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NASA NTRS1975

Parameter adaptive estimation of random processes

This paper is concerned with the parameter adaptive least squares estimation of random processes. The main result is a general representation theorem for the conditional expectation of a random variable on a product probability space. Using this theorem along with the general likelihood ratio expression, the least squares estimate of the process is found in terms of the parameter conditioned estimates. The stochastic differential for the a posteriori probability and the stochastic differential equation for the a posteriori density are found by using simple stochastic calculus on the representations obtained. The results are specialized to the case when the parameter has a discrete distribution. The results can be used to construct an implementable recursive estimator for certain types of nonlinear filtering problems. This is illustrated by some simple examples.

Caglayan, A. K.↗

NASA NTRS1976

Illinois crop-acreage estimation experiment

The University of Illinois and the U.S. Department of Agriculture have collaborated to examine the feasibility of Landsat imagery analysis for USDA crop-acreage estimation purposes. The region chosen for the experiment was ten western counties of Illinois. Preliminary crop-acreage estimates derived from the ILLIAC IV-ARPA Network analysis of Landsat data are presented for these ten counties. Assuming the practicality of similar analyses covering the entire state, a procedure is discussed for evaluating statistically the information to be gained by estimating state crop-acreage totals from Landsat imagery classification results where SRS sample survey data are used as ground truth information for classification training as opposed to estimating state crop-acreage totals directly from SRS survey data alone.

Ray, R. M., III↗

NASA NTRS1977

A simulation of air pollution model parameter estimation using data from a ground-based LIDAR remote sensor

One way to obtain estimates of the unknown parameters in a pollution dispersion model is to compare the model predictions with remotely sensed air quality data. A ground-based LIDAR sensor provides relative pollution concentration measurements as a function of space and time. The measured sensor data are compared with the dispersion model output through a numerical estimation procedure to yield parameter estimates which best fit the data. This overall process is tested in a computer simulation to study the effects of various measurement strategies. Such a simulation is useful prior to a field measurement exercise to maximize the information content in the collected data. Parametric studies of simulated data matched to a Gaussian plume dispersion model indicate the trade offs available between estimation accuracy and data acquisition strategy.

Kibler, J. F.↗

NASA NTRS1977

Two phase sampling for wheat acreage estimation

A two phase LANDSAT-based sample allocation and wheat proportion estimation method was developed. This technique employs manual, LANDSAT full frame-based wheat or cultivated land proportion estimates from a large number of segments comprising a first sample phase to optimally allocate a smaller phase two sample of computer or manually processed segments. Application to the Kansas Southwest CRD for 1974 produced a wheat acreage estimate for that CRD within 2.42 percent of the USDA SRS-based estimate using a lower CRD inventory budget than for a simulated reference LACIE system. Factor of 2 or greater cost or precision improvements relative to the reference system were obtained.

Thomas, R. W.↗

NASA NTRS1978

Estimation from incomplete multinomial data

The vector of multinomial cell probabilities was estimated from incomplete data, incomplete in that it contains partially classified observations. Each such partially classified observation was observed to fall in one of two or more selected categories but was not classified further into a single category. The data were assumed to be incomplete at random. The estimation criterion was minimization of risk for quadratic loss. The estimators were the classical maximum likelihood estimate, the Bayesian posterior mode, and the posterior mean. An approximation was developed for the posterior mean. The Dirichlet, the conjugate prior for the multinomial distribution, was assumed for the prior distribution.

Credeur, K. R.↗

NASA NTRS1978

Aerodynamic derivatives for an oblique wing aircraft estimated from flight data by using a maximum likelihood technique

There are several practical problems in using current techniques with five degree of freedom equations to estimate the stability and control derivatives of oblique wing aircraft from flight data. A technique was developed to estimate these derivatives by separating the analysis of the longitudinal and lateral directional motion without neglecting cross coupling effects. Although previously applied to symmetrical aircraft, the technique was not expected to be adequate for oblique wing vehicles. The application of the technique to flight data from a remotely piloted oblique wing aircraft is described. The aircraft instrumentation and data processing were reviewed, with particular emphasis on the digital filtering of the data. A complete set of flight determined stability and control derivative estimates is presented and compared with predictions. The results demonstrated that the relatively simple approach developed was adequate to obtain high quality estimates of the aerodynamic derivatives of such aircraft.

Maine, R. E.↗

NASA NTRS1977

Structured estimation - Sample size reduction for adaptive pattern classification

The Gaussian two-category classification problem with known category mean value vectors and identical but unknown category covariance matrices is considered. The weight vector depends on the unknown common covariance matrix, so the procedure is to estimate the covariance matrix in order to obtain an estimate of the optimum weight vector. The measure of performance for the adapted classifier is the output signal-to-interference noise ratio (SIR). A simple approximation for the expected SIR is gained by using the general sample covariance matrix estimator; this performance is both signal and true covariance matrix independent. An approximation is also found for the expected SIR obtained by using a Toeplitz form covariance matrix estimator; this performance is found to be dependent on both the signal and the true covariance matrix.

Morgera, S.↗

NASA NTRS1977

Parameter estimating state reconstruction

Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. These systems must be observable. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a Space Shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.

George, E. B.↗

NASA NTRS1977

Estimation of spectral reflectance curves from multispectral image data

A technique is presented for estimating spectral reflectance curves from multispectral image data even if the spectral samples are obtained from channels whose spectral responsivity is not narrowband. It is demonstrated that these reflectance estimates can be written as a linear combination of the spectral samples and that, analogous to Shannon's sampling theorem, if the spectral reflectance is a natural cubic spline, it can be estimated exactly provided the number of spectral channels is sufficiently large. Simulation results suggest that the accuracy of the spectral reflectance estimates is quite good and very insensitive to the spectral responsivity shapes.

Park, S. K.↗

NASA NTRS1978

Microwave scatter and sea state estimation - Two-scale ocean wave models

The efficient estimation of ocean wave-structure parameters with a remote, narrow-beam, pulsed, microwave radar at intermediate incidence angles is discussed. The sea surface is described as the sum of random small- and large-scale structures (waves), the latter the sum of a sinusoid and a random field. It is shown that the small-scale structure is responsible for scattering and that the scatter depends parametrically on the large-scale structure. For the estimation problem it is assumed, reasonably, that the received signal is normally distributed: a relatively simple processor which will efficiently estimate parameters of the sinusoidal structure is illustrated and its performance discussed. A brief comparison is made with a normal incidence system with which the variance of the large-scale random roughness can be estimated.

Harger, R. O.↗

NASA NTRS1978

Rain-rate estimates for an attenuating radar

An iterative method has been used to produce rain-rate estimates for an attenuating frequency radar. An infinite number of higher-order estimates are shown to converge in the limit to the Hitschfeld-Bordan solution under certain conditions. An error analysis was performed by a model accounting for the randomness of the radar return power, the k-Z, Z-R relations, and offsets in the radar calibration constant. Since the behavior of the estimates strongly depends on system errors, the choice of the best estimate requires a knowledge of the variance and range of offsets in meteorological data and the calibration constant. As the errors increase, the use of the lower orders avoids significant overpredictions. In order to obtain reliable rain-rate predictions in the presence of realistic errors, an antenna pointing angles away from the horizontal at frequencies in the lower end of the X-band may be used. Such antenna configurations insure low attenuation.

Meneghini, R.↗

NASA NTRS1977

Two phase sampling for wheat acreage estimation

A two phase Landsat-based sample allocation and wheat proportion estimation method was developed. This technique employs manual, Landsat full frame-based wheat or cultivated land proportion estimates from a large number of segments comprising a first sample phase to optimally allocate a smaller phase two sample of computer or manually processed segments. Application to the Kansas Southwest CRD for 1974 produced a wheat acreage estimate for that CRD within 2.42 percent of the USDA SRS-based estimate using a lower CRD inventory budget than for a simulated reference LACIE system. Factor of 2 or greater cost or precision improvements relative to the reference system were obtained

Thomas, R. W.↗

NASA NTRS1977

Crop identification and area estimation by computer-aided analysis of Landsat data

This report describes the results of a study involving the use of computer-aided analysis techniques applied to Landsat MSS data for identification and area estimation of winter wheat in Kansas and corn and soybeans in Indiana. Key elements of the approach included use of aerial photography for classifier training, stratification of Landsat data and extension of training statistics to areas without training data, and classification of a systematic sample of pixels from each county. Major results and conclusions are: (1) Landsat data was adequate for accurate identification and area estimation of winter wheat in Kansas, but corn and soybean estimates for Indiana were less accurate; (2) computer-aided analysis techniques can be effectively used to extract crop identification information from Landsat MSS data, and (3) systematic sampling of entire counties made possible by computer classification methods resulted in very precise area estimates at county as well as district and state levels.

Bauer, M. E.↗

NASA NTRS1978

Area estimation of crops by digital analysis of Landsat data

The study for which the results are presented had these objectives: (1) to use Landsat data and computer-implemented pattern recognition to classify the major crops from regions encompassing different climates, soils, and crops; (2) to estimate crop areas for counties and states by using crop identification data obtained from the Landsat identifications; and (3) to evaluate the accuracy, precision, and timeliness of crop area estimates obtained from Landsat data. The paper describes the method of developing the training statistics and evaluating the classification accuracy. Landsat MSS data were adequate to accurately identify wheat in Kansas; corn and soybean estimates for Indiana were less accurate. Systematic sampling of entire counties made possible by computer classification methods resulted in very precise area estimates at county, district, and state levels.

Bauer, M. E.↗

NASA NTRS1979

Determination of stability and control parameters of a light airplane from flight data using two estimation methods

Two identification methods, the equation error method and the output error method, are used to estimate stability and control parameter values from flight data for a low-wing, single-engine, general aviation airplane. The estimated parameters from both methods are in very good agreement primarily because of sufficient accuracy of measured data. The estimated static parameters also agree with the results from steady flights. The effect of power different input forms are demonstrated. Examination of all results available gives the best values of estimated parameters and specifies their accuracies.

Klein, V.↗

NASA NTRS1979

Multiple scene attitude estimator performance for LANDSAT-1

Initial results are presented to demonstrate the performance of a linear sequential estimator (Kalman Filter) used to estimate a LANDSAT 1 spacecraft attitude time series defined for four scenes. With the revised estimator a GCP poor scene - a scene with no usable geodetic control points (GCPs) - can be rectified to higher accuracies than otherwise based on the use of GCPs in adjacent scenes. Attitude estimation errors was determined by the use of GCPs located in the GCP-poor test scene, but which are not used to update the Kalman filter. Initial results achieved indicate that errors of 500m (rms) can be attained for the GCP-poor scenes. Operational factors are related to various scenarios.

Rifman, S. S.↗

NASA NTRS1979

Convective rainfall estimation from digital GOES-1 infrared data

An investigation was conducted to determine the feasibility of developing and objective technique for estimating convective rainfall from digital GOES-1 infrared data. The study area was a 240 km by 240 km box centered on College Station, Texas (Texas A and M University). The Scofield and Oliver (1977) rainfall estimation scheme was adapted and used with the digital geostationary satellite data. The concept of enhancement curves with respect to rainfall approximation is discussed. Raingage rainfall analyses and satellite-derived rainfall estimation analyses were compared. The correlation for the station data pairs (observed versus estimated rainfall amounts) for the convective portion of the storm was 0.92. It was demonstrated that a fairly accurate objective rainfall technique using digital geostationary infrared satellite data is feasible. The rawinsonde and some synoptic data that were used in this investigation came from NASA's Atmospheric Variability Experiment, AVE 7.

Sickler, G. L.↗

NASA NTRS1979

Optimal estimation of large structure model errors

In-flight estimation of large structure model errors is usually required as a means of detecting inevitable deficiencies in large structure controller/estimator models. The present paper deals with a least-squares formulation which seeks to minimize a quadratic functional of the model errors. The properties of these error estimates are analyzed. It is shown that an arbitrary model error can be decomposed as the sum of two components that are orthogonal in a suitably defined function space. Relations between true and estimated errors are defined. The estimates are found to be approximations that retain many of the significant dynamics of the true model errors. Current efforts are directed toward application of the analytical results to a reference large structure model.

Rodriguez, G.↗