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.     

Motion Analysis in SAR Images of Unfocused Objects Using Time–Frequency Methods

Synthetic aperture radar (SAR) image formation processing assumes that the scene is stationary, and to focus an object, one coherently sums a large number of independent returns. Any target motion introduces phases that distort and/or translate the target's image. Target motion produces a smear primarily in the azimuth direction of the SAR image. Time-frequency (TF) modeling is used to analyze and correct the residual phase distortions. An interactive focusing algorithm based on TF modeling demonstrates how to correct the phase and to rapidly focus the mover. This is demonstrated on two watercraft observed in a SAR image. Then, two time-frequency representations (TFRs) are applied to estimate the motion parameters of the movers or refocus them or both. The first is the short-time Fourier transform, from which a velocity profile is constructed based on the length of the smear. The second TFR is the time-frequency distribution series, which is a robust derivative of the Wigner-Ville distribution that works well in this SAR environment. The smear is a modulated chirp, from which a velocity profile is plotted and the phase corrections are integrated to focus the movers. The relationship between these two methods is discussed. Both methods show good agreement on the example.     

TAZ-level variation in work trip mode choice between 1990 and 2000 and the presence of rail transit

Rail transit continues to be a popular alternative for cities as a tool for alleviating automobile congestion and for redeveloping areas into transit and pedestrian-friendly environments. Ideally, rail transit will draw trips away from cars, but the quantitative work that tests this notion has often been either case studies of neighborhoods, in which conclusions are tough to generalize, or citywide comparisons where important spatial variation is lost in aggregation. This study seeks to narrow this gap in the research by using multivariate analysis of covariance to isolate the effect of covariates and cities on changes in work trip mode choice at the traffic analysis zone (TAZ) level for nine cities between 1990 and 2000. The results suggest differences by city in the change at the TAZ level of the proportion of people driving alone and taking transit. Increases in transit usage were associated with cities that built rail transit, while increases in automobile commuting and decreases in transit usage were associated with cities that did not.     

SIMD correlator library for GNSS software receivers

Software receivers have had a discernable impact on the GNSS research community. Often such receivers are implemented in a compiled programming language, such as C or C++. A software receiver must emulate the digital signal processing (DSP) algorithms executed on dedicated hardware in a traditional receiver. The DSP algorithms, most notably correlation, have a high computational cost; this burden precludes many software receivers from running in real time. However, the computational cost can be lessened by utilizing single instruction multiple data (SIMD) operations found on modern ×86 processors. The following demonstrates how C/C++ compatible code can be written to directly utilize the SIMD instructions. First, an analysis is carried out to demonstrate why real time operation is not possible when using traditional C/C++ code is carried out. Secondly a tutorial outlines how to write and insert ×86 assembly, with SIMD operations, into C/C++ code. Performance gains achieved via SIMD operations are then demonstrated, and pseudo code outlines how SIMD operations can be employed to perform correlation. Finally, a C/C++ compatible SIMD enabled arithmetic library is added to the GPS Toolbox for use in software receivers.     

Illumination effects on the differenced Normalized Burn Ratio's optimality for assessing fire severity

The influence of illumination effects on the optimality of the dNBR (differenced Normalized Burn Ratio) was evaluated for the case of the 2007 Peloponnese (Greece) wildfires using a pre/post-fire Landsat TM (Thematic Mapper) image couple. Well-illuminated pixels (south and south-east facing slopes) exhibited more optimal displacements in the bi-spectral feature space than more shaded pixels (north and north-west exposed slopes). Moreover, pixels experiencing a small image-to-image difference in illumination obtained a higher optimality than pixels with a relatively large difference in illumination. To correct for illumination effects, the c-correction method and a modified c-correction technique were applied. The resulting median dNBR optimality of uncorrected, c-corrected and modified c-correction data was respectively 0.58, 0.60 and 0.71 (differences significant for p < 0.001). The original c-correction method improved the optimality of badly illuminated pixels while deteriorating the optimality of well-illuminated pixels. In contrast, the modified c-correction technique improved the optimality of all the pixels while retaining the prime characteristic of topographic correction techniques, i.e. detrending the illumination–reflectance relationship. For a minority of the data, for shaded pixels and/or pixels with a high image-to-image difference in illumination, the original c-correction outperformed the modified c-correction technique. In this study conducted in rugged terrain and with a bi-temporal image acquisition scheme that deviated up to two months from the ideal anniversary date scheme the modified c-correction technique resulted in a more reliable change detection.     

Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data

A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth’s gravity field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree 2,190, may reach amplitudes of 10 cm and more for height anomalies. The present paper proposes the utilisation of high-resolution residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05) and GPS/levelling data as references, demonstrate that RTM-based omission error estimates improve EGM2008 height anomaly differences by 10 cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates these findings with an improvement rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application, RTM omission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling data.     

Modeling preferential flow in reactive barriers: implications for performance and design

Reactive barriers are passive and in situ ground water treatment systems. Heterogeneities in hydraulic conductivity (K) within the aquifer-reactive barrier system will result in higher flux rates, and reduced residence times, through portions of the barrier. These spatial variations in residence time will affect the treatment capacity of the barrier. A numerical flow model was used to evaluate the effects of spatial variations in K on preferential flow through barriers. The simulations indicate that the impact of heterogeneities in K will be a function of their location and distribution; the more localized the high K zone, the greater the preferential flow. The geometry of the reactive barrier will also strongly influence flow distribution. Aquifer heterogeneities will produce greater preferential flow in thinner barriers compared to thicker barriers. If the barrier K is heterogeneous, greater preferential flow will occur in thicker barriers. The K of the barrier will affect the flow distribution; decreasing the K of the barrier can result in more even distribution of flow. Results indicate that less variable flow will be attained utilizing thicker, homogeneous barriers. The addition of homogeneous zones to thinner barriers will be effective at redistributing flow only if installed immediately adjacent to both the up- and downgradient faces of the barrier.