The optical slit sensor as a standard sensor for spacecraft attitude determination

The basic concept of an optical slit sensor as a standard altitude sensor is considered for any missions using a spinning spacecraft or where rotating sensors or mirrors could be used. Information available from a single sensor or from two sensors is analyzed. A standard slit sensor package is compared with the altitude package flown on the first synchronous meteorological satellite

Almost Eigenvalues and Eigenvectors of Almost Mathieu Operators

The almost Mathieu operator is the discrete Schr\"odinger operator $H_{\alpha,\beta,\theta}$ on $\ell^2(\mathbb{Z})$ defined via $(H_{\alpha,\beta,\theta}f)(k) = f(k + 1) + f(k - 1) + \beta \cos(2\pi \alpha k + \theta) f(k)$. We derive explicit estimates for the eigenvalues at the edge of the spectrum of the finite-dimensional almost Mathieu operator. We furthermore show that the (properly rescaled) $m$-th Hermite function $\phi_m$ is an approximate eigenvector of this operator, and that it satisfies the same properties that characterize the true eigenvector associated to the $m$-th largest eigenvalue. Moreover, a properly translated and modulated version of $\phi_m$ is also an approximate eigenvector of this operator, and it satisfies the properties that characterize the true eigenvector associated to the $m$-th largest (in modulus) negative eigenvalue. The results hold at the edge of the spectrum, for any choice of $\theta$ and under very mild conditions on $\alpha$ and $\beta$. We also give precise estimates for the size of the "edge", and extend some of our results to the infinite dimensional case. The ingredients for our proofs comprise Taylor expansions, basic time-frequency analysis, Sturm sequences, and perturbation theory for eigenvalues and eigenvectors. Numerical simulations demonstrate the tight fit of the theoretical estimates

pySPT: a package dedicated to the source position transformation

The modern time-delay cosmography aims to infer the cosmological parameters with a competitive precision from observing a multiply imaged quasar. The success of this technique relies upon a robust modeling of the lens mass distribution. Unfortunately strong degeneracies between density profiles that lead to almost the same lensing observables may bias precise estimate for the Hubble constant. The source position transformation (SPT), which covers the well-known mass sheet transformation (MST) as a special case, defines a new framework to investigate these degeneracies. In this paper, we present pySPT, a Python package dedicated to the SPT. We describe how it can be used to evaluate the impact of the SPT on lensing observables. We review most of its capabilities and elaborate on key features that we used in a companion paper regarding SPT and time delays. pySPT also comes with a sub-package dedicated to simple lens modeling. It can be used to generate lensing related quantities for a wide variety of lens models, independently from any SPT analysis. As a first practical application, we present a correction to the first estimate of the impact on time delays of the SPT, which has been experimentally found in Schneider and Sluse (2013) between a softened power-law and a composite (baryons + dark matter) lenses. We find that the large deviations predicted in Schneider and Sluse (2014) have been overestimated due to a minor bug (now fixed) in the public lens modeling code lensmodel (v1.99). We conclude that the predictions for the Hubble constant deviate by $\sim 7$\%, first and foremost caused by an MST. The latest version of pySPT is available at https://github.com/owertz/pySPT. We also provide tutorials to describe in detail how making the best use of pySPT at https://github.com/owertz/pySPT_tutorials.Comment: 9 pages, 5 figure

Alternatives with stronger convergence than coordinate-descent iterative LMI algorithms

In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other optimization methods better equipped to deal with such problems (having theoretical convergence guarantees and/or being more efficient in practice). This fact, already outlined at several places in the literature, still appears to be disregarded by a sizable part of the systems and control community. Thus, main elements on this issue and better optimization alternatives are presented and illustrated by means of an example.Comment: 3 pages. Main experimental results reproducible from files available on http://www.mathworks.com/matlabcentral/fileexchange/33219 This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Ambiguities in gravitational lens models: impact on time delays of the source position transformation

The central ambition of the modern time delay cosmography consists in determining the Hubble constant $H_0$ with a competitive precision. However, the tension with $H_0$ obtained from the Planck satellite for a spatially-flat $\Lambda$CDM cosmology suggests that systematic errors may have been underestimated. The most critical one probably comes from the degeneracy existing between lens models that was first formalized by the well-known mass-sheet transformation (MST). In this paper, we assess to what extent the source position transformation (SPT), a more general invariance transformation which contains the MST as a special case, may affect the time delays predicted by a model. To this aim we use pySPT, a new open-source python package fully dedicated to the SPT that we present in a companion paper. For axisymmetric lenses, we find that the time delay ratios between a model and its SPT-modified counterpart simply scale like the corresponding source position ratios, $\Delta \hat{t}/ \Delta t \approx \hat{\beta}/\beta$, regardless of the mass profile and the isotropic SPT. Similar behavior (almost) holds for non-axisymmetric lenses in the double image regime and for opposite image pairs in the quadruple image regime. In the latter regime, we also confirm that the time delay ratios are not conserved. In addition to the MST effects, the SPT-modified time delays deviate in general no more than a few percent for particular image pairs, suggesting that its impact on time-delay cosmography seems not be as crucial as initially suspected. We also reflected upon the relevance of the SPT validity criterion and present arguments suggesting that it should be reconsidered. Even though a new validity criterion would affect the time delays in a different way, we expect from numerical simulations that our conclusions will remain unchanged.Comment: 15 pages, 14 figure

Measuring the initial impacts on deforestation of Mato Grosso's program for environmental control

Although private forest use in Brazil has been regulated at least since the Forest Code of 1965, cumulative deforestation in the Brazilian Amazon reached 653,000 km2 by 2003 (INPE 2004). Much of this deforestation is illegal. In 1999, the State Foundation of the Environment (FEMA) in Mato Grosso introduced an innovative licensing and enforcement system to increase compliance with land use regulations. If successful, the program would deter deforestation that contravenes those regulations, including deforestation of riverine and hillside forest (permanent preservation areas), and reduction of a property's forest cover below a specified limit (the legal forest reserve requirement). This study seeks to assess whether introduction of the program affected landholder behavior in the desired direction. Simple before/after comparisons are not suitable for this purpose, because there is considerable year to year variation in deforestation due to climatic and economic conditions. Nor is it valid to assess program impacts by comparing licensed and unlicensed landholders, even though the program focused its enforcement efforts on the former. This is because, first, landholders with no intention of deforesting may choose to become licensed; and second, unlicensed landholders may be deterred from deforestation by the mere existence of a serious program that aims for universal licensing. To meet these challenges, the study applies a difference-in-difference approach to geographically explicit data. It looks for, and confirms, post-program declines in deforestation in high-priority enforcement areas relative to other areas; in more easily observed areas relative to less easily observed areas; and in areas of low remaining forest cover (where further deforestation is probably illegal) relative to high remaining forest cover. Thus, even against a backdrop of higher aggregate deforestation (driven in part by higher agricultural prices), there is evidence that the program in its early stages (before 2002) did shift landholder behavior in a direction consistent with reduced illegal deforestation. (The legality of deforestation was not however directly observed). The study hypothesizes that this behavioral change resulted from an initial perception of increased likelihood of the detection and prosecution of illegal deforestation, following announcement of the program. The study does not assess Mato Grosso's new system for environmental regulation (SLAPR) impacts following the change of state administration in 2003.Energy and Environment,Environment and Energy Efficiency,Environmental Economics&Policies,Forestry,Ecosystems and Natural Habitats

Fully autonomous navigation for the NASA cargo transfer vehicle

A great deal of attention has been paid to navigation during the close approach (less than or equal to 1 km) phase of spacecraft rendezvous. However, most spacecraft also require a navigation system which provides the necessary accuracy for placing both satellites within the range of the docking sensors. The Microcosm Autonomous Navigation System (MANS) is an on-board system which uses Earth-referenced attitude sensing hardware to provide precision orbit and attitude determination. The system is capable of functioning from LEO to GEO and beyond. Performance depends on the number of available sensors as well as mission geometry; however, extensive simulations have shown that MANS will provide 100 m to 400 m (3(sigma)) position accuracy and 0.03 to 0.07 deg (3(sigma)) attitude accuracy in low Earth orbit. The system is independent of any external source, including GPS. MANS is expected to have a significant impact on ground operations costs, mission definition and design, survivability, and the potential development of very low-cost, fully autonomous spacecraft

Fast Selection of Spectral Variables with B-Spline Compression

The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal approach of testing all possible subsets of variables with the prediction model is intractable, an incremental selection approach using a nonparametric statistics is a good option, as it avoids the computationally intensive use of the model itself. It has two drawbacks however: the number of groups of variables to test is still huge, and colinearities can make the results unstable. To overcome these limitations, this paper presents a method to select groups of spectral variables. It consists in a forward-backward procedure applied to the coefficients of a B-Spline representation of the spectra. The criterion used in the forward-backward procedure is the mutual information, allowing to find nonlinear dependencies between variables, on the contrary of the generally used correlation. The spline representation is used to get interpretability of the results, as groups of consecutive spectral variables will be selected. The experiments conducted on NIR spectra from fescue grass and diesel fuels show that the method provides clearly identified groups of selected variables, making interpretation easy, while keeping a low computational load. The prediction performances obtained using the selected coefficients are higher than those obtained by the same method applied directly to the original variables and similar to those obtained using traditional models, although using significantly less spectral variables