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.     

GI Science, Disasters, and Emergency Management

Societal responses to disasters begin with the initial post‐event rescue and relief operations, followed by recovery, reconstruction, and then transcend into mitigation actions including the development of pre‐impact preparedness measures, collectively known as the emergency response cycle. This paper highlights some of the applications of GI Science to the emergency response cycle, citing examples from natural hazards and from the World Trade Center disaster on 11th September 2001. More importantly, the paper describes some of the constraints on the utilization of GI Science by the practitioner community: understandable user interfaces; data quantity, quality, and integration; real‐time data and information. Finally, the paper suggests some important GI Science research areas based on the needs of the disasters and emergency management research and practitioner communities.     

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     

Similar single-difference model and its algorithm for solving GPS monitoring deformation directly at single epoch

A new similar singledifference mathematical model ( SS-DM) and its corresponding algorithm are advanced to solve the deformation of monitoring point directly in single epoch. The method for building the SSDM is introduced in detail, and the main error sources affecting the accuracy of deformation measurement are analyzed briefly, and the basic algorithm and steps of solving the deformation are discussed. In order to validate the correctness and the accuracy of the similar single-difference model, the test with five dual frequency receivers is carried out on a slideway which moved in plane in Feb. 2001. In the test, five sessions are observed. The numerical results of test data show that the advanced model is correct.     

Hedonic price models with omitted variables and measurement errors: a constrained autoregression–structural equation modeling approach with application to urban Indonesia

Omitted variables and measurement errors in explanatory variables frequently occur in hedonic price models. Ignoring these problems leads to biased estimators. In this paper, we develop a constrained autoregression–structural equation model (ASEM) to handle both types of problems. Standard panel data models to handle omitted variables bias are based on the assumption that the omitted variables are time-invariant. ASEM allows handling of both time-varying and time-invariant omitted variables by constrained autoregression. In the case of measurement error, standard approaches require additional external information which is usually difficult to obtain. ASEM exploits the fact that panel data are repeatedly measured which allows decomposing the variance of a variable into the true variance and the variance due to measurement error. We apply ASEM to estimate a hedonic housing model for urban Indonesia. To get insight into the consequences of measurement error and omitted variables, we compare the ASEM estimates with the outcomes of (1) a standard SEM, which does not account for omitted variables, (2) a constrained autoregression model, which does not account for measurement error, and (3) a fixed effects hedonic model, which ignores measurement error and time-varying omitted variables. The differences between the ASEM estimates and the outcomes of the three alternative approaches are substantial.     

Land Cover Mapping for Namdapha National Park (Arunachal Pradesh), India Using Harmonized Land Cover Legends

Since last few decades RS-GIS is playing vital role in studying and mapping spatiotemporal responses of land cover, however, as a matter of fact, the mapping outputs largely depend on the expert's/user's preferences because location specific and people specific land cover classification systems are adopted autonomously for image classification in GIS. This may actually lead to an ambiguous definition of a particular land cover type when such different maps are compared at global level. In 1993, FAO and UNEP started efforts for development of a software tool know as LCCS which is a comprehensive standardized tool capable of providing land cover characterization to all possible land cover types in the world regardless of spatial relevance, mapping scale, data collection method etc. Adding to the global efforts of land cover legend harmonization and mapping, this study presents development of harmonized land cover legends for Namdapha National Park located in north-eastern Indian Himalayan region using LCCS and subsequent mapping. The potential of Remote Sensing (RS) and Geographical Information Systems (GIS) in forest/land cover mapping is very well recognized. Therefore, adopting the developed harmonized legends for the study area, land cover mapping was done using RS-GIS approach.     

Non-linear motions of Australian geodetic stations induced by non-tidal ocean loading and the passage of tropical cyclones

We investigate daily and sub-daily non-tidal oceanic and atmospheric loading (NTOAL) in the Australian region and put an upper bound on potential site motion examining the effects of tropical cyclone Yasi that crossed the Australian coast in January/February 2011. The dynamic nature of the ocean is important, particularly for northern Australia where the long-term scatter due to daily and sub-daily oceanic changes increases by 20–55 % compared to that estimated using the inverted barometer (IB) assumption. Correcting the daily Global Positioning System (GPS) time series for NTOAL employing either a dynamic ocean model or the IB assumption leads to a reduction of up to 52 % in the weighted scatter of daily coordinate estimates. Differences between the approaches are obscured by seasonal variations in the GPS precision along the northern coast. Two compensating signals during the cyclone require modelling at high spatial and temporal resolution: uplift induced by the atmospheric depression, and subsidence induced by storm surge. The latter dominates ( \(>\) 135 %) the combined net effect that reaches a maximum of 14 mm, and 10 mm near the closest GPS site TOW2. Here, 96 % of the displacement is reached within 15 h due to the rapid transit of cyclones and the quasi-linear nature of the coastline. Consequently, estimating sub-daily NTOAL is necessary to properly account for such a signal that can be 3.5 times larger than its daily-averaged value. We were unable to detect the deformation signal in 2-hourly GPS processing and show that seasonal noise in the Austral summer dominates and precludes GPS detection of the cyclone-related subsidence.     

Automatic placement of GIS vector map annotation in area feature by long-diagonal

This paper discusses the placement of Chinese annotation from point of view of graphics. Area Feature is classified as simple polygon, complex polygon and special polygon. For simple ones, annotations are placed along the longest edge. For complex ones, firstly the polygon are simplified according to close points, then the longest diagonal is gotten by comparing length, lastly, annotations are placed along long-diagonal. For special ones, the polygon are partitioned into several parts by a certain rule for getting their sub-diagonals, then their annotation are placed by means of the second.     

Monitoring of salt affected soils — A case study using aerial photographs,salyut‐7 space photographs,and landsat TM data

Soils of part of Ukai‐kakarapar Command area, Gujarat (India) have been mapped at 1:25, 000 scale using aerial photographs of December 1977. It was observed that about 36.3% of the area was affected by soil salinity/alkalinity. The test area has been remapped using Salyut‐7 space photographs taken during Indo‐Soviet joint flight in April, 1984. The area affected by soil salinity/alkalinity was found to be substantially higher (80.3%). The earlier mapping using aerial photographs was done when the soil surface was compartively moist (December 1977) as compared to date of Salyut‐7 photography (April 1984), when the soil surface was likely to be devoid of moisture and the salts moved to the surface. To have easy comparision with the map prepared by using aerial photographs, Landsat TM data of December, 1985 was used in which 45.7% of the total area was mapped as salt affected. The extent of area delineated using Landsat TM was higher than that of 1977 but much lesser than the area delineated using Salyut‐7 (MKF‐6M) photographs. This indicated that the increase in the extent of salt affected area in the map prepared using the MKF‐6M photographs might be partly due to actual increase in the salinity/alkalinity and partly due to the seasonal affects. Among the various bands of MKF‐6M, band ‐4 was found to be the best for delineating the salt affected soils. The boundaries were sharper in the FCC and band No.4 of MKF‐6M than in the aerial photographs.