Consideration of time-correlated errors in a Kalman filter applicable to GNSS

An algorithm for considering time-correlated errors in a Kalman filter is presented. The algorithm differs from previous implementations in that it does not suffer from numerical problems; does not contain inherent time latency or require reinterpretation of Kalman filter parameters, and gives full consideration to additive white noise that is often still present but ignored in previous implementations. Simulation results indicate that the application of the new algorithm yields more realistic and therefore useful state and covariance information than the standard implementation. Results from a field test of the algorithm applied to the problem of kinematic differential GPS demonstrate that the algorithm provides slightly pessimistic covariance estimates whereas the standard Kalman filter provides optimistic covariance estimates.     

Representation of Uncertainty and Integration of PGIS-based Grazing Intensity Maps Using Evidential Belief Functions

In a project to classify livestock grazing intensity using participatory geographic information systems (PGIS), we encountered the problem of how to synthesize PGIS-based maps of livestock grazing intensity that were prepared separately by local experts. We investigated the utility of evidential belief functions (EBFs) and Dempster's rule of combination to represent classification uncertainty and integrate the PGIS-based grazing intensity maps. These maps were used as individual sets of evidence in the application of EBFs to evaluate the proposition that " This area or pixel belongs to the high, medium, or low grazing intensity class because the local expert(s) says (say) so ". The class-area-weighted averages of EBFs based on each of the PGIS-based maps show that the lowest degree of classification uncertainty is associated with maps in which "vegetation species" was used as the mapping criterion. This criterion, together with local landscape attributes of livestock use may be considered as an appropriate standard measure for grazing intensity. The maps of integrated EBFs of grazing intensity show that classification uncertainty is high when the local experts apply at least two mapping criteria together. This study demonstrates the usefulness of EBFs to represent classification uncertainty and the possibility to use the EBF values in identifying and using criteria for PGIS-based mapping of livestock grazing intensity.     

Triangulated spherical splines for geopotential reconstruction

We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations. The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite. Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n _max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics of satellite coverage, which could not be done using a global spherical harmonic representation. The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577.     

Land damage assessment - a case study

The paper discusses the land damage assessment and change detection analysis with reference to a mineral bearing zone in Manjhi, Manuni and Churan valleys. The area is located in environmentally sensitive and fragile region of Himalaya and constitutes of nearly 400 small-scale mines of slate, which were operative since last one hundred years and are stopped by court of law since 1995 on account of environment deterioration. The status of land degradation has been studied using IRS-1B satellite data of 1988,1992 and 1995. The geo-coded data on 1:50,000 scale has been interpreted and an increase in land degradation status was noticed. Finally, the management strategy for arresting the further land damage in a broader perspective is suggested.     

Remote Sensing Study of Sittampundi Anorthosite Complex,India

In the present study, The Landsat 7 ETM satellite data was collected for the Sittampundi anorthosites complex and digital image analysis was carried out. The anorthositic rocks available at Sittampundi complex is considered as an equivalent of lunar highland rocks. Hence, a remote sensing study comprises of image analysis and spectral profile analysis was carried out. The satellite data was digitally processed and generated various outputs like band combinations, color composites, stretched outputs, and PCA. The suitable processed outputs were identified for delineating the anorthosite complex. The diagnostic absorption features of reflectance spectra are the sensitive indicators of mineralogy and chemical composition of rocks, which are interest to the planetary scientists. The spectral profile of Landsat ETM plotted for pure and mixed anorthosite pixels and compared with the field and lab reflectance spectra. The percentages of image spectra vary from 30% to 60% for Sittampundi anorthosite. The spectral bands 2, 4 and 6 have low reflectance and bands 3 and 5 have high reflectance. The spectral range of bands 2,3,4,5 and 6 are 525 nm–605 nm, 630 nm–690 nm, 750 nm–900 nm, 1550 nm–1750 nm and 10400 nm–12500 nm respectively. The field spectral curve has weak absorptions at 650 nm and 1000 nm due to the iron transition absorption and low ca- pyroxene respectively available in the anorthosite, matching with the image spectra. However, hyperspectal image with narrow bandwidth could be more useful in selecting the suitable spectrum for remotely mapping the anorthosite region, as equivalent test site for lunar highland region.     

Mental maps and travel behaviour: meanings and models

In this paper, the “mental map” concept is positioned with regard to individual travel behaviour to start with. Based on Ogden and Richards’ triangle of meaning (The meaning of meaning: a study of the influence of language upon thought and of the science of symbolism. International library of psychology, philosophy and scientific method. Routledge and Kegan Paul, London, 1966) distinct thoughts, referents and symbols originating from different scientific disciplines are identified and explained in order to clear up the notion’s fuzziness. Next, the use of this concept in two major areas of research relevant to travel demand modelling is indicated and discussed in detail: spatial cognition and decision-making. The relevance of these constructs to understand and model individual travel behaviour is explained and current research efforts to implement these concepts in travel demand models are addressed. Furthermore, these mental map notions are specified in two types of computational models, i.e. a Bayesian Inference Network (BIN) and a Fuzzy Cognitive Map (FCM). Both models are explained, and a numerical and a real-life example are provided. Both approaches yield a detailed quantitative representation of the mental map of decision-making problems in travel behaviour.     

Water Harvesting Structure Positioning by Using Geo-Visualization Concept and Prioritization of Mini-Watersheds Through Morphometric Analysis in the Lower Tapi Basin

Geo-visualization concept has been used for positioning water harvesting structures in Varekhadi watershed consisting of 26 mini watersheds, falling in Lower Tapi Basin (LTB), Surat district, Gujarat state. For prioritization of the mini watersheds, morphometric analysis was utilized by using the linear parameters such as bifurcation ratio (R_b), drainage density (D_d), stream frequency (F_u), texture ratio (T), length of overland flow (L_o) and the shape parameter such as form factor (R_f), shape factor (B_s), elongation ratio (R_e), compactness constant (C_c) and circularity ratio (R_c). The different prioritization ranks were assigned after evaluation of the compound factor. 3 Dimensional (3D) Elevation Model (DEM) from Shuttle Radar Topography Mission (SRTM) and DEM from topo contour were analyzed in ArcScene 9.1 and the fly tool was utilized for the Geo-visualization of Varekhadi mini watersheds as per the priority ranks. Combining this with soil map and slope map, the best feasibility of positioning check dams in mini-watershed no. 1, 5 and 24 has been proposed, after validation of the sites.     

Spectral Reflectance Characteristics of the Soils on Basaltic Terrain of Central Indian Plateau

In-situ spectral reflectance characteristics of soils were studied under field conditions with Multiband Ground Truth Radiometer covering 0.45?C0.52, 0.52?C0.59, 0.62?C0.68, and 0.77?C0.86 ??m spectral bands. Twenty-two surface soil samples were studied in laboratory for their spectral reflectance characteristics using ISCO Model S.R. Spectroradiometer in visible wavelength (450?C725 nm), with 25 nm bandwidth, and in infrared wavelength (750?C1550 nm), with 50 nm bandwidth. The Bidirectional reflectance factor representative of spectral reflectance varied from 3.78 to 11.3???m in band 1, 6.09 to 15.41???m in band 2, 8.05 to 19.41???m in band 3, and 12.18 to 31.2???m in band 4. In-situ spectral reflectance in general increases with the wavelength from visible to infrared bands for all the soils. Black soils have relatively lower reflectance as compared to red soils, which is attributed to the variation in the physicochemical properties of soils. Spectral reflectance, under laboratory conditions, for all the soils increases with wavelength from visible to infrared region except at 950 nm and 1200 nm, where reflectance decreased in all soils, due to weaker water absorption bands and also at 1350 nm, due to strong water absorption at this band. The spectral reflectance of red soils were higher, in-situ as well as under laboratory conditions, as compared to black soils, which is attributed to variation in soil colour, organic matter and clay content of soils. It is observed that the spectral reflectance decrease due to moisture content in soils in all the spectral bands because of darker appearance of soils at moist conditions. Laboratory reflectance measurements serve to define the extent to which intrinsic spectral information is available from soils as a consequence of their composition.     

Geoid determination using adapted reference field, seismic Moho depths and variable density contrast

 The traditional remove-restore technique for geoid computation suffers from two main drawbacks. The first is the assumption of an isostatic hypothesis to compute the compensation masses. The second is the double consideration of the effect of the topographic–isostatic masses within the data window through removing the reference field and the terrain reduction process. To overcome the first disadvantage, the seismic Moho depths, representing, more or less, the actual compensating masses, have been used with variable density anomalies computed by employing the topographic–isostatic mass balance principle. In order to avoid the double consideration of the effect of the topographic–isostatic masses within the data window, the effect of these masses for the used fixed data window, in terms of potential coefficients, has been subtracted from the reference field, yielding an adapted reference field. This adapted reference field has been used for the remove–restore technique. The necessary harmonic analysis of the topographic–isostatic potential using seismic Moho depths with variable density anomalies is given. A wide comparison among geoids computed by the adapted reference field with both the Airy–Heiskanen isostatic model and seismic Moho depths with variable density anomaly and a geoid computed by the traditional remove–restore technique is made. The results show that using seismic Moho depths with variable density anomaly along with the adapted reference field gives the best relative geoid accuracy compared to the GPS/levelling geoid. Received: 3 October 2001 / Accepted: 20 September 2002 Correspondence to: H.A. Abd-Elmotaal     

A study on the combination of satellite, airborne, and terrestrial gravity data

Satellite gravity missions, such as CHAMP, GRACE and GOCE, and airborne gravity campaigns in areas without ground gravity will enhance the present knowledge of the Earths gravity field. Combining the new gravity information with the existing marine and ground gravity anomalies is a major task for which the mathematical tools have to be developed. In one way or another they will be based on the spectral information available for gravity data and noise. The integration of the additional gravity information from satellite and airborne campaigns with existing data has not been studied in sufficient detail and a number of open questions remain. A strategy for the combination of satellite, airborne and ground measurements is presented. It is based on ideas independently introduced by Sjöberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions. In addition, the original approach of Sjöberg and Wenzel is extended to more than two measurement types, combining the Meissl scheme with the least-squares spectral combination. Satellite (or geopotential) harmonics, ground gravity anomalies and airborne gravity disturbances are used as measurement types, but other combinations are possible. Different error characteristics and measurement-type combinations and their impact on the final solution are studied. Using simulated data, the results show a geoid accuracy in the centimeter range for a local test area.