Multi-reference evaluation of uncertainty in earth orientation parameter measurements

Uncertainties in polar motion and length-of-day measurements are evaluated empirically using several data series from the space-geodetic techniques of the global positioning system (GPS), satellite laser ranging (SLR), and very long baseline interferometry (VLBI) during 1997–2002. In the evaluation procedure employed here, known as the three-corner hat (TCH) technique, the signal common to each series is eliminated by forming pair-wise differences between the series, thus requiring no assumed values for the “truth” signal. From the variances of the differenced series, the uncertainty of each series can be recovered when reasonable assumptions are made about the correlations between the series. In order to form the pair-wise differences, the series data must be given at the same epoch. All measurement data sets studied here were sampled at noon (UTC); except for the VLBI series, whose data are interpolated to noon and whose UT1 values are also numerically differentiated to obtain LOD. The numerical error introduced to the VLBI values by the interpolation and differentiation is shown to be comparable in magnitude to the values determined by the TCH method for the uncertainties of the VLBI series. The TCH estimates for the VLBI series are corrupted by such numerical errors mostly as a result of the relatively large data intervals. Of the remaining data sets studied here, it is found that the IGS Final combined series has the smallest polar motion and length-of-day uncertainties.     

GGM02 – An improved Earth gravity field model from GRACE

A new generation of Earth gravity field models called GGM02 are derived using approximately 14 months of data spanning from April 2002 to December 2003 from the Gravity Recovery And Climate Experiment (GRACE). Relative to the preceding generation, GGM01, there have been improvements to the data products, the gravity estimation methods and the background models. Based on the calibrated covariances, GGM02 (both the GRACE-only model GGM02S and the combination model GGM02C) represents an improvement greater than a factor of two over the previous GGM01 models. Error estimates indicate a cumulative error less than 1 cm geoid height to spherical harmonic degree 70, which can be said to have met the GRACE minimum mission goals. Electronic Supplementary Material Supplementary material is available in the online version of this article at     

Interannual variability of low-degree gravitational change, 1980–2002

Time variations in the Earths gravity field at periods longer than 1 year, for degree-two spherical harmonics, C₂₁, S₂₁, and C₂₀, are estimated from accurately measured Earth rotational variations. These are compared with predictions of atmospheric, oceanic, and hydrologic models, and with independent satellite laser ranging (SLR) results. There is remarkably good agreement between Earth rotation and model predictions of C₂₁ and S₂₁ over a 22-year period. After decadal signals are removed, Earth-rotation-derived interannual C₂₀ variations are dominated by a strong oscillation of period about 5.6 years, probably due to uncertainties in wind and ocean current estimates. The model-predicted C₂₀ agrees reasonably well with SLR observations during the 22-year period, with the exception of the recent anomaly since 1997/1998.     

Performance of the improved Abel transform to estimate electron density profiles from GPS occultation data

The Abel inversion is a straightforward tool to retrieve high-resolution vertical profiles of electron density from GPS radio occultations gathered by low earth orbiters (LEO). Nevertheless, the classical approach of this technique is limited by the assumption that the electron density in the vicinity of the occultation depends only on height (i.e., spherical symmetry), which is not realistic particularly in low-latitude regions or during ionospheric storms. Moreover, with the advent of recent satellite missions with orbits placed around 400 km (such as CHAMP satellite), an additional issue has to be dealt with: the treatment of the electron content above the satellite orbits. This paper extends the performance study of a method, proposed by the authors in previous works, which tackles both problems using an assumption of electron-density separability between the vertical total electron content and a shape function. This allows introducing horizontal information into the classic Abel inversion. Moreover, using both positive and negative elevation data makes it feasible to take into account the electron content above the LEO as well. Different data sets involving different periods of the solar cycle, periods of the day and satellites are studied in this work, confirming the benefits of this improved Abel transform approach.     

Combined Digital Photogrammetry and Time-of-Flight Laser Scanning for Monitoring Cliff Evolution

Although cliffs form approximately 75% of the world's coastline, the understanding of the processes through which they evolve remains limited because of a lack of quantitative data on the morphological changes they undergo. In this paper the combination of terrestrial time-of-flight laser scanning with high-resolution digital photogrammetry is examined to generate high-quality data-sets pertaining to the geomorphic processes governing cliff development. The study was undertaken on a section of hard rock cliffs in North Yorkshire, UK, which has been monitored over a 12-month period. High-density, laser-scanned point clouds have been used to produce an accurate representation of these complex surfaces, free from the optical variations that degrade photographic data. These data-sets have been combined with high-resolution photographic monitoring, resampled with the fixed accuracies of the terrestrial laser survey, to generate a new approach to recording the volumetric changes in complex coastal cliffs. This has led to significant improvements in the understanding of the activity patterns of coastal cliffs.     

THE NEW DECADE: DIGITS AND DIVERSITY

The President of the Photogrammetric Society, Mr. I Newton, chaired a panel discussion concerned with those developments in photogrammetry which may take place during the 1990s.     

Wet tropospheric effects on precise relative GPS height determination

Summary Considerable interest has been generated recently in the use of the Global Positioning System (GPS) for precise height determination. A major error source in these measurements is the propagation delay due to atmospheric water vapour. In order to achieve the high precisions required for such applications as absolute sea-level monitoring improvement of wet delay modelling is necessary. Results from a GPS campaign show a significant correlation (0.91) between the variability of the wet delay measured using a water vapour radiometer (WVR) at the Onsala site and the absolute value of the residual error in the height determination of a 134 km baseline from Onsala to Jönköping. This correlation indicates that the atmosphericvariability as inferred from the WVR data includes information on the quality of the GPS height estimate. During periods of high atmospheric activity, e.g., during the passage of a weather front, the use of a six-parameter gradient model reduces the spread for the vertical coordinate from 40 mm to 20 mm (with standard deviations of 17 mm and 9 mm respectively) over the 134 km baseline (less than 1 × 10^–7) using 8 hour data spans on 11 different days over a six month period.     

On AGV's navigation in 3-dimensional space

This paper deals with position estimation and path control for Autonomous Guided Vehicles (AGV). To enable a vehicle or a mobile robot in following a continuous virtual path without human control, these techniques play an important role. The relationship between the vehicle's motion in 3-dimensional space and the shape of a curved surface is described. In particular, the introduction of a digital terrain model in dead reckoning is considered. Moreover, a possible nonlinear control is developed based on curvilinear path coordinates, and the proof for global stability is given. To achieve general validity, these topics are treated here independently of the cart's special mechanization (the configuration of steered wheels and driven wheels). Simulation studies are presented to illustrate the investigations.     

Spectrum estimation using maximum entropy and multiresolution considerations

Summary Given a sample autocovariance sequence of finite length for some observed random process, the spectrum estimation problem involves the extension of this sequence for the required Fourier transformation. The maximum entropy approach which is based on the optimal use of information contents, leads to a dual sequence of reflection coefficients with reciprocal spectrum of the process. The estimation of the maximum entropy spectrum implies results identical to those using autoregressive modeling in one dimension under appropriate white noise assumptions. In cases of a non-white noise component, the approach is generalized to an autoregressive-moving-average model. Recent developments in multiresolution analysis with spectral domain decompositions also offer possibilities of subband spectrum estimation for specific applications. Using a simulated data sequence with two close frequencies, the estimated spectrum from a two-level decomposition with autoregressive modeling shows better resolution than with conventional processing. Geodetic and geophysical applications are briefly indicated.     

Closed form solution to the twin P4P or the combined three dimensional resection-intersection problem in terms of Möbius barycentric coordinates

The twin perspective 4 point (twin P4P) problem – also called the combined three dimensional resection-intersection problem – is the problem of finding the position of a scene object from 4 correspondence points and a scene stereopair. While the perspective centers of the left and right scene image are positioned by means of a double three dimensional resection, the position of the scene object imaged on the left and right photograph is determined by a three dimensional intersection based upon given resected perspective centers. Here we present a new algorithm solving the twin P4P problem by means of M?bius barycentric coordinates. In the first algorithmic step we determine the distances between the perspective centers and the unknown intersected point by solving a linear system of equations. Typically, area elements of the left and right image build up the linear equation system. The second algorithmic step allows for the computation of the M?bius barycentric coordinates of the unknown intersected point which are thirdly converted into three dimensional object space coordinates {X,Y,Z} of the intersected point. Typically, this three-step algorithm based upon M?bius barycentric coordinates takes advantage of the primary double resection problem from which only distances from four correspondence points to the left and right perspective centre are needed. No orientation parameters and no coordinates of the left and right perspective center have to be made available. Received 1 May 1996; Accepted 13 September 1996