Statistical evaluation of primary relevellings

For the following problems

- estimating the statistical parameters of the precise levelling,

- adjusting the primary levelling networks and

- estimating vertical crustal movements

mathematical models are being sketched out. Results obtained in evaluating primary relevellings in the G.D.R. are reported.     

La determination du rayon terrestre par J. PICARD en 1669–1671

The French astronomerJean PICARD (1620–1682) was certainly one of the leading scientists of his time. Friend of Huygens, of Hevelius, of Oldenburg, master of Römer, indefatigable traveller, he played a very important part in the development of positional astronomy and geodesy.

- He first, had the idea of comparing the length units to a reproductible physical quantity, namely the length of the one second pendulum at Paris, and measured that length.

- He conceived the first cross wire telescopes and adapted them on geodetic and astronomical instruments of his own, used throughout one century until 1780.

- He obtained the first really reliable value of the earth radius, in his famous measurement of the meridional arc PARIS-AMIENS, being the original cell of the French triangulations.

The following article is devoted to a recomputation and evaluation of the accuracy of that work, as compared with further operations, but independently concludes that this achievement gave the necessary impulse to the development of geodesy in France and probably abroad.     

ITG-CHAMP01: a CHAMP gravity field model from short kinematic arcs over a one-year observation period

Global gravity field models have been determined based on kinematic orbits covering an observation period of one year beginning from March 2002. Three different models have been derived up to a maximum degree of n=90 of a spherical harmonic expansion of the gravitational potential. One version, ITG-CHAMP01E, has been regularized beginning from degree n=40 upwards, based on the potential coefficients of the gravity field model EGM96. A second model, ITG-CHAMP01K, has been determined based on Kaulas rule of thumb, also beginning from degree n=40. A third version, ITG-CHAMP01S, has been determined without any regularization. The physical model of the gravity field recovery technique is based on Newtons equation of motion, formulated as a boundary value problem in the form of a Fredholm-type integral equation. The observation equations are formulated in the space domain by dividing the one-year orbit into short sections of approximately 30-minute arcs. For every short arc, a variance factor has been determined by an iterative computation procedure. The three gravity field models have been validated based on various criteria, and demonstrate the quality of not only the gravity field recovery technique but also the kinematically determined orbits.     

Pre-zero-epoch covariance matrix in sequential analysis of deformations

A sequential adjustment procedure is proposed for the direct estimation of point—velocities in deformation analysis networks. At any intermediate stage of the adjustment the up-to-date covariance matrix of those velocities tells the evolving story of the network in terms of solvability and reliability. A pre-zero-epoch covariance matrix is utilized for a smooth and flexible treatment of two characteristic problems of deformation analysis:

- high turnover of points in the network

- processing variable and generally incomplete observational batches.

A small numerical example is presented at the end as an illustration.     

Reducing the draconitic errors in GNSS geodetic products

Systematic errors at harmonics of the GPS draconitic year have been found in diverse GPS-derived geodetic products like the geocenter $Z$ -component, station coordinates, $Y$ -pole rate and orbits (i.e. orbit overlaps). The GPS draconitic year is the repeat period of the GPS constellation w.r.t. the Sun which is about 351 days. Different error sources have been proposed which could generate these spurious signals at the draconitic harmonics. In this study, we focus on one of these error sources, namely the radiation pressure orbit modeling deficiencies. For this purpose, three GPS+GLONASS solutions of 8 years (2004–2011) were computed which differ only in the solar radiation pressure (SRP) and satellite attitude models. The models employed in the solutions are: (1) the CODE (5-parameter) radiation pressure model widely used within the International GNSS Service community, (2) the adjustable box-wing model for SRP impacting GPS (and GLONASS) satellites, and (3) the adjustable box-wing model upgraded to use non-nominal yaw attitude, specially for satellites in eclipse seasons. When comparing the first solution with the third one we achieved the following in the GNSS geodetic products. Orbits: the draconitic errors in the orbit overlaps are reduced for the GPS satellites in all the harmonics on average 46, 38 and 57 % for the radial, along-track and cross-track components, while for GLONASS satellites they are mainly reduced in the cross-track component by 39 %. Geocenter $Z$ -component: all the odd draconitic harmonics found when the CODE model is used show a very important reduction (almost disappearing with a 92 % average reduction) with the new radiation pressure models. Earth orientation parameters: the draconitic errors are reduced for the $X$ -pole rate and especially for the $Y$ -pole rate by 24 and 50 % respectively. Station coordinates: all the draconitic harmonics (except the 2nd harmonic in the North component) are reduced in the North, East and Height components, with average reductions of 41, 39 and 35 % respectively. This shows, that part of the draconitic errors currently found in GNSS geodetic products are definitely induced by the CODE radiation pressure orbit modeling deficiencies.     

Prospects for gradiometric aiding of inertial survey systems

The state of current and proposed moving-base gravity gradiometer instruments is briefly reviewed. The review perspective is directed toward their deployment as a source of additional gravimetric data during inertial surveys. In such gradiometer-aided surveys, the additional gravity gradient information could be used to:

1. Improve surveyed gravity vector accuracy
2. Extend the interval between zero velocity update stops
3. Accomplish varying combinations of the above.

The paper examines potential survey improvements associated with gradiometers having noise levels observed in laboratory prototypes. The additional improvements possible with future gradiometers are also discussed. These results are interpreted in light of present and likely future inertial survey system technology.     

A note on adjustment of free networks

The present paper deals with the least-squares adjustment where the design matrix (A) is rank-deficient. The adjusted parameters \(\hat x\) as well as their variance-covariance matrix ( \(\sum _{\hat x} \) ) can be obtained as in the “standard” adjustment whereA has the full column rank, supplemented with constraints, \(C\hat x = w\) , whereC is the constraint matrix andw is sometimes called the “constant vector”. In this analysis only the inner adjustment constraints are considered, whereC has the full row rank equal to the rank deficiency ofA, andAC ^T =0. Perhaps the most important outcome points to the three kinds of results

1. A general least-squares solution where both \(\hat x\) and \(\sum _{\hat x} \) are indeterminate corresponds tow=arbitrary random vector.
2. The minimum trace (least-squares) solution where \(\hat x\) is indeterminate but \(\sum _{\hat x} \) is detemined (and trace \(\sum _{\hat x} \) corresponds tow=arbitrary constant vector.
3. The minimum norm (least-squares) solution where both \(\hat x\) and \(\sum _{\hat x} \) are determined (and norm \(\hat x\) , trace \(\sum _{\hat x} \) corresponds tow?0

     

Remote Sensing Data Acquisition,Platforms and Sensor Requirements

Although data available from various earth observation systems have been routinely used in many resource applications, however there have been gaps, and data needs of applications at different levels of details have not been met. There is a growing demand for availability of data at higher repetivity, at higher spatial resolution, in more and narrower spectral bands etc. Some of the thrust areas of applications particularly in the Indian context are;

1. Management of natural resources to ensure sustainable increase in agricultural production,
2. Study the state of the environment, its monitoring and assessment of the impact of. various development actions on the environment,
3. Updating and generation of large scale topographical maps.
4. Exploration/exploitation of marine and mineral resources and
5. Operational meteorology and studying various land and oceanic processes to understand/predict global climate changes.

Each of these thrust area of application has many components, related to basic resource areas such as agriculture, forestry, water resources, minerals, marine resources etc. and the field of cartography. Observational requirements for major applications have been summarized as under. Monitoring vegetation health from space remains the most important observational parameter with applications, in agriculture, forestry, environment, hydrology etc. Vegetation extent, quantity and temporal changes are the three main requirements which are not fully realized with RS data available. Vegetation productivity, forest biomass, canopy moisture status, canopy biogeochemistry are some examples. Crop production forecasting is an important application area. Remotely sensed data has been used for identification of crops and their acreage estimation. Fragmented holdings, large spread in crop calendars and different management practices continue to pose a challenge lo remote sensing. Remotely sensed data at much higher spatial resolution than hitherto available as well as at greater repetivity are required to meet this need. Non-availability of cloud-free data in the kharif season is one of the serious problems in operational use of remote sensing for crop inventory. Synthetic aperture radar data al X & Ku bands is necessary to meet this demand. Nutrient stress/disease detection requires observations in narrow spectral bands. In case of forestry applications, multispectral data at high spatial resolution of the order of 5 to 10 metres is required to make working plans at forest compartment level. Observations from space for deriving tree height are required for volume estimation. Observations in the middle infrared region would greatly enhance capability of satellite remote sensing in forest fire detection. Temporal, spatial and spectral observational requirements in various applications on vegetation viewing are diverse, as they address processes at different spatial and time scales. Hence, it would be worthwhile to address this issue in three broad categories. a) Full coverage, moderate spatial resolution with high repetivity (drought, large scale deforestation, forest phenology....). b) Full coverage, moderate to high spatial resolution and high repetivity (crop forecasting, vegetation productivity). c) Selected viewing at high spatial resolution, moderate to high repetivity and with new dimensions to imaging (narrow spectral bands, different viewing angles). A host of agrometeorological parameters are needed to be measured from space for their effective use in development of yield models. Estimation of root-zone soil moisture is an important area requiring radar measurements from space. Surface meteorological observations from space at the desired spatial and temporal distributions has not developed because of heavy demands placed on the sensor as well as analytical operational models. Agrometeorology not only provides quantitative inputs to other applications such as crop forecasting, hydrological models but also could be used for farmer advisory services by local bodies. Mineral exploration requires information on geological structures, geomorphology and lithology. Surface manifestation over localized regions requires large scale mapping while the lithology can be deciphered from specific narrow bands in visible. NIR, MIR and TIR regions. Sensors identified for mapping/cartography in conjunction with imaging spectrometer would seem to cover requirements of this application. Narrow spectral bands in the short regions which provide diagnostics of relevant geological phenomenon are necessary for mineral exploration. Thermal inertia measurements help in better discrimination of different rock units. Measurements from synthetic aperture data which would provide information on geological structures and geomorphology are necessary for mineral exploration. The applications related to marine environment fall in three major areas: (i) Ocean colour and productivity, biological resources; (ii) Land-ocean interface, this includes coastal landforms, bathymetry, littoral transport processes, etc. and; (iii) Physical oceanography, sea surface temperature, winds, wave spectra, energy and mass exchange between atmosphere and ocean. Measurement of chlorophyll concentration accurately on daily basis, sea surface temperature with an accuracy of 0.5 °K. and information on current patterns arc required for developing better fishery forecast models. Improved spatial resolution data are desirable for studying sediment and other coastal processes. Cartography is another important application area. The major problems encountered in relation to topographic map updation are location and geometric accuracy and information content. Two most important requirements for such an application are high spatial resolution data of 1 to 2 metre and stereo capability to provide vertical resolution of 1 metre. This requirement places stringent demands on the sensor specifications, geometric processing, platform stability and automated digital cartography. The requirements for the future earth observation systems based on different application needs can be summarized as follows:

1. Moderate spatial resolution (l50-300m), high repetivity (2 Days), minimum set of spectral bands (VIS, NIR, MIR. TIR) full coverage.
2. Moderate to high spatial resolution (20-40m), high repetivity (4-6 Days), spectral bands (VIS, MR, MIR, TIR) full coverage.
3. High spatial resolution (5-10m) muitispectral data with provision for selecting specific narrow bands (VIS, N1R. MIR), viewing from different angles.
4. Synthetic aperture radar operating in at least two frequencies (C, X, Ku), two incidence angles/polarizations, moderate to high spatial resolution (20-40m), high repetivity (4-6 Days).
5. Very high spatial resolution (1-2m) data in panchromatic band to provide terrain details at cadastral level (1:10,000).
6. Stereo capability (1-2m height resolution) to help planning/execution of development plans.
7. Moderate resolution sensor operating in VIS, NIR, MIR on a geostationary platform for observations at different sun angles necessary for the development of canopy reflectance inversion models.
8. Diurnal (at least two i.e. pre-dawn and noon) temperature measurements of the earth surface.
9. Ocean colour monitor with daily coverage.
10. Multi-frequency microwave radiometer, scatterometer. altimeter, atmospheric sounder, etc.

     

Observable quantities in satellite gradiometry

Deriving the observables for satellite gravity gradiometry, several workers have identified the invariants under spatial rotation of the gravitation gradient tensor for obtaining quantities insensitive to the precise (unrecoverable) attitude of the satellite. Extending this work we show:

1. Considering that an approximate (not precise) attitude recovery for these, three-axes-stabilised, satellites is to be expected, one can identifythree independent invariants instead of two.
2. Besides studying gradient tensor invariants for one observation time, one should also study (as withGPS observables) first and seconddifferences between successive tensor component values in time. Bias and trend patterns in the measured tensor components caused by satellite rotation uncertainty, and by attitude uncertainty in some cross components, are shown to cancel. Information thus obtained is exclusively high-frequency, however.

Observation equations for gradiometry are derived taking three satellite attitude angles into account. Various alternatives for the satellite’s nominalattitude law are discussed.     

Geology of the area around Katta,sindhudurg district,Maharashtra. Based on aerospace data

Geological studies of the area around Katta, in the southern part of the Ratnagiri District of Maharashtra, were carried out with the help of visual remote sensing techniques using LANDSAT imageries on 1:250,000 scale and aerial photographs on 1:60,000 scale. The major stratigraphic units represented in the area under study are the Archean Complex, Kaladgi Supergroup, Deccan Trap, Laterite and Alluvium. The Kaladgis unconformably overlie the Archean metasediments and also at places exhibit faulted contacts with the latter. The major part of the area is covered by a thick evergreen vegetation. The interpretation followed by field work and laboratory work revealed the following:

1. The different lithologic units could be delineated on the aerial photographs.
2. Different lineaments marked on the imagery were found to be due either to faults or fracture zones. Some of the older faults appear to have been rejuvenated after the formation of the laterites.
3. Some of the lithologic horizons can be identified on the Landsat imagery by virtue of their spatial signatures.

These studies indicate that even in the area covered with thick vegetation, aerospace imagery in appropriate band and data scale can provide significant geological information.     

Contribution of Starlette,Stella, and AJISAI to the SLR-derived global reference frame

The contribution of Starlette, Stella, and AJISAI is currently neglected when defining the International Terrestrial Reference Frame, despite a long time series of precise SLR observations and a huge amount of available data. The inferior accuracy of the orbits of low orbiting geodetic satellites is the main reason for this neglect. The Analysis Centers of the International Laser Ranging Service (ILRS ACs) do, however, consider including low orbiting geodetic satellites for deriving the standard ILRS products based on LAGEOS and Etalon satellites, instead of the sparsely observed, and thus, virtually negligible Etalons. We process ten years of SLR observations to Starlette, Stella, AJISAI, and LAGEOS and we assess the impact of these Low Earth Orbiting (LEO) SLR satellites on the SLR-derived parameters. We study different orbit parameterizations, in particular different arc lengths and the impact of pseudo-stochastic pulses and dynamical orbit parameters on the quality of the solutions. We found that the repeatability of the East and North components of station coordinates, the quality of polar coordinates, and the scale estimates of the reference are improved when combining LAGEOS with low orbiting SLR satellites. In the multi-SLR solutions, the scale and the \(Z\) component of geocenter coordinates are less affected by deficiencies in solar radiation pressure modeling than in the LAGEOS-1/2 solutions, due to substantially reduced correlations between the \(Z\) geocenter coordinate and empirical orbit parameters. Eventually, we found that the standard values of Center-of-mass corrections (CoM) for geodetic LEO satellites are not valid for the currently operating SLR systems. The variations of station-dependent differential range biases reach 52 and 25 mm for AJISAI and Starlette/Stella, respectively, which is why estimating station-dependent range biases or using station-dependent CoM, instead of one value for all SLR stations, is strongly recommended. This clearly indicates that the ILRS effort to produce CoM corrections for each satellite, which are site-specific and depend on the system characteristics at the time of tracking, is very important and needs to be implemented in the SLR data analysis.     

Investigations on the accuracy concerning the derivation of absolute gravimetric height anomalies and deflections of the vertical based on the theory of Molodensky

The investigations refer to the compartment method by using mean terrestrial free air anomalies only. Three main error influences of remote areas (distance from the fixed point >9°) on height anomalies and deflections of the vertical are being regarded:

1. The prediction errors of mean terrestrial free air anomalies have the greatest influence and amount to about ±0″.2 in each component for deflections of the vertical and to ±3 m for height anomalies;
2. The error of the compartment method, which originates from converting the integral formulas of Stokes and Vening-Meinesz into summation formulas, can be neglected if the anomalies for points and gravity profiles are compiled to 5°×5° mean values.
3. The influences of the mean gravimetric correction terms of Arnold—estimated for important mountains of the Earth by means of an approximate formula—on height anomalies may amount to 1–2 m and on deflections of the vertical to 0″0.5–0″.1, and, therefore, they have to be taken into account for exact calculations.

The computations of errors are carried out using a global covariance function of point free air anomalies.     

Sensitivity of GPS and GLONASS orbits with respect to resonant geopotential parameters

The Center for Orbit Determination in Europe (CODE) has been involved in the processing of combined GPS/GLONASS data during the International GLONASS Experiment (IGEX). The resulting precise orbits were analyzed using the program SORBDT. Introducing one satellites positions as pseudo-observations, the program is capable of fitting orbital arcs through these positions using an orbit improvement procedure based on the numerical integration of the satellites orbit and its partial derivative with respect to the orbit parameters. For this study, the program was enhanced to estimate selected parameters of the Earths gravity field. The orbital periods of the GPS satellites are —in contrast to those of the GLONASS satellites – 2:1 commensurable (P _Sid:P _GPS) with the rotation period of the Earth. Therefore, resonance effects of the satellite motion with terms of the geopotential occur and they influence the estimation of these parameters. A sensitivity study of the GPS and GLONASS orbits with respect to the geopotential coefficients reveals that the correlations between different geopotential coefficients and the correlations of geopotential coefficients with other orbit parameters, in particular with solar radiation pressure parameters, are the crucial issues in this context. The estimation of the resonant geopotential terms is, in the case of GPS, hindered by correlations with the simultaneously estimated radiation pressure parameters. In the GLONASS case, arc lengths of several days allow the decorrelation of the two parameter types. The formal errors of the estimates based on the GLONASS orbits are a factor of 5 to 10 smaller for all resonant terms. AcknowledgmentsThe authors would like to thank all the organizations involved in the IGS and the IGEX campaign, in particular those operating an IGS or IGEX observation site and providing the indispensable data for precise orbit determination.     

Homogeneous reprocessing of GPS,GLONASS and SLR observations

The International GNSS Service (IGS) provides operational products for the GPS and GLONASS constellation. Homogeneously processed time series of parameters from the IGS are only available for GPS. Reprocessed GLONASS series are provided only by individual Analysis Centers (i. e. CODE and ESA), making it difficult to fully include the GLONASS system into a rigorous GNSS analysis. In view of the increasing number of active GLONASS satellites and a steadily growing number of GPS+GLONASS-tracking stations available over the past few years, Technische Universität Dresden, Technische Universität München, Universität Bern and Eidgenössische Technische Hochschule Zürich performed a combined reprocessing of GPS and GLONASS observations. Also, SLR observations to GPS and GLONASS are included in this reprocessing effort. Here, we show only SLR results from a GNSS orbit validation. In total, 18 years of data (1994–2011) have been processed from altogether 340 GNSS and 70 SLR stations. The use of GLONASS observations in addition to GPS has no impact on the estimated linear terrestrial reference frame parameters. However, daily station positions show an RMS reduction of 0.3 mm on average for the height component when additional GLONASS observations can be used for the time series determination. Analyzing satellite orbit overlaps, the rigorous combination of GPS and GLONASS neither improves nor degrades the GPS orbit precision. For GLONASS, however, the quality of the microwave-derived GLONASS orbits improves due to the combination. These findings are confirmed using independent SLR observations for a GNSS orbit validation. In comparison to previous studies, mean SLR biases for satellites GPS-35 and GPS-36 could be reduced in magnitude from \(-35\) and \(-38\)  mm to \(-12\) and \(-13\)  mm, respectively. Our results show that remaining SLR biases depend on the satellite type and the use of coated or uncoated retro-reflectors. For Earth rotation parameters, the increasing number of GLONASS satellites and tracking stations over the past few years leads to differences between GPS-only and GPS+GLONASS combined solutions which are most pronounced in the pole rate estimates with maximum 0.2 mas/day in magnitude. At the same time, the difference between GLONASS-only and combined solutions decreases. Derived GNSS orbits are used to estimate combined GPS+GLONASS satellite clocks, with first results presented in this paper. Phase observation residuals from a precise point positioning are at the level of 2 mm and particularly reveal poorly modeled yaw maneuver periods.     

On the use of heterogeneous noisy data in spectral gravity field modeling methods

Spectral methods have been a standard tool in physical geodesy applications over the past decade. Typically, they have been used for the efficient evaluation of convolution integrals, utilizing homogeneous, noise-free gridded data. This paper answers the following three questions:

1. Can data errors be propagated into the results?
2. Can heterogeneous data be used?
3. Is error propagation possible with heterogeneous data?

The answer to the above questions is yes and is illustrated for the case of two input data sets and one output. Firstly, a solution is obtained in the frequency domain using the theory of a two-input, single-output system. The assumption here is that both the input signals and their errors are stochastic variables with known PSDs. The solution depends on the ratios of the error PSD and the signal PSD, i.e., the noise-to-signal ratios of the two inputs. It is shown that, when the two inputs are partially correlated, this solution is equivalent to stepwise collocation. Secondly, a solution is derived in the frequency domain by a least-squares adjustment of the spectra of the input data. The assumption is that only the input errors are stochastic variables with known power spectral density functions (PSDs). It is shown that the solution depends on the ratio of the noise PSDs. In both cases, there exists the non-trivial problem of estimating the input noise PSDs, given that we only have available the error variances of the data. An effective but non-rigorous way of overcoming this problem in practice is to approximate the noise PSDs by simple stationary models.     

Self-consistent treatment of tidal variations in the geocenter for precise orbit determination

We show that the current levels of accuracy being achieved for the precise orbit determination (POD) of low-Earth orbiters demonstrate the need for the self-consistent treatment of tidal variations in the geocenter. Our study uses as an example the POD of the OSTM/Jason-2 satellite altimeter mission based upon Global Positioning System (GPS) tracking data. Current GPS-based POD solutions are demonstrating root-mean-square (RMS) radial orbit accuracy and precision of \({<}1\)  cm and 1 mm, respectively. Meanwhile, we show that the RMS of three-dimensional tidal geocenter variations is \({<}6\)  mm, but can be as large as 15 mm, with the largest component along the Earth’s spin axis. Our results demonstrate that GPS-based POD of Earth orbiters is best performed using GPS satellite orbit positions that are defined in a reference frame whose origin is at the center of mass of the entire Earth system, including the ocean tides. Errors in the GPS-based POD solutions for OSTM/Jason-2 of \({<}4\)  mm (3D RMS) and \({<}2\)  mm (radial RMS) are introduced when tidal geocenter variations are not treated consistently. Nevertheless, inconsistent treatment is measurable in the OSTM/Jason-2 POD solutions and manifests through degraded post-fit tracking data residuals, orbit precision, and relative orbit accuracy. For the latter metric, sea surface height crossover variance is higher by \(6~\hbox {mm}^{2}\) when tidal geocenter variations are treated inconsistently.     

Short-arc analysis of intersatellite tracking data in a gravity mapping mission

 A technique for the analysis of low–low intersatellite range-rate data in a gravity mapping mission is explored. The technique is based on standard tracking data analysis for orbit determination but uses a spherical coordinate representation of the 12 epoch state parameters describing the baseline between the two satellites. This representation of the state parameters is exploited to allow the intersatellite range-rate analysis to benefit from information provided by other tracking data types without large simultaneous multiple-data-type solutions. The technique appears especially valuable for estimating gravity from short arcs (e.g. less than 15 minutes) of data. Gravity recovery simulations which use short arcs are compared with those using arcs a day in length. For a high-inclination orbit, the short-arc analysis recovers low-order gravity coefficients remarkably well, although higher-order terms, especially sectorial terms, are less accurate. Simulations suggest that either long or short arcs of the Gravity Recovery and Climate Experiment (GRACE) data are likely to improve parts of the geopotential spectrum by orders of magnitude. Received: 26 June 2001 / Accepted: 21 January 2002     

The effect of seasonal and long-period geopotential variations on the GPS orbits

We examine the impact of using seasonal and long-period time-variable gravity field (TVG) models on GPS orbit determination, through simulations from 1994 to 2012. The models of time-variable gravity that we test include the GRGS release RL02 GRACE-derived 10-day gravity field models up to degree and order 20 (grgs20x20), a 4 × 4 series of weekly coefficients using GGM03S as a base derived from SLR and DORIS tracking to 11 satellites (tvg4x4), and a harmonic fit to the above 4 × 4 SLR–DORIS time series (goco2s_fit2). These detailed models are compared to GPS orbit simulations using a reference model (stdtvg) based on the International Earth Rotation Service (IERS) and International GNSS Service (IGS) repro1 standards. We find that the new TVG modeling produces significant along, cross-track orbit differences as well as annual, semi-annual, draconitic and long-period effects in the Helmert translation parameters (Tx, Ty, Tz) of the GPS orbits with magnitudes of several mm. We show that the simplistic TVG modeling approach used by all of the IGS Analysis Centers, which is based on the models provided by the IERS standards, becomes progressively less adequate following 2006 when compared to the seasonal and long-period TVG models.     

A technique for routinely updating the ITU-R database using radio occultation electron density profiles

Well credited and widely used ionospheric models, such as the International Reference Ionosphere or NeQuick, describe the variation of the electron density with height by means of a piecewise profile tied to the F2-peak parameters: the electron density, $N_m \mathrm{F2}$ N m F 2 , and the height, $h_m \mathrm{F2}$ h m F 2 . Accurate values of these parameters are crucial for retrieving reliable electron density estimations from those models. When direct measurements of these parameters are not available, the models compute the parameters using the so-called ITU-R database, which was established in the early 1960s. This paper presents a technique aimed at routinely updating the ITU-R database using radio occultation electron density profiles derived from GPS measurements gathered from low Earth orbit satellites. Before being used, these radio occultation profiles are validated by fitting to them an electron density model. A re-weighted Least Squares algorithm is used for down-weighting unreliable measurements (occasionally, entire profiles) and to retrieve $N_m \mathrm{F2}$ N m F 2 and $h_m \mathrm{F2}$ h m F 2 values—together with their error estimates—from the profiles. These values are used to monthly update the database, which consists of two sets of ITU-R-like coefficients that could easily be implemented in the IRI or NeQuick models. The technique was tested with radio occultation electron density profiles that are delivered to the community by the COSMIC/FORMOSAT-3 mission team. Tests were performed for solstices and equinoxes seasons in high and low-solar activity conditions. The global mean error of the resulting maps—estimated by the Least Squares technique—is between $0.5\times 10^{10}$ 0.5 × 10 10 and $3.6\times 10^{10}$ 3.6 × 10 10 elec/m $^{-3}$ ? 3 for the F2-peak electron density (which is equivalent to 7 % of the value of the estimated parameter) and from 2.0 to 5.6 km for the height ( $\sim $ ～ 2 %).     

Evaluation of GPS orbit prediction strategies for the IGS Ultra-rapid products

The International GNSS Service (IGS) provides Ultra-rapid GPS & GLONASS orbits every 6 h. Each product is composed of 24 h of observed orbits with predicted orbits for the next 24 h. We have studied how the orbit prediction performance varies as a function of the arc length of the fitted observed orbits and the parameterization strategy used to estimate the empirical solar radiation pressure (SRP) effects. To focus on the dynamical aspects of the problem, nearly ideal conditions have been adopted by using IGS Rapid orbits and known earth rotation parameters (ERPs) as observations. Performance was gauged by comparison with Rapid orbits as truth by examining WRMS and median orbit differences over the first 6-h and the full 24-h prediction intervals, as well as the stability of the Helmert frame alignment parameters. Two versions of the extended SRP orbit model developed by the Centre for Orbit Determination in Europe (CODE) were tested. Adjusting all nine SRPs (offsets plus once-per-revolution sines and cosines in each satellite-centered frame direction) for each satellite shows smaller mean sub-daily, scale, and origin translation differences. On the other hand, eliminating the four once-per-revolution SRP parameters in the sun-ward and the solar panel axis directions yields orbit predictions that are much more rotationally stable. We found that observed arc lengths of 40–45 h produce the most stable and accurate predictions during 2010. A combined strategy of rotationally aligning the 9 SRP results to the 5 SRP frame should give optimal predictions with about 13 mm mean WRMS residuals over the first 6 h and 50 mm over 24 h. Actual Ultra-rapid performance will be degraded due to the unavoidable rotational errors from ERP predictions.