Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.     

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.     

On the topographic bias in geoid determination by the external gravity field

The topographic bias is defined as the error/bias committed by continuing the external gravity field inside the topographic masses by a harmonic function. We study the topographic bias given by a digital terrain model defined by a spherical template, and we show that the topographic bias is given only by the potential of an inner-zone cap, and it equals the bias of the Bouguer shell, independent of the size of the cap. Then we study the effect on the real Earth by decomposing its topography into a template, and we show also in this case that the topographic bias is that of the Bouguer shell, independent of the shape of the terrain. Finally, we show that the topographic potential of the terrain at the geoid can be determined to any precision by a Taylor expansion outside the Earth’s surface. The last statement is demonstrated by a Taylor expansion to fourth order.     

Estimating sagebrush cover in semi-arid environments using Landsat Thematic Mapper data

Sagebrush ecosystems of the western US provide important habitat for several ungulate and vertebrate species. As a consequence of energy development, these ecosystems in Wyoming have been subjected to a variety of anthropogenic disturbances. Land managers require methodology that will allow them to consistently catalog sagebrush ecosystems and evaluate potential impact of proposed anthropogenic activities. This study addresses the utility of remotely sensed and ancillary geospatial data to estimate sagebrush cover using ordinal logistic regression. We demonstrate statistically significant prediction of ordinal sagebrush cover categories using spectral (χ² = 113; p < 0.0001) and transformed indices (χ² = 117; p < 0.0001). Both Landsat spectral bands (c-value = 0.88) and transformed indices (c-value = 0.89) can distinguish sites with closed, moderate and open cover sagebrush cover categories from no cover. The techniques described in this study can be used for estimating categories of sagebrush cover in arid ecosystems.     

A bootstrap based space–time surveillance model with an application to crime occurrences

This study proposes a bootstrap-based space–time surveillance model. Designed to find emerging hotspots in near-real time, the bootstrap based model is characterized by its use of past occurrence information and bootstrap permutations. Many existing space–time surveillance methods, using population at risk data to generate expected values, have resulting hotspots bounded by administrative area units and are of limited use for near-real time applications because of the population data needed. However, this study generates expected values for local hotspots from past occurrences rather than population at risk. Also, bootstrap permutations of previous occurrences are used for significant tests. Consequently, the bootstrap-based model, without the requirement of population at risk data, (1) is free from administrative area restriction, (2) enables more frequent surveillance for continuously updated registry database, and (3) is readily applicable to criminology and epidemiology surveillance. The bootstrap-based model performs better for space–time surveillance than the space–time scan statistic. This is shown by means of simulations and an application to residential crime occurrences in Columbus, OH, year 2000.     

Using spectral information from the NIR water absorption features for the retrieval of canopy water content

Canopy water content (CWC) is important for mapping and monitoring the condition of the terrestrial ecosystem. Spectral information related to the water absorption features at 970 nm and 1200 nm offers possibilities for deriving information on CWC. In this study, we compare the use of derivative spectra, spectral indices and continuum removal techniques for these regions. Hyperspectral reflectance data representing a range of canopies were simulated using the combined PROSPECT + SAILH model. Best results in estimating CWC were obtained by using spectral derivatives at the slopes of the 970 nm and 1200 nm water absorption features. Real data from two different test sites were analysed. Spectral information at both test sites was obtained with an ASD FieldSpec spectrometer, whereas at the second site HyMap airborne imaging spectrometer data were also acquired. Best results were obtained for the derivative spectra. In order to avoid the potential influence of atmospheric water vapour absorption bands the derivative of the reflectance on the right slope of the canopy water absorption feature at 970 nm can best be used for estimating CWC.     

The design and the development of a hyperspectral and multispectral airborne mapping system

Flexible and cost-effective tools for rapid image acquisition and natural resource mapping are needed by land managers. This paper describes the hardware and software architecture of a low-cost system that can be deployed on a light aircraft for rapid data acquisition. The Hyperspectral and Multispectral Cameras for Airborne Mapping (HAMCAM) was designed and developed in the Geospatial Laboratory for Environmental Dynamics at the University of Idaho as a student-learning tool, and to enhance the existing curriculum currently offered. The system integrates a hyperspectral sensor with four multispectral cameras, an Inertial Navigation System (INS), a Wide Area Augmentation System (WAAS)-capable Global Positioning System (GPS), a data acquisition computer, and custom software for running the sensors in a variety of different modes. The outputs include very high resolution imagery obtained in four adjustable visible and near-infrared bands from the multispectral imager. The hyperspectral sensor acquires 240 spectral bands along 2.7 nm intervals within the 445–900 nm range. The INS provides aircraft pitch, roll and yaw information for rapid geo-registration of the imagery. This paper will discuss the challenges associated with the development of the system and the integration of components and software for implementation of this system for natural resource management applications. In addition, sample imagery acquired by the sensor will be presented.     

On a global integrated fundamental network

Editor's comment: This letter has been received fromDr. E.H. Knickmeyer, University of Calgary, Dep. of Surveying Engineering, 2500 University Dr. N. Calgary, Alberta, Canada T2N 1N4, in April 1988. A response to this letter has been written byDr. C. Boucher, who represents the Central Bureau ofIERS andIAG SSG 5.123. Similar letters, dealing with matters of interest for geodesy and for IAG will in the future be published in Bulletin Géodésique with an answer by the person or committee in IAG which is most closely related to or responsible for the matter being dealt with in the letter.     

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.