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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Optical Communications Channel Combiner

NASA has identified deep-space optical communications links as an integral part of a unified space communication network in order to provide data rates in excess of 100 Mb/s. The distances and limited power inherent in a deep-space optical downlink necessitate the use of photon-counting detectors and a power-efficient modulation such as pulse position modulation (PPM). For the output of each photodetector, whether from a separate telescope or a portion of the detection area, a communication receiver estimates a log-likelihood ratio for each PPM slot. To realize the full effective aperture of these receivers, their outputs must be combined prior to information decoding. A channel combiner was developed to synchronize the log-likelihood ratio (LLR) sequences of multiple receivers, and then combines these into a single LLR sequence for information decoding. The channel combiner synchronizes the LLR sequences of up to three receivers and then combines these into a single LLR sequence for output. The channel combiner has three channel inputs, each of which takes as input a sequence of four-bit LLRs for each PPM slot in a codeword via a XAUI 10 Gb/s quad optical fiber interface. The cross-correlation between the channels LLR time series are calculated and used to synchronize the sequences prior to combining. The output of the channel combiner is a sequence of four-bit LLRs for each PPM slot in a codeword via a XAUI 10 Gb/s quad optical fiber interface. The unit is controlled through a 1 Gb/s Ethernet UDP/IP interface. A deep-space optical communication link has not yet been demonstrated. This ground-station channel combiner was developed to demonstrate this capability and is unique in its ability to process such a signal.

Quirk, Kevin J.↗
NASA NTRS1973

Detection and Estimation of an Optical Image by Photon-Counting Techniques

Statistical description of a photoelectric detector is given. The photosensitive surface of the detector is divided into many small areas, and the moment generating function of the photo-counting statistic is derived for large time-bandwidth product. The detection of a specified optical image in the presence of the background light by using the hypothesis test is discussed. The ideal detector based on the likelihood ratio from a set of numbers of photoelectrons ejected from many small areas of the photosensitive surface is studied and compared with the threshold detector and a simple detector which is based on the likelihood ratio by counting the total number of photoelectrons from a finite area of the surface. The intensity of the image is assumed to be Gaussian distributed spatially against the uniformly distributed background light. The numerical approximation by the method of steepest descent is used, and the calculations of the reliabilities for the detectors are carried out by a digital computer.

Wang, Lily Lee↗
NASA NTRS1975

An ERTS-1 investigation for Lake Ontario and its basin

The author has identified the following significant results. Methods of manual, semi-automatic, and automatic (computer) data processing were evaluated, as were the requirements for spatial physiographic and limnological information. The coupling of specially processed ERTS data with simulation models of the watershed precipitation/runoff process provides potential for water resources management. Optimal and full use of the data requires a mix of data processing and analysis techniques, including single band editing, two band ratios, and multiband combinations. A combination of maximum likelihood ratio and near-IR/red band ratio processing was found to be particularly useful.

Polcyn, F. C.↗
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.↗
NASA NTRS2012

Combining Ratio Estimation for Low Density Parity Check (LDPC) Coding

The Low Density Parity Check (LDPC) Code decoding algorithm make use of a scaled receive signal derived from maximizing the log-likelihood ratio of the received signal. The scaling factor (often called the combining ratio) in an AWGN channel is a ratio between signal amplitude and noise variance. Accurately estimating this ratio has shown as much as 0.6 dB decoding performance gain. This presentation briefly describes three methods for estimating the combining ratio: a Pilot-Guided estimation method, a Blind estimation method, and a Simulation-Based Look-Up table. The Pilot Guided Estimation method has shown that the maximum likelihood estimates of signal amplitude is the mean inner product of the received sequence and the known sequence, the attached synchronization marker (ASM) , and signal variance is the difference of the mean of the squared received sequence and the square of the signal amplitude. This method has the advantage of simplicity at the expense of latency since several frames worth of ASMs. The Blind estimation method s maximum likelihood estimator is the average of the product of the received signal with the hyperbolic tangent of the product combining ratio and the received signal. The root of this equation can be determined by an iterative binary search between 0 and 1 after normalizing the received sequence. This method has the benefit of requiring one frame of data to estimate the combining ratio which is good for faster changing channels compared to the previous method, however it is computationally expensive. The final method uses a look-up table based on prior simulated results to determine signal amplitude and noise variance. In this method the received mean signal strength is controlled to a constant soft decision value. The magnitude of the deviation is averaged over a predetermined number of samples. This value is referenced in a look up table to determine the combining ratio that prior simulation associated with the average magnitude of the deviation. This method is more complicated than the Pilot-Guided Method due to the gain control circuitry, but does not have the real-time computation complexity of the Blind Estimation method. Each of these methods can be used to provide an accurate estimation of the combining ratio, and the final selection of the estimation method depends on other design constraints.

Mahmoud, Saad↗
NASA NTRS2021

Sequential Wald Test Employing a Constrained Filter Bank: Application to Spacecraft Conjunctions

A binary Wald sequential probability ratio test that uses the residuals of norm-inequality-constrained Kalman filters for its likelihood ratio may be employed for a class of compound hypothesis tests on non-stationary systems. The hypotheses concern an inequality constraint on the norm of some elements of the system state. Each of two filters minimizes the summed-squares of its estimation errors subject to one or the other direction of the inequality constraint. This solution is motivated by the problem of satellite conjunction assessment, wherein the constraint concerns the close approach distance between two space objects. The outcome of the test can inform decisions concerning risk mitigation maneuvers.

J. Russell Carpenter↗
NASA NTRS1987

Efficient computation of parameter confidence intervals

An important step in system identification of aircraft is the estimation of stability and control derivatives from flight data along with an assessment of parameter accuracy. When the maximum likelihood estimation technique is used, parameter accuracy is commonly assessed by the Cramer-Rao lower bound. It is known, however, that in some cases the lower bound can be substantially different from the parameter variance. Under these circumstances the Cramer-Rao bounds may be misleading as an accuracy measure. This paper discusses the confidence interval estimation problem based on likelihood ratios, which offers a more general estimate of the error bounds. Four approaches are considered for computing confidence intervals of maximum likelihood parameter estimates. Each approach is applied to real flight data and compared.

Murphy, Patrick C.↗
NASA NTRS2013

Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data

We propose a Wald Sequential Probability Ratio Test for analysis of commonly available predictions associated with spacecraft conjunctions. Such predictions generally consist of a relative state and relative state error covariance at the time of closest approach, under the assumption that prediction errors are Gaussian. We show that under these circumstances, the likelihood ratio of the Wald test reduces to an especially simple form, involving the current best estimate of collision probability, and a similar estimate of collision probability that is based on prior assumptions about the likelihood of collision.

Carpenter, J. Russell↗
NASA NTRS1977

Land use/land cover mapping (1:25000) of Taiwan, Republic of China by automated multispectral interpretation of LANDSAT imagery

Three methods were tested for collection of the training sets needed to establish the spectral signatures of the land uses/land covers sought due to the difficulties of retrospective collection of representative ground control data. Computer preprocessing techniques applied to the digital images to improve the final classification results were geometric corrections, spectral band or image ratioing and statistical cleaning of the representative training sets. A minimal level of statistical verification was made based upon the comparisons between the airphoto estimates and the classification results. The verifications provided a further support to the selection of MSS band 5 and 7. It also indicated that the maximum likelihood ratioing technique can achieve more agreeable classification results with the airphoto estimates than the stepwise discriminant analysis.

Sung, Q. C.↗
NASA NTRS2009

Hardware Implementation of Serially Concatenated PPM Decoder

A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.

Moision, Bruce↗
NASA NTRS1968

Maximum Likelihood Properties

Maximum likelihood properties and asymptotic distributions for limiting distribution of likelihood ratio statistic under class of local alternatives

Lever, W. E.↗
NASA NTRS1970

The development of spectro-signature indicators of root disease impacts on forest stands

A field research program was begun in 1969 and intensified in 1970 on the physiology and biophysical responses of second-growth Douglas fir infected with root rot fungus. A double tramway system was suspended between three 100-foot instrument towers to carry sensors for measuring the energy response from above both healthy and infected trees. Processing and analysis was completed of airborne multispectral scanner imagery collected over the Wind River research area in 1969. Likelihood ratio processing of three-channel infrared data and Euclidean distance analysis of ten-channel spectrometer data did not identify incipient root rot infection outside the training sets. In all cases infected fir was misclassified as healthy fir. It was concluded from careful examination of physiological data that Poria root rot infection has little effect on water metabolism and energy exchange. What was identified was a low-grade stress that affects respiration and metabolism over long periods of time. This led to minor changes in the external physical symptoms of Poria-infected trees which was revealed only in the shortwave reflectance data.

Weber, F. P.↗
NASA NTRS1971

Mapping soil types from multispectral scanner data.

Multispectral remote sensing and computer-implemented pattern recognition techniques were used for automatic ?mapping' of soil types. This approach involves subjective selection of a set of reference samples from a gray-level display of spectral variations which was generated by a computer. Each resolution element is then classified using a maximum likelihood ratio. Output is a computer printout on which the researcher assigns a different symbol to each class. Four soil test areas in Indiana were experimentally examined using this approach, and partially successful results were obtained.

Kristof, S. J.↗
NASA NTRS1972

Optimum detection of an optical image on a photoelectric surface

The detection of an optical image in the presence of uniform background light is based on a likelihood ratio formed of the numbers of photoelectrons emitted from small elements of a photoelectric surface onto which the image is focused. When diffraction is negligible and the surface has unit quantum efficiency, this detector is equipollent with the optimum detector of the image forming light. Its performance is compared with that of the threshold detector and that of a detector basing its decisions on the total number of photoelectrons from a finite area of the image. The illuminance of the image is postulated to have a Gaussian spatial distribution. All three detectors exhibit nearly the same reliability.

Helstrom, C. W.↗
NASA NTRS1973

Estimation and detection of signals in multiplicative noise

A class of detection-estimation problems on matrix Lie groups is defined in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear in nature, it is possible to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite dimensional optimal solution to a nonlinear estimation problem and can be viewed as consisting of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid body rotational control system.

Willsky, A. S.↗
NASA NTRS1974

Computer-implemented land use classification with pattern recognition software and ERTS digital data

Significant progress has been made in the classification of surface conditions (land uses) with computer-implemented techniques based on the use of ERTS digital data and pattern recognition software. The supervised technique presently used at the NASA Earth Resources Laboratory is based on maximum likelihood ratioing with a digital table look-up approach to classification. After classification, colors are assigned to the various surface conditions (land uses) classified, and the color-coded classification is film recorded on either positive or negative 9 1/2 in. film at the scale desired. Prints of the film strips are then mosaicked and photographed to produce a land use map in the format desired. Computer extraction of statistical information is performed to show the extent of each surface condition (land use) within any given land unit that can be identified in the image. Evaluations of the product indicate that classification accuracy is well within the limits for use by land resource managers and administrators. Classifications performed with digital data acquired during different seasons indicate that the combination of two or more classifications offer even better accuracy.

Joyce, A. T.↗