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NASA NTRS1976

A non-gaussian model of continuous atmospheric turbulence for use in aircraft design

A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.

Reeves, P. M.↗

NASA NTRS1999

Fluid Physics in a Fluctuating Acceleration Environment

Our program of research aims at developing a stochastic description of the residual acceleration field onboard spacecraft (g-jitter) to describe in quantitative detail its effect on fluid motion. Our main premise is that such a statistical description is necessary in those cases in which the characteristic time scales of the process under investigation are long compared with the correlation time of g-jitter. Although a clear separation between time scales makes this approach feasible, there remain several difficulties of practical nature: (i), g-jitter time series are not statistically stationary but rather show definite dependences on factors such as active or rest crew periods; (ii), it is very difficult to extract reliably the low frequency range of the power spectrum of the acceleration field. This range controls the magnitude of diffusive processes; and (iii), models used to date are Gaussian, but there is evidence that large amplitude disturbances occur much more frequently than a Gaussian distribution would predict. The lack of stationarity does not constitute a severe limitation in practice, since the intensity of the stochastic components changes very slowly during space missions (perhaps over times of the order of hours). A separate analysis of large amplitude disturbances has not been undertaken yet, but it does not seem difficult a priori to devise models that may describe this range better than a Gaussian distribution. The effect of low frequency components, on the other hand, is more difficult to ascertain, partly due to the difficulty associated with measuring them, and partly because they may be indistinguishable from slowly changing averages. This latter effect is further complicated by the lack of statistical stationarity of the time series. Recent work has focused on the effect of stochastic modulation on the onset of oscillatory instabilities as an example of resonant interaction between the driving acceleration and normal modes of the system, and on cavity flow as an example of how an oscillatory response under periodic driving becomes diffusive if the forcing is random instead. This paper describes three different topics that illustrate behavior that is peculiar to a stochastic acceleration field. In the first case, we show that g-jitter can induce effective attractive or repulsive forces between a pair of spherical particles that are suspended in an incompressible fluid of different density provided that the momentum diffusion length is larger than the interparticle separation (as in the case in most colloidal suspensions). Second, a stochastic modulation of the control parameter in the vicinity of a pitchfork or supercritical bifurcation is known not to affect the location of the threshold. We show, however, that resonance between the modulation and linearly stable modes close to onset can lead to a shift in threshold. Finally, we discuss the classical problem of vorticity diffusion away from a plane boundary that is being vibrated along its own plane. Periodic motion with zero average vorticity production results in an exponential decay of the vorticity away from the boundary. Random vibration, on the other hand, results in power law decay away from the boundary even if vorticity production averages to zero.

Drolet, Francois↗

NASA NTRS2019

Automated Classification of Transient Contamination in Stationary Acoustic Data

An automated procedure for the classification of transient contamination of stationary acoustic data is proposed and analyzed. The procedure requires the assumption that the stationary acoustic data of interest can be modeled as a band-limited, Gaussian random process. It also requires that the transient contamination be of higher variance than the acoustic data of interest. When these assumptions are satisfied, it is a blind separation procedure, aside from the initial input specifying how to subdivide the time series of interest. No a priori threshold criterion is required. Simulation results show that for a sufficient number of blocks, the method performs well, as long as the occasional false positive or false negative is acceptable. The effectiveness of the procedure is demonstrated with an application to experimental wind tunnel acoustic test data which are contaminated by hydrodynamic gusts.

Bahr, Christopher J.↗

NASA NTRS2019

Automated Classification of Transient Contamination in Stationary Acoustic Data

binary classification↗

NASA NTRS1976

Some new results on the statistics of radio wave scintillation. I - Empirical evidence for Gaussian statistics

This paper presents an analysis of ionospheric scintillation data which shows that the underlying statistical structure of the signal can be accurately modeled by the additive complex Gaussian perturbation predicted by the Born approximation in conjunction with an application of the central limit theorem. By making use of this fact, it is possible to estimate the in-phase, phase quadrature, and cophased scattered power by curve fitting to measured intensity histograms. By using this procedure, it is found that typically more than 80% of the scattered power is in phase quadrature with the undeviated signal component. Thus, the signal is modeled by a Gaussian, but highly non-Rician process. From simultaneous UHF and VHF data, only a weak dependence of this statistical structure on changes in the Fresnel radius is deduced. The signal variance is found to have a nonquadratic wavelength dependence. It is hypothesized that this latter effect is a subtle manifestation of locally homogeneous irregularity structures, a mathematical model proposed by Kolmogorov (1941) in his early studies of incompressible fluid turbulence.

Rino, C. L.↗

NASA NTRS2021

Hot planets around cool stars – two short-period mini-Neptunes transiting the late K-dwarf TOI-1260

We present the discovery and characterization of two sub-Neptunes in close orbits, as well as a tentative outer planet of a similar size, orbiting TOI-1260 – a low metallicity K6 V dwarf star. Photometry from Transiting Exoplanet Survey Satellite(TESS) yields radii of R(b) = 2.33 ± 0.10 and R(c) = 2.82 ± 0.15 Rꚛ, and periods of 3.13 and 7.49 d for TOI-1260 b and TOI-1260 c, respectively. We combined the TESS data with a series of ground-based follow-up observations to characterize the planetary system. From HARPS-N high-precision radial velocities we obtain M(b) = 8.6(+1.4,−1.5) and M(c) = 11.8(+3.4,−3.2) Mꚛ. The star is moderately active with a complex activity pattern, which necessitated the use of Gaussian process regression for both the light-curve detrending and the radial velocity modelling, in the latter case guided by suitable activity indicators. We successfully disentangle the stellar-induced signal from the planetary signals, underlining the importance and usefulness of the Gaussian process approach. We test the system’s stability against atmospheric photoevaporation and find that the TOI-1260 planets are classic examples of the structure and composition ambiguity typical for the 2–3 Rꚛ range.

I Y Georgieva↗

NASA NTRS1971

Two stochastic models for simulation of correlated random processes

Mathematical models for simulation of correlated stochastic processes with stationary Gaussian properties

Hoshiya, M.↗

NASA NTRS1977

A qualitative assessment of a random process proposed as an atmospheric turbulence model

A random process is formed by the product of two Gaussian processes and the sum of that product with a third Gaussian process. The resulting total random process is interpreted as the sum of an amplitude modulated process and a slowly varying, random mean value. The properties of the process are examined, including an interpretation of the process in terms of the physical structure of atmospheric motions. The inclusion of the mean value variation gives an improved representation of the properties of atmospheric motions, since the resulting process can account for the differences in the statistical properties of atmospheric velocity components and their gradients. The application of the process to atmospheric turbulence problems, including the response of aircraft dynamic systems, is examined. The effects of the mean value variation upon aircraft loads are small in most cases, but can be important in the measurement and interpretation of atmospheric turbulence data.

Sidwell, K.↗

NASA NTRS2012

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Mashiku, Alinda↗

NASA NTRS2004

Unfolding of Proteins: Thermal and Mechanical Unfolding

We have employed a Hamiltonian model based on a self-consistent Gaussian appoximation to examine the unfolding process of proteins in external - both mechanical and thermal - force elds. The motivation was to investigate the unfolding pathways of proteins by including only the essence of the important interactions of the native-state topology. Furthermore, if such a model can indeed correctly predict the physics of protein unfolding, it can complement more computationally expensive simulations and theoretical work. The self-consistent Gaussian approximation by Micheletti et al. has been incorporated in our model to make the model mathematically tractable by signi cantly reducing the computational cost. All thermodynamic properties and pair contact probabilities are calculated by simply evaluating the values of a series of Incomplete Gamma functions in an iterative manner. We have compared our results to previous molecular dynamics simulation and experimental data for the mechanical unfolding of the giant muscle protein Titin (1TIT). Our model, especially in light of its simplicity and excellent agreement with experiment and simulation, demonstrates the basic physical elements necessary to capture the mechanism of protein unfolding in an external force field.

Hur, Joe S.↗

NASA NTRSDate not supplied

Estimation With Range Dependent Sensor Model

This paper focuses on the improvement of target tracking accuracy taking into account the sensor’s reading degradation as the relative range increases. The approach is based on the assumption that range measurement error depends on the actual range. Specifically, we model the measurement error as a proportional to the actual range term plus a zero-mean, Gaussian distributed, and uncorrelated process. We present two approaches to tracking a target with constant velocity model. The first approach uses Extended Kalman Filter (EKF) framework to estimate target's states and the unknown proportionality coefficient with linearization on the observation model on the predicted states at each time step. The second one uses a measurement conversion method to estimate the target's scaled by the unknown constant term states, which is shown to be unbiased. This conversion results in linear state and observation models, hence the standard Kalman filter can be applied. The actual target state is computed by application of back scaling with the estimate of unknown scale factor. We evaluate the approaches in desktop simulations.

Target tracking↗

NASA NTRS1977

A mathematical study of a random process proposed as an atmospheric turbulence model

A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

Sidwell, K.↗

NASA NTRS1995

Improved Gaussian Beam-Scattering Algorithm

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Lock, James A.↗

NASA NTRSDate not supplied

PM 2.5 Concentrations over Major Metropolitan Regions Inferred from Airborne High Spectral Resolution Lidar Measurements Using Machine Learning Regression

We use measurements of near-surface aerosol backscatter, extinction, and depolarization acquired by four NASA Langley Research Center airborne High Spectral Resolution Lidars (HSRLs) to develop a machine learning regression methodology to infer PM2.5 concentrations at the surface and aloft. These airborne HSRL measurements were acquired over major metropolitan regions in the United States and Asia during more than 170 flights since 2010. Hourly surface PM2.5 measurements from the EPA air quality system and similar networks in other countries acquired within 10 km and 15 minutes of these near-surface HSRL measurements are used to train models that compute PM2.5 concentrations from the HSRL measurements. We examine several regression methods and find that exponential Gaussian Process algorithms consistently give the best performance in terms of the lowest root-mean-square (RMS) errors and the highest correlations. Model performance varies significantly depending on various combinations of HSRL aerosol measurements (e.g., aerosol backscatter, extinction, depolarization, backscatter color ratios, lidar ratios, aerosol optical thickness) and retrievals (e.g., mixed layer height, aerosol type) used in the regressions. Models that use near-surface measurements of aerosol backscatter and aerosol intensive properties such as depolarization, backscatter color ratio, and lidar ratio typically give the best performance with RMS errors around 4 mg/m3 and correlation coefficients above 0.9. HSRL measurements were often acquired when the aircraft flew systematic “raster-scan” patterns for several hours over these cities. These flight patterns enabled measurements of the spatial, temporal, and vertical variabilities in the distributions of aerosol backscatter and aerosol intensive properties and allowed us to derive the corresponding variabilities in PM2.5 concentrations. We present examples of such variabilities over urban areas in the United States as well as Asia. We describe also how the distribution of surface PM2.5 varies with aerosol type and use these retrievals to examine model simulations of surface PM2.5 in these metropolitan regions. We also discuss how this methodology may be applied to measurements from satellite lidars such as CALIOP on CALIPSO and ATLID on EarthCARE.

lidar↗

NASA NTRS2022

Searching for Quasi-periodic Oscillations in Astrophysical Transients Using Gaussian Processes

Analyses of quasi-periodic oscillations(QPOs)are important to understanding the dynamic behavior in manyastrophysical objects during transient events like gamma-ray bursts, solarflares, magnetarflares, and fast radiobursts. Astrophysicists often search for QPOs with frequency-domain methods such as(Lomb–Scargle)periodograms, which generally assume power-law models plus some excess around the QPO frequency. Time-series data can alternatively be investigated directly in the time domain using Gaussian process(GP)regression.While GP regression is computationally expensive in the general case, the properties of astrophysical data andmodels allow fast likelihood strategies. Heteroscedasticity and nonstationarity in data have been shown to causebias in periodogram-based analyses. GPs can take account of these properties. Using GPs, we model QPOs as astochastic process on top of a deterministicflare shape. Using Bayesian inference, we demonstrate how to infer GPhyperparameters and assign them physical meaning, such as the QPO frequency. We also perform model selectionbetween QPOs and alternative models such as red noise and show that this can be used to reliablyfind QPOs. Thismethod is easily applicable to a variety of different astrophysical data sets. We demonstrate the use of this methodon a range of short transients: a gamma-ray burst, a magnetarflare, a magnetar giantflare, and simulated solarflare data.

Moritz Hubner↗

NASA NTRS1997

Predictive Attitude Estimation Using Global Positioning System Signals

In this paper, a new algorithm is developed for attitude estimation using Global Positioning System (GPS) signals. The new algorithm is based on a predictive filtering scheme designed for spacecraft without rate measuring devices. The major advantage of this new algorithm over traditional Kalman filter approaches is that the model error is not assumed to represented by an unbiased Gaussian noise process with known covariance, but instead is determined during the estimation process. This is achieved by simultaneously solving system optimality conditions and an output error constraint. This approach is well suited for GPS attitude estimation since some error sources that contribute to attitude inaccuracy, such as signal multipath, are known to be non-Gaussian processes. Also, the predictive filter scheme can use either GPS signals or vector observations or a combination of both for attitude estimation, so that performance characteristics can be maintained during periods of GPS attitude sensor outage. The performance of the new algorithm is tested using flight data from the REX-2 spacecraft. Results are shown using the predictive filter to estimate the attitude from both GPS signals and magnetometer measurements, and comparing that solution to a magnetometer-only based solution. Results using the new estimation algorithm indicate that GPS-based solutions are verified to within 2 degrees using the magnetometer cross-check for the REX-2 spacecraft. GPS attitude accuracy of better than 1 degree is expected per axis, but cannot be reliably proven due to inaccuracies in the magnetic field model.

Crassidis, John L.↗

NASA NTRS2005

Adaptive Filtering Using Recurrent Neural Networks

A method for adaptive (or, optionally, nonadaptive) filtering has been developed for estimating the states of complex process systems (e.g., chemical plants, factories, or manufacturing processes at some level of abstraction) from time series of measurements of system inputs and outputs. The method is based partly on the fundamental principles of the Kalman filter and partly on the use of recurrent neural networks. The standard Kalman filter involves an assumption of linearity of the mathematical model used to describe a process system. The extended Kalman filter accommodates a nonlinear process model but still requires linearization about the state estimate. Both the standard and extended Kalman filters involve the often unrealistic assumption that process and measurement noise are zero-mean, Gaussian, and white. In contrast, the present method does not involve any assumptions of linearity of process models or of the nature of process noise; on the contrary, few (if any) assumptions are made about process models, noise models, or the parameters of such models. In this regard, the method can be characterized as one of nonlinear, nonparametric filtering. The method exploits the unique ability of neural networks to approximate nonlinear functions. In a given case, the process model is limited mainly by limitations of the approximation ability of the neural networks chosen for that case. Moreover, despite the lack of assumptions regarding process noise, the method yields minimum- variance filters. In that they do not require statistical models of noise, the neural- network-based state filters of this method are comparable to conventional nonlinear least-squares estimators.

Parlos, Alexander G.↗

NASA NTRS1996

Report on 3 and 4-point correlation statistics in the COBE DMR anisotrophy maps

As part of the work performed under NASA contract # NAS5-32648, we have computed the 3-point and 4-point correlation functions of the COBE-DNIR 2-year and 4-year anisotropy maps. The motivation for this study was to search for evidence of non-Gaussian statistical fluctuations in the temperature maps: skewness or asymmetry in the case of the 3-point function, kurtosis in the case of the 4-point function. Such behavior would have very significant implications for our understanding of the processes of galaxy formation, because our current models of galaxy formation predict that non-Gaussian features should not be present in the DMR maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data. Our computation and analysis of 3-point correlations in the 2-year DMR maps was published in the Astrophysical Journal Letters, volume 446, page L67, 1995. Our computation and analysis of 3-point correlations in the 4-year DMR maps will be published, together with some additional tests, in the June 10, 1996 issue of the Astrophysical Journal Letters. Copies of both of these papers are attached as an appendix to this report.

Hinshaw, Gary↗