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At least 199 records · Page 11

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Canavos, G. C.↗

Aircraft System Identification from Multisine Inputs and Frequency Responses

A frequency-domain approach is described for estimating parameters, such as stability and control derivatives, in aircraft flight dynamic models from measured input and output data. The approach uses orthogonal phase-optimized multisines for moving the aircraft control effectors, Fourier analysis for computing multiple-input multiple-output frequency responses, and a maximum likelihood estimator called frequency response error (FRE) for determining values and uncertainties for the model parameters. The approach is demonstrated using flight test data for two subscale airplanes: the T-2 generic transport model and the X-56A aeroelastic demonstrator. Results and comparisons with the output-error method indicated that the approach produced accurate estimates of stability and control derivatives and their uncertainties from flight test data.

Grauer, Jared A.↗

Distributed parameter estimation for NASA Mini-Mast truss through displacement measurements

Most methods of system identification of large flexible structures by far are based on the lumped parameter approach. Because of the considerable computational burden due to the large number of unknown parameters, distributed parameter approach, which greatly decreases the number of unknowns, has being investigated. In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss has been formulated. Both Bernoulli-Euler beam and Timoshenko beam equations are used to characterize the lateral bending vibrations of the truss. The measurement of the lateral displacement at the tip of the truss is provided to the maximum likelihood estimator. Closed-form solutions of the partial differential equations and closed-form expressions of the sensitivity functions are derived so that the estimation algorithm is highly efficient. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from finite element analysis.

Huang, Jen-Kuang↗

Estimation of Aircraft Nonlinear Unsteady Parameters From Wind Tunnel Data

Aerodynamic equations were formulated for an aircraft in one-degree-of-freedom large amplitude motion about each of its body axes. The model formulation based on indicial functions separated the resulting aerodynamic forces and moments into static terms, purely rotary terms and unsteady terms. Model identification from experimental data combined stepwise regression and maximum likelihood estimation in a two-stage optimization algorithm that can identify the unsteady term and rotary term if necessary. The identification scheme was applied to oscillatory data in two examples. The model identified from experimental data fit the data well, however, some parameters were estimated with limited accuracy. The resulting model was a good predictor for oscillatory and ramp input data.

Klein, Vladislav↗

Aerodynamic parameter estimation via Fourier modulating function techniques

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Pearson, A. E.↗

The New NASA Orbital Debris Engineering Model ORDEM2000

The NASA Orbital Debris Program Office at Johnson Space Center has developed a new computer-based orbital debris engineering model, ORDEM2000, which describes the orbital debris environment in the low Earth orbit region between 200 and 2000 km altitude. The model is appropriate for those engineering solutions requiring knowledge and estimates of the orbital debris environment (debris spatial density, flux, etc.). ORDEM2000 can also be used as a benchmark for ground-based debris measurements and observations. We incorporated a large set of observational data, covering the object size range from 10 mm to 10 m, into the ORDEM2000 debris database, utilizing a maximum likelihood estimator to convert observations into debris population probability distribution functions. These functions then form the basis of debris populations. We developed a finite element model to process the debris populations to form the debris environment. A more capable input and output structure and a user-friendly graphical user interface are also implemented in the model. ORDEM2000 has been subjected to a significant verification and validation effort. This document describes ORDEM2000, which supersedes the previous model, ORDEM96. The availability of new sensor and in situ data, as well as new analytical techniques, has enabled the construction of this new model. Section 1 describes the general requirements and scope of an engineering model. Data analyses and the theoretical formulation of the model are described in Sections 2 and 3. Section 4 describes the verification and validation effort and the sensitivity and uncertainty analyses. Finally, Section 5 describes the graphical user interface, software installation, and test cases for the user.

Liou, Jer-Chyi↗

Statistics of Sxy estimates

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

Freilich, M. H.↗

Uncertainties in Estimates of the Risks of Late Effects from Space Radiation

The health risks faced by astronauts from space radiation include cancer, cataracts, hereditary effects, and non-cancer morbidity and mortality risks related to the diseases of the old age. Methods used to project risks in low-Earth orbit are of questionable merit for exploration missions because of the limited radiobiology data and knowledge of galactic cosmic ray (GCR) heavy ions, which causes estimates of the risk of late effects to be highly uncertain. Risk projections involve a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Within the linear-additivity model, we use Monte-Carlo sampling from subjective uncertainty distributions in each factor to obtain a Maximum Likelihood estimate of the overall uncertainty in risk projections. The resulting methodology is applied to several human space exploration mission scenarios including ISS, lunar station, deep space outpost, and Mar's missions of duration of 360, 660, and 1000 days. The major results are the quantification of the uncertainties in current risk estimates, the identification of factors that dominate risk projection uncertainties, and the development of a method to quantify candidate approaches to reduce uncertainties or mitigate risks. The large uncertainties in GCR risk projections lead to probability distributions of risk that mask any potential risk reduction using the "optimization" of shielding materials or configurations. In contrast, the design of shielding optimization approaches for solar particle events and trapped protons can be made at this time, and promising technologies can be shown to have merit using our approach. The methods used also make it possible to express risk management objectives in terms of quantitative objective's, i.e., the number of days in space without exceeding a given risk level within well defined confidence limits.

Cucinotta, F. A.↗

Local neighborhood transition probability estimation and its use in contextual classification

The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques for obtaining the optimal value of the parameter Theta as a maximum likelihood estimate from the local neighborhood of the pattern under consideration are developed.

Chittineni, C. B.↗

Technical guidance and analytic services in support of SEASAT-A

The design of a high resolution radar for altimetry and ocean wave height estimation was studied. From basic principles, it is shown that a short pulse wide beam radar is the most appropriate and recommended technique for measuring both altitude and ocean wave height. To achieve a topographic resolution of + or - 10 cm RMS at 5.0 meter RMS wave heights, as required for SEASAT-A, it is recommended that the altimeter design include an onboard adaptive processor. The resulting design, which assumes a maximum likelihood estimation (MLE) processor, is shown to satisfy all performance requirements. A design summary is given for the recommended radar altimeter, which includes a full deramp STRETCH pulse compression technique followed by an analog filter bank to separate range returns as well as the assumed MLE processor. The feedback loop implementation of the MLE on a digital computer was examined in detail, and computer size, estimation accuracies, and bias due to range sidelobes are given for the MLE with typical SEASAT-A parameters. The standard deviation of the altitude estimate was developed and evaluated for several adaptive and nonadaptive split-gate trackers. Split-gate tracker biases due to range sidelobes and transmitter noise are examined. An approximate closed form solution for the altimeter power return is derived and evaluated. The feasibility of utilizing the basic radar altimeter design for the measurement of ocean wave spectra was examined.

Brooks, W. L.↗

Cramer-Rao Bound for Gaussian Random Processes and Applications to Radar Processing of Atmospheric Signals

Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimates of the mean frequency, signal power, and spectral width of Doppler radar/lidar signals (a Gaussian random process) are presented. Approximate CRB's are derived using the Discrete Fourier Transform (DFT). These approximate results are equal to the exact CRB when the DFT coefficients are mutually uncorrelated. Previous high SNR limits for CRB's are shown to be inaccurate because the discrete summations cannot be approximated with integration. The performance of an approximate maximum likelihood estimator for mean frequency approaches the exact CRB for moderate signal to noise ratio and moderate spectral width.

Frehlich, Rod↗

A novel multistage estimation of the signal parameters of a possibly data-modulated sinusoid under very high dynamics

A novel multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data, and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity, acceleration and jerk of the GPS receiver. In the proposed multistage scheme, the first stage estimator operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second state of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first stage algorithm is selected to be a modified least squares algorithm operating upon the differential signal model and referred to as differential least squares. This estimation stage provides relatively coarse estimates of the frequency and its derivatives. The second algorithm is simply an extended Kalman filter which also yields the estimate of the phase along with a more refined estimate of frequency as well. A major advantage of the proposed algorithm is a reduction in the threshold on received carrier power-to-noise power spectral density ratio as compared to the threshold achievable by either of these algorithms alone. In fact, it appears from the simulations that for the case of an unmodulated carrier, the proposed scheme achieves the same threshold as for an almost exact and computationally intensive implementation of the maximum likelihood estimator.

Kumar, Rajendra↗

Predicting the Redshift 2 H-Alpha Luminosity Function Using [OIII] Emission Line Galaxies

Upcoming space-based surveys such as Euclid and WFIRST-AFTA plan to measure Baryonic Acoustic Oscillations (BAOs) in order to study dark energy. These surveys will use IR slitless grism spectroscopy to measure redshifts of a large number of galaxies over a significant redshift range. In this paper, we use the WFC3 Infrared Spectroscopic Parallel Survey (WISP) to estimate the expected number of H-alpha emitters observable by these future surveys. WISP is an ongoing Hubble Space Telescope slitless spectroscopic survey, covering the 0.8 - 1.65 micrometers wavelength range and allowing the detection of H-alpha emitters up to z approximately equal to 1.5 and [OIII] emitters to z approximately equal to 2.3. We derive the H-alpha-[OIII] bivariate line luminosity function for WISP galaxies at z approximately equal to 1 using a maximum likelihood estimator that properly accounts for uncertainties in line luminosity measurement, and demonstrate how it can be used to derive the H-alpha luminosity function from exclusively fitting [OIII] data. Using the z approximately equal to 2 [OIII] line luminosity function, and assuming that the relation between H-alpha and [OIII] luminosity does not change significantly over the redshift range, we predict the H-alpha number counts at z approximately equal to 2 - the upper end of the redshift range of interest for the future surveys. For the redshift range 0.7 less than z less than 2, we expect approximately 3000 galaxies per sq deg for a flux limit of 3 x 10(exp −16) ergs per sec per sq cm (the proposed depth of Euclid galaxy redshift survey) and approximately 20,000 galaxies per sq deg for a flux limit of approximately 10(exp −16) ergs per sec per sq cm (the baseline depth of WFIRST galaxy redshift survey).

Redshift↗

The application of parameter estimation to flight measurements to obtain lateral-directional stability derivatives of an augmented jet-flap STOL airplane

Flight experiments with an augmented jet flap STOL aircraft provided data from which the lateral directional stability and control derivatives were calculated by applying a linear regression parameter estimation procedure. The tests, which were conducted with the jet flaps set at a 65 deg deflection, covered a large range of angles of attack and engine power settings. The effect of changing the angle of the jet thrust vector was also investigated. Test results are compared with stability derivatives that had been predicted. The roll damping derived from the tests was significantly larger than had been predicted, whereas the other derivatives were generally in agreement with the predictions. Results obtained using a maximum likelihood estimation procedure are compared with those from the linear regression solutions.

Stephenson, J. D.↗

Radar satellite altimetry and ocean wave height estimation

The design of a radar satellite altimeter having a plus or minus 10 cm topographic resolution at 20 meter (peak-to-trough) ocean wave heights is described. In addition to altimetry, the resulting design also provides a measurement of significant wave height over the range of 1.0 to 20 meters to within plus or minus 10%. A full deramp pulse compression technique followed by an analog filter bank to separate individual range returns is used in the radar transmitter/receiver design to reduce the A/D converter bandwidth from a rather impractical 330 MHz to less than 1 MHz. The altimeter design utilizes an onboard maximum likelihood estimate (MLE) processor to achieve the plus or minus 10 cm topographic resolution. It is shown that an MLE processor provides simultaneous optimum (minimum variance) estimates of satellite altitude, ocean wave height and electromagnetic ocean surface reflectivity.

Dooley, R. P.↗

Distributed parameter modeling of the structural dynamics of the Solar Array Flight Experiment

A distributed-parameter model of the structural dynamics of the space-shuttle-deployed Solar Array Flight Experiment is developed and used to produce estimates of the modal frequencies and mode shapes. A lumped parameter version of the distributed model is used to estimate model characteristics by analyzing the measured responses of 32 targets. To make the modeling more tenable, a distributed parameter system is used to reduce the number of unknown parameters, a modified Newton-Raphson technique is used for rapid convergence, and a parallel processing supercomputer is used for more efficient computation. The performances of computers with a high-speed serial processor and with a high-speed parallel processor are compared. The best results are obtained with the modeling approach in which maximum likelihood estimation is applied to distributed parameter models.

Taylor, L. W., Jr.↗

Top-of-atmosphere radiative fluxes - Validation of ERBE scanner inversion algorithm using Nimbus-7 ERB data

The ERBE algorithm is applied to the Nimbus-7 earth radiation budget (ERB) scanner data for June 1979 to analyze the performance of an inversion method in deriving top-of-atmosphere albedos and longwave radiative fluxes. The performance is assessed by comparing ERBE algorithm results with appropriate results derived using the sorting-by-angular-bins (SAB) method, the ERB MATRIX algorithm, and the 'new-cloud ERB' (NCLE) algorithm. Comparisons are made for top-of-atmosphere albedos, longwave fluxes, viewing zenith-angle dependence of derived albedos and longwave fluxes, and cloud fractional coverage. Using the SAB method as a reference, the rms accuracy of monthly average ERBE-derived results are estimated to be 0.0165 (5.6 W/sq m) for albedos (shortwave fluxes) and 3.0 W/sq m for longwave fluxes. The ERBE-derived results were found to depend systematically on the viewing zenith angle, varying from near nadir to near the limb by about 10 percent for albedos and by 6-7 percent for longwave fluxes. Analyses indicated that the ERBE angular models are the most likely source of the systematic angular dependences. Comparison of the ERBE-derived cloud fractions, based on a maximum-likelihood estimation method, with results from the NCLE showed agreement within about 10 percent.

Suttles, John T.↗

Fan Beam Emission Tomography for Estimating Scalar Properties in Laminar Flames

A new method of estimating temperatures and gas species concentrations (CO2 and H2O) in a laminar flame is reported. The path-integrated, spectral radiation intensities emitted from a laminar flame at multiple wavelengths and view angles are calculated using a narrow band radiation model. Synthetic data, in the form of radial profiles of temperature and gas concentrations, are used in these calculations. The calculations mimic measurements that would theoretically be obtained using a mid-infrared spectrometer with a scanner. The path integrated spectral radiation intensities are deconvoluted using a maximum likelihood estimation method in conjunction with an iterative scheme. The deconvolution algorithm accounts for the self-absorption of radiation by the intervening gases, and provides the local temperature and gas species concentrations. The deconvoluted temperatures and gas concentrations are compared with the synthetic data used for calculating the spectral radiation intensities. The deconvoluted temperatures and gas species concentrations are within 0.5 % of the synthetic data. The deconvolution algorithm is expected to provide combustion researchers with an easy method of obtaining the radial profiles of major gas species concentrations and temperatures in laminar flames non-intrusively using a mid-infrared spectrometer with a scanner.

Lim, Jongmook↗