Airborne gravimetry used in precise geoid computations by ring integration

Two detailed geoids have been computed in the region of North Jutland. The first computation used marine data in the offshore areas. For the second computation the marine data set was replaced by the sparser airborne gravity data resulting from the AGMASCO campaign of September 1996. The results of comparisons of the geoid heights at on-shore geometric control showed that the geoid heights computed from the airborne gravity data matched in precision those computed using the marine data, supporting the view that airborne techniques have enormous potential for mapping those unsurveyed areas between the land-based data and the off-shore marine or altimetrically derived data. Received: 7 July 1997 / Accepted: 22 April 1998     

Generalized inverses of nonlinear mappings and the nonlinear geodetic datum problem

Motivated by the existing theory of the geometric characteristics of linear generalized inverses of linear mappings, an attempt is made to establish a corresponding mathematical theory for nonlinear generalized inverses of nonlinear mappings in finite- dimensional spaces. The theory relies on the concept of fiberings consisting of disjoint manifolds (fibers) in which the domain and range spaces of the mappings are partitioned. Fiberings replace the quotient spaces generated by some characteristic subspaces in the linear case. In addition to the simple generalized inverse, the minimum-distance and the x ₀-nearest generalized inverse are introduced and characterized, in analogy with the least-squares and the minimum-norm generalized inverses of the linear case. The theory is specialized to the geodetic mapping from network coordinates to observables and the nonlinear transformations (Baarda's S-transformations) between different solutions are defined with the help of transformation parameters obtained from the solution of nonlinear equations. In particular, the transformations from any solution to an x ₀-nearest solution (corresponding to Meissl's inner solution) are given for two- and three-dimensional networks for both the similarity and the rigid transformation case. Finally the nonlinear theory is specialized to the linear case with the help of the singular-value decomposition and algebraic expressions with specific geometric meaning are given for all possible types of generalized inverses. Received: 11 April 1996 / Accepted: 19 April 1997     

Space orientation and geodetic azimuths of long lines from observations of the ANNA Satellite

The space orientation and geodetic azimuths of lines ranging from 300 km to 1400 km have been determined from simultaneous optical observations of the ANNA Flashing Satellite. The results of this test prove that the azimuth and the space direction between two stations can be achieved to an accuracy of 0.5″ and 0.8″ second respectively with only a limited amount of data. The reason for the high accuracy is attributed to two factors: [1] the metric quality of the PC-1000's stellar cameras, and [2] the “perfect” simultaneity in the observations provided by the ANNA flashing light. Much of this work was accomplished by the writer while employed by the Geodesy and Gravity Branch of Cambridge Research Laboratories.     

Automatic Selection of Landmarks for Navigation Guidance

Although current navigation services provide significant benefits to people's mobility, the turn‐by‐turn instructions they provide are sometimes ineffective. These instructions require people to maintain a high level of attention and cognitive workload while performing distance or angle measurements on their own mental map. To overcome this problem, landmarks have been identified as playing a major role in turn‐by‐turn instructions. This requires the availability of landmarks in navigation databases. Landmarks are commonly selected manually, which involves time‐consuming and tedious tasks. Automatic selection of landmarks has recently gained the attention of researchers but currently there are only a few techniques that can select appropriate landmarks. In this article, we present a technique based on a neural network model, where both static and dynamic features are used for selecting landmarks automatically. To train and test this model, two labeling approaches, manual labeling and rule‐based labeling, are also discussed. Experiments on the developed technique were conducted and the results show that rule‐based labeling has a precision of approximately 90%, which makes the technique suitable and reliable for automatic selection of landmarks.     

Towards a Better Understanding of Dynamic Interaction Metrics for Wildlife: a Null Model Approach

The ability to measure dynamic interactions, such as attraction or avoidance, is crucial to understanding socio‐spatial behaviors related to territoriality and mating as well as for exploring resource use and the potential spread of infectious epizootic diseases. In spite of the importance of measuring dynamic interactions, it has not been a main research focus in movement pattern analysis. With very few exceptions (see Benhamou et al. 2014), no new metrics have been developed in the past 20 years to accommodate the fundamental shift in the type of animal movement data now being collected and there have been few comparison or otherwise critical studies of existing dynamic interaction metrics (but see Long et al. 2014; Miller 2012). This research borrows from the null model approach commonly used in community ecology to compare six currently used dynamic interaction metrics using data on five brown hyena dyads in Northern Botswana. There was disconcerting variation among the dynamic interaction results depending on which metric and which null model was used, and these results highlight the need for more extensive research on measuring and interpreting dynamic interactions in order to avoid making potentially misleading inferences about socio‐spatial behaviors.     

Semi-automatic delineation of badlands using contrast in vegetation activity: a case study in the lower Chambal valley,India

Population growth worldwide leads to an increasing pressure on the land. Recent studies reported that many areas covered by badlands are decreasing because parts of badlands are being levelled and converted into arable land. It is important to monitor these changes for environmental planning. This paper proposes a remote-sensing-based detection method which allows mapping of badland dynamics based on seasonal vegetation changes in the lower Chambal valley, India. Supervised classification was applied on three Landsat (Thematic Mapper) images, from 3 different seasons; January (winter), April (summer) and October (post-monsoon). Different band selection methods were applied to get the best classification. Validation was done by ground referencing and a GeoEye-1 satellite image. The image from January performed best with overall accuracy of 87% and 0.69 of kappa. This method opens the possibilities of using semi-automatic classification for the Chambal badlands which is so far mapped with manual interpretations only.     

A scoping review on the multiplicity of scale in spatial analysis

Journal of Geographical Systems - Scale is a central concept in the geographical sciences and is an intrinsic property of many spatial systems. It also serves as an essential thread in the fabric...     

Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame

This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84(3):165–178, 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first- and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first- and second-order derivatives in terms of the geopotential coefficients. These equations are converted into recurrent relations from which the coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission.