ALBERT

Notes: Summary The method for predicting x, y, and UT1-UTC as conceived and implemented by the Subbureau for Rapid Service and Prediction of the International Earth Rotation Service (IERS) is shown. For polar motion, the method is an extrapolation of an annual ellipse and Chandler circle. The method for UT1-UTC involves a simple differencing technique.

Notes: Summary The procedure for computing Earth orientation parameters (EOPs) implemented by the Subbureau for Rapid Service and Prediction of the International Earth Rotational Service (IERS) is described. This scheme involves the use of weighted cubic splines and provides smoothing of observations consistent with the agreement between contributed data sets.

Notes: Summary Two iterative algorithms for transformation from geocentric to geodetic coordinates are compared for numerical efficiency: the well known Bowring's algorithm of 1976, which employs the method of simple iteration, and the recent (1989) algorithm by Borkowski, which employs the Newton-Raphson method. The results of numerical tests suggest that the simple iteration method implemented in Bowring's algorithm executes approximately 30% faster than the Newton-Raphson method implemented in Borkowski's algorithm. Only two iterations of each algorithm are considered. Two iterations are sufficient to produce coordinates accurate to the comparable level of 1E-9 m, which exceeds the requirements of any practical application. Therefore, in the class of iterative methods, the classical Bowring's algorithm should be the method of choice.

Notes: Summary Following the introduction to the RETrig project and its history, the data included in the adjustment, as well as some test procedures concerning the data are, presented. Then the formulae for the combined solution of terrestrial and space data, originally published by Wolf, but used for the ED87 with modifications, are outlined. The resulting coordinate set was approved by the IAG as the European Datum 1987 (ED87). The strength of the figure is investigated by relative error ellipses between selected points. Finally, the first iteration of the numerical solution resulting in shifts for the ED87 coordinates is presented. This article is a résumé of the final report of ED87 calledthe ED87 Coordinates, Ehrnsperger (1989).

Notes: Summary A new approach has been developed for determining consistent satellite-tracking data weights in solutions for the satellite-only gravitational models. The method employs subset least-squares solutions of the satellite data contained within the complete solution and requires that the differences of the parameters of subset solutions and the complete solution to be in agreement with their error estimates by adjusting the data weights. GEM-T2 model was recently computed and adjusted through a direct application of this method. The estimated data weights are markedly smaller than the weights implied by the formal uncertainties of the measurements. Orbital arc tests as well as surface gravity comparisons show significant improvements for solutions when more realistic data weighting is achieved.

Notes: Summary A globally distributed network of high-precision receivers which obtain data from the full Global Positioning System (GPS) configuration of 18 or more satellites may soon become an efficient and economical method for the rapid determination of short-term variations in Earth orientation. A covariance analysis has been performed to evaluate the errors associated with GPS monitoring of Earth orientation. Earth orientation parameters were modeled either as constants over observing windows of various lengths, or as stochastic process-noise variables. The sensitivity of Earth orientation estimates to systematic errors in selected model parameters was also examined. GPS measurements appear to be highly competitive with those from other techniques, and have the potential to generate nearly continuous centimeter-level Earth orientation information to aid both spacecraft navigation and the study of high-frequency Earth orientation-related processes.

Notes: Abstract The mean sea level along the Swedish coast has been recomputed, taking into account the effect of the permanent tide on the height system. The recomputed data show the deviation of mean sea level (1960) from the mean geoid, i.e. the oceanographic deviation of mean sea level, with NAP as zero. On the basis of a conversion between the Finnish and Swedish height systems, mean sea level data from the Finnish coast are reduced to the same system as on the Swedish coast. The geodetically determined mean sea level values are compared with oceanographic model calculations. On the whole, the agreement between geodesy and oceanography is found to be good. Nevertheless, oceanography tends to yield somewhat larger deviations of the mean sea level than geodesy, especially in the extreme parts of both the Gulf of Bothnia and the Gulf of Finland. This might indicate that the oceanographic model has overestimated some effect. However, across the Gulf of Bothnia the oceanographic model predicts slightly smaller mean sea level differences than the geodetic data suggest.

Notes: Abstract The design of an integrated navigation system requires that various aspects are taken into consideration. In this paper the aspect of reliability (in the statistical sense) is more closely investigated. A particular measure of reliability, the Minimal Detectable Bias (MDB), is considered. Its use as a design tool for integrated navigation systems is described and is illustrated by an example.

Notes: Abstract Six sources of error in the use of Fourier methods for the conversion of geoid heights to gravity anomalies are considered. The errors due to spherical approximation are unimportant. The errors due to approximations in Stokes' integral may be eliminated by use of the gravity coating rather than the gravity anomaly. The chord-to-arc error and the truncation error may be reduced by using a reference field. Tapering of the edges of the measurement window reduces the truncation error. The long-wavelength components of the high degree spherical harmonics cause small offsets in the resulting gravity anomalies. The errors due to the plane approximation can be reduced by appropriate choice of map projection and area of integration.

Notes: Summary The significant coordinate difference changes of the same baselines, measured in different observing sessions, may be interpreted as the rotation around the station held fixed during the differenced processing, if the length changes of these baselines show random behavior. These rotation errors can significantly bias the final network adjustment based on redundant observing sessions and a relative approach. The Gauss-Helmert model with the estimation of the stochastic properties of the rotation errors is the most effective investigated approach. The standard deviation of the baseline length differences between those derived from a precise geodetic network and derived by Trimvec relative positioning software improved by a factor 2.4 after the final network adjustment using the introduced Gauss-Helmert model.

Notes: Summary The logistical difficulties and expense of measuring gravity over the surface of the earth or ocean provides the motivation for developing techniques for airborne data acquisition. To meet this need, the U.S. Naval Research Laboratory has had an active research program in airborne gravimetry since 1979. This paper provides a brief history, current status and proposed future directions of the program.

Notes: Abstract Characteristic frequencies and frequency bands are identified in the output of the inertial sensor block in a Ring Laser Gyro Strapdown Survey System by using Fast Fourier Transformation and are related to physical causes such as vehicle motion, environmental noise and sensor errors. A significant disturbance in the gyro and accelerometer outputs caused by the dither mechanism of the laser gyro is discussed. A frequency filtering approache to decrease the disturbing frequencies are studied. The effect of the filtering on the system performance is presented for field test results.

Notes: Abstract Classical least squares Bayesian estimation consists of minimizing the sum of the squared residuals of observations and the corrections to prior estimates of parameters.Many authors have produced more robust versions of this estimation by replacing the square by something else, such as the absolute value. In this article, three robust (M-LS, LS-M and M-M) estimators for three corresponding error models are described based on the principle of maximum likelihood type estimates (M-estimates). The influence functions of the three robust Bayesian estimators are given. The algorithm implementation problems are discussed and the expressions for the posterior variance-covariance are derived.

Notes: Abstract The concept of optimal filtering of observations collected with a dual frequency GPS P-code receiver is investigated in comparison to an approach for C/A-code units. The filter presented here uses only data gathered between one receiver and one satellite. The estimated state vector consists of a one-way pseudorange, ionospheric influence, and ambiguity biases. Neither orbit information nor station information is required. The independently estimated biases are used to form double differences where, in case of a P-code receiver, the wide lane integer ambiguities are usually recovered successfully except when elevation angles are very small. An elevation dependent uncertainty for pseudorange measurements was discovered for different receiver types. An exponential model for the pseudorange uncertainty was used with success in the filter gain computations.

Notes: Abstract Ray-tracing is used to examine the accuracy of several well known models for tropospheric delay prediction under varying atmospheric conditions. The models considered include the Hopfield zenith delay model and related mapping functions, the Saastamoinen zenith delay model and mapping function, and three empirical mapping functions based upon the Marini continued fraction form. Modelled delays are benchmarked against ray-tracing solutions for representative atmospheric profiles at various latitudes and seasons. Numerical results are presented in light of the approximations inherent in model formulation. The effect of approximations to the temperature, pressure and humidity structure of the neutral atmosphere are considered; the impact of surface layer anomalies (i.e., inversions) on prediction accuracy is examined; and errors resulting from the neglect of ray bending are illustrated. The influence of surface meteorological parameter measurement error is examined. Finally, model adaptability to local conditions is considered. Recommendations concerning the suitability of the models for GPS relative positioning and their optimal application are made based upon the results presented.

Notes: Summary The signals transmitted by Block II satellites of the Global Positioning System (GPS) can be degraded to limit the highest accuracy of the system (10 m or better point positioning) to authorized users. This mode of degraded operation is called “Selective Availability” (S/A). S/A involves the degradation in the quality of broadcast orbits and satellite clock dithering. We monitored the dithered satellite oscillator and investigated the effect of this clock dithering on high accuracy relative positioning. The effect was studied over short 3-meter and zero-baselines with two GPS receivers. The equivalent S/A effects for baselines ranging from 0 to 〉10,000 km can be examined with short test baselines if the receiver clocks are deliberately mis-synchronized by a known and varying amount. Our results show that the maximum effect of satellite clock dithering on GPS double difference phase residuals grows as a function of the clock synchronization error according to: S/A effect =0.04 cm/msec, and it increases as a function of baseline length like: S/A effect =0.014 cm/100 km. These are equations for maximum observed values of post-fit residuals due to S/A. The effect on GPS baselines is likely to be smaller than the 0.14 mm for a baseline separation of 100 km. We therefore conclude, for our limited data set, and for the level of S/A during our tests, that S/A clock dithering has negligible effect on all terrestrial GPS baselines if double difference processing techniques are employed and if the GPS receivers remain synchronized to better than 10 msec. S/A may constitute a problem, however, if accurate point processing is required, or if GPS receivers are not synchronized. We suggest and test two different methods to monitor satellite frequency offsets due to S/A. S/A modulates GPS carrier frequencies in the range of-2 Hz to +2 Hz over time periods of several minutes. The methods used in this paper to measure the satellite clock dither could be applied by the civilian GPS community to continuously monitor S/A clock dithering. The monitored frequencies may aid high accuracy point positioning applications in a postprocessing mode (Malys and Ortiz 1989), and differential GPS with poorly synchronized receivers (Feigl et al. 1991).

Notes: Summary Absolute measurements of gravity have been made at 6 locations ranging from Ottawa, Ont., in southern Canada, to Alert, N.W.T., the world's most northerly permanent settlement, as part of a program to provide scale and level for the Canadian Gravity Standardization Network (CGSN). Except at Resolute, N.W.T., CGSN-74 gravity values, upon which our gravity reductions are currently based, agree with the absolute gravity meter results to within about .25µm/s2. The scale of our CGSN-80 gravity network, upon which our spring-balance type gravity meter scale constants are derived, agrees with the scale defined by the absolute gravity measurements to within about one part in ten thousand.

Notes: Abstract In October 1987 a four day satellite GPS campaign was performed over the Åland archipelago to test the possibility of connecting the Swedish and Finnish national height systems. This paper summarizes the gained experiences using 5 WM 101 GPS receivers and the PoPS software. The computing results for the connection between the two height systems are considerably dependent on the choice of geoidal undulation model and systematic error parameter model. Using the NKG Scandinavian geoid 1989, which is probably the most accurate geoid available for the region, and a bias and tilt parameter model the difference between the Swedish RH70 system and the Finnish N60 system is estimated to 11.4 ± 4.0 cm. An independent check is provided by two connecting border bench marks in northern Scandinavia yielding the difference 19.2 ± 4.2 cm. In view of that merely single frequency GPS receivers were used together with the PoPS software, we consider this result most satisfactory.

Notes: Abstract The capability of the recently developed SAGEM ULISS-30 inertial survey system for performing local surveys at high accuracies have been tested in a field campaign carried out November 1989 on the island of Fyn, Denmark, in cooperation with the Swedish National Land Survey. In the test a number of lines between existing national geodetic control points were surveyed, along with points in the less reliably determined cadastral network, forming an irregular network pattern of 10–15 km extent. The survey involved frequent offset measurements (up to 50–100 m) with an ISS-integrated total station. The profile geometries were not particularly suited for inertial surveys, with narrow and rather winding roads, necessitating frequent vehicle turns. In addition to the pure inertial surveys a kinematic GPS/inertial test was also carried out, using a pair of Ashtech L-XII receivers. The inertial survey results, analyzed with a smoothing algoritm utilizing common points on forward/backward runs, indicate that 5-cm accuracies are possible on reasonably straight profiles of 5 km length, corresponding to a 10 ppm “best-case” accuracy for double-run traverses. On longer, more winding traverses error levels of 10–20 cm are typical. To handle the inertial data optimally, proper network adjustments are required. A discussion of suitable adjustment models of both conventional and collocation type is included in the paper.

Notes: Abstract At different European institutes software has been developed for evaluation of the gravitational potential of the Earth using high degree spherical harmonic expansions. In this report the results of a comparison of a number of these software packages are presented. We compared the results for the second order derivatives (gravity gradients). It appeared that one of the most critical points in these computations is the definition of the coordinates, which should be as accurate as possible. Machine dependency and algorithm setup were of less importance, the former being only reflected in CPU timing results.

Notes: Abstract An experiment was conducted in 1987 in search for a possible non-Newtonian component to gravity. The test compared accurately measured gravity values on a 600 m tower with upward continued surface gravity. The results indicated a dominant attractive non-Newtonian force that asymptotically approached -540 µGal at the top of the tower. An exhaustive search of possible error sources led to the discovery that our surface data did not accurately represent some of the local topographic features. The surface survey was supplemented by gravity data to remove some of the biases that were caused by the misrepresentation. In addition, a rigorous terrain correction was applied to the surface data resulting in terrain-corrected Bouguer anomalies. These anomalies were then upward continued using two independent techniques. The terrain effect was added back to the predicted values at altitude. With this procedure almost the entire non-Newtonian effect was explained. Currently we find no conclusive evidence for a non-Newtonian force over the range of several hundred meters.

Notes: Abstract The part of the Baltic Shield located within Finland consists mainly of two tectonic units: the Archaean basement and the Proterozoic bedrock formed by various types of granitoids, and metamorphosed sedimentary and volcanic rocks. These are further divided into smaller subblocks. Horizontal relative movements between and within the main units have been detected by comparison of original terrestrial triangulation and repeated trilateration observations with time interval on the average 30 years (12 to 46 years). The strain pattern obtained is in agreement with geological structures as well as with a completely independently determined crustal uplift pattern.

Notes: Abstract In October 1990, several airborne GPS tests were conducted in the Ottawa region by the Canada Centre for Surveying (CCS) and the Canada Centre for Remote Sensing (CCRS). Ashtech XII receivers were located at up to three monitor stations with baseline lengths to the aircraft ranging from 1–200 km. Approximately two hours of airborne data, collected at a 2 Hz rate, were available for each of the three test days. Post-processing of the differential data was done using the University of Calgary's SEMIKIN package which utilizes a Kalman filter algorithm to estimate both the remote receiver's position and velocity. Comparisons were made between the aircraft position and velocity determined from each of the monitor stations to assess the consistency of differential GPS when different reference stations are used. Results show that the degree of consistency is dependent upon the distance to the monitor stations. Agreement at the decimetre-level is achieved in position when the baseline lengths are within 100 km. Agreement in velocity is usually better than 1 cm s−1 (RMS).

Notes: Summary In the last three years, the European Geodetic Very Long Baseline Interferometry (VLBI) Network has grown to a total of six fixed antennas placed in Germany, Italy, Spain and Sweden, all equipped with the standard geodetic VLBI instrumentation and data recording systems. During this period of time, several experiments have been carried out using this interferometer providing data of very high quality due to the excellent sensitivity and performance of the European stations. The purpose of this paper is to study the consistency of the VLBI geodetic results on the European baselines with respect to the different degrees of freedom in the analysis procedure. In order to complete this study we have made use of both real and simulated data sets, two different software packages (OCCAM 3.0 and CALC 7.4/SOLVE) and a variety of strategies in the data analysis. The results we have obtained show that the repeatability of the VLBI estimates of the baseline lengths in the European network is better than one centimeter, independent of the different analysis methods, and is consistent with the formal error levels expected from the data analysis. This consistency should be enough to produce geophysically significant information in Europe from VLBI data within a relatively short time span.

Notes: Abstract An analysis of the quasi-stationary sea surface topography (QSST) is carried out in the Norwegian Sea region (54°〈ø〈72°, -25°〈λ〈20°) using marine gravimetry and one year of Geosat ERM altimetry. As reference models the geopotential model OSU91A and the QSST model OSU89D were used. Two procedures to extract the QSST from mean sea surface heights and gravity anomalies were tested. Spherical FFT techniques were applied in both procedures. The results show that QSST associated with wavelength shorter than 4000 km exists. Relative to the OSU89D model the QSST was found to have a variance of (0.219 m)2 and a correlation length of 1.105°. The circulation pattern recovered in this paper agree with results of oceanographic analysis.

Notes: Abstract The Global Positioning System (GPS) is considered in conjunction with a strapdown Inertial Measurement Unit (IMU) for measuring the gravity vector. A comparison of this system in space and on an airborne platform shows the relative importance of each system element in these two different acceleration environments. With currently available instrumentation, the acceleration measurement accuracy is the deciding factor in space, while on an Earth-bound (including airborne) platform, the attitude error of the IMU is most critical. A simulation shows that GPS-derived accelerations in space can be accurate to better than 0.1mgal for a 30s integration time, leading to estimates of 1° mean gravity anomalies on the Earth's surface with an accuracy of 4–5 mgal. On an airborne platform, the horizontal gravity estimation error is tightly coupled to the attitude error of the platform, which can only be bounded by external attitude updates. Horizontal gravity errors of 5mgal are achievable if the attitude is maintained to an accuracy of 1arcsec.

Notes: Abstract Least-squares collocation and Stokes integral formula, as implemented using the Fast Fourier Technique, handle the harmonic downward continuation problem quite differently. FFT furthermore requires gridded data, amplifying the difference of methods. We have in this paper studied numerically the effects of downward continuation and gridding in a mountainous area in central Norway. Topographically smoothed data were used in order to reduce these effects. Despite the smoothing, it was found that the vertical gravity gradient had values up to -11 mgal/km. The corresponding differences between geoid heights and the height anomalies at altitude reached 12 cm. The differences between geoid heights obtained using collocation or FFT with gravity data at terrain level or sea level showed differences between the values of up to 10 cm r.m.s. A part of this difference was a consequence of different data areas used in the FFT and collocation solution, though. Major discrepancies between the solutions were found in areas where the topographic smoothing could not be applied (deep fjords with no depth information in the used DTM) or where there seemed to be gross errors in the data. We conclude that proper handling of harmonic continuation is important, even when we as here have used a 1 km resolution DTM for the calculation of topographic effects. The effect of data gridding, required for the FFT method, seems not to be as serious as the need to limit the data distribution area, required when least squares collocation is used with randomly distributed data.

Notes: Abstract The computational requirements in the simulations of geopotential estimation from satellite gravity gradiometry are discussed. Fast algorithms for spherical harmonic synthesis and least squares accumulation on a vectorizing supercomputers are presented. Using these methods, in a test case estimation of 2595 coefficients of a degree and order 50 gravity field, sustained program execution speeds of 275 Mflops (87 % peak machine speed) on a single processor of a CRAY Y-MP were achieved, with spherical harmonics computation accounting for less than 1 % of total cost. From the results, it appears that brute-force estimation of a degree and order 180 field would require 537 Million Words of memory and 85 hours of CPU time, assuming mission duration of 1 month, and execution speed of 1 Gflops. Both memory size and execution speed requirements are within the capabilities of modern multi-processor supercomputers.

Notes: Abstract Two water tube clinometers are installed in a deep mine in Lohja, Finland. One, lying in an E-W direction, is 177 m long and the other, lying in a N-S direction, is 62 m long. These instruments are used for tidal records and research. Because the station was on the zone of totality of the 1990 solar eclipse, the instruments offered a suitable tool for investigating whether there was any shielding effect on the direction of the vertical. During the eclipse, the resolution of the instruments was increased to 0.00001″ and 0.00004″, respectively. p ]Recordings and data evaluation are discussed, and the results obtained show that no gravitational shielding was found at the level of the above accuracy.

Notes: Summary Many GPS networks which were initially surveyed with Texas Instruments TI-4100 receivers have now been resurveyed with mixtures of TI-4100 and Trimble 4000 receivers or exclusively with Trimble receivers. In order to make confident tectonic interpretation of displacements observed between such surveys, it is necessary to understand any biases which may be introduced by using different receiver types or by mixing receivers within a network. Therefore, one of the primary objectives of the Ecuador 1990 GPS campaign (February 1990) was to provide a direct long baseline comparison between the TI-4100 and Trimble 4000SDT GPS receivers. p ]During this campaign, TI and Trimble receivers were co-located at each end of a 1323 kilometer baseline (Jerusalen to Baltra). Solutions for this baseline show no variation with receiver type. Zero-length baseline solutions showed no evidence for any intrinsic bias caused by mixing the two receiver types. Short baseline solutions indicate a bias of -34±10 mm in the baseline vertical component; the sign of the bias indicates that either the assumed phase center location for the TI is too low or the assumed location for the Trimble is too high. The bias is explainable if the phase centers of the Trimble SDT and SST antennas are similarly located. p ]Solutions for baselines measured with codeless receivers (such as the Trimble) should be as precise as those for baselines measured with P-code receivers (such as the TI) as long as it is possible to resolve ambiguities. Resolution of the widelane ambiguity is the limiting factor in ambiguity resolution with any codeless receiver, and in the February 1990 campaigns it was not successful fore baselines longer than 100 km. Without explicit modeling of the ionospheric effect on the widelane, ambiguity resolution with codeless receivers will not be successful for baselines longer than about 100 km, depending on the local ionospheric conditions.

Notes: Abstract The variance component estimation (VCE) method as developed by Helmert has been applied to the global SLR data set for the year 1987. In the first part of this study the observations have been divided into two groups: those from ruby and YAG laser systems, and their weights estimated over several months. It was found that the weights of both sets of stations altered slightly from month to month, but that, not surprisingly, the YAG systems consistently outperformed those based on ruby lasers. The major part of this paper then considers the estimation of the variance components (i.e. weights) at each SLR station from month to month. These were tested using the F-statistic and, although it indicated that most stations had significant temporal variations, they were generally small compared with the differences between the stations themselves, i.e. the method has been shown to be capable of discriminating between the precision with which the various laser stations are operating. The station coordinates and baseline lengths computed using both a priori, and estimated, weights where also compared and this showed that changes in the weights can have significant effects on the estimation of the station positions, particularly in the z component, and on the baseline lengths - so proving the importance of proper stochastic modelling when processing SLR data.

Notes: Abstract In this paper several ordering algorithms for the unknowns in geodetic least squares systems are compared. The comparison is restricted to the case of the well known Cholesky factorization of the normal matrixA into a lower triangular factorL. p ]The algorithms which were investigated are: minimum degree, minimum deficiency, nested dissection, reverse Cuthill-McKee, King's-, Snay's-, and Levy's-banker's and Gibbs-King. p ]Also some strategies are presented to reduce the time needed to compute the ordering using a priori information about the way the unknowns are connected to each other. p ]The algorithms are applied to normal matrices of the least squares adjustment of 2D geodetic terrestrial networks, photogrammetric bundle-block adjustments, and a photogrammetric adjustment using independent models. p ]The results show that ordering the unknowns yields a considerable decrease of the cpu time for computing the Cholesky factor, and that in general the minimum degree and Snay's banker's ordering perform best. Furtheron they show that a priori information about the connection structure of the unknowns speeds up the computation of the ordering substantially.

Notes: Abstract Some selected test areas in the Austrian territory are presented. Free-air and Bouguer anomalies as well as isostatic anomalies (based on Vening Meinesz' isostatic model) are computed. Statistics of these anomalies are given. Also, an extensive comparison between their empirical covariance functions is made and will be discussed. The results show that the isostatic anomalies for our test areas still contain, in general, a trend part.

Notes: Summary For several years polar motion has been routinely monitored with the technique of geodetic Very Long Baseline Interferometry (VLBI) at five-day intervals. Here we present the results of the first two series of VLBI measurements for polar motion monitoring observed on a quasi daily basis employing only a single baseline. The high sensitivity of the long north-south baseline between radio telescopes at Wettzell in Germany and Hartebeesthock in South Africa for both components of polar motion permitted relatively short and inexpensive measurements of only two hours duration per session. The results of this series agree very well with the pole path determined with the IRIS network using 4 observatories in each observing session of 24 hour duration. With the polar motion results of the two series spanning about 35 days each, spectral analyses were performed which have shown a fortnightly period with a high degree of probability. These measurements demonstrate the potential of long north-south VLBI baselines for monitoring polar motion with very high temporal resolution for studies of short period fluctuations.

Notes: Abstract One year (November 1986 to October 1987) of Geosat altimeter data with improved orbits produced at The Ohio State University has been used to define sea surface heights for 22 ERM and one year averaged Geosat track. All sea surface heights were referenced to the single reference track through the application of geoid gradient corrections. The root mean square (RMS) gradient correction was on the order of ±1 cm although it could reach 20 cm with data points in trench areas. 10 values used to form the mean were considered. Although this study was initially driven by a need for a good reference sea surface for geodetic applications the formation of the reference track yields information on the variability of the ocean surface in the first year of the Geosat ERM. The RMS point variability was ± 12.6 cm with only a very small number of values exceeding 50 cm when a depth editing criteria was used. Global plots of the sea surface variability clearly reveal the major ocean currents and their variations in position in the year. Examination of the 1° × 1° averaged sea surface height variations show average and maximum variability values as follows: Gulf Stream (29 and 50 cm); Kurshio Current (24 and 49 cm); Agulhas Current (24 and 52 cm) and the Gulf of Mexico (18 and 31 cm). These magnitudes may be dependent on the radial orbit correction procedure. To investigate this effect sea slope variations were also computed. These results also showed clear current structures but also high frequency gravity field information despite efforts to average out such information. The data described in the paper is available from the authors for numerous other studies, some of which are suggested in the paper.

Notes: Abstract The determination of a representative refractive index for the wave path is the main limitation of the attainable accuracy in electronic distance measurement. To overcome this limitation the length ratio method was initially proposed and later developed into the local scale parameter (LSP) method. In this paper, the mathematical model of the LSP method is derived for electro-optical distance measurement from first principles based on the physics of the atmospheric boundary layer. The model does not rely on ‘standard atmospheres’. It is shown that atmospheric temperatures and pressures must be observed at instrument stations but not at reflector stations. Appropriate LSP field procedures and the results of some field experiments are summarized. The method consistently produces accuracies of better than ±1 ppm. Use of the method is recommended for high precision (trilateration) networks, which need to be measured repeatedly and where absolute scale is not relevant.

Notes: Abstract In order to find short periodic oscillations in the Earth's rate of rotation, atmospheric angular momentum, solar activity the Maximum Entropy Spectral Analysis — MESA (Burg, 1967) has been applied. The MESA with moving autoregressive order has been introduced in order to detect more accurately periods of very weak short periodic variations. Oscillations with periods of about 75, 50, 27 and 18 days have been found in length of day — LOD, from which tidal oscillations were removed up to 35 days — LODR computed by the Center for Space Research — CSR from Lageos Laser Ranging data, in the axial component of atmospheric angular momentum — χ3 determined by the U.S. National Meteorological Center — NMC and in the geomagnetic activity represented by the geomagnetic index —A p (Lincoln, 1967). These oscillations computed by Ormsby band pass filter (Ormsby, 1961) are in a very good phase agreement in the case of oscillations with periods of 50 and 18 days in these 3 series. The MESA of the cross covariance estimations between LODR- χ3, χ3-A p,A p-LODR, LODR-FLUX, χ3-FLUX, andA p-FLUX has confirmed the existence of common oscillations with periods of 70, 50, 27 and 18 days. This indicates a possible relationship between solar activity and the short periodic exchange of angular momentum between the atmosphere and the solid Earth.

Notes: Abstract It is considered that precise geoid determination is one of the main current geodetic problems in Turkey since GPS defined coordinates require geoidal heights in practice. In order to determine the geoid by least squares collocation (LSC) the area covering Turkey was divided into 114 blocks of size 1° × 1°. LSC approximation to the geoid based upon the tailored geopotential model GPM2-T1 is constructed within each block. The model GPM2-T1 complete to degree and order 200 has been developed by tailoring of the model GPM2 to mean free-air anomalies and mean heights of one degree blocks in Turkey. Terrain effect reduced point gravity data spaced 5′ × 5′ within each block which the sides extended 0°.5 were used in LSC. Residual terrain model (RTM) depends on point heights at 15″×20″ griding and 5′×5′ and 15′×15′ mean heights has been carried out in terrain effect reduction. Indirect effect of RTM on geoid is also taken into account. The geoid, called Turkish Geoid 1991 (TG-91), referenced to GRS-80 ellipsoid has been computed at 3′ × 3′ griding nodes within each block. The quality of the TG-91 is also evaluated by comparing computed and GPS derived geoidal height differences, and 2.1 – 2.6 ppm accuracy for average baseline lenght of 45 km is obtained.

Notes: Abstract Gravity data inversion methods using spatial source distributions are frequently investigated and applied in Geodesy. Nearly all of them construct a fixed geometry for the sources. It was shown that this is not at all necessary. We give an approach to the problem of geoid determination based on free-positioned point masses. The algorithm available is extended and refined in order to make it applicable to more ill-designed and complex problems than addressed so far. We introduce concepts to handle different data accuracies, non-uniform data coverages, and different data types. The Gulf of Bothnia serves as an area of investigation. We determine a pure gravimetric geoid solution as well as a combined solution based on gravimetric and altimetric data. The problem of gross error detection in the altimetry is treated. The prediction accuracies obtained prove the method to be suitable for such a problem.

Notes: Summary A small and light-weight military land navigation system (Litton LLN-83 strapdown inertial unit with Litef IBAG control unit) was tested for its suitability for inertial surveying applications with moderate accuracy requirements. Field tests with a minivan were carried out on linear test courses of 1 km and 7 km length. The performance of the system was assessed on the basis of double-run accuracy (against true coordinates, after simple adjustment of measured data onto end points). On the 1-km course (sealed road, average spacing of points: 118 m) an accuracy of 0.4 m in E and N and 0.25 m in elevation was achieved. On two 7-km courses (unsealed roads, average spacing of points: 1.0 km) a pooled accuracy of 1.2 m in E and N and 0.4 m in elevation was obtained. The system proved extremely reliable. Susceptibility to rough roads (likely due to the lack of a rigid attachment of the system to the host vehicle) led to the abortion of two missions.

Notes: Summary The least-squares collocation method has been used for the computation of a geoid solution in central Spain, combining a geopotential model complete to degree and order 360, gravity anomalies and topographic information. The area has been divided in two 1°× 1° blocks and predictions have been done in each block with gravity data spacing about 5′ × 5′ within each block, extended 1/2°. Topographic effects have been calculated from 6″ × 9″ heights using an RTM reduction with a reference terrain model of 30′ × 30′ mean heights.

Notes: Abstract In addition to the on-line data evaluation during the measurements with the absolute gravity meter JILAG-3, a subsequently more intensive examination of the measured time/distance data pairs is performed. This allows an additional assessment of the gravity results, the station quality and the measurement conditions. Sinusoidal disturbances in the raw data deteriorate the determination of gravity. Incoming microseisms affect the mean result of the free-fall experiments randomly after a large number of measurements. Instrumental vibrations of the gravity meter during the measurement procedure may influence the gravity result systematically. A station comparison indicates that a 30 Hz frequency is triggered by JILAG-3 itself and influences the measurements depending on the stability of the foundation. Using a mathematical filter it is possible to separate the deteriorations from the gravity acceleration. Up to now an improvement in the absolute accuracy of gravity after filtering could not be proved, but an increase of the precision is indicated.

Notes: Abstract In order to study the Baltic Sea Level change and to unify national height systems a two week GPS campaign was performed in the region in Autumn 1990. Parties from Denmark, Finland, Germany, Poland and Sweden carried out GPS measurements at 26 tide gauges along the Baltic sea and 8 VLBI and SLR fiducial stations with baseline lengths ranging from 230 km to 1600 km. The observations were processed in the network mode with the Bernese version 3.3 software using orbit improvement techniques. To get rid of the scale error introduced by the ionospheric refraction from single-frequency data, the local models of the ionosphere were estimated using L4 observations. The tropospheric zenith corrections were also considered. The preliminary results show average root mean square (RMS) errors of about ±3 cm in the horizontal position and ±7 cm in the vertical position relative to the Potsdam SLR station in ITRF89 system. After transformation of the GPS results to geoid heights using the levelled heights, an absolute comparison with gravimetric geoid heights using the least squares modification of Stokes' formula (LSMS), the modified Molodensky and the NKG Scandinavian geoid 1989 (NGK-89) models gives a standard deviation of the difference of ±7cm to ±9cm for the NKG-89 model and of ±9cm to ±30cm for the LSMS and the modified Molodensky model. The Swedish height system is found to be about 8-37cm higher than those of the other Baltic countries for NKG-89 model.

Notes: Abstract In view of a uniform European geoid determination with centimeter accuracy the situation of the geodetic reference systems in Eastern Europe is described. For the necessary transformations into a uniform reference system the relevant relations are specified.

Notes: Abstract The representation of the topography is usually made by digital height models and digital density models. Therefore, one can produce the so-called digital Moho model (DMM) by applying a certain isostatic hypothesis. The attraction of such compensating masses is deducted. Also, some special cases are treated. The effect of neglecting the height of the computational point only on calculating the attraction of the compensating masses is studied. The results show that the height of the computational point must be taken into account on calculating the attraction of the compensating masses specially for high mountainous areas.

Notes: Abstract Six days of data from the GIG'91 experiment have been analyzed with a fiducial strategy. The results obtained with our orbital software GEOSAT, show daily horizontal and length repeatabilities at the level of 1 part in 109 plus 2 mm for baseline lengths up to 4000 km. A direct comparison with results from the GIPSY software shows, with some exceptions, mean differences at the sub-cm level. After transformation to ITRF'90 the rms of the coordinate differences is 14.8 mm. Studies of orbital predictions and comparisons with external high precision orbits indicate a mean orbit precision and accuracy of around 35 cm in each cartesian coordinate. Correlations between the GEOSAT and GIPSY solutions indicate some common model deficiencies.

Notes: Abstract A new set of formulas has been developed for the computation of geoid undulations and terrain corrections by FFT when the input gravity anomalies and heights are mean gridded values. The effects of the analytical and the discrete spectra of kernel functions and that of zero-padding on the computation of geoid undulations and terrain corrections are studied in detail. Numerical examples show that the discrete spectrum is superior to the analytically-defined one. By using the discrete spectrum and 100% zero-padding, the RMS differences are 0.000 m for the FFT geoid undulations and 0.200 to 0.000 mGal for the FFT terrain corrections compared with results obtained by numerical integration.

Notes: Abstract In this paper a new method to compute in a fast and reliable way the collocation solution is presented. In order to speed up the numerical procedures, some restrictions on input data are needed. The basic assumption is that data are gridded and homogeneous; this implies that the autocovariance matrix entering in the collocation formula is of Toeplitz type. In particular, if observations are placed on a two dimensional planar grid, the autocovariance matrix is a symmetric block Toeplitz matrix and each block is itself a symmetric Toeplitz matrix (Toeplitz/Toeplitz structure). The analysis can be extended to a regular geographical grid, considered as a generalization of the planar one, taking into account the distortions on the Toeplitz/Toeplitz structure induced by the convergence of the meridians. The devised method is based on a combined application of the Preconditioned Conjugate Gradient Method and of the Fast Fourier Transform. This allows a proper exploitation of the Toeplitz/Toeplitz structure of the autocovariance matrix in computing the collocation solution. The numerical tests proved that the application of this algorithm leads to a relevant decrease in CPU time if compared with standard methods used to solve a collocation problem (Cholesky, Levinson).

Notes: Abstract In view of the smallness of the atmospheric mass compared to the mass variations within the Earth, it is generally assumed in physical geodesy that the terrain effects are negligible. Subsequently most models assume a spherical or ellipsoidal layering of the atmosphere. The removal and restoring of the atmosphere in solving the exterior boundary value problems thus correspond to gravity and geoid corrections of the order of 0.9 mGal and -0.7 cm, respectively. We demonstrate that the gravity terrain correction for the removal of the atmosphere is of the order of 50µGal/km of elevation with a maximum close to 0.5 mGal at the top of Mount Everest. The corresponding effect on the geoid may reach several centimetres in mountainous regions. Also the total effect on geoid determination for removal and restoring the atmosphere may contribute significantly, in particular by long wavelengths. This is not the case for the quasi geoid in mountainous regions.

Notes: Summary A local model of the geoid in NE Italy and its section along the “Venice” ground track of the ERS-1 satellite of the European Space Agency is presented. The observational data consist of geoid undulations determined with a network of 25 stations of known orthometric (by spirit leveling) and ellipsoidal (by GPS differential survey) and of 13 deflections of the vertical measured at sites of the network for which, besides the ellipsoidal (WGS84) coordinates, also astronomic coordinates were known. The network covers an area of 1×1 degrees and is tied to a vertical and horizontal datum: one vertex of the network is the tide gauge of Punta Salute, in Venice, providing a tie to a mean sea level; a second vertex is the site for mobile laser systems at Monte Venda, on the Euganei Hills, for which geocentric coordinates resulted from the analysis of several LAGEOS passes.The interpolation algorithm used to map sparse and heterogeneous data to a regular grid of geoid undulations is based on least squares collocation and the autocorrelation function of the geoid undulations is modeled by a third order Markov process on flat earth. The algorithm has been applied to the observed undulations and deflections of the vertical after subtraction of the corresponding predictions made on the basis of the OSU91A global geoid model of the Ohio State University, complete to degree and order 360. The locally improved geoid results by adding back, at the nodes of a regular grid, the predictions of the global field to the least squares interpolated values. Comparison of the model values with the raw data at the observing stations indicates that the mean discrepancy is virtually zero with a root mean square dispersion of 8 cm, assuming that the ellipsoidal heights and vertical deflections data are affected by a random error of 3 cm and 0″.5 respectively. The corrections resulting from the local data and added to the “background” 360×360 global model are described by a smooth surface with excursions from the reference surface not larger than ±30 cm.

Notes: Summary The 1986 GPS survey of Iceland aimed to: (1) establish geodetic control in the South Iceland Seismic Zone (SISZ), to study destructive earthquakes there, (2) measure a country-wide network to form the basis of a new first order national network. 51 points were surveyed, with 20–30 km spacings within the SISZ and 100 km spacings elsewhere. The data were processed using the Bernese GPS software Version 3. Analysis was difficult due to poor satellite geometry and short-period ionospheric variations. However, an ambiguity-fixed, ionosphere-free solution gave accuracies of 1–2 cm in the horizontal and 2–3 cm in the vertical for the SISZ network and an ambiguity-free, ionosphere-free solution yielded accuracies of about 5 cm for the country-wide network. An ionosphere-free solution for the total survey with ambiguities fixed for the SISZ network only gave marginal additional improvements over the two separate solutions. GPS surveying has continued annually in Iceland with measurements in South Iceland in 1989 and 1992 (Hackman 1991; Sigmundsson 1992) and in North Iceland in 1987, 1990 and 1992 (Jahn et al. 1992; Foulger et al. 1992).

Notes: Summary A low cost lunar Satellite-to-Satellite radio tracking mission in a low-low configuration could considerably improve the existing knowledge about the lunar gravity field. The impact of various mission parameters that may contribute to the recovery of the gravity field, such as satellite altitude, satellite separation, mission duration, measurement precision and sampling interval were quantified using the Jekeli-Rapp algorithm. Preliminary results indicate that the gravity field resolution up to harmonic degree 40 to 80 is feasible depending on various mission configurations. Radio tracking data from a six-month mission with a precision of 1 mm s−1 every 10 s and 300 km satellite separation at 150 km altitude will permit the determination of 5o×5o mean gravity anomalies with an error of approximately 15 mgals. Consideration of other unaccounted error sources of instrumental, operational as well as environmental nature may lower this resolution.

Notes: Abstract Carrier phase ambiguity resolution on the fly is investigated using two receiver technologies, namely dual-frequency P code and high performance, single frequency, C/A code receivers. Both receiver types were used simultaneously in a series of land kinematic trials. A least-squares search technique is used to find the correct double difference carrier phase ambiguities. Both C/A and single frequency P code technologies are found to be equivalent and capable of resolving the integer ambiguities on the fly using some 30 to 200 seconds of data under benign multipath conditions. Successful ambiguity resolution on the fly results in cm-level accuracy kinematic positioning. The ambiguity resolution time required and success rate are however found to be strongly dependent on the level of carrier phase multipath and, as a consequence, on the error variance assigned to the carrier phase measurements. The use of widelaning with the dual frequency P code results in ambiguity resolution in seconds. The performance of widelaning is also superior in a comparatively high carrier phase multipath environment.

Notes: Abstract Some time ago it was agreed to set up a European GPS Traverse from Tromsö (Norway) to Syracuse (Sicily), to improve the definition of the European geoid. An outline of the Italian portion of this Traverse is summarized here, with special reference to the sections from the Brenner Pass to Taranto — carried out in 1989 — and for those from Taranto to Syracuse-Noto, recently completed. The observing procedures and results are reported here. A comparison with the results of the ITALGEO '90 geoid, and a tentative profile of the Italian geoid along the whole traverse are also sketched. Furthermore, a net of similar traverses, a “first order geoidal net” in Italy is proposed, in order to support the existing and new geoid determinations. In such a way a sub-decimetric accuracy in the Italian GPS derived orthometric heights may probably be achieved

Notes: Abstract A method based on multi-antennae linked to a common GPS receiver is proposed. The goal of the technique is to improve height determination for baselines a few kilometres in length. The advantage of this technique resides in the elimination of relative clock parameters in the “between-antenna” single difference observations. Because single difference observations are free of clock errors more geometrical strength remains to determine the baseline components. This statement is valid as long as intercable biases can be carefully calibrated. For millimetre height determination, the intercable calibration must be done at the same level of accuracy. Under this assumption it is shown that in general the height standard deviation improves by a factor of about three compared to standard GPS data processing. With the proposed method, the effect of relative tropospheric zenith delay errors becomes a bit smaller (in absolute value), compared to standard data processing. To absorb this error, a relative tropospheric zenith delay parameter may be estimated. Even with this additional parameter in the solution the height standard deviation remains two times smaller than the results of standard processing techniques (without tropospheric zenith delay parameter), and at least five times smaller than in the results obtained from standard processing including one tropospheric zenith delay parameter.

Notes: Abstract The Southwest Pacific GPS Project (SWP) is using the Global Positioning System (GPS) to monitor crustal motion across and within a plate boundary complex between the Australian and Pacific plates. GPS field campaigns were conducted in 1988, 1989 and 1990, to observe networks of increasing size and complexity. The 1990 campaign consisted of two periods, or “Bursts”, and this paper focuses on the analysis of data collected during the nine day Burst 1 in July, 1990, a period in which GPS Selective Availability was activated. During Burst 1, baselines that spanned the Tonga Trench and the Lau Basin were observed, and only one station (Espiritu Santo, Vanuatu) was located west of Fiji in the network. The lengths of the baselines observed fall mainly between 300 km and 1600 km, but some lines are as long as 3500 km. A total of 78 station-days of field site data and approximately 150 station-days of global fiducial data were processed from predominantly codeless receivers. A global fiducial network of 20 sites was used to provide orbit control and accuracy assessment for the 13 available satellites. The daily solutions for 45 baselines between 10 SWP sites have an RMS scatter in the length of 24 mm plus 6 parts per billion. This scatter provides an estimate of baseline precision for the Burst 1 “nominal solution.” Experiments were conducted to investigate a variety of possible effects on the SWP Network baseline estimates, including the influence of a reduced global fiducial network for the purpose of assessing the quality of results obtained in 1988 and 1989 in which the fiducial network was smaller than in 1990. These experiments produced results that agreed with the nominal solution at the level of the precision estimate. Furthermore, estimates for selected baselines in Australia, the Central Pacific, North America and Europe, also measured by VLBI and SLR, were used for an external accuracy evaluation. The GPS and VLBI or SLR determinations of length agreed at a level consistent with the nominal solution precision estimate.

Notes: Summary In May 1989 and April 1990 the radio telescopes of the Wettzell Geodetic Fundamental Station in Germany and of the Shanghai Observatory near Seshan in China observed two series of daily VLBI experiments of short duration for precise determination of UT1. In 1990 a few experiments were complemented by the Hartebeesthoek Radio Astronomy Observatory in South Africa and the Medicina telescope of the Bologna Istituto di Radioastronomia in Italy. Employing the South African station together with the east-west baseline formed by the observatories of Seshan and Medicina permitted simultaneous determinations of UT1 and polar motion. Here we report on the results of these observations. Comparing the UT1 results with those of the IRIS Intensive series gives a clear indication of the absolute accuracy of such short duration VLBI measurements which is estimated to be of the order of ±60µs.

Notes: Abstract The effects of residual ocean tide signals on altimetric mesoscale variability estimates are analyzed in the north east Atlantic region using one year of Geosat Exact Repeat Mission data. The variability is evaluated along collinear tracks and covariance functions are determined. Initial results show that the average variability is about 10 cm. Variability values of 15–20 cm are found between Iceland and the Faeroe Islands and values up to 1/2 m are found near the coast of the UK. Then a procedure for estimation of ocean tide signals combined with the collinear analyses was tested. A separation of the estimated tide residuals associated with M2, S2, and N2 resulted in a significant reduction of the variability. The average variability decreased to 5 cm and the temporal correlations vanished. A reduction of the large variability values from 15–50 cm to 5–10 cm demonstrates that significant residual ocean tide signals can be estimated and removed efficiently in a collinear analysis of the mesoscale ocean variability.