctuations in the radiometer receiver. To examine the application of NADA using calibrated noise, a Receiver Gain Modulation Circuit (RGMC) was designed and built to modulate the gain of a radiometer receiver using an external signal. In 2010, an RGMC was installed and operated at the National Institute of Standards and Techniques (NIST) using their Noise Figure Radiometer (NFRad) and national standard noise references. The data collected is the first known set of calibrated noise measurements from a receiver with an externally modulated gain. As an initial step, sinusoidal and step-function signals were used to modulate the receiver gain, to evaluate the circuit characteristics and to study the performance of a variety of calibration algorithms. The receiver noise temperature and time-bandwidth product of the NFRad are calculated from the data. Statistical analysis using temporal-dependent calibration algorithms reveals that the natural occurring fluctuations in the receiver are stationary over long intervals (100s of seconds); however the receiver exhibits local non stationarity over the interval over which one set of reference measurements are collected. A variety of calibration algorithms have been applied to the data to assess algorithms' performance with the gain fluctuation signals. This presentation will describe the RGMC, experiment design and a comparative analysis of calibration algorithms.

Racette, Paul↗
NASA NTRS1996

Sea WiFS Technical Report Series: The fourth SeaWIFS Intercalibration Round-Robin Experiment (SIRREX-4), May 1995

This report documents the fourth Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Intercalibration Round-Robin Experiment (SIRREX-4), which was held at the National Institute of Standards and Technology (NIST) on 3-10 May 1995. The agenda for SIRREX-4 was established by a consensus reached at the conclusion of SIRREX-3: there should be an emphasis on training and work to foster and encourage uniform use of accepted protocols for calibrating radiometric instruments in the laboratory. The goal was to host the activity in a setting where proper techniques could be discussed and demonstrated. It seemed appealing to split the day between morning lectures and afternoon laboratory exercises or practicals. The former gave the user community a chance to present what was important to them and discuss it with acknowledged experts in radiometry, while the latter presented a unique opportunity for training and evaluation in the presence of these same experts. The five laboratory sessions were concerned with (1) determining the responsivity of a spectroradiometer and the spectral radiance of an unknown integrating sphere source, (2) demonstrating spectral field calibration procedures for an integrating sphere using three different instruments, (3) measuring spectral radiance using the plaque method, (4) setting up and aligning lamp calibration transfer standards using the NIST specifications for irradiance measurements, and (5) characterizing radiometric instruments. In addition to documenting some supplemental studies performed outside the laboratory sessions, this report includes an evaluation of the hardware that has been used during the SIRREX activities plus a critical evaluation of SIRREX objectives.

Johnson, B. Carol↗
NASA NTRS1989

Radiation thermometry at NIST: An update of services and research activities

An overview of activities at the National Institute of Standards and Terminology (NIST) in radiation thermometry and related temperature scale research is presented. An expansion of calibration services for pyrometers will be described as well as efforts to develop calibration services for blackbody simulators. Research relevant to the realization of the new international temperature scale (ITS 90) will be discussed.

Hillard, G. Barry↗
NASA NTRS1990

The use of precise ephemerides, ionospheric data, and corrected antenna coordinates in a long-distance GPS time transfer

Over intercontinental distances, the accuracy of The Global Positioning System (GPS) time transfers ranges from 10 to 20 ns. The principal error sources are the broadcast ionospheric model, the broadcast ephemerides and the local antenna coordinates. For the first time, the three major error sources for GPS time transfer can be reduced simultaneously for a particular time link. Ionospheric measurement systems of the National Institute of Standards and Technology (NIST) type are now operating on a regular basis at the National Institute of Standards and Technology in Boulder and at the Paris Observatory in Paris. Broadcast ephemerides are currently recorded for time-transfer tracks between these sites, this being necessary for using precise ephemerides. At last, corrected local GPS antenna coordinates are now introduced in GPS receivers at both sites. Shown here is the improvement in precision for this long-distance time comparison resulting from the reduction of these three error sources.

Lewandowski, Wlodzimierz W.↗