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NASA NTRS1989

Frequency estimation techniques for high dynamic trajectories

A comparison is presented of four different estimation techniques applied to the problem of continuously estimating the rapidly varying parameters of a sinusoidal signal, observed in the presence of additive noise. Frequency estimates are emphasized, although phase and/or frequency rate are also estimated by some of the algorithms. These parameters are related to the velocity, position, and acceleration of the maneuvering receiver or transmitter. Estimated performance at low carrier-to-noise ratios and high dynamics is investigated for the purpose of determining the useful operating range of an approximate maximum-likelihood estimator, an extended Kalman filter, a cross-product automatic frequency loop, and a phase-locked loop. Numerical simulations are used to evaluate performance while tracking a common trajectory exhibiting high dynamics.

Vilnrotter, Victor A.↗

NASA NTRS2010

Using MERRA Gridded Innovations for Quantifying Uncertainties in Analysis Fields and Diagnosing Observing System Inhomogeneities

MERRA is a NASA reanalysis for the satellite era using a major new version of the Goddard Earth Observing System Data Assimilation System Version 5 (GEOS-5). The project focuses on historical analyses of the hydrological cycle on a broad range of weather and climate time scales and places the NASA EOS suite of observations in a climate context. The characterization of uncertainty in reanalysis fields is a commonly requested feature by users of such data. While intercomparison with reference data sets is common practice for ascertaining the realism of the datasets, such studies typically are restricted to long term climatological statistics and seldom provide state dependent measures of the uncertainties involved. In principle, variational data assimilation algorithms have the ability of producing error estimates for the analysis variables (typically surface pressure, winds, temperature, moisture and ozone) consistent with the assumed background and observation error statistics. However, these "perceived error estimates" are expensive to obtain and are limited by the somewhat simplistic errors assumed in the algorithm. The observation minus forecast residuals (innovations) by-product of any assimilation system constitutes a powerful tool for estimating the systematic and random errors in the analysis fields. Unfortunately, such data is usually not readily available with reanalysis products, often requiring the tedious decoding of large datasets and not so-user friendly file formats. With MERRA we have introduced a gridded version of the observations/innovations used in the assimilation process, using the same grid and data formats as the regular datasets. Such dataset empowers the user with the ability of conveniently performing observing system related analysis and error estimates. The scope of this dataset will be briefly described. We will present a systematic analysis of MERRA innovation time series for the conventional observing system, including maximum-likelihood estimates of background and observation errors, as well as global bias estimates. Starting with the joint PDF of innovations and analysis increments at observation locations we propose a technique for diagnosing bias among the observing systems, and document how these contextual biases have evolved during the satellite era covered by MERRA.

da Silva, Arlindo↗

NASA NTRS1971

Estimating the proportions of objects within a single resolution element of a multispectral scanner.

Description of a procedu*e designed to estimate the proportions of objects and materials contained in the instantaneous field of view (IFOV) of an airborne multispectral device. A mathematical model is derived to relate the signature of a combination of materials in a resolution cell to the signatures of the individual materials considered. Estimation algorithms are generated and digital computer programs are prepared to apply the algorithms in the description of the effects which are observed when several objects are viewed simultaneously. The maximum likelihood estimate of the proportions of various individual materials in an IFOV is discussed. A simulation program is proposed for such estimates. A procedure for analyzing the geometric relations of signatures which affect the accuracy of estimates is set forth.

Horwitz, H. M.↗

NASA NTRS1973

Estimation of proportions of objects and determination of training sample-size in a remote sensing application

A multichannel scanning device may fail to observe objects because of obstructions blocking the view, or different categories of objects may make up a resolution element giving rise to a single observation. Ground truth will be required on any such categories of objects in order to estimate their expected proportions associated with various classes represented in the remote sensing data. Considering the classes to be distributed as multivariate normal with different mean vectors and common covariance, maximum likelihood estimates are given for the expected proportions of objects associated with different classes, using the Bayes procedure for classification of individuals obtained from these classes. An approximate solution for simultaneous confidence intervals on these proportions is given, and thereby a sample-size needed to achieve a desired amount of accuracy for the estimates is determined.

Chhikara, R. S.↗

NASA NTRS1972

Evaluation of errors in prior mean and variance in the estimation of integrated circuit failure rates using Bayesian methods

The critical point of any Bayesian analysis concerns the choice and quantification of the prior information. The effects of prior data on a Bayesian analysis are studied. Comparisons of the maximum likelihood estimator, the Bayesian estimator, and the known failure rate are presented. The results of the many simulated trails are then analyzed to show the region of criticality for prior information being supplied to the Bayesian estimator. In particular, effects of prior mean and variance are determined as a function of the amount of test data available.

Fletcher, B. C.↗

NASA NTRS1997

Extraction of Lateral-Directional Stability and Control Derivatives for the Basic F-18 Aircraft at High Angles of Attack

The results of parameter identification to determine the lateral-directional stability and control derivatives of an F-18 research aircraft in its basic hardware and software configuration are presented. The derivatives are estimated from dynamic flight data using a specialized identification program developed at NASA Dryden Flight Research Center. The formulation uses the linearized aircraft equations of motions in their continuous/discrete form and a maximum likelihood estimator that accounts for both state and measurement noise. State noise is used to model the uncommanded forcing function caused by unsteady aerodynamics, such as separated and vortical flows, over the aircraft. The derivatives are plotted as functions of angle of attack between 3 deg and 47 deg and compared with wind-tunnel predictions. The quality of the derivative estimates obtained by parameter identification is somewhat degraded because the maneuvers were flown with the aircraft's control augmentation system engaged, which introduced relatively high correlations between the control variables and response variables as a result of control motions from the feedback control system.

Iliff, Kenneth W.↗

NASA NTRS1990

Experiments in on-orbit identification for control of space structures

Two extensions to an earlier work on system identification for large flexible structures are presented. The first extension applies an integrated frequency-domain ID approach to experiments utilizing rib root actuators for full system excitation of both 'boom-dish' and 'dish' modes of the structure; while the second extension employs a time-domain identification, utilizing frequency-domain results obtained for initialization of the parameter estimates. For the first extension, the results show that in the presence of closely packed modes, the curve-fit algorithm employed can distinguish modes with frequency separation as small as 0.04 Hz. The maximum likelihood estimation used in the second extension produce estimates close to the parametric modal values of frequencies and damping.

Yam, Y.↗

NASA NTRS1991

A finite mixtures algorithm for finding classes in images

The authors describe an algorithm for estimating the proportions of classes in a SAR (synthetic aperture radar) image without any user interaction. The method assumes that the image is a mixture of a known number of different pixel types. A maximum likelihood estimate of the parameters of the resulting mixture distribution is then used to find the proportions for the various classes. The technique was successfully applied to aircraft SAR images of sea ice. Computer simulations were used to determine the relative errors of the technique. The technique performs well even with extremely noisy images.

Samadani, Ramin↗

NASA NTRS2012

Achievable Precision for Optical Ranging Systems

Achievable RMS errors in estimating the phase, frequency, and intensity of a direct-detected intensity-modulated optical pulse train are presented. For each parameter, the Cramer-Rao-Bound (CRB) is derived and the performance of the Maximum Likelihood estimator is illustrated. Approximations to the CRBs are provided, enabling an intuitive understanding of estimator behavior as a function of the signaling parameters. The results are compared to achievable RMS errors in estimating the same parameters from a sinusoidal waveform in additive white Gaussian noise. This establishes a framework for a performance comparison of radio frequency (RF) and optical science. Comparisons are made using parameters for state-of-the-art deep-space RF and optical links. Degradations to the achievable errors due to clock phase noise and detector jitter are illustrated.

estimation theory↗

NASA NTRS1978

Estimation of the sea surface's two-scale backscatter parameters

The relationship between the sea-surface normalized radar cross section and the friction velocity vector is determined using a parametric two-scale scattering model. The model parameters are found from a nonlinear maximum likelihood estimation. The estimation is based on aircraft scatterometer measurements and the sea-surface anemometer measurements collected during the JONSWAP '75 experiment. The estimates of the ten model parameters converge to realistic values that are in good agreement with the available oceanographic data. The rms discrepancy between the model and the cross section measurements is 0.7 db, which is the rms sum of a 0.3 db average measurement error and a 0.6 db modeling error.

Wentz, F. J.↗

NASA NTRS1986

Application of parameter estimation to highly unstable aircraft

This paper discusses the application of parameter estimation to highly unstable aircraft. It includes a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

Maine, R. E.↗

NASA NTRS1986

Application of parameter estimation to highly unstable aircraft

The application of parameter estimation to highly unstable aircraft is discussed. Included are a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

Maine, R. E.↗

NASA NTRS1986

First diurnal results from the Earth Radiation Budget Experiment

Early results are reported from measurements of the diurnal variability of total and clear-sky regional radiative parameters by the ERBE instruments on one dedicated satellite and the polar-orbiting NOAA-9 satellite. Attention is focused on November 1984, the first complete data set. The scene is identified in terms of longwave and shortwave radiances (daytime) or longwave radiation (night) and maximum likelihood estimates carried out with the addition of Earth Radiation Budget data from Nimbus-7. Analysis of the first data set revealed significant differences between total and clear-sky albedo. The clear-sky and LRE both reach maximum around noon and minimum values at midnight.

Harrison, E. F.↗

NASA NTRS1988

Modal identification using single-mode projection filters and comparison with ERA and MLE results

The Single-Mode Projection Filter (SPF) is a newly developed algorithm for eigensystem parameter identification from both analytical results and test data. The SPF is formulated with a single mode only and practical for parallel processing implementation. Explicit formulations of SPF are derived for the multi-input multi-output (MIMO) system by using the orthogonal matrices of the controllability and observability matrices in the general sense. The modal parameters of SPF are initially obtained from an analytical model in modal space. The experimental data are then processed through SPF to update its modal parameters and to minimize a cost function defined by the norm of an error matrix. The updated modal parameters represent the characteristics of the test data. A two-dimensional global minimum optimization algorithm is developed and applied for the filter update by using the interval analysis method. The SPF is developed based on a single-mode subsystem and identifies only one modal frequency and one modal damping within a specified region. For an n-modes structure, n SPF can be implemented for parallel processing to reduce the computational burden. The SPF is applied to analyze the simulated data for the MAST beam structure. The estimated modal parameters are comparable to those from the Eigensystem Realization Algorithm (ERA) and repeated modal frequencies are identified. The modal analysis of the Spacecraft Control Laboratory Experiment (SCOLE) data is also performed by using the ERA and the Maximum Likelihood Estimate (MLE). The result shows that the first five modal frequencies are very close from ERA and MLE. However, there are slight disparities in the damping rates and the computational burdens are quite different among these two algorithms.

Huang, Jen-Kuang↗

NASA NTRS1973

Bayesian estimation of life parameters in the Weibull distribution.

Development of a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter theta, Bayesian estimates of theta and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results (1967) for the one-parameter exponential life-testing distribution are reduced to a special case of these results. A fully Bayesian analysis of both the scale and shape parameters is developed by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of Monte Carlo simulation and numerical-integration techniques. In both cases, a computer simulation is carried out, and a comparison is made between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.

Canavos, G. C.↗

NASA NTRS1993

Lunar gravitational field estimation and the effects of mismodeling upon lunar satellite orbit prediction

Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.

Davis, John H.↗

NASA NTRS1981

Estimation of proportions in mixed pixels through their region characterization

A region of mixed pixels can be characterized through the probability density function of proportions of classes in the pixels. Using information from the spectral vectors of a given set of pixels from the mixed pixel region, expressions are developed for obtaining the maximum likelihood estimates of the parameters of probability density functions of proportions. The proportions of classes in the mixed pixels can then be estimated. If the mixed pixels contain objects of two classes, the computation can be reduced by transforming the spectral vectors using a transformation matrix that simultaneously diagonalizes the covariance matrices of the two classes. If the proportions of the classes of a set of mixed pixels from the region are given, then expressions are developed for obtaining the estmates of the parameters of the probability density function of the proportions of mixed pixels. Development of these expressions is based on the criterion of the minimum sum of squares of errors. Experimental results from the processing of remotely sensed agricultural multispectral imagery data are presented.

Chittineni, C. B.↗

NASA NTRS1973

Estimation in a modified binomial distribution

Estimation techniques in a modified binomial distribution, developed to describe thunderstorm activity over a small area at Cape Kennedy, Florida, are compared. A compound model is also developed and compared with the original model. The minimum Chi square technique is compared with the maximum likelihood and method of moments techniques. The minimum Chi square technique, although useful in complicated models, compared poorly compared to the other techniques. The maximum likelihood and method of moments were comparable. The compound model fit better in every case based on a likelihood ratio test comparing the compound model with the modified binomial model using maximum likelihood estimators.

Carter, M. C.↗