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NASA NTRS2014

Acoustics Research of Propulsion Systems

The liftoff phase induces high acoustic loading over a broad frequency range for a launch vehicle. These external acoustic environments are used in the prediction of the internal vibration responses of the vehicle and components. Present liftoff vehicle acoustic environment prediction methods utilize stationary data from previously conducted hold-down tests to generate 1/3 octave band Sound Pressure Level (SPL) spectra. In an effort to update the accuracy and quality of liftoff acoustic loading predictions, non-stationary flight data from the Ares I-X were processed in PC-Signal in two flight phases: simulated hold-down and liftoff. In conjunction, the Prediction of Acoustic Vehicle Environments (PAVE) program was developed in MATLAB to allow for efficient predictions of sound pressure levels (SPLs) as a function of station number along the vehicle using semi-empirical methods. This consisted of generating the Dimensionless Spectrum Function (DSF) and Dimensionless Source Location (DSL) curves from the Ares I-X flight data. These are then used in the MATLAB program to generate the 1/3 octave band SPL spectra. Concluding results show major differences in SPLs between the hold-down test data and the processed Ares I-X flight data making the Ares I-X flight data more practical for future vehicle acoustic environment predictions.

Gao, Ximing↗

NASA NTRS1990

On recursive least-squares filtering algorithms and implementations

In many real-time signal processing applications, fast and numerically stable algorithms for solving least-squares problems are necessary and important. In particular, under non-stationary conditions, these algorithms must be able to adapt themselves to reflect the changes in the system and take appropriate adjustments to achieve optimum performances. Among existing algorithms, the QR-decomposition (QRD)-based recursive least-squares (RLS) methods have been shown to be useful and effective for adaptive signal processing. In order to increase the speed of processing and achieve high throughput rate, many algorithms are being vectorized and/or pipelined to facilitate high degrees of parallelism. A time-recursive formulation of RLS filtering employing block QRD will be considered first. Several methods, including a new non-continuous windowing scheme based on selectively rejecting contaminated data, were investigated for adaptive processing. Based on systolic triarrays, many other forms of systolic arrays are shown to be capable of implementing different algorithms. Various updating and downdating systolic algorithms and architectures for RLS filtering are examined and compared in details, which include Householder reflector, Gram-Schmidt procedure, and Givens rotation. A unified approach encompassing existing square-root-free algorithms is also proposed. For the sinusoidal spectrum estimation problem, a judicious method of separating the noise from the signal is of great interest. Various truncated QR methods are proposed for this purpose and compared to the truncated SVD method. Computer simulations provided for detailed comparisons show the effectiveness of these methods. This thesis deals with fundamental issues of numerical stability, computational efficiency, adaptivity, and VLSI implementation for the RLS filtering problems. In all, various new and modified algorithms and architectures are proposed and analyzed; the significance of any of the new method depends crucially on specific application.

Hsieh, Shih-Fu↗

NASA NTRS2019

Time Series Analysis in the Search for Other Worlds Through Transit Photometry

The Kepler Mission launched in June 2009 to commence NASA's first mission to search for potentially habitable, Earth-size planets orbiting Sun-like stars. Kepler discovered explanets via the transit method: searching for minute (100 ppm) drops in brightness lasting 1 - 13 hours corresponding to occasions where the planet crosses the face of its host star from Kepler's point of view. The exquisite precision required to carry out the Kepler mission (20 ppm in 6.5 hours) pushed astronomical time series analysis to the limits, and motivated the development of novel algorithmic approaches. Transit signatures of rocky planets are often dwarfed by the intrinsic stellar variability, which is not white noise, and often is non-stationary, and by instrumental systematic effects, which can include transients and electronic artifacts. Surmounting this challenging regime of weak, temporally compact, periodic signals in observation noise with strong systematics and other sources of variability motivated the development of 1) an overcomplete, non-decimated, wavelet-based matched filter to jointly estimate the properties of the non-stationary, non-white observation noise process, and 2) a multi-scale, maximum a posteriori (msMAP) approach to identifying and removing instrumental systematic effects. After over nine years of observations, the Kepler spacecraft finally ran out of fuel in November 2018, ending its data collection activities. Over 2300 planets were discovered by Kepler in its primary mission, and over 355 have been discovered by K2, the repurposed mission that followed Kepler's primary mission after the loss of a second reaction wheel in May 2013. We have ported the Kepler science pipeline for the Transiting Exoplanet Survey Satellite (TESS) Mission, which began science observations in July 2019, and report initial results and performance of the modified science pipeline.The Kepler and TESS Missions are supported by NASA's Science Mission Directorate.

transit surveys↗

DOE OSTI2023

Is land use producing robust signals in future projections from Earth system models, all else being equal?

Abstract We use six Earth system models (ESMs) run under SSP3-7.0, a scenario characterized by a relatively large land use change (LUC) over the 21st century, and under a variant of the same scenario where a significantly different pattern of LUC, taken from SSP1-2.6, was used, all else being equal. Our goal is to identify changes in climate extremes between the two scenarios that are statistically significant and robust across the ESMs. The motivation for this study is to test a long-held assumption of the shared socio-economic pathway-representative concentration pathway (SSP-RCP) scenario framework: that the signal from LUC can be safely disregarded when pairing different SSPs to the compatible RCPs, where compatibility only considers global radiative forcing, predominantly determined by well-mixed greenhouse gasses emissions. We analyze extremes of daily minimum and maximum temperatures and precipitation, after fitting non-stationary generalized extreme value distributions in a way that borrows strength along the length of the simulation (2015–2100) and across initial condition ensembles. We consider changes in the 20 year return levels (RL20s) of these metrics by 2100, and focus on eight locations where LUC is large within each scenario, and strongly differs between scenarios, averaging the RL20s over a neighborhood characterized by the same LUC to enhance the signal to noise. We find that precipitation extremes do not show significant differences attributable to LUC differences. For temperature extremes (cold and hot) results are mixed, with some location-index combination showing significant results for some of the ESMs but not all, and not many coherent changes appearing for indices across regions, or regions across indices. These ESMs are representative of what is typically adopted as the source of climate information for impact studies, when the SSP-RCP framework is put to use. Overall, our analysis suggests that the hypothesis to pair SSPs to RCPs in a flexible fashion is overall defensible. However, the appearance of some coherence in a few locations and for some indices invites further investigation.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2011

Receiver Gain Modulation Circuit

A receiver gain modulation circuit (RGMC) was developed that modulates the power gain of the output of a radiometer receiver with a test signal. As the radiometer receiver switches between calibration noise references, the test signal is mixed with the calibrated noise and thus produces an ensemble set of measurements from which ensemble statistical analysis can be used to extract statistical information about the test signal. The RGMC is an enabling technology of the ensemble detector. As a key component for achieving ensemble detection and analysis, the RGMC has broad aeronautical and space applications. The RGMC can be used to test and develop new calibration algorithms, for example, to detect gain anomalies, and/or correct for slow drifts that affect climate-quality measurements over an accelerated time scale. A generalized approach to analyzing radiometer system designs yields a mathematical treatment of noise reference measurements in calibration algorithms. By treating the measurements from the different noise references as ensemble samples of the receiver state, i.e. receiver gain, a quantitative description of the non-stationary properties of the underlying receiver fluctuations can be derived. Excellent agreement has been obtained between model calculations and radiometric measurements. The mathematical formulation is equivalent to modulating the gain of a stable receiver with an externally generated signal and is the basis for ensemble detection and analysis (EDA). The concept of generating ensemble data sets using an ensemble detector is similar to the ensemble data sets generated as part of ensemble empirical mode decomposition (EEMD) with exception of a key distinguishing factor. EEMD adds noise to the signal under study whereas EDA mixes the signal with calibrated noise. It is mixing with calibrated noise that permits the measurement of temporal-functional variability of uncertainty in the underlying process. The RGMC permits the evaluation of EDA by modulating the receiver gain using an external signal. Without the RGMC, samples of calibrated references from radiometers form an ensemble data set of the natural occurring fluctuations within a receiver. By driving the gain of an otherwise stable receiver with an external signal, the conceptual framework and generalization of the mathematics of EDA can be tested. A series of measurements was conducted to evaluate and characterize the performance of the RGMC. Test signals stepped the RGMC across its dynamic range of performance using a radiometer that sampled four noise references; analysis indicates that the RGMC successfully modulated the receiver gain with an external signal. Calibration algorithms applied to four noise references demonstrate the RGMC produced ensemble data sets of the external signal.

Jones, Hollis↗

NASA NTRS2014

Device and Method for Gathering Ensemble Data Sets

An ensemble detector uses calibrated noise references to produce ensemble sets of data from which properties of non-stationary processes may be extracted. The ensemble detector comprising: a receiver; a switching device coupled to the receiver, the switching device configured to selectively connect each of a plurality of reference noise signals to the receiver; and a gain modulation circuit coupled to the receiver and configured to vary a gain of the receiver based on a forcing signal; whereby the switching device selectively connects each of the plurality of reference noise signals to the receiver to produce an output signal derived from the plurality of reference noise signals and the forcing signal.

Racette, Paul E.↗

NASA NTRS2015

Progress Towards Improved Analysis of TES X-ray Data Using Principal Component Analysis

The traditional method of applying a digital optimal filter to measure X-ray pulses from transition-edge sensor (TES) devices does not achieve the best energy resolution when the signals have a highly non-linear response to energy, or the noise is non-stationary during the pulse. We present an implementation of a method to analyze X-ray data from TESs, which is based upon principal component analysis (PCA). Our method separates the X-ray signal pulse into orthogonal components that have the largest variance. We typically recover pulse height, arrival time, differences in pulse shape, and the variation of pulse height with detector temperature. These components can then be combined to form a representation of pulse energy. An added value of this method is that by reporting information on more descriptive parameters (as opposed to a single number representing energy), we generate a much more complete picture of the pulse received. Here we report on progress in developing this technique for future implementation on X-ray telescopes. We used an 55Fe source to characterize Mo/Au TESs. On the same dataset, the PCA method recovers a spectral resolution that is better by a factor of two than achievable with digital optimal filters.

Low-temperature detectors A[center dot] Transition↗

DOE OSTI2022

Utilization of the CW magnetrons as coherent RF sources for superconducting RF accelerators

CW magnetrons designed and optimized for industrial heaters, driven by an injection-locking signal, were suggested to power Superconducting RF (SRF) cavities. However, the CW magnetrons, which are regenerative generators, are intended to operate in self-excitation mode, so, for reliable starting they use a large regenerative gain, causing a large regenerative instability in operation. Thus, power supply ripple, even shot noise, etc., lead to multiple sidebands forming a quasi-continuous noise spectrum at the carrier frequency. Therefore, in the traditionally used mode of operation and control, such magnetrons are inapplicable for powering high Q-factor SRF cavities. A new approach to operation and control of CW magnetrons considering non-stationary processes during start-up and operation makes it possible to find a mode of almost coherent RF generation of tubes with a significant reduction in regenerative instability and noise and increased efficiency. In our work is presented substantiation for the newly developed mode with an analysis of the new approach based on experimental results. •In this article, for the first time, non-stationary, regenerative processes are considered during the start-up and operation of CW magnetrons for powering high-Q superconducting RF cavities.•An analytical study, confirmed by experiments, showed that the traditionally used modes of starting and operating CW magnetrons are not suitable for powering high-Q superconducting RF cavities.•In fact, to make CW magnetrons suitable for such cavities, the physics of starting and operating CW magnetrons must be changed. This has been demonstrated in our work.•In developing the Stimulated Coherent Generation Mode [NIM A 980 (2020) 164366], we have shown the suitability of this mode for starting and operating CW magnetrons for high-Q superconducting RF cavities.•Analytical analysis, verified experimentally, substantiates in our article the suitability of the “Mode of stimulated coherent generation” of CW magnetrons for powering high-Q superconducting cavities in pulsed and continuous modes.

43 PARTICLE ACCELERATORS↗

NASA NTRS2010

Platform for Post-Processing Waveform-Based NDE

Signal- and image-processing methods are commonly needed to extract information from the waves, improve resolution of, and highlight defects in an image. Since some similarity exists for all waveform-based nondestructive evaluation (NDE) methods, it would seem that a common software platform containing multiple signal- and image-processing techniques to process the waveforms and images makes sense where multiple techniques, scientists, engineers, and organizations are involved. NDE Wave & Image Processor Version 2.0 software provides a single, integrated signal- and image-processing and analysis environment for total NDE data processing and analysis. It brings some of the most useful algorithms developed for NDE over the past 20 years into a commercial-grade product. The software can import signal/spectroscopic data, image data, and image series data. This software offers the user hundreds of basic and advanced signal- and image-processing capabilities including esoteric 1D and 2D wavelet-based de-noising, de-trending, and filtering. Batch processing is included for signal- and image-processing capability so that an optimized sequence of processing operations can be applied to entire folders of signals, spectra, and images. Additionally, an extensive interactive model-based curve-fitting facility has been included to allow fitting of spectroscopy data such as from Raman spectroscopy. An extensive joint-time frequency module is included for analysis of non-stationary or transient data such as that from acoustic emission, vibration, or earthquake data.

Roth, Don J.↗

NASA NTRS2022

How Well do Multisatellite Products Capture the Space-Time Dynamics of Precipitation? Part II: Building an Error Model Through Spectral System Identification

Satellite precipitation products, as all quantitative estimates, come with some inherent degree of uncertainty. To associate a quantitative value of the uncertainty to each individual estimate, error modeling is necessary. Most of the error models proposed so far compute the uncertainty as a function of precipitation intensity only, and only at one specific spatio-temporal scale. We propose a spectral error model which accounts for the neighboring space-time dynamics of precipitation into the uncertainty quantification. Systematic distortions of the precipitation signal and random errors are characterized distinctively in every frequency-wavenumber band in the Fourier domain, to accurately characterize error across scales. The systematic distortions are represented as a deterministic space-time linear filtering term. The random errors are represented as a non-stationary additive noise. The spectral error model is applied to the IMERG multi satellite precipitation product and its parameters are estimated empirically through a system identification approach using the GV-MRMS gauge-radar measurements as reference (“truth”) over the eastern United States. The filtering term is found to be essentially low-pass. While traditional error models attribute most of the error variance to random errors, it is found here that the systematic filtering term explains 48% of the error variance at the native resolution of IMERG. This fact confirms that, at high resolution, filtering effects in satellite precipitation products cannot be ignored, and that the error cannot be represented as a purely random additive or multiplicative term. An important consequence is that precipitation estimates derived from totally different sources shall not be expected to automatically have statistically independent errors.

Precipitation↗

NASA NTRS1988

Digital spectral estimation and modeling of Space Shuttle flight data

Application of the digital signal processing technique of autoregressive-moving-average (ARMA) modeling to the estimation of power spectra and shock spectra from Space Shuttle lift-off flight accelerograms is described in this paper. The background for application to ARMA of lift-off accelerograms which are non-stationary in nature is exemplified through a step-by-step discussion of actual numerical results. Included is a discussion of pertinent mathematical background for the ARMA approximations. Potential areas for application of ARMA modeling in payload integration activities are suggested.

Spanos, P. D.↗

NASA NTRS1992

Experiments with recursive estimation in astronomical image processing

Recursive estimation concepts were applied to image enhancement problems since the 70's. However, very few applications in the particular area of astronomical image processing are known. These concepts were derived, for 2-dimensional images, from the well-known theory of Kalman filtering in one dimension. The historic reasons for application of these techniques to digital images are related to the images' scanned nature, in which the temporal output of a scanner device can be processed on-line by techniques borrowed directly from 1-dimensional recursive signal analysis. However, recursive estimation has particular properties that make it attractive even in modern days, when big computer memories make the full scanned image available to the processor at any given time. One particularly important aspect is the ability of recursive techniques to deal with non-stationary phenomena, that is, phenomena which have their statistical properties variable in time (or position in a 2-D image). Many image processing methods make underlying stationary assumptions either for the stochastic field being imaged, for the imaging system properties, or both. They will underperform, or even fail, when applied to images that deviate significantly from stationarity. Recursive methods, on the contrary, make it feasible to perform adaptive processing, that is, to process the image by a processor with properties tuned to the image's local statistical properties. Recursive estimation can be used to build estimates of images degraded by such phenomena as noise and blur. We show examples of recursive adaptive processing of astronomical images, using several local statistical properties to drive the adaptive processor, as average signal intensity, signal-to-noise and autocorrelation function. Software was developed under IRAF, and as such will be made available to interested users.

Busko, I.↗

NASA NTRS2016

The Mexican Drought Atlas: Tree-Ring Reconstructions of the Soil Moisture Balance During the Late Pre-Hispanic, Colonial, and Modern Eras

Mexico has suffered a long history and prehistory of severe sustained drought. Drought over Mexico is modulated by ocean-atmospheric variability in the Atlantic and Pacific, raising the possibility for long-range seasonal climate forecasting, which could help mediate the economic and social impacts of future dry spells. The instrumental record of Mexican climate is very limited before 1920, but tree-ring chronologies developed from old-growth forests in Mexico can provide an excellent proxy representation of the spatial pattern and intensity of past moisture regimes useful for the analysis of climate dynamics and climate impacts. The Mexican Drought Atlas (MXDA) has been developed from an extensive network of 252 climate sensitive tree-ring chronologies in and near Mexico. The MXDA reconstructions extend from 1400 CE-2012 and were calibrated with the instrumental summer (JJA) self-calibrating Palmer Drought Severity Index (scPDSI) on a 0.5deg latitude/longitude grid extending over land areas from 14 to 34degN and 75-120degW using Ensemble Point-by-Point Regression (EPPR) for the 1944-1984 period. The grid point reconstructions were validated for the period 1920-1943 against instrumental gridded scPDSI values based on the fewer weather station observations available during that interval. The MXDA provides a new spatial perspective on the historical impacts of moisture extremes over Mexico during the past 600-years, including the Aztec Drought of One Rabbit in 1454, the drought of El Ano de Hambre in 1785-1786, and the drought that preceded the Mexican Revolution of 1909-1910. The El Nino/Southern Oscillation (ENSO) is the most important ocean-atmospheric forcing of moisture variability detected with the MXDA. In fact, the reconstructions suggest that the strongest central equatorial Pacific sea surface temperature (SST) teleconnection to the soil moisture balance over North America may reside in northern Mexico. This ENSO signal has stronger and more time-stable correlations than computed for either the Atlantic Multidecadal Oscillation or Pacific Decadal Oscillation. The extended Multivariate ENSO Index is most highly correlated with reconstructed scPDSI over northern Mexico, where warm events favor moist conditions during the winter, spring, and early summer. This ENSO teleconnection to northern Mexico has been strong over the past 150 years, but it has been comparatively weak and non-stationary in the MXDA over central and southern Mexico where eastern tropical Pacific and Caribbean/tropical Atlantic SSTs seem to be more important. The ENSO teleconnection to northern Mexico is weaker in the available instrumental PDSI, but analyses based on the millennium climate simulations with the Community Earth System Model suggest that the moisture balance during the winter, spring, and early summer over northern Mexico may indeed be particularly sensitive to ENSO forcing. Nationwide drought is predicted to become more common with anthropogenic climate change, but the MXDA reconstructions indicate that intense "All Mexico" droughts have been rare over the past 600 years and their frequency does not appear to have increased substantially in recent decades.

El Nino↗

NASA NTRSDate not supplied

Assessing Potential Geophysical and Environmental Impacts from Frequent Rocket Launch Missions at Kennedy Space Center

Kennedy Space Center (KSC) in Florida has been utilized for space missions over many years with a gradually increasing number of rocket launches. There have been multiple studies where air-coupled acoustic waves and infrasound originating from launched rockets were used for operational purposes, such as locating booster trajectories as a function of changing atmospheric conditions. However, no study has utilized the acoustoelastic waves as a signal source for subsurface seismic investigations. We conducted a dispersion analysis using the seismic energy recorded from the Artemis I rocket launch at KSC in November 2022, and from these results we generated depth-sensitivity kernels at different wave frequencies. The kernels were compared with sedimentary core data to verify boundaries of carbonate layers above the Floridan Aquifer System. Accumulative information of bedrock-sediment boundary across the sedimentary platform could especially provide geo-structural evidence that manifests the configuration of coastal features. Continuous dispersion analysis of seismic recordings from consecutive rocket launches also has potential to identify non-stationary environmental effects, such as reorientation of sedimentary structures and fluctuation of the saltwater/groundwater lens from gravitational tides, which may affect erosional susceptibility of coastal features.

Han Byul Woo↗

NASA NTRSDate not supplied

Assessing Potential Geophysical and Environmental Impacts from Frequent Rocket Launch Missions at Kennedy Space Center

Rocket Launch Seismicity↗

NASA NTRS2021

Accuracy Assessment of Global Internal-Tide Models Using Satellite Altimetry Models Using Satellite Altimetry

Altimeter measurements are corrected for several geophysical parameters in order to access ocean signals of interest, like mesoscale or sub-mesoscale variability. The ocean tide is one of the most critical corrections due to the amplitude of the tidal elevations and to the aliasing phenomena of high-frequency signals into the lower-frequency band, but the internal-tide signatures at the ocean surface are not yet corrected globally. Internal tides can have a signature of several centimeters at the surface with wavelengths of about 50–250 km for the first mode and even smaller scales for higher-order modes. The goals of the upcoming Surface Water Ocean Topography (SWOT) mission and other high-resolution ocean measurements make the correction of these small-scale signals a challenge, as the correction of all tidal variability becomes mandatory to access accurate measurements of other oceanic signals. In this context, several scientific teams are working on the development of new internal-tide models, taking advantage of the very long altimeter time series now available, which represent an unprecedented and valuable global ocean database. The internal-tide models presented here focus on the coherent internal-tide signal and they are of three types: empirical models based upon analysis of existing altimeter missions, an assimilative model and a three-dimensional hydrodynamic model. A detailed comparison and validation of these internal-tide models is proposed using existing satellite altimeter databases. The analysis focuses on the four main tidal constituents: M2, K1, O1 and S2. The validation process is based on a statistical analysis of multi-mission altimetry including Jason-2 and Cryosphere Satellite-2 data. The results show a significant altimeter variance reduction when using internal-tide corrections in all ocean regions where internal tides are generating or propagating. A complementary spectral analysis also gives some estimation of the performance of each model as a function of wavelength and some insight into the residual non-stationary part of internal tides in the different regions of interest. This work led to the implementation of a new internal-tide correction (ZARON'one) in the next geophysical data records version-F (GDR-F) standards.

Loren Carrere↗

NASA NTRS2002

An Exploration of Discontinuous Time Synchronous Averaging for Helicopter HUMS Using Cruise and Terminal Area Vibration Data

Recent research using NASA Ames AH-1 and OH-58C helicopters, and NASA Glenn test rigs, has shown that in-flight vibration data are typically non-stationary [l-4]. The nature and extent of this non-stationarity is most likely produced by several factors operating simultaneously. The aerodynamic flight environment and pilot commands provide continuously changing inputs, with a complex dynamic response that includes automatic feedback control from the engine regulator. It would appear that the combined effects operate primarily through an induced torque profile, which causes concomitant stress modulation at the individual internal gear meshes in the transmission. This notion is supported by several analyses, which show that upwards of 93% of the vibration signal s variance can be explained by knowledge of torque alone. That this relationship is stronger in an AH-1 than an OH-58, where measured non-stationarity is greater, suggests that the overall mass of the vehicle is an important consideration. In the lighter aircraft, the unsteady aerodynamic influences transmit relatively greater unsteady dynamic forces on the mechanical components, quite possibly contributing to its greater non-stationarity . In a recent paper using OH-58C pinion data [5], the authors have shown that in computing a time synchronous average (TSA) for various single-value metric computations, an effective trade-off can be obtained between sample size and measured stationarity by using data from only a single mesh cycle. A mesh cycle, which is defined as the number of rotations required for the gear teeth to return to their original mating position, has the property of representing all of the discrete phase angles of the opposing gears exactly once in the average. Measured stationarity is probably maximized because a single mesh cycle of the pinion gear occurs over a very short span of time, during which time-dependent non-stationary effects are kept to a minimum. Clearly, the advantage of local stationarity diminishes as the temporal duration of the cycle increases. This is most evident for a planetary mesh cycle, which can take several minutes to complete.

Huff, Edward M.↗

NASA NTRS2010

Transiting Planet Search in the Kepler Pipeline

The Kepler Mission simultaneously measures the brightness of more than 160,000 stars every 29.4 minutes over a 3.5-year mission to search for transiting planets. Detecting transits is a signal-detection problem where the signal of interest is a periodic pulse train and the predominant noise source is non-white, non-stationary (1/f) type process of stellar variability. Many stars also exhibit coherent or quasi-coherent oscillations. The detection algorithm first identifies and removes strong oscillations followed by an adaptive, wavelet-based matched filter. We discuss how we obtain super-resolution detection statistics and the effectiveness of the algorithm for Kepler flight data.

Jenkins, Jon M.↗