Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters

The Earth's non-spherical mass distribution and atmospheric drag cause the strongest perturbations on very low-Earth orbiting satellites (LEOs). Models of gravitational and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is also possible to derive LEO positions based on GPS precise point positioning without dynamical information. We use the reduced-dynamic technique for LEO POD, which combines the geometric strength of the GPS observations with the force models, and investigate the performance of different pseudo-stochastic orbit parametrizations, such as instantaneous velocity changes (pulses), piecewise constant accelerations, and continuous piecewise linear accelerations. The estimation of such empirical orbit parameters in a standard least-squares adjustment process of GPS observations, together with other relevant parameters, strives for the highest precision in the computation of LEO trajectories. We used the procedures for the CHAMP satellite and found that the orbits may be validated by means of independent SLR measurements at the level of 3.2cm RMS. Validations with independent accelerometer data revealed correlations at the level of 95% in the along-track direction. As expected, the empirical parameters compensate to a certain extent for deficiencies in the dynamic models. We analyzed the capability of pseudo-stochastic parameters for deriving information about the mismodeled part of the force field and found evidence that the resulting orbits may be used to recover force field parameters, if the number of pseudo-stochastic parameters is large enough. Results based on simulations showed a significantly better performance of acceleration-based orbits for gravity field recovery than for pulse-based orbits, with a quality comparable to a direct estimation if unconstrained accelerations are set up every 30

Propagation of atmospheric model errors to gravity potential harmonics—impact on GRACE de-aliasing

High-frequency, time-varying mass redistributions in the ocean and atmosphere have an impact on GRACE gravity field solutions due to the space-time sampling characteristics of signal and orbit. Consequently, aliasing of these signals into the GRACE observations is present and needs to be taken into account during data analysis by applying atmospheric and oceanic model data (de-aliasing). As the accuracy predicted prior to launch could not yet be achieved in the analysis of real GRACE data, the de-aliasing process and related geophysical model uncertainties are regarded as a potential error source in GRACE gravity field determination. Therefore, this study aims to improve the de-aliasing process in order to obtain a more accurate GRACE gravity field time-series. As these time-series provide estimates for the integrated mass transport in the Earth system, like the global water cycle and solid Earth geophysical processes, any increase in accuracy will lead to improvements in the geophysical interpretation of the results. So in conclusion, improving the de-aliasing is of relevance for a better understanding of geophysical processes. By no longer regarding the atmosphere and ocean model output as error-free, deeper insight into the impact of such uncertainties on the de-aliasing and on the resulting GRACE gravity field models can be obtained. For this purpose, in a first step, a full error propagation of the atmospheric and oceanic model parameters up to the de-aliasing gravity field coefficients is performed and the GRACE K-Band-Satellite-to-Satellite Tracking (KBR-SST) residuals, as an intermediate gravity field result, are analysed. The paper reviews the standard GRACE de-aliasing process and presents the mathematical model applied for the error propagation. Specifically, the effect of uncertainties in the atmospheric input parameters (temperature, surface pressure, specific humidity, geopotential) on the gravity field potential coefficients used for de-aliasing is shown in several scenarios. Finally, the impact of de-aliasing products (with and without error propagation) on a GRACE gravity field solution is investigated on the level of observation residuals. From the results obtained in this study it can be concluded that with respect to the current GRACE error budget, atmospheric model uncertainties do not play a prominent role in the error budget of current GRACE gravity field solutions. Nevertheless, in order to fully exploit the GRACE measurements towards the baseline accuracy, an optimized de-aliasing is needed. In this case, GRACE gravity field solutions are sensitive to uncertainties in atmospheric and oceanic models. Thus, the associated geophysical model errors shall be taken into account in the de-aliasing proces

High-rate GPS clock corrections from CODE: support of 1Hz applications

GPS zero-difference applications with a sampling rate up to 1Hz require corresponding high-rate GPS clock corrections. The determination of the clock corrections in a full network solution is a time-consuming task. The Center for Orbit Determination in Europe (CODE) has developed an efficient algorithm based on epoch-differenced phase observations, which allows to generate high-rate clock corrections within reasonably short time (<2h) and with sufficient accuracy (on the same level as the CODE rapid or final clock corrections, respectively). The clock determination procedure at CODE and the new algorithm is described in detail. It is shown that the simplifications to speed up the processing are not causing a significant loss of accuracy for the clock corrections. The high-rate clock corrections have in essence the same quality as clock corrections determined in a full network solution. In order to support 1Hz applications 1-s clock corrections would be needed. The computation time, even for the efficient algorithm, is not negligible, however. Therefore, we studied whether a reduced sampling is sufficient for the GPS satellite clock corrections to reach the same or only slightly inferior level of accuracy as for the full 1-s clock correction set. We show that high-rate satellite clock corrections with a spacing of 5s may be linearly interpolated resulting in less than 2% degradation of accurac

Efficient satellite orbit modelling using pseudo-stochastic parameters

If the force field acting on an artificial Earth satellite is not known a priori with sufficient accuracy to represent its observations on their accuracy level, one may introduce so-called pseudo-stochastic parameters into an orbit determination process, e.g. instantaneous velocity changes at user-defined epochs or piecewise constant accelerations in user-defined adjacent time subintervals or piecewise linear and continuous accelerations in adjacent time subintervals. The procedures, based on standard least-squares, associated with such parameterizations are well established, but they become inefficient (slow) if the number of pseudo-stochastic parameters becomes large. We develop two efficient methods to solve the orbit determination problem in the presence of pseudo-stochastic parameters. The results of the methods are identical to those obtained with conventional least-squares algorithms. The first efficient algorithm also provides the full variance-covariance matrix; the second, even more efficient algorithm, only parts of i

Evaluation of HCMM data for assessing soil moisture and water table depth

Soil moisture in the 0-cm to 4-cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop in eastern South Dakota. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the soil temperature. Corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. Shallow alluvial aquifers were located with HCMM predawn data. After correcting the data for vegetation differences, equations were developed for predicting water table depths within the aquifer. A finite difference code simulating soil moisture and soil temperature shows that soils with different moisture profiles differed in soil temperatures in a well defined functional manner. A significant surface thermal anomaly was found to be associated with shallow water tables

Evaluation of HCMM data for assessing soil moisture and water table depth

Data were analyzed for variations in eastern South Dakota. Soil moisture in the 0-4 cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop (% cover ranging from 30% to 90%) with an r squared = 0.81. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the 1-mm soil temperature, r squared = 0.88. The corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the 0-4 cm soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. HCMM data were used to estimate the soil moisture for four dates with an r squared = 0.55 after correction for crop conditions. Location of shallow alluvial aquifers could be accomplished with HCMM predawn data. After correction of HCMM day data for vegetation differences, equations were developed for predicting water table depths within the aquifer (r=0.8)

Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals

We present a method to integrate the equations of motion that govern bound, accelerated orbits in Schwarzschild spacetime. At each instant the true worldline is assumed to lie tangent to a reference geodesic, called an osculating orbit, such that the worldline evolves smoothly from one such geodesic to the next. Because a geodesic is uniquely identified by a set of constant orbital elements, the transition between osculating orbits corresponds to an evolution of the elements. In this paper we derive the evolution equations for a convenient set of orbital elements, assuming that the force acts only within the orbital plane; this is the only restriction that we impose on the formalism, and we do not assume that the force must be small. As an application of our method, we analyze the relative motion of two massive bodies, assuming that one body is much smaller than the other. Using the hybrid Schwarzschild/post-Newtonian equations of motion formulated by Kidder, Will, and Wiseman, we treat the unperturbed motion as geodesic in a Schwarzschild spacetime whose mass parameter is equal to the system's total mass. The force then consists of terms that depend on the system's reduced mass. We highlight the importance of conservative terms in this force, which cause significant long-term changes in the time-dependence and phase of the relative orbit. From our results we infer some general limitations of the radiative approximation to the gravitational self-force, which uses only the dissipative terms in the force.Comment: 18 pages, 6 figures, final version to be published in Physical Review

Public Price Reporting, Marketing Channel Selection, and Price Discovery: The Perspective of Cow/Calf Producers in the Dakotas

Cow/calf producers operating in the Dakotas were surveyed on their price discovery strategies, marketing channel preferences, and their perceptions of how regime change in the public price reporting system for fed cattle affected the beef industry in general and the cow/calf industry in particular. Survey results indicate cow/calf producers consider local institutions (auction barns, etc.) to be more reliable for price discovery than regional or national institutions (futures market, USDA public price reports, satellite auctions, etc.). The auction barn marketing channel is the preferred channel for marketing cattle and is considered the most reliable source of market information by producers. Dakota cow/calf producers perceive livestock mandatory price reporting as benefiting the beef industry in general, but consider public price reports to be less reliable than local sources of market information.beef supply chain, cow-calf marketing, marketing channel, price discovery, public price reporting, Livestock Production/Industries,

Negaton and Positon Solutions of the KDV Equation

We give a systematic classification and a detailed discussion of the structure, motion and scattering of the recently discovered negaton and positon solutions of the Korteweg-de Vries equation. There are two distinct types of negaton solutions which we label $[S^{n}]$ and $[C^{n}]$, where $(n+1)$ is the order of the Wronskian used in the derivation. For negatons, the number of singularities and zeros is finite and they show very interesting time dependence. The general motion is in the positive $x$ direction, except for certain negatons which exhibit one oscillation around the origin. In contrast, there is just one type of positon solution, which we label $[\tilde C^n]$. For positons, one gets a finite number of singularities for $n$ odd, but an infinite number for even values of $n$. The general motion of positons is in the negative $x$ direction with periodic oscillations. Negatons and positons retain their identities in a scattering process and their phase shifts are discussed. We obtain a simple explanation of all phase shifts by generalizing the notions of ``mass" and ``center of mass" to singular solutions. Finally, it is shown that negaton and positon solutions of the KdV equation can be used to obtain corresponding new solutions of the modified KdV equation.Comment: 20 pages plus 12 figures(available from authors on request),Latex fil

Impact of the Method of G6PD Deficiency Assessment on Genetic Association Studies of Malaria Susceptibility

BACKGROUND:Clinical association studies have yielded varied results regarding the impact of glucose-6-phosphate dehydrogenase (G6PD) deficiency upon susceptibility to malaria. Analyses have been complicated by varied methods used to diagnose G6PD deficiency. METHODOLOGY/PRINCIPAL FINDINGS:We compared the association between uncomplicated malaria incidence and G6PD deficiency in a cohort of 601 Ugandan children using two different diagnostic methods, enzyme activity and G6PD genotype (G202A, the predominant East African allele). Although roughly the same percentage of males were identified as deficient using enzyme activity (12%) and genotype (14%), nearly 30% of males who were enzymatically deficient were wild-type at G202A. The number of deficient females was three-fold higher with assessment by genotype (21%) compared to enzyme activity (7%). Heterozygous females accounted for the majority (46/54) of children with a mutant genotype but normal enzyme activity. G6PD deficiency, as determined by G6PD enzyme activity, conferred a 52% (relative risk [RR] 0.48, 95% CI 0.31-0.75) reduced risk of uncomplicated malaria in females. In contrast, when G6PD deficiency was defined based on genotype, the protective association for females was no longer seen (RR = 0.99, 95% CI 0.70-1.39). Notably, restricting the analysis to those females who were both genotypically and enzymatically deficient, the association of deficiency and protection from uncomplicated malaria was again demonstrated in females, but not in males (RR = 0.57, 95% CI 0.37-0.88 for females). CONCLUSIONS/SIGNIFICANCE:This study underscores the impact that the method of identifying G6PD deficient individuals has upon association studies of G6PD deficiency and uncomplicated malaria. We found that G6PD-deficient females were significantly protected against uncomplicated malaria, but this protection was only seen when G6PD deficiency is described using enzyme activity. These observations may help to explain the discrepancy in some published association studies involving G6PD deficiency and uncomplicated malaria