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Maximum likelihood estimation of label imperfection probabilities and its use in the identification of mislabeled patterns

Estimating label imperfections and the use of estimations in the identification of mislabeled patterns are discussed. Expressions are presented for the asymptotic variances of the probability of correct classification and proportion, and for the maximum likelihood estimates of classification errors and a priori probabilities. Models are developed for imperfections in the labels and classification errors, and expressions are derived for the probability of imperfect label identification schemes resulting in wrong decisions. The expressions are used in computing thresholds and the techniques are given practical applications. The imperfect label identification scheme in the multiclass case is found to amount to establishing a region around each decision surface, and decisions of the label correction scheme are found in close agreement with the analyst-interpreter interpretations of the imagery films. As an example, the application of the maximum likelihood estimation to the processing of Landsat MSS data is discussed.

Chittineni, C. B.↗

Monte Carlo studies of ocean wind vector measurements by SCATT: Objective criteria and maximum likelihood estimates for removal of aliases, and effects of cell size on accuracy of vector winds

The scatterometer on the National Oceanic Satellite System (NOSS) is studied by means of Monte Carlo techniques so as to determine the effect of two additional antennas for alias (or ambiguity) removal by means of an objective criteria technique and a normalized maximum likelihood estimator. Cells nominally 10 km by 10 km, 10 km by 50 km, and 50 km by 50 km are simulated for winds of 4, 8, 12 and 24 m/s and incidence angles of 29, 39, 47, and 53.5 deg for 15 deg changes in direction. The normalized maximum likelihood estimate (MLE) is correct a large part of the time, but the objective criterion technique is recommended as a reserve, and more quickly computed, procedure. Both methods for alias removal depend on the differences in the present model function at upwind and downwind. For 10 km by 10 km cells, it is found that the MLE method introduces a correlation between wind speed errors and aspect angle (wind direction) errors that can be as high as 0.8 or 0.9 and that the wind direction errors are unacceptably large, compared to those obtained for the SASS for similar assumptions.

Pierson, W. J.↗

Further observations on maximum likelihood estimates of stability and control characteristics obtained from flight data

A maximum likelihood estimation method for flight test data is described. Flight results based on 3000 maneuvers from 30 aircraft on the effect of resolution and sampling rate on the estimates, on understanding the discrepancies previously observed in the magnitude of the Cramer-Rao bounds, on the scale effects on the derivative estimates obtained from dynamic aircraft flight maneuvers, and on the analysis of lateral-directional maneuvers obtained in turbulence, are presented.

Iliff, K. W.↗

An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities

An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm.

Murphy, P. C.↗

Maximum-likelihood analysis of the COBE angular correlation function

We have used maximum-likelihood estimation to determine the quadrupole amplitude Q(sub rms-PS) and the spectral index n of the density fluctuation power spectrum at recombination from the COBE DMR data. We find a strong correlation between the two parameters of the form Q(sub rms-PS) = (15.7 +/- 2.6) exp (0.46(1 - n)) microK for fixed n. Our result is slightly smaller than and has a smaller statistical uncertainty than the 1992 estimate of Smoot et al.

Seljak, Uros↗

Maximum Likelihood Estimation of Spectra Information from Multiple Independent Astrophysics Data Sets

The Maximum Likelihood (ML) statistical theory required to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments is developed in this paper. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral information based on the combination of data sets. The procedure is of significant value to both existing data sets and those to be produced by future astrophysics missions consisting of two or more detectors by allowing instrument developers to optimize each detector's design parameters through simulation studies in order to design and build complementary detectors that will maximize the precision with which the science objectives may be obtained. The benefits of this ML theory and its application is measured in terms of the reduction of the statistical errors (standard deviations) of the spectra information using the multiple data sets in concert as compared to the statistical errors of the spectra information when the data sets are considered separately, as well as any biases resulting from poor statistics in one or more of the individual data sets that might be reduced when the data sets are combined.

Howell, Leonard W., Jr.↗

The Implementation of Maximum Likelihood Estimation in Space Launch System Vehicle Design

The Space Launch System uses a Maximum Likelihood Estimation process in conjunction with Design of Experiments to develop statistically representative vehicles for the Block 1 configuration. These vehicles are then used to estimate maximum load conditions for simulating stressing cases in other simulations. This paper discusses the modeling process and how SLS captures manufacturing uncertainty in the launch vehicle design. It also provides an overview of the differences between Block 1 statistical representations. This paper also discusses proper grid choice as well as which uncertainties drive the vehicle design.

Stein, W. B.↗

Practical aspects of a maximum likelihood estimation method to extract stability and control derivatives from flight data

A maximum likelihood estimation method was applied to flight data and procedures to facilitate the routine analysis of a large amount of flight data were described. Techniques that can be used to obtain stability and control derivatives from aircraft maneuvers that are less than ideal for this purpose are described. The techniques involve detecting and correcting the effects of dependent or nearly dependent variables, structural vibration, data drift, inadequate instrumentation, and difficulties with the data acquisition system and the mathematical model. The use of uncertainty levels and multiple maneuver analysis also proved to be useful in improving the quality of the estimated coefficients. The procedures used for editing the data and for overall analysis are also discussed.

Iliff, K. W.↗

Maximum likelihood tuning of a vehicle motion filter

This paper describes the use of maximum likelihood parameter estimation unknown parameters appearing in a nonlinear vehicle motion filter. The filter uses the kinematic equations of motion of a rigid body in motion over a spherical earth. The nine states of the filter represent vehicle velocity, attitude, and position. The inputs to the filter are three components of translational acceleration and three components of angular rate. Measurements used to update states include air data, altitude, position, and attitude. Expressions are derived for the elements of filter matrices needed to use air data in a body-fixed frame with filter states expressed in a geographic frame. An expression for the likelihood functions of the data is given, along with accurate approximations for the function's gradient and Hessian with respect to unknown parameters. These are used by a numerical quasi-Newton algorithm for maximizing the likelihood function of the data in order to estimate the unknown parameters. The parameter estimation algorithm is useful for processing data from aircraft flight tests or for tuning inertial navigation systems.

Trankle, Thomas L.↗