Attitude determination and sensor alignment via weighted least squares affine transformations

Attitude determination and sensor alignment via weighted least squares affine transformation

A vector approach to the algebra of rotations with applications

Vector analysis approach to algebra of rotations with applications to least-squares rotation and rigid body motio

Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal. In this paper, we attempt to bridge this gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that offers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework. We provide theoretical guarantees and practical insight into the use of this dictionary for recovery of sampled multiband signals from compressive measurements

Algorithm for in-flight gyroscope calibration

An optimal algorithm for the in-flight calibration of spacecraft gyroscope systems is presented. Special consideration is given to the selection of the loss function weight matrix in situations in which the spacecraft attitude sensors provide significantly more accurate information in pitch and yaw than in roll, such as will be the case in the Hubble Space Telescope mission. The results of numerical tests that verify the accuracy of the algorithm are discussed

Signal Space CoSaMP for Sparse Recovery with Redundant Dictionaries

Compressive sensing (CS) has recently emerged as a powerful framework for acquiring sparse signals. The bulk of the CS literature has focused on the case where the acquired signal has a sparse or compressible representation in an orthonormal basis. In practice, however, there are many signals that cannot be sparsely represented or approximated using an orthonormal basis, but that do have sparse representations in a redundant dictionary. Standard results in CS can sometimes be extended to handle this case provided that the dictionary is sufficiently incoherent or well-conditioned, but these approaches fail to address the case of a truly redundant or overcomplete dictionary. In this paper we describe a variant of the iterative recovery algorithm CoSaMP for this more challenging setting. We utilize the D-RIP, a condition on the sensing matrix analogous to the well-known restricted isometry property. In contrast to prior work, the method and analysis are "signal-focused"; that is, they are oriented around recovering the signal rather than its dictionary coefficients. Under the assumption that we have a near-optimal scheme for projecting vectors in signal space onto the model family of candidate sparse signals, we provide provable recovery guarantees. Developing a practical algorithm that can provably compute the required near-optimal projections remains a significant open problem, but we include simulation results using various heuristics that empirically exhibit superior performance to traditional recovery algorithms

Engineering and fabrication cost considerations for cryogenic wind tunnel models

Design and fabrication cost drivers for cryogenic transonic wind tunnel models are defined. The major cost factors for wind tunnel models are model complexity, tolerances, surface finishes, materials, material validation, and model inspection. The cryogenic temperatures require the use of materials with relatively high fracture toughness but at the same time high strength. Some of these materials are very difficult to machine, requiring extensive machine hours which can add significantly to the manufacturing costs. Some additional engineering costs are incurred to certify the materials through mechanical tests and nondestructive evaluation techniques, which are not normally required with conventional models. When instrumentation such as accelerometers and electronically scanned pressure modules is required, temperature control of these devices needs to be incorporated into the design, which requires added effort. Additional thermal analyses and subsystem tests may be necessary, which also adds to the design costs. The largest driver to the design costs is potentially the additional static and dynamic analyses required to insure structural integrity of the model and support system

Magnetometry of random AC magnetic fields using a single Nitrogen-Vacancy center

We report on the use of a single NV center to probe fluctuating AC magnetic fields. Using engineered currents to induce random changes in the field amplitude and phase, we show that stochastic fluctuations reduce the NV center sensitivity and, in general, make the NV response field-dependent. We also introduce two modalities to determine the field spectral composition, unknown a priori in a practical application. One strategy capitalizes on the generation of AC-field-induced coherence 'revivals', while the other approach uses the time-tagged fluorescence intensity record from successive NV observations to reconstruct the AC field spectral density. These studies are relevant for magnetic sensing in scenarios where the field of interest has a non-trivial, stochastic behavior, such as sensing unpolarized nuclear spin ensembles at low static magnetic fields.Comment: 11 pages, 3 figure

HUMAN GROWTH CURVE

The human growth curve shows two (and only two) outstanding periods of accelerated growth—the circumnatal and the adolescent. The circumnatal growth cycle attains great velocity, which reaches a maximum at the time of birth. The curve of this cycle is best fitted by a theoretical skew curve of Pearson's Type I. It has a theoretical range of 44 months and a standard deviation of 5.17 months. The modal velocity is 10.2 kilos per year. The adolescent growth cycle has less maximum velocity and greater range in time than the circumnatal cycle. The best fitting theoretical curve is a normal frequency curve ranging over about 10 years with a standard deviation of about 21 months and a modal velocity of 4.5 kilos per year. The two great growth accelerations are superimposed on a residual curve of growth which measures a substratum of growth out of which the accelerations arise. This probably extends from conception to 55 years, on the average. It is characterized by low velocity, averaging about 2 kilos per year from 2 to 12 years. It is interpreted as due to many growth operations coincident or closely blending in time. Our curve shows no third marked period of acceleration at between the 3rd and 6th years. The total growth in weight of the body is the sum of the weight of its constituent organs. In some cases these keep pace with the growth of the body as a whole; great accelerations of body growth are due to great accelerations in growth of the constituent organs. In other cases one of the organs of the body (like the thymus gland) may undergo a change in weight that is not in harmony with that of the body as a whole. The development of the weight in man is the resultant of many more or less elementary growth processes. These result in two special episodes of growth and numerous smaller, blending, growth operations. Hypotheses are suggested as to the basis of the special growth accelerations