Obervational Model for Microarcsecond Astrometry with the Space Interferometry Mission

The Space Interferometry Mission (SIM) is a space-based long-baseline optical interferometer for precision astrometry. One of the primary objectives of the SIM instrument is to accurately determine the directions to a grid of stars, together with their proper motions and parallaxes, improving a priori knowledge by nearly three orders of magnitude. The basic astrometric observable of the instrument is the pathlength delay, a measurement made by a combination of internal metrology measurements that determine the distance the starlight travels through the two arms of the interferometer and a measurement of the white light stellar fringe to find the point of equal pathlength. Because this operation requires a non--negligible integration time to accurately measure the stellar fringe position, the interferometer baseline vector is not stationary over this time period, as its absolute length and orientation are time--varying. This conflicts with the consistency condition necessary for extracting the astrometric parameters which requires a stationary baseline vector. This paper addresses how the time-varying baseline is ``regularized'' so that it may act as a single baseline vector for multiple stars, and thereby establishing the fundamental operation of the instrument.Comment: 24 pages, 6 figure

A factorization on the semi-infinite interval I: General theory

AbstractThis paper extends the methods of special factorization to treat a class of factorization problems on the half-line. Factorizations involving integral operators with stationary and nonstationary kernels are presented. A simple “time domain” connection between the factorization problem and the stable regulator problem in Hilbert space is developed

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered

Design optimization of the JPL Phase B testbed

Increasingly complex spacecraft will benefit from integrated design and optimization of structural, optical, and control subsystems. Integrated design optimization will allow designers to make tradeoffs in objectives and constraints across these subsystems. The location, number, and types of passive and active devices distributed along the structure can have a dramatic impact on overall system performance. In addition, the manner in which structural mass is distributed can also serve as an effective mechanism for attenuating disturbance transmission between source and sensitive system components. This paper presents recent experience using optimization tools that have been developed for addressing some of these issues on a challenging testbed design problem. This particular testbed is one of a series of testbeds at the Jet Propulsion Laboratory under the sponsorship of the NASA Control Structure Interaction (CSI) Program to demonstrate nanometer level optical pathlength control on a flexible truss structure that emulates a spaceborne interferometer

Observational Model for Precision Astrometry with the Space Interferometry Mission

The Space Interferometry Mission (SIM) is a space-based 10-m baseline Michelson optical interferometer operating in the visible waveband that is designed to achieve astrometric accuracy in the single digits of the microarcsecond domain. Over a narrow field of view SIM is expected to achieve a mission accuracy of 1 microarcsecond. In this mode SIM will search for planetary companions to nearby stars by detecting the astrometric "wobble" relative to a nearby reference star. In its wide-angle mode, SIM will provide 4 microarcsecond precision absolute position measurements of stars, with parallaxes to comparable accuracy, at the end of its 5-year mission. The expected proper motion accuracy is around 3 microarcsecond/year, corresponding to a transverse velocity of 10 m/ s at a distance of 1 kpc. The basic astrometric observable of the SIM instrument is the pathlength delay. This measurement is made by a combination of internal metrology measurements that determine the distance the starlight travels through the two arms of the interferometer, and a measurement of the white light stellar fringe to find the point of equal pathlength. Because this operation requires a non-negligible integration time, the interferometer baseline vector is not stationary over this time period, as its absolute length and orientation are time varying. This paper addresses how the time varying baseline can be "regularized" so that it may act as a single baseline vector for multiple stars, as required for the solution of the astrometric equations

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference

Active control and parameter updating techniques for nonlinear thermal network models

The present article reports on active control and parameter updating techniques for thermal models based on the network approach. Emphasis is placed on applications where radiation plays a dominant role. Examples of such applications are the thermal design and modeling of spacecrafts and space-based science instruments. Active thermal control of a system aims to approximate a desired temperature distribution or to minimize a suitably defined temperature-dependent functional. Similarly, parameter updating aims to update the values of certain parameters of the thermal model so that the output approximates a distribution obtained through direct measurements. Both problems are formulated as nonlinear, least-square optimization problems. The proposed strategies for their solution are explained in detail and their efficiency is demonstrated through numerical tests. Finally, certain theoretical results pertaining to the characterization of solutions of the problems of interest are also presented

High-Precision Narrow Angle Astrometry with a Space-Borne Interferometer

This paper develops an observing and processing scheme for narrow angle astrometry using a single baseline interferometer without the aid of "grid" stars to characterize the interferometer baseline vector in inertial space. The basic concept derives from the recognition that over a narrow field the set of fundamental unknown instrument parameters that arise because the interferometer baseline vector has large uncertainties (since there are no grid star measurements) is indistinguishable from a particular set of unobservable errors in the determination of star positions within the field. Reference stars within the narrow field of regard are used to circumvent the unobservable modes. Feasibility of the approach is demonstrated through analysis and example simulations

Nodal temperature estimation algorithms for nonlinear thermal network models

Algorithms for estimating temperatures at arbitrary nodes of steady-state thermal network models, given noisy measured values of a subset of the nodes of the network, are described. Applications where temperature estimation is desired include correlation of test and analysis results, thermal-stress estimation, and others. An optimization problem is formulated to recover the temperatures at the unobservable nodes. This problem is an example of nonlinear, least-squares minimization with a single quadratic constraint (imposed by the measured data) and is solved with the method of Lagrange multipliers. New algorithms are developed that find local minima of the cost functional through a Newton-type iteration procedure. At each iteration a least-squares problem with a quadratic inequality is solved with a fast and memory-efficient method. The proposed algorithms are shown to be at least an order of magnitude faster than standard algorithms. Their accuracy and speed are examined through a series of tests on thermal models from ongoing NASA mission

Optimization methods for thermal modeling of optomechanical systems

Numerical techniques for a class of optimization problems associated with the thermal modeling of optomechanical systems are presented. Emphasis is placed on applications where radiation plays a dominant role. This work is motivated by the need for incorporating thermal analysis into integrated modeling of high-precision, space-borne optical systems. The specific problems of interest are thermal control to minimize the wavefront error by application of external heat loads, and the temperature estimation problem of predicting temperatures at arbitrary nodes of the model given noisy measurements on a subset of nodes. The proposed numerical techniques are briefly described and compared to existing algorithms. Their accuracy and robustness are demonstrated through numerical tests with models from ongoing NASA missions