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NASA NTRS1974

Binary signaling over channels containing quadratic nonlinearities

This paper examines the transmission of binary data signals over channels which contain quadratic nonlinearities and additive Gaussian noise. We consider the case where the channel is nonlinear with memory and where the signal is passed through an input receiver filter and sampled once every signaling interval. The samples are represented by a discrete Volterra series and a special case where the received sample contains a single quadratic distortion term is examined. The optimum (maximum-likelihood) receiver (processor) is derived and upper and lower performance bounds obtained. The performance of a practical, suboptimum receiver is examined by means of computer simulation and is shown to be very close to the lower bound of the optimum receiver. Next we examine the case where the received sample contains two quadratic distortion terms. Again, upper and lower performance bounds are obtained.

Lawless, W. J.↗
NASA NTRS1974

Numerical modelling of instantaneous plate tectonics

Assuming lithospheric plates to be rigid, 68 spreading rates, 62 fracture zones trends, and 106 earthquake slip vectors are systematically inverted to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum-likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable.

Minster, J. B.↗
NASA NTRS1974

Free distance bounds for convolutional codes

The best asymptotic bounds presently known on free distance for convolutional codes are presented from a unified point of view. Upper and lower bounds for both time-varying and fixed codes are obtained. A comparison is made between bounds for nonsystematic and systematic codes which shows that more free distance is available with nonsystematic codes. This result is important when selecting codes for use with sequential or maximum-likelihood (Viterbi) decoding since the probability of decoding error is closely related to the free distance of the code. An ancillary result, used in proving the lower bound on free distance for time-varying nonsystematic codes, furnishes a generalization of two earlier bounds on the definite decoding minimum distance of convolutional codes.

Costello, D. J., Jr.↗
NASA NTRS1974

A Bayesian analysis of two probability models describing thunderstorm activity at Cape Kennedy, Florida

A Bayesian analysis of the two discrete probability models, the negative binomial and the modified negative binomial distributions, which have been used to describe thunderstorm activity at Cape Kennedy, Florida, is presented. The Bayesian approach with beta prior distributions is compared to the classical approach which uses a moment method of estimation or a maximum-likelihood method. The accuracy and simplicity of the Bayesian method is demonstrated.

Williford, W. O.↗
NASA NTRS1974

Single-tone parameter estimation from discrete-time observations

Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramer-Rao bounds and maximum-likelihood (ML) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practial algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.

Rife, D. C.↗
NASA NTRS1975

Geological mapping in northwestern Saudi Arabia using LANDSAT multispectral techniques

Various computer enhancement and data extraction systems using LANDSAT data were assessed and used to complement a continuing geologic mapping program. Interactive digital classification techniques using both the parallel-piped and maximum-likelihood statistical approaches achieve very limited success in areas of highly dissected terrain. Computer enhanced imagery developed by color compositing stretched MSS ratio data was constructed for a test site in northwestern Saudi Arabia. Initial results indicate that several igneous and sedimentary rock types can be discriminated.

Blodget, H. W.↗
NASA NTRS1975

Geological mapping in northwestern Saudi Arabia using LANDSAT multispectral techniques

Various computer enhancement and data extraction systems using LANDSAT data were assessed and used to complement a continuing geologic mapping program. Interactive digital classification techniques using both the maximum-likelihood and thresholding statistical approaches achieve very limited success in areas of highly dissected terrain. Computer enhanced imagery developed by color compositing stretched MSS ratio data was constructed for a test site in northwestern Saudi Arabia. Initial results indicate that several igneous and sedimentary rock-types can be discriminated.

Blodget, H. W.↗
NASA NTRS1975

A general non-parametric classifier applied to discriminating surface water from terrain shadows

A general non-parametric classifier is described in the context of discriminating surface water from terrain shadows. In addition to using non-parametric statistics, this classifier permits the use of a cost matrix to assign different penalties to various types of misclassifications. The approach also differs from conventional classifiers in that it applies the maximum-likelihood criterion to overall class probabilities as opposed to the standard practice of choosing the most likely individual subclass. The classifier performance is evaluated using two different effectiveness measures for a specific set of ERTS data.

Eppler, W. G.↗
NASA NTRS1975

A random search algorithm for laboratory computers

The small laboratory computer is ideal for experimental control and data acquisition. Postexperimental data processing is often performed on large computers because of the availability of sophisticated programs, but costs and data compatibility are negative factors. Parameter optimization can be accomplished on the small computer, offering ease of programming, data compatibility, and low cost. A previously proposed random-search algorithm ('random creep') was found to be very slow in convergence. A method is proposed (the 'random leap' algorithm) which starts in a global search mode and automatically adjusts step size to speed convergence. A FORTRAN executive program for the random-leap algorithm is presented which calls a user-supplied function subroutine. An example of a function subroutine is given which calculates maximum-likelihood estimates of receiver operating-characteristic parameters from binary response data. Other applications in parameter estimation, generalized least squares, and matrix inversion are discussed.

Curry, R. E.↗
NASA NTRS1975

A note on the consistency of maximum likelihood estimates for finite families of stochastic processes

The note considers families of stochastic processes indexed by a finite number of alternative parameter values. For general classes of stochastic processes, it is shown that maximum-likelihood estimates converge almost surely to the correct parameter value. This is established by use of a submartingale property of the sequence of maximized-likelihood ratios together with a technique first employed by Wald (1949) in the case of independent identically distributed random variables.

Caines, P. E.↗
NASA NTRS1976

Curve fitting of aeroelastic transient response data with exponential functions

The extraction of frequency, damping, amplitude, and phase information from unforced transient response data is considered. These quantities are obtained from the parameters determined by fitting the digitized time-history data in a least-squares sense with complex exponential functions. The highlights of the method are described, and the results of several test cases are presented. The effects of noise are considered both by using analytical examples with random noise and by estimating the standard deviation of the parameters from maximum-likelihood theory.

Bennett, R. M.↗
NASA NTRS1976

Filtering and smoothing techniques for parameter estimation

In this paper filtering and smoothing criteria for maximum-likelihood parameter estimation are described and compared. It is shown that the parameter estimate using the smoothing criterion may be obtained independently of the smoothed state estimate. Monte Carlo test results are presented comparing the efficiency of the estimation procedures.

Bach, R. E., Jr.↗
NASA NTRS1977

On the error probability of general trellis codes with applications to sequential decoding

An upper bound on the average probability of error for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n with distinction between memory length and tail length is given. It is shown that the bound is independent of the length L of the information sequence if the memory length exceeds the tail length by a specified amount that depends on L. Sequential decoding simulations using the stack algorithm were conducted to test the dependence of the undetected error probability on tail length and memory length, and the results corroborated the theory.

Johannesson, R.↗
NASA NTRS1977

The effect of the atmosphere on the classification of satellite observations to identify surface features

The effect of differences in atmospheric turbidity on the classification of Landsat 1 observations of a rural scene is presented. The observations are classified by an unsupervised clustering technique. These clusters serve as a training set for use of a maximum-likelihood algorithm. The measured radiances in each of the four spectral bands are then changed by amounts measured by Landsat 1. These changes can be associated with a decrease in atmospheric turbidity by a factor of 1.3. The classification of 22% of the pixels changes as a result of the modification. The modified observations are then reclassified as an independent set. Only 3% of the pixels have a different classification than the unmodified set. Hence, if classification errors of rural areas are not to exceed 15%, a new training set has to be developed whenever the difference in turbidity between the training and test sets reaches unity.

Fraser, R. S.↗
NASA NTRS1976

Performance of convolutionally encoded noncoherent MFSK modem in fading channels

The performance of a convolutionally encoded noncoherent multiple-frequency shift-keyed (MFSK) modem utilizing Viterbi maximum-likelihood decoding and operating on a fading channel is described. Both the lognormal and classical Rician fading channels are considered for both slow and time-varying channel conditions. Primary interest is in the resulting bit error rate as a function of the ratio between the energy per transmitted information bit and noise spectral density, parameterized by both the fading channel and code parameters. Fairly general upper bounds on bit error probability are provided and compared with simulation results in the two extremes of zero and infinite channel memory. The efficacy of simple block interleaving in combatting channel memory effects are thoroughly explored. Both quantized and unquantized receiver outputs are considered.

Modestino, J. W.↗
NASA NTRS1978

Quasi-Newton Methods

The problem to be solved is formulated precisely and the introduction of quasi-Newton methods is motivated by considering the classical Newton and secant methods and their properties. Three highly successful quasi-Newton methods are surveyed: Broyden's method for the solution of general nonlinear equations, and the Davidon-Fletcher-Powell and Broyden-Fletcher-Goldfarb-Shanno procedures for unconstrained minimization. Finally, the properties of these methods are compared to those of Newton's method and UHMLE in potential applications to maximum-likelihood estimation of parameters in mixture distributions.

Walker, H. F.↗
NASA NTRS1978

A comparative study of optimum and suboptimum direct-detection laser ranging receivers

A summary of previously proposed receiver strategies for direct-detection laser ranging receivers is presented. Computer simulations are used to compare performance of candidate implementation strategies in the 1- to 100-photoelectron region. Under the condition of no background radiation, the maximum-likelihood and minimum mean-square error estimators were found to give the same performance for both bell-shaped and rectangular optical-pulse shapes. For signal energies greater than 100 photoelectrons, the root-mean-square range error is shown to decrease as Q to the -1/2 power for bell-shaped pulses and Q to the -1 power for rectangular pulses, where Q represents the average pulse energy. Of several receiver implementations presented, the matched-filter peak detector was found to be preferable. A similar configuration, using a constant-fraction discriminator, exhibited a signal-level dependent time bias.

Abshire, J. B.↗
NASA NTRS1977

Landsat-D thematic mapper simulation using aircraft multispectral scanner data

A simulation of imagery from the upcoming Landsat-D Thematic Mapper was accomplished by using selected channels of aircraft 24-channel multispectral scanner data. The purpose was to simulate Thematic Mapper 30-meter resolution imagery, to compare its spectral quality with the original aircraft MSS data, and to determine changes in thematic classification accuracy for the simulated imagery. The original resolution of approximately 7.5 meters IFOV and simulated resolution of 15, 30, and 60 meters were used to indicate the trend of spectral quality and classification accuracy. The study was based in a 6.5 square kilometer area of urban Los Angeles having a diversity of land use. The original imagery was reduced in resolution by two related methods: pixel matrix averaging, and matrix smoothing with a unity box filter, followed by matrix averaging. Thematic land use classification using training sites and a Bayesian maximum-likelihood algorithm was performed at three levels of standard deviation - 1.0, 2.0, and 3.0 sigma. Plots of relative standard deviation showed that for larger training sites with a normal distribution of data, as the resolution decreased, the distribution range of density values decreased. Also, the classification accuracies for three levels of standard deviation increased as resolution decreased. However, the indication is that a point of diminishing returns had been reached, and 30 meters IFOV should be the best for multispectral classification of urban scenes.

Clark, J.↗