Polyhedral approximations in physical geodesy

Summary A procedure is derived for the upward continuation of unevenly spaced gravity data. The topographic relief is approximated by a polyhedron with triangular faces and vertices placed at small distances around the surface of a sphere. The usual Fredholm integral equation of the second kind is modified considering the discontinuity of the normal vector. It is solved by successive approximations assuming the unknown function is linear inside each face at every step of the iteration process. An approximate formula to obtain the anomalous potential from the Bouguer anomaly is discussed. The potential of a homogeneous polyhedron is derived and used to compute relief corrections to the geoid undulations. Numerical applications are presented with respect to the Romanian territory.Partially presented at theJoint Symposium of IGC and IGC, Graz, Austria, 11–17 September 1994     

Avoiding numerical stability problems of long duration DGPS/INS Kalman filters

A current pursuit of the geodetic community is the optimal integration of differential GPS (DGPS) and inertial navigation system (INS) data streams for precise and efficient position and gravity vector surveying. Therein a complete INS and multiple-antenna GPS receiver payload, mounted on a moving platform, is used in conjunction with a network of ground-fixed single antenna GPS receivers. This paper presents a complete, GPS-based, external updating measurement model for the applicable Kalman filter. The model utilizes four external observation types for every GPS satellite in-view: DGPS range differences, single phase differences, and single phase-rate differences; as well as the mobile, multipleantenna GPS receiver's measurement of theerrors in the INS's estimate of the phase difference between any two vehicle-borne GPS antennae. Although not widely conveyed in the geodetic world, the inertial navigation community has long known that traditional Kalman filter covariance propagation recurrences are inherently unstable when such highly accurate external updates are repeatedly applied (every 1 second) over long time durations. A hybrid square root covariance/U — D covariance factorization approach is a numerically stable alternative and is reviewed herein. The hybrid makeup of the algorithm is necessitated by the correlated nature of the fourth type of GPS external measurement listed above (each vehicle-borne GPS antenna formstwo baselines). Such measurement correlations require a functional transformation of the overall external updating model to permit the multiple updates (simultaneously available at each updating epoch) to be sequentially (and efficiently) processed. An appropriate transformation is given. Stable covariance propagation relationships are presented and the transformed Kalman gain is also furnished and its use in the determination of the externally updated error states is discussed. Specific DGPS/INS instabilities produced by the traditional recurrences are displayed. The stable alternative method requires about 25% more CPU time than the traditional Kalman recurrences. With the ever-increasing computational speeds of microprocessors, this added CPU time is of no real concern.     

Theory of satellite ground-track crossovers

The fundamental geometry of satellite ground tracks and their crossover problem are investigated. For idealized nominal ground tracks, the geometry is governed by a few constant parameters whose variations lead to qualitative changes in the crossover solutions. On the basis that the theory to locate crossovers has not been studied in sufficient detail, such changes are described in regard to the number of crossover solutions in conjunction with their bifurcations. Employing the spinor algebra as a tool for establishing the ground-track crossing condition, numerical methodologies to locate crossovers appearing in general dual-satellite ground-track configurations are also presented. The methodologies are applied to precisely determined orbital ephemerides of the GEOSAT, ERS-1, and TOPEX/POSEIDON altimeter satellites. Received: 19 November 1996 / Accepted: 12 May 1997     

Surveying Stonehenge By Photogrammetry

For centuries the ruins of Stonehenge have proved to be both a source of fascination and mystery for the many visitors to this World Heritage Site. The monument itself sets a puzzle that even to this day has not been solved, although there have been numerous theories suggested as to its construction. There is little accurate survey data currently available on the stones themselves, against which these many theories could be tested. The Photogrammetric Unit of English Heritage was therefore requested, in 1993, to commence a project to digitally map all the external faces of all the stones that form the visible remains of this internationally important monument. Photogrammetry was the chosen survey technique and this paper outlines the work of the Unit in using the latest digital photogrammetric equipment to generate a basic three dimensional model of Stonehenge.     

Quantification of suspended solids in Dal lake,Srinagar using remote sensing technology

Indian Remote Sensing satellite (IRS)-1B, Linear Imaging Self Scanner (LISS)-II spectral digital data was analysed to determine the feasibility of quantifying the concentration of suspended solids in the surface water of inland water body, Dal lake, in Srinagar, India. The water samples collected in concurrent with IRS-1B overpass, were analysed to determine the concentration of suspended solids. The results indicate that a positive functional relationship exist between the concentration of suspended solids and the visible wave length bands 1 and 3 and near infrared band 4. It has been observed that as the concentration of suspended solids increase, the spectral response also increases. It is concluded that IRS LISS-H data can be effectively used to quantify suspended sediment concentration in the Dal lake surface water.     

Urban change detection related to earthquakes using an adaptive nonlinear mapping of high-resolution images

We propose a nonlinear mapping method for detecting geographical changes. In our system, two images photographed at different points of time are checked based on an iterative nonlinear mapping. The system automatically extracts feature changes of aerial imageries by computing distribution of the image matching score. We evaluate the change detection ability by using the receiver operating characteristic under misregistration cases, including rotational misalignments.     

Boreal forest coherence-based measures of interferometric pair suitability for operational stem volume retrieval

The performance of interferometric synthetic aperture radar (INSAR)-based boreal forest stem volume retrieval is strongly affected by weather conditions around the time of the SAR image acquisitions. Since weather conditions cannot be controlled, the suitability of a particular interferometric pair for stem volume retrieval can only be assessed afterward. In this letter, four objective measures based on observed forest coherence were compared in assessing the suitability of interferometric pairs for stem volume retrieval. These suitability measures can be used to identify the best and worst pairs, i.e., the ones with the most and least favorable weather conditions. Stem volume retrievals were performed using single European Remote Sensing (ERS-1/2) Tandem interferometric pairs by inverting a backscattering-coherence model for boreal forests. A total of 14 ERS Tandem image pairs acquired in varying weather conditions were studied, and the stem volume retrieval performance was assessed against ground-based stem volume estimates on 134 boreal forest stands. Stem volume retrieval performance as measured by R/sup 2/-values between INSAR-estimated stem volumes and ground truth was found to be directly proportional to boreal forest coherence. The interferometric coherence-contrast (ICC), i.e., the difference in coherence between sparsest and densest boreal forest stands was found to be the best of the four studied suitability measures. The ICC could be used as a suitability parameter in the selection of the best interferometric pairs for operational boreal forest stem volume retrieval.     

Neuralizing target superresolution algorithms

Tatem et al. (2001) have designed a Hopfield network-based algorithm for superresolving discrete targets that are larger than the sample spacing of an image. The algorithm iteratively minimizes a criterion function that contains a sigmoidal activation term. We have altered their algorithm to bring it in line with Hopfield's original network by reducing the pseudotemperature of the sigmoid. We found that smaller values of the pseudotemperature lead to faster convergence to a solution and resulting solutions that are more accurate.     

Wheat growth profile: satellite monitoring and crop yield modelling

The most important advantage of the low resolution National Oceanic and Atmospheric Administration’s Advanced Very High Resolution Radiometer (NOAA AVHRR) data is its high temporal frequency and high radiometric sensitivity which helps in vegetation detection in the visible and near-infrared spectral regions. In areas where most of the crop cultivation is in large contiguous areas, and if the AVHRR data are selected for time period such that the crop of interest is well discriminated from other crops, these data can be used for monitoring vegetative growth and condition very effectively. The present study deals with the application of AVHRR data for the monitoring of the wheat crop in its seventeen main growing districts of the Rajasthan state. The fourteen date AVHRR data covering the entire growth period have been used to generate the normalized difference vegetation index (NDV1) growth profile for the crop by masking the non-crop pixels following the two-date NDVI change method. The growth profile parameters and other derived parameters, such as post-anthesis senescence rate and areas under the entire growth profile or under selected growth periods have been related to the district average wheat yield through statistical regression models. Various methods adopted for wheat pixels masking have been critically evaluated. It is found that the wheat yield can be predicted well by the area under the profile in different growth periods.     

Analysis of temporal sar and optical data for rice mapping

This study investigates the potential of multi-temporal signature analysis of satellite imagery to map rice area in South 24 Paraganas district of West Bengal. Two optical data (IRS ID LISS III) and three RADARSAT SAR data of different dates were acquired during 2001. Multi-temporal SAR backscatter signatures of different landcovers were incorporated into knowledge based decision rules and kharif landcover map was generated. Based on the spectral variation in signature, the optical data acquired during rabi (January) and summer (March) season were classified using supervised maximum likelihood classifier. A co-incidence matrix was generated using logical approach for a combined “rabi-summer” and “kharif-rabi-summer” landcover mapping. The major landcovers obtained in South 24 Paraganas using remote sensing data are rice, water, aquaculture ponds, homestead, mangrove, and urban area. The classification accuracy of rice area was 98.2% using SAR data. However, while generating combined “kharif-rabi-summer” landcovers, the classification accuracy of rice area was improved from 81.6% (optical data) to 96.6% (combined SAR-Optical). The primary aim of the study is to achieve better accuracy in classifying rice area using the synergy between the two kinds of remotely sensed data.