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NASA NTRS2020

Dynamic Scheduling: Target of Opportunity Observations of Gravitational Wave Events

The simultaneous detection of electromagnetic and gravitational waves from the coalescence of two neutron stars (GW170817 and GRB170817A) has ushered in a new era of ‘multimessenger’ astronomy, with electromagnetic detections spanning from gamma to radio. This great opportunity for new scientific investigations raises the issue of how the available multimessenger tools can best be integrated to constitute a powerful method to study the transient Universe in particular. To facilitate the classification of possible optical counterparts to gravitational wave events, it is important to optimize the scheduling of observations and the filtering of transients, both key elements of the follow-up process. In this work, we describe the existing workflow whereby telescope networks such as GRANDMA and GROWTH are currently scheduled; we then present modifications we have developed for the scheduling process specifically, so as to face the relevant challenges that have appeared during the latest observing run of Advanced LIGO and Advanced Virgo. We address issues with scheduling more than one epoch for multiple fields within a skymap, especially for large and disjointed localizations. This is done in two ways: by optimizing the maximum number of fields that can be scheduled and by splitting up the lobes within the skymap by right ascension to be scheduled individually. In addition, we implement the ability to take previously observed fields into consideration when rescheduling. We show the improvements that these modifications produce in making the search for optical counterparts more efficient, and we point to areas needing further improvement.

Gravitational waves↗
NASA NTRS1989

Stable Kalman filters for processing clock measurement data

Kalman filters have been used for some time to process clock measurement data. Due to instabilities in the standard Kalman filter algorithms, the results have been unreliable and difficult to obtain. During the past several years, stable forms of the Kalman filter have been developed, implemented, and used in many diverse applications. These algorithms, while algebraically equivalent to the standard Kalman filter, exhibit excellent numerical properties. Two of these stable algorithms, the Upper triangular-Diagonal (UD) filter and the Square Root Information Filter (SRIF), have been implemented to replace the standard Kalman filter used to process data from the Deep Space Network (DSN) hydrogen maser clocks. The data are time offsets between the clocks in the DSN, the timescale at the National Institute of Standards and Technology (NIST), and two geographically intermediate clocks. The measurements are made by using the GPS navigation satellites in mutual view between clocks. The filter programs allow the user to easily modify the clock models, the GPS satellite dependent biases, and the random noise levels in order to compare different modeling assumptions. The results of this study show the usefulness of such software for processing clock data. The UD filter is indeed a stable, efficient, and flexible method for obtaining optimal estimates of clock offsets, offset rates, and drift rates. A brief overview of the UD filter is also given.

Clements, P. A.↗
NASA NTRS1983

Optimal processing of satellite-derived magnetic anomaly data

It is shown how the concept of the power spectrum can be extended to two-dimensional spatial power spectra and how it can be used in determining optimal data processing methods for satellite-derived magnetic anomaly data and planning missions to obtain such data. The analysis techniques are applied to the data set and data-processing procedure described by Mayhew et al. (1980), a study that treats magnetic anomaly data for Australia and the surrounding ocean obtained by the polar orbit POGO series satellites. It is shown that the data-processing method used by Mayhew et al. is approximately equivalent to an invariant two-dimensional linear filter and that it is reasonably close to optimal with respect to accuracy, although some possible improvements are suggested. However, as is usual when filtering data, some real 'signal' is unavoidably removed along with the 'noise' resulting in errors that can be quite large. A method for reducing these errors by using additional data from a medium inclination orbit satellite (for example, 60 deg inclination) is proposed.

Mcleod, M. G.↗
NASA NTRS2009

Recent Results on "Approximations to Optimal Alarm Systems for Anomaly Detection"

An optimal alarm system and its approximations may use Kalman filtering for univariate linear dynamic systems driven by Gaussian noise to provide a layer of predictive capability. Predicted Kalman filter future process values and a fixed critical threshold can be used to construct a candidate level-crossing event over a predetermined prediction window. An optimal alarm system can be designed to elicit the fewest false alarms for a fixed detection probability in this particular scenario.

Martin, Rodney Alexander↗
NASA NTRS2008

Adaptive Key Component Control of Nonlinear Evolving Flexible Structures

An optimal alarm system and its approximations may use Kalman filtering for univariate linear dynamic systems driven by Gaussian noise to provide a layer of predictive capability. Predicted Kalman filter future process values and a fixed critical threshold can be used to construct a candidate level-crossing event over a predetermined prediction window. An optimal alarm system can be designed to elicit the fewest false alarms for a fixed detection probability in this particular scenario.

Balas, Mark↗
NASA NTRS1998

Design and Specification of Optical Bandpass Filters for Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS)

Advanced optical bandpass filters for the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) have been developed on a filter-by-filter basis through detailed studies which take into account the instrument's science goals, available optical filter fabrication technology, and developments in ACS's charge-coupled-device (CCD) detector technology. These filters include a subset of filters for the Sloan Digital Sky Survey (SDSS) which are optimized for astronomical photometry using today's charge-coupled-devices (CCD's). In order for ACS to be truly advanced, these filters must push the state-of-the-art in performance in a number of key areas at the same time. Important requirements for these filters include outstanding transmitted wavefront, high transmittance, uniform transmittance across each filter, spectrally structure-free bandpasses, exceptionally high out of band rejection, a high degree of parfocality, and immunity to environmental degradation. These constitute a very stringent set of requirements indeed, especially for filters which are up to 90 mm in diameter. The highly successful paradigm in which final specifications for flight filters were derived through interaction amongst the ACS Science Team, the instrument designer, the lead optical engineer, and the filter designer and vendor is described. Examples of iterative design trade studies carried out in the context of science needs and budgetary and schedule constraints are presented. An overview of the final design specifications for the ACS bandpass and ramp filters is also presented.

Leviton, Douglas B.↗
NASA NTRS1992

Robust control of flexible space vehicles with minimum structural excitation: On-off pulse control of flexible space vehicles

Both feedback and feedforward control approaches for uncertain dynamical systems (in particular, with uncertainty in structural mode frequency) are investigated. The control objective is to achieve a fast settling time (high performance) and robustness (insensitivity) to plant uncertainty. Preshaping of an ideal, time optimal control input using a tapped-delay filter is shown to provide a fast settling time with robust performance. A robust, non-minimum-phase feedback controller is synthesized with particular emphasis on its proper implementation for a non-zero set-point control problem. It is shown that a properly designed, feedback controller performs well, as compared with a time optimal open loop controller with special preshaping for performance robustness. Also included are two separate papers by the same authors on this subject.

Wie, Bong↗
NASA NTRS1973

Improved detection technique of a band-limited PCM/NRZ signal.

A simple tapped-delay-line filter in tandem with the receiver that optimally detects a single pulse over a band-limited channel in the presence of Gaussian noise is proposed for reducing the effect of the intersymbol interference in an ideal band-limited PCM/NRZ system. The improvement is described in terms of the gain in signal-to-noise ratio for a specific bit-error probability.

Shehadeh, N. M.↗
NASA NTRS1974

Selection of sampling rate for digital control of aircrafts

The considerations in selecting the sample rates for digital control of aircrafts are identified and evaluated using the optimal discrete method. A high performance aircraft model which includes a bending mode and wind gusts was studied. The following factors which influence the selection of the sampling rates were identified: (1) the time and roughness response to control inputs; (2) the response to external disturbances; and (3) the sensitivity to variations of parameters. It was found that the time response to a control input and the response to external disturbances limit the selection of the sampling rate. The optimal discrete regulator, the steady state Kalman filter, and the mean response to external disturbances are calculated.

Katz, P.↗
NASA NTRS1977

Optimum performance of suppressed carrier receivers with Costas loop tracking

The performance of suppressed carrier receivers with Costas loop tracking is optimized by proper choice of loop arm filter bandwidth. In particular, it is shown that for a variety of passive arm filter types, there exists, for a given data rate and data signal-to-noise ratio, an optimum filter bandwidth in the sense of minimizing the loop's squaring loss. For the linear theory case, this is equivalent to minimizing the loop's tracking jitter. When symbol synchronization is known, it is shown that by replacing the passive arm filters with active filters, i.e., integrate-and-dump circuits, one can achieve an improvement in carrier-to-noise ratio of as much as 4 to 6 dB depending on the passive arm filter type used for comparison and the value of data signal-to-noise ratio.

Simon, M. K.↗
NASA NTRS1981

Near optimum delay-line detection filters for serial detection of MSK signals

A method for designing transversal delay-line filter approximations to the matched filter for the serial detection of minimum-shift keyed (MSK) modulated signals is given. Two configurations are characterized in terms of signal-to-noise ratio degradation at a bit error rate (BER) of 10 to the -6th. One is shown to depart less than 0.3 dB from the ideal matched filter performance when its parameter values are optimized. A lumped-element equivalent is also given and shown to provide a degradation of less than 0.4 dB at a BER of 10 to the -6th

Ziemer, R. E.↗
NASA NTRS1988

The Mark III stellar interferometer

The Mark III interferometer is an operational long baseline stellar interferometer on Mt. Wilson with four-possible baseline configurations from 9m NE-SW to 20m N-S. The interferometer was designed to be a highly automated astronomical instrument to measure stellar positions and diameters to a magnitude limit of seven. Initial fringe observations were made in September 1986 with a 12-m N-S baseline. In the following months, semi-automated astrometric and stellar diameter measurements were also made. This paper describes the hardware and software components of the instrument and its operational characteristics. The interferometer has several novel features. One is the use of optimal estimation and control algorithms (e.g. Kalman filters) in the control loops. Another is the ability to operate both as a closed-loop phased interferometer and eventually as an open-loop or absolute coherent interferometer. High thermal stability and mechanical accuracy should permit the instrument to point blind at an astronomical object and maintain optical path equality to within the limits set by the atmosphere. In this absolute interferometric mode of operation, it should be possible to observe faint astronomical objects that are too dim for phase tracking. In theory, measurements of amplitude, group delay, and closure phase will be possible to 14 mag.

Shao, M.↗
NASA NTRS1995

On-line estimation of error covariance parameters for atmospheric data assimilation

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.

Dee, Dick P.↗
NASA NTRS1995

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Melott, A. L.↗
NASA NTRS2011

Kalman Orbit Optimized Loop Tracking

Under certain conditions of low signal power and/or high noise, there is insufficient signal to noise ratio (SNR) to close tracking loops with individual signals on orbiting Global Navigation Satellite System (GNSS) receivers. In addition, the processing power available from flight computers is not great enough to implement a conventional ultra-tight coupling tracking loop. This work provides a method to track GNSS signals at very low SNR without the penalty of requiring very high processor throughput to calculate the loop parameters. The Kalman Orbit-Optimized Loop (KOOL) tracking approach constitutes a filter with a dynamic model and using the aggregate of information from all tracked GNSS signals to close the tracking loop for each signal. For applications where there is not a good dynamic model, such as very low orbits where atmospheric drag models may not be adequate to achieve the required accuracy, aiding from an IMU (inertial measurement unit) or other sensor will be added. The KOOL approach is based on research JPL has done to allow signal recovery from weak and scintillating signals observed during the use of GPS signals for limb sounding of the Earth s atmosphere. That approach uses the onboard PVT (position, velocity, time) solution to generate predictions for the range, range rate, and acceleration of the low-SNR signal. The low- SNR signal data are captured by a directed open loop. KOOL builds on the previous open loop tracking by including feedback and observable generation from the weak-signal channels so that the MSR receiver will continue to track and provide PVT, range, and Doppler data, even when all channels have low SNR.

Young, Lawrence E.↗
NASA NTRS1994

Reflective Filters Design for Self-Filtering Narrowband Ultraviolet Imaging Experiment Wide-Field Surveys (NUVIEWS) Project

We report the design of multilayer reflective filters for the self-filtering cameras of the NUVIEWS project. Wide angle self-filtering cameras were designed to image the C IV (154.9 nm) line emission, and H2 Lyman band fluorescence (centered at 161 nm) over a 20 deg x 30 deg field of view. A key element of the filter design includes the development of pi-multilayers optimized to provide maximum reflectance at 154.9 nm and 161 nm for the respective cameras without significant spectral sensitivity to the large cone angle of the incident radiation. We applied self-filtering concepts to design NUVIEWS telescope filters that are composed of three reflective mirrors and one folding mirror. The filters with narrowband widths of 6 and 8 rim at 154.9 and 161 nm, respectively, have net throughputs of more than 50 % with average blocking of out-of-band wavelengths better than 3 x 10(exp -4)%.

Park, Jung- Ho↗