Groebner-basis solution of the three-dimensional resection problem (P4P)

The three-dimensional (3-D) resection problem is usually solved by first obtaining the distances connecting the unknown point P{X,Y,Z} to the known points P_i{X_i,Y_i,Z_i}i=1,2,3 through the solution of the three nonlinear Grunert equations and then using the obtained distances to determine the position {X,Y,Z} and the 3-D orientation parameters {,, }. Starting from the work of the German J. A. Grunert (1841), the Grunert equations have been solved in several substitutional steps and the desire as evidenced by several publications has been to reduce these number of steps. Similarly, the 3-D ranging step for position determination which follows the distance determination step involves the solution of three nonlinear ranging (`Bogenschnitt') equations solved in several substitution steps. It is illustrated how the algebraic technique of Groebner basis solves explicitly the nonlinear Grunert distance equations and the nonlinear 3-D ranging (`Bogenschnitt') equations in a single step once the equations have been converted into algebraic (polynomial) form. In particular, the algebraic tool of the Groebner basis provides symbolic solutions to the problem of 3-D resection. The various forward and backward substitution steps inherent in the classical closed-form solutions of the problem are avoided. Similar to the Gauss elimination technique in linear systems of equations, the Groebner basis eliminates several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of a univariate polynomial whose roots can be determined by existing programs e.g. by using the roots command in Matlab.Acknowledgments.The first author wishes to acknowledge the support of JSPS (Japan Society of Promotion of Science) for the financial support that enabled the completion of the write-up of the paper at Kyoto University, Japan. The author is further grateful for the warm welcome and the good working atmosphere provided by his hosts Professors S. Takemoto and Y. Fukuda of the Department of Geophysics, Graduate School of Science, Kyoto University, Japan.     

Nonlinear Adjustment of GPS Observations of Type Pseudo-Ranges

The nonlinear adjustment of GPS observations of type pseudo-ranges is performed in two steps. In step one a combinatorial minimal subset of observations is constructed which is rigorously converted into station coordinates by means of Groebner basis algorithm or the multipolynomial resultant algorithm. The combinatorial solution points in a polyhedron are reduced to their barycentric in step two by means of their weighted mean. Such a weighted mean of the polyhedron points in ℝ³ is generated via the Error Propagation law/variance-covariance propagation. The Fast Nonlinear Adjustment Algorithm (FNon Ad Al) has been already proposed by Gauss whose work was published posthumously and Jacobi (1841). The algorithm, here referred to as the Gauss-Jacobi Combinatorial algorithm, solves the over-determined GPS pseudo-ranging problem without reverting to iterative or linearization procedure except for the second moment (Variance-Covariance propagation). The results compared well with the solutions obtained using the linearized least squares approach giving legitimacy to the Gauss-Jacobi combinatorial procedure. ? 2002 Wiley Periodicals, Inc.     

GPS network monitors the Western Alps' deformation over a five-year period: 1993–1998

  The Western Alps are among the best studied collisional belts with both detailed structural mapping and also crustal geophysical investigations such as the ECORS and EGT seismic profile. By contrast, the present-day kinematics of the belt is still largely unknown due to small relative motions and the insufficient accuracy of the triangulation data. As a consequence, several tectonic problems still remain to be solved, such as the amount of N–S convergence in the Occidental Alps, the repartition of the deformation between the Alpine tectonic units, and the relation between deformation and rotation across the Alpine arc. In order to address these problems, the GPS ALPES group, made up of French, Swiss and Italian research organizations, has achieved the first large-scale GPS surveys of the Western Alps. More than 60 sites were surveyed in 1993 and 1998 with a minimum observation of 3 days at each site. GPS data processing has been done by three independent teams using different software. The different solutions have horizontal repeatabilities (N–E) of 4–7 mm in 1993 and 2–3 mm in 1998 and compare at the 3–5-mm level in position and 2-mm/yr level in velocity. A comparison of 1993 and 1998 coordinates shows that residual velocities of the GPS marks are generally smaller than 2 mm/yr, precluding a detailed tectonic interpretation of the differential motions. However, these data seem to suggest that the N–S compression of the Western Alps is quite mild (less than 2 mm/yr) compared to the global convergence between the African and Eurasian plate (6 mm/yr). This implies that the shortening must be accomodated elsewhere by the deformation of the Maghrebids and/or by rotations of Mediterranean microplates. Also, E–W velocity components analysis supports the idea that E–W extension exists, as already suggested by recent structural and seismotectonic data interpretation. Received: 27 November 2000 / Accepted: 17 September 2001     

Use of the L2C signal for inversions of GPS radio occultation data in the neutral atmosphere

Results from processing FORMOSAT-3/COSMIC radio occultations (RO) with the new GPS L2C signal acquired both in phase locked loop (PLL) and open loop (OL) modes are presented. Analysis of L2P, L2C, and L1CA signals acquired in PLL mode shows that in the presence of strong ionospheric scintillation not only L2P tracking, but also L1CA tracking often fails, while L2C tracking is most stable. The use of L2C improves current RO processing in the neutral atmosphere mainly by increasing the number of processed occultations (due to significant reduction in the number of L2 tracking failures) and marginally by a reduction in noise in statistics. The latter is due to the combination of reduced L2C noise (compared to L2P) and increased L1CA noise in those occultations where L2P would have failed. This result suggests application of OL tracking for L1CA and L2C signals throughout an entire occultation to optimally acquire RO data. Two methods of concurrent processing of L1CA and L2C RO signals are considered. Based on testing of individual occultations, these methods allow: (1) reduction in uncertainty of bending angles retrieved by wave optics in the lower troposphere and (2) reduction in small-scale residual errors of the ionospheric correction in the stratosphere.     

A GIS-based glacier inventory for the Antarctic Peninsula and the South Shetland Islands —A first case study on King George Island

The aim of the international project “Global Land Ice Measurements from Space (GLIMS)” headed by the US Geological Survey is to establish a world wide glacier inventory based on satellite imagery. This data set will form a first digital baseline study for future glacier monitoring. The presented GIS-based glacier inventory for King George Island is a case study for the area of the Antarctic Peninsula. In the database of the glacier inventory topographic information, specific glaciological parameters as well as metadata will be included. The topographic data consists of drainage basin limits, basin areas, altitudinal ranges, perimeters and mean lengths. Glaciological data sets should comprise information on glacier retreat in different periods, glacier velocities, ice thickness and bedrock topography as well as derived parameters. Modelled and measured mass balance parameters could be included as additional data layers. In particular, these metadata records must comprise background information on data accuracy and data sources and should be compatible with a future data model for the King George Island GIS (KGIS). Three examples illustrate that the GLIMS database will not only contain information valuable for glaciological applications, but also other environmental studies on the island will benefit from this standardised remote sensing data sets. Therefore, a very close link between the data models of KGIS and GLIMS has to be established to enable these synergisms. Finally, better access to historic aerial photography would enable a continuous record of glacier retreat from the beginning of the 1950's onward.     

Determination of turbidity patterns of the Zhujiang estuarine region,South China,using satellite images and a GIS approach

Landsat MSS images and SPOT HRV data were employed to map the changes in turbidity levels in the Zhujiang estuarine region, South China, during the dry season in the period 1973–1987 at low and high tides. Analysis of turbidity trends and changes in the spatial pattern of high turbidity class was carried out with a GIS software—IDRISI. It was concluded that with the use of OVERLAY and RECLASS functions in the GIS approach a large number of turbidity maps could be easily compared and the turbidity trend determined. The GIS approach further permitted evaluation of the importance of such factors as water depths, mean tidal differences, and water salinity to sedimentation in the study region.     

THE MULTIPLICITY PRINCIPLE IN MODERN REMOTE SENSING METHODS AND ITS APPLICATION TO AGRICULTURAL IMAGE INTERPRETATION

The authors elaborate upon the “multiplicity principle” in remote sensing, i.e., the need for repeated imaging at a variety of scales, spatial resolutions, spectral bands, and times of imaging in order to attain the maximum information possible. They then explore the ways it can be applied in agricultural research, through two different image comparison and interpretation strategies. A detailed example is presented of the use of a multitemporal imaging strategy for the recognition of several agricultural crops from false color composite imagery. Translated by Edward Torrey, Alexandria, VA 22308 from: G. V. Dobrovol'skiy and V. L. Andronikov, eds., Aerokosmicheskiye metody v pochvo-vedenii i ikh ispol'zovaniye v sel'skom khozyaystve: sbornik nauchnykh trudov [Remote Sensing Methods in Soil Science and Their Utilization in Agriculture: A Collection of Scientific Works]. Moscow: Nauka, 1990, pp. 47-55.     

COMPUTATION AND MAPPING OF THE ELEMENTS OF THE WATER-ICE BUDGET OF GLACIERS

Two general approaches for compiling maps of components of the water-ice budget in regions of glacier nourishment are compared and the resulting maps are analyzed. The compilation of raw data is based on field measurements rather than remote sensing information. Translated by Edward Torrey, Alexandria, VA 22308 from: Materialy glyatsiologicheskikh issledovaniy, 1991, No. 72, pp. 94-102.