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NASA NTRS1982

Topics in global convergence of density estimates

The problem of estimating a density f on R sup d from a sample Xz(1),...,X(n) of independent identically distributed random vectors is critically examined, and some recent results in the field are reviewed. The following statements are qualified: (1) For any sequence of density estimates f(n), any arbitrary slow rate of convergence to 0 is possible for E(integral/f(n)-fl); (2) In theoretical comparisons of density estimates, integral/f(n)-f/ should be used and not integral/f(n)-f/sup p, p 1; and (3) For most reasonable nonparametric density estimates, either there is convergence of integral/f(n)-f/ (and then the convergence is in the strongest possible sense for all f), or there is no convergence (even in the weakest possible sense for a single f). There is no intermediate situation.

Devroye, L.↗
NASA NTRS1983

Estimating proportions of materials using mixture models

An approach to proportion estimation based on the notion of a mixture model, appropriate parametric forms for a mixture model that appears to fit observed remotely sensed data, methods for estimating the parameters in these models, methods for labelling proportion determination from the mixture model, and methods which use the mixture model estimates as auxiliary variable values in some proportion estimation schemes are addressed.

Heydorn, R. P.↗
NASA NTRS1982

Validation of Nimbus-7 temperature-humidity infrared radiometer estimates of cloud type and amount

Estimates of clear and low, middle and high cloud amount in fixed geographical regions approximately (160 km) squared are being made routinely from 11.5 micron radiance measurements of the Nimbus-7 Temperature-Humidity Infrared Radiometer (THIR). The purpose of validation is to determine the accuracy of the THIR cloud estimates. Validation requires that a comparison be made between the THIR estimates of cloudiness and the 'true' cloudiness. The validation results reported in this paper use human analysis of concurrent but independent satellite images with surface meteorological and radiosonde observations to approximate the 'true' cloudiness. Regression and error analyses are used to estimate the systematic and random errors of THIR derived clear amount.

Stowe, L. L.↗
NASA NTRS1982

Least-squares sequential parameter and state estimation for large space structures

This paper presents the formulation of simultaneous state and parameter estimation problems for flexible structures in terms of least-squares minimization problems. The approach combines an on-line order determination algorithm, with least-squares algorithms for finding estimates of modal approximation functions, modal amplitudes, and modal parameters. The approach combines previous results on separable nonlinear least squares estimation with a regression analysis formulation of the state estimation problem. The technique makes use of sequential Householder transformations. This allows for sequential accumulation of matrices required during the identification process. The technique is used to identify the modal prameters of a flexible beam.

Thau, F. E.↗
NASA NTRS1983

Applications of state estimation in aircraft flight-data analysis

This paper traces the evolution of the use of state estimation in the analysis of aircraft flight data and discusses some recent applications associated with airline turbulence upsets and high-angle-of-attack flight tests. A unifying mathematical framework for state estimation is reviewed, and several examples are shown that illustrate a general approach for estimating variables that are difficult to measure. It is hoped that the diversity of the applications discussed and the examples presented will make the flight-data analyst mindful of the potential advantages of using state estimation methods.

Bach, R. E., Jr.↗
NASA NTRS1983

On-board estimation technology for space station - Current status and future developments.

Design considerations and projected solutions to on-board automated estimation techniques for advanced technology controls on a space station are described, with emphasis on the state estimator. The space station is modelled as a collection of rigid and flexible bodies connected at a finite number of hinges. The systems dynamics are characterized by angular velocities of the base body, gimbal angles, and deflections of the flexible appendages. The state estimator evolution is projected to occur in four generations, with the first being control logic in the Viking and Voyager spacecraft, the second in the Shuttle and Galileo probe, the third being large antennas and the prototype space station, the last, around the year 2000, for the actual space station. Considerations for attitude, ephemeris, shape determination, and position estimation through each generation are discussed.

Rodriguez, G.↗
NASA NTRS1984

A comparison of two position estimate algorithms that use ILS localizer and DME information. Simulation and flight test results

Simulation and flight tests were conducted to compare the accuracy of two algorithms designed to compute a position estimate with an airborne navigation computer. Both algorithms used ILS localizer and DME radio signals to compute a position difference vector to be used as an input to the navigation computer position estimate filter. The results of these tests show that the position estimate accuracy and response to artificially induced errors are improved when the position estimate is computed by an algorithm that geometrically combines DME and ILS localizer information to form a single component of error rather than by an algorithm that produces two independent components of error, one from a DMD input and the other from the ILS localizer input.

Knox, C. E.↗
NASA NTRS1984

Signal-to-noise Ratio and Combiner Weight Estimation for Symbol Stream Combining

A method is presented for signal to noise ratio (SNR) and symbol stream combiner weight estimation. The SNR estimator employs absolute value moments as in an earlier method. The main contribution is that a new algorithm is derived for the combiner weight estimator to remove the large bias at low SNRs. The new algorithm is simulated to combine two independent symbol streams at various SNRs. As an example, the combining two symbol streams at SNRs of -1 dB and -7 dB, conbiner weight estimates using 1000 samples for the -1 dB stream and 10,000 samples for the -7 dB stream achieve an output SNR of -0.039 dB, which is just 0.012 dB below the theoretical limit achievable with perfect knowledge of the SNRs.

Vo, Q. D.↗
NASA NTRS1983

Crop area estimation based on remotely-sensed data with an accurate but costly subsample

Alternatives to sampling-theory stratified and regression estimators of crop production and timber biomass were examined. An alternative estimator which is viewed as especially promising is the errors-in-variable regression estimator. Investigations established the need for caution with this estimator when the ratio of two error variances is not precisely known.

Gunst, R. F.↗
NASA NTRS1984

Crop moisture estimation over the southern Great Plains with dual polarization 1.66 centimeter passive microwave data from Nimbus 7

Moisture content of snow-free, unfrozen soil is inferred using passive microwave brightness temperatures from the scanning multichannel microwave radiometer (SMMR) on Nimbus-7. Investigation is restricted to the two polarizations of the 1.66 cm wavelength sensor. Passive microwave estimates of soil moisture are of two basic categories; those based upon soil emissivity and those based upon the polarization of soil emission. The two methods are compared and contrasted through the investigation of 54 potential functions of polarized brightness temperatures and, in some cases, ground-based temperature measurements. Of these indices, three are selected for the estimated emissivity, the difference between polarized brightness temperatures, and the normalized polarization difference. Each of these indices is about equally effective for monitoring soil moisture. Using an antecedent precipitation index (API) as ground control data, temporal and spatial analyses show that emissivity data consistently give slightly better soil moisture estimates than depolarization data. The difference, however, is not statistically significant. It is concluded that polarization data alone can provide estimates of soil moisture in areas where the emissivity cannot be inferred due to nonavailability of surface temperature data.

Mcfarland, M. J.↗
NASA NTRS1984

The electrical conductivity of the upper mantle as estimated from satellite magnetic field data

The electrical conductivity of the upper mantle is estimated from low-latitude magnetic field variations caused by large fluctuations in the equatorial ring current. The data base is derived from magnetic field magnitude data measured by satellites OGO 2, 4, and 6, which offer better global coverage than land-based observatories. The procedures of analysis consist of: (1) separation of the disturbance field into internal and external parts relative to the surface of the earth, (2) estimation of an electromagnetic response function Q(omega) which relates the internally generated magnetic field variations to the external variations due to the ring current, and (3) interpretation of the estimated response function using theoretical response functions for assumed conductivity profiles. Special consideration is given to possible oceanic and ionospheric effects. Best estimates of the geomagnetic response function Q(omega) for 0.2 to 2.0 cpd indicate an upper mantle conductivity of the order of 0.01 S/m.

Didwall, E. M.↗
NASA NTRS1984

Effect of mixed (boundary) pixels on crop proportion estimation

In estimating acreage proportions of crop types in a segment using Landsat data, considerable problem is caused by the presence of mixed pixels. Due to lack of understanding of their spectral characteristics, mixed pixels have been treated in the past as pure while clustering and classifying the segment data. This paper examines this approach of treating mixed pixels as pure pixels and the effect of mixed pixels on the bias and variance of a crop type proportion estimate. First, the spectral response of a boundary pixel is modeled and an analytical expression for the bias and variance of a proportion estimate is obtained. This is followed by a numerical illustration of the effect of mixed pixels on bias and variance. It is shown that as the size of the mixed pixel class increases in a segment, the variance increases, however, such increase does not always affect the bias of the proportion estimate.

Chhikara, R. S.↗
NASA NTRS1984

More than you may want to know about maximum likelihood estimation

A discussion is undertaken concerning the maximum likelihood estimator and the aircraft equations of motion it employs, with attention to the application of the concepts of minimization and estimation to a simple computed aircraft example. Graphic representations are given for the cost functions to help illustrate the minimization process. The basic concepts are then generalized, and estimations obtained from flight data are evaluated. The example considered shows the advantage of low measurement noise, multiple estimates at a given condition, the Cramer-Rao bounds, and the quality of the match between measured and computed data.

Iliff, K. W.↗
NASA NTRS1984

Multi crop area estimation in Idaho using EDITOR

The use of LANDSAT multispectral scanner digital data for multi-crop acreage estimation in the central Snake River Plain of Idaho was examined. Two acquisitions of LANDSAT data covering ground sample units selected from a U.S. Department of Agriculture sampling frame in a four country study site were used to train a maximum likelihood classifier which, subsequently, classified all picture elements in the study site. Acreage estimates for six major crops, by county and for the four counties combined, were generated from the classification using the Battesse-Fuller model for estimation by regression in small areas. Results from the regression analysis were compared to those obtained by direct expansion of the ground data. Using the LANDSAT data significantly decreased the errors associated with the estimates for the three largest acreage crops. The late date of the second LANDSAT acquisition may have contributed to the poor results for three summer crops.

Sheffner, E. J.↗
NASA NTRS1985

Completely monotone regression estimates of software failure rates

A method for estimating the present failure rate of a program is presented. A crude nonparameter estimate of the failure rate function is obtained from past failure times. This estimate is then smoothed by fitting a completely monotonic function, which is the solution of a quadratic programming problem. The value of the smoothed function at present time is used as the estimate of present failure rate. Results of a Monte Carlo study of performance are given.

Miller, D. R.↗
NASA NTRS1984

Early season spring small grains proportion estimation

An accurate, automated method for estimating early season spring small grains from Landsat MSS data is discussed. The method is summarized and the results of its application to 100 sample segment-years of data from the US Northern Great Plains in 1976, 1977, 1978, and 1979 are summarized. The results show that this estimator provides accurate estimates earlier in the growing season than previous methods. Ground truth is required only in the estimator development, and data storage, transmission, preprocessing, and processing requirements are minimal.

Phinney, D. E.↗
NASA NTRS1983

Simulations as a tool for evaluating Landsat-based crop area estimation systems

An important use of remotely sensed data is in the estimation of agricultural production in foreign areas. Evaluation of such production estimates is difficult because of the lack of independent crop inventories. This paper presents simulation software developed to assess the effects of various factors on the performance of Landsat-based agricultural crop area estimators. An application of the simulator to determine whether the interaction of weather cycles with the Landsat orbital period could induce a systematic bias in large area crop estimates is discussed in detail. The simulation study was performed for the spring grains growing region of the Soviet Union.

Ramey, D. B.↗
NASA NTRS1985

Estimating the weight of generally configured dual wing systems

Formulas available for the weight estimation of monoplane wings cannot be said to be appropriate for the estimation of generally configured dual wing systems. In the present paper a method is described which simultaneously generates a structural weight estimate and a fully stressed, quasi-optimal structure for a model of a dual wing system. The method is fast and inexpensive. It is ideally suited to preliminary design. To illustrate the method, a dual wing system and a conventional wing system are sized. Numerical computation is shown to be suitably fast for both cases and, for both cases, convergence to a final configuration is shown to be quite rapid. To illustrate the validity of the method, a conventional wing is sized and its weight obtained by the present method is compared to its weight determined by a reputable weight estimation formula. The results are shown to be very close.

Cronin, D. L.↗