Search NASA⌕ Search

SEARCH · Search NASA

Results for “Likelihood Function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Radar optimization for sea surface and geodetic measurements

The efficient estimation of geoid and sea state parameters is discussed, and the optimum processing structures, including maximum likelihood estimators, and their accuracy limits are given for a model. The model accounts for random surface reflectivity, sea height, and additive noise, and allows for arbitrary radar system parameters, based on the assumption the received signal is a sample function of a normal random process. The integral equation associated with the Gaussian signal in Gaussian noise inference problem was solved. It is shown that the optimum processing is generally a mixture of coherent and incoherent integrations which may be viewed as a weighted summation of received power of the match-filtered received data. When estimates are correlated, the strongest correlation appears between geoid and asymmetry estimates, and between wave height standard deviation and reflectivity estimates.

Harger, R. O.↗
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 NTRS1981

The effect of noisy carrier reference on telemetry with baseband arraying

Imperfect carrier reference causes a degradation in detection performance in coherent communication systems. A measure of this degradation is the radio loss, which is the amount of increase in data signal to noise ratio (SNR) per bit required to achieve the same bit error rate when carrier reference is perfect. Performance analysis and numerical results are obtained for the Voyager high rate telemetry link with maximum likelihood convolutional decoding. The arraying of antennas provides not only improved performance due to an increase in effective antenna aperture, but also a decrease in radio loss with respect to a single antenna. This telemetry link performance improvement is a function of the carrier loop SNR and data bit error rate. When the carrier loop SNR's are low, it provides a significant improvement in the telemetry link performance since the decrease in radio loss with respect to a single station is substantial.

Divsalar, D.↗
NASA NTRS1987

Statistics of Sxy estimates

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

Freilich, M. H.↗
NASA NTRS1997

Flight-Determined Subsonic Longitudinal Stability and Control Derivatives of the F-18 High Angle of Attack Research Vehicle (HARV) with Thrust Vectoring

The subsonic longitudinal stability and control derivatives of the F-18 High Angle of Attack Research Vehicle (HARV) are extracted from dynamic flight data using a maximum likelihood parameter identification technique. The technique uses the linearized aircraft equations of motion in their continuous/discrete form and accounts for state and measurement noise as well as thrust-vectoring effects. State noise is used to model the uncommanded forcing function caused by unsteady aerodynamics over the aircraft, particularly at high angles of attack. Thrust vectoring was implemented using electrohydraulically-actuated nozzle postexit vanes and a specialized research flight control system. During maneuvers, a control system feature provided independent aerodynamic control surface inputs and independent thrust-vectoring vane inputs, thereby eliminating correlations between the aircraft states and controls. Substantial variations in control excitation and dynamic response were exhibited for maneuvers conducted at different angles of attack. Opposing vane interactions caused most thrust-vectoring inputs to experience some exhaust plume interference and thus reduced effectiveness. The estimated stability and control derivatives are plotted, and a discussion relates them to predicted values and maneuver quality.

Iliff, Kenneth W.↗
NASA NTRS1973

An empirical Bayes approach for the Poisson life distribution.

A smooth empirical Bayes estimator is derived for the intensity parameter (hazard rate) in the Poisson distribution as used in life testing. The reliability function is also estimated either by using the empirical Bayes estimate of the parameter, or by obtaining the expectation of the reliability function. The behavior of the empirical Bayes procedure is studied through Monte Carlo simulation in which estimates of mean-squared errors of the empirical Bayes estimators are compared with those of conventional estimators such as minimum variance unbiased or maximum likelihood. Results indicate a significant reduction in mean-squared error of the empirical Bayes estimators over the conventional variety.

Canavos, G. C.↗
NASA NTRS1979

Atmospheric effects on cluster analyses

Ground reflected radiance, from which information is extracted through techniques of cluster analyses for remote sensing application, is altered by the atmosphere when it reaches the satellite. Therefore it is essential to understand the effects of the atmosphere on Landsat measurements, cluster characteristics and analysis accuracy. A doubling model is employed to compute the effective reflectivity, observed from the satellite, as a function of ground reflectivity, solar zenith angle and aerosol optical thickness for standard atmosphere. The relation between the effective reflectivity and ground reflectivity is approximately linear. It is shown that for a horizontally homogeneous atmosphere, the classification statistics from a maximum likelihood classifier remains unchanged under these transforms. If inhomogeneity is present, the divergence between clusters is reduced, and correlation between spectral bands increases. Radiance reflected by the background area surrounding the target may also reach the satellite. The influence of background reflectivity on effective reflectivity is discussed.

Kiang, R. K.↗
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 NTRS2019

Method for Tracking and Communicating Aggregate Risk Through the Use of Model-Based Systems Engineering (MBSE) Tools

Large, complex projects can identify a significant number and variety of risks, throughout the project life cycle. These risks are analyzed, mitigated, closed or accepted as independent uncertainties. Once closed or accepted, it is easy for projects to lose awareness of their impact. In reality, each of these risks contributes some amount to the overall risk posture of the project. The ability to track and effectively communicate this aggregate risk has represented a challenge to project management. There have been previous attempts to create a schema to communicate the aggregate effect of risks, without notable success. Most of these attempts have centered on some additive metric derived from the scoring of likelihood and consequence values. This, in and of itself, is a logical approach, but all too often the scores were then aggregated to a level where all context was lost. One weakness has been a lack of attempt to create linkages or logical groups of the risks upon which useful aggregation could then occur. The overall move to model-based (systems) engineering (MBSE) has opened up a vast frontier of opportunities to better integrate all project data. MBSE provides an underlying layer that links data items to each other. Objectives link to requirements, which then link to functions, functions to physical architecture items, and so on, as far down as projects want to model. While it started with a focus on modeling requirements based on things like use cases, efforts are now underway to integrate safety and mission assurance (S&MA) information and analyses, such as risks. This effort, called Model Based Mission Assurance (MBMA), is yielding models that are more useful and are a more accurate representations of the systems. MBSE models, with this ability to link related items, provide a new means of tracking and communicating aggregate risks. In the proposed method, risks are added into the models as distinct items, having attributes that communicate a scoring derived from the likelihood and consequence values as charted on the standard NASA 5x5 risk matrix. Like earlier efforts, each box in the 5x5 has an associated scoring, which may include both a current score and potential post-mitigation/control score. The risk items are then linked to elements of the model, such as system objectives/goals, requirements, functions, or physical architecture items, with "Risk to" relationships. These risks will then be communicated by use of reports generated from the model, detailing all risks and/or hazards linked to model elements. These reports can include aggregate impacts, including a current scoring and potential future state scoring based on the planned mitigations and/or controls. These reports will show all risks, open, accepted, and closed, linked to project objectives or requirements. When run as part of an upcoming risk acceptance discussion, these reports will serve to remind the team of all previous risks that relate to the effected portion of the system. When included as part of periodic program or project reviews, risk reviews, and safety reviews, this method can improve the overall understanding of the system's true risk posture. This proposed method takes full advantage of the advances that modern modeling techniques provide, with a minimal investment of additional time. Utilizing the model environment also enables a near constant access to current state of aggregate risks.

model based mission assurance↗
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 NTRS1990

A search for anisotropy in the cosmic microwave radiation at medium angular scales

The results are reported from a search for anisotropy in the cosmic microwave radiation (CMR) at angular scales of 0.5 to 5 deg. No temperature fluctuations are detected, and limits are placed on intrinsic CMR anisotropy. These limits are expressed in terms of two models which describe the temperature fluctuations. For models specified by a Gaussian-shaped correlation function, the fluctuation amplitude is found to be 1.1 x 10 to the -4th or less at 1.1 deg; for models with monochromatic fluctuations it is 7.5 x 10 to the -5th or less at 1.7 deg. These limits satisfy the likelihood ratio test at the 95 percent confidence level. The implications of the results for large-scale structure information scenarios are discussed.

Timbie, Peter T.↗
NASA NTRS1993

Variability of the occurrence frequency of solar flares as a function of peak hard X-ray rate

We study the occurrence frequency of solar flares as a function of the hard X-ray peak count rate, using observations of the Solar Maximum Mission. The size distributions are well represented by power-law distributions with negative indices. As a better alternative to the conventional method, we devise a maximum likelihood method of determining the power-law index of the size distribution. We find that the power-law index of the size distribution changes with time and with the phase of the 154-day periodicity. The size distribution is steeper during the maximum years of solar cycle 21 (1980 and 1981) than during the declining phase (1982-1984). The size distribution, however, is flatter during the maximum phase of the 154-day periodicity than during the minimum phase. The implications of these findings are discussed.

Bai, T.↗
NASA NTRS2012

Current-State Constrained Filter Bank for Wald Testing of Spacecraft Conjunctions

We propose a filter bank consisting of an ordinary current-state extended Kalman filter, and two similar but constrained filters: one is constrained by a null hypothesis that the miss distance between two conjuncting spacecraft is inside their combined hard body radius at the predicted time of closest approach, and one is constrained by an alternative complementary hypothesis. The unconstrained filter is the basis of an initial screening for close approaches of interest. Once the initial screening detects a possibly risky conjunction, the unconstrained filter also governs measurement editing for all three filters, and predicts the time of closest approach. The constrained filters operate only when conjunctions of interest occur. The computed likelihoods of the innovations of the two constrained filters form a ratio for a Wald sequential probability ratio test. The Wald test guides risk mitigation maneuver decisions based on explicit false alarm and missed detection criteria. Since only current-state Kalman filtering is required to compute the innovations for the likelihood ratio, the present approach does not require the mapping of probability density forward to the time of closest approach. Instead, the hard-body constraint manifold is mapped to the filter update time by applying a sigma-point transformation to a projection function. Although many projectors are available, we choose one based on Lambert-style differential correction of the current-state velocity. We have tested our method using a scenario based on the Magnetospheric Multi-Scale mission, scheduled for launch in late 2014. This mission involves formation flight in highly elliptical orbits of four spinning spacecraft equipped with antennas extending 120 meters tip-to-tip. Eccentricities range from 0.82 to 0.91, and close approaches generally occur in the vicinity of perigee, where rapid changes in geometry may occur. Testing the method using two 12,000-case Monte Carlo simulations, we found the method achieved a missed detection rate of 0.1%, and a false alarm rate of 2%.

Carpenter, J. Russell↗
NASA NTRS1991

Coding gains and error rates from the Big Viterbi Decoder

A prototype hardware Big Viterbi Decoder (BVD) was completed for an experiment with the Galileo Spacecraft. Searches for new convolutional codes, studies of Viterbi decoder hardware designs and architectures, mathematical formulations, and decompositions of the deBruijn graph into identical and hierarchical subgraphs, and very large scale integration (VLSI) chip design are just a few examples of tasks completed for this project. The BVD bit error rates (BER), measured from hardware and software simulations, are plotted as a function of bit signal to noise ratio E sub b/N sub 0 on the additive white Gaussian noise channel. Using the constraint length 15, rate 1/4, experimental convolutional code for the Galileo mission, the BVD gains 1.5 dB over the NASA standard (7,1/2) Maximum Likelihood Convolution Decoder (MCD) at a BER of 0.005. At this BER, the same gain results when the (255,233) NASA standard Reed-Solomon decoder is used, which yields a word error rate of 2.1 x 10(exp -8) and a BER of 1.4 x 10(exp -9). The (15, 1/6) code to be used by the Cometary Rendezvous Asteroid Flyby (CRAF)/Cassini Missions yields 1.7 dB of coding gain. These gains are measured with respect to symbols input to the BVD and increase with decreasing BER. Also, 8-bit input symbol quantization makes the BVD resistant to demodulated signal-level variations which may cause higher bandwidth than the NASA (7,1/2) code, these gains are offset by about 0.1 dB of expected additional receiver losses. Coding gains of several decibels are possible by compressing all spacecraft data.

Onyszchuk, I. M.↗
NASA NTRS1992

ERS-1 scatterometer calibration and validation activities at ECMWF. B: From radar backscatter characteristics to wind vector solutions

Calibration and validation activities for the ERS-1 scatterometer were carried out at ECMWF (European Center for Medium range Weather Forecast) complementary to the 'Haltenbanken' field campaign off the coast of Norway. At a Numerical Weather Prediction (NWP) center a wealth of verifying data is available both in time and space. This data is used to redefine the wind retrieval procedure given the instrumental characteristics. It was found that a maximum likelihood estimation procedure to obtain the coefficients of a reformulated sigma deg to wind relationship should use radar measurements in logarithmic rather than physical space, and use winds as the wind components rather than wind speed and direction. Doing this, a much more accurate transfer function than the one currently operated by ESA was derived. Sigma deg measurement space shows no signature of a separation in an upwind solution cone and a downwind solution cone. As such signature was anticipated in ESA's wind direction ambiguity removal algorithm, reconsideration of the procedure is necessary. Despite the fact that revisions have to be made in the process of wind retrieval; a grid potential is shown for scatterometry in meteorology and climatology.

Stoffelen, AD↗
NASA NTRS1998

Role of metabolic gases in bubble formation during hypobaric exposures

Our hypothesis is that metabolic gases play a role in the initial explosive growth phase of bubble formation during hypobaric exposures. Models that account for optimal internal tensions of dissolved gases to predict the probability of occurrence of venous gas emboli were statistically fitted to 426 hypobaric exposures from National Aeronautics and Space Administration tests. The presence of venous gas emboli in the pulmonary artery was detected with an ultrasound Doppler detector. The model fit and parameter estimation were done by using the statistical method of maximum likelihood. The analysis results were as follows. 1) For the model without an input of noninert dissolved gas tissue tension, the log likelihood (in absolute value) was 255.01. 2) When an additional parameter was added to the model to account for the dissolved noninert gas tissue tension, the log likelihood was 251.70. The significance of the additional parameter was established based on the likelihood ratio test (P < 0.012). 3) The parameter estimate for the dissolved noninert gas tissue tension participating in bubble formation was 19. 1 kPa (143 mmHg). 4) The additional gas tissue tension, supposedly due to noninert gases, did not show an exponential decay as a function of time during denitrogenation, but it remained constant. 5) The positive sign for this parameter term in the model is characteristic of an outward radial pressure of gases in the bubble. This analysis suggests that dissolved gases other than N2 in tissues may facilitate the initial explosive bubble-growth phase.

NASA Center JSC↗
NASA NTRS2009

Gaussian and Lognormal Models of Hurricane Gust Factors

A document describes a tool that predicts the likelihood of land-falling tropical storms and hurricanes exceeding specified peak speeds, given the mean wind speed at various heights of up to 500 feet (150 meters) above ground level. Empirical models to calculate mean and standard deviation of the gust factor as a function of height and mean wind speed were developed in Excel based on data from previous hurricanes. Separate models were developed for Gaussian and offset lognormal distributions for the gust factor. Rather than forecasting a single, specific peak wind speed, this tool provides a probability of exceeding a specified value. This probability is provided as a function of height, allowing it to be applied at a height appropriate for tall structures. The user inputs the mean wind speed, height, and operational threshold. The tool produces the probability from each model that the given threshold will be exceeded. This application does have its limits. They were tested only in tropical storm conditions associated with the periphery of hurricanes. Winds of similar speed produced by non-tropical system may have different turbulence dynamics and stability, which may change those winds statistical characteristics. These models were developed along the Central Florida seacoast, and their results may not accurately extrapolate to inland areas, or even to coastal sites that are different from those used to build the models. Although this tool cannot be generalized for use in different environments, its methodology could be applied to those locations to develop a similar tool tuned to local conditions.

Merceret, Frank↗
NASA NTRS2009

Defining Nitrogen Kinetics for Air Break in Prebreathe

Actual tissue nitrogen (N2) kinetics are complex; the uptake and elimination is often approximated with a single half-time compartment in statistical descriptions of denitrogenation [prebreathe (PB)] protocols. Air breaks during PB complicate N2 kinetics. A comparison of symmetrical versus asymmetrical N2 kinetics was performed using the time to onset of hypobaric decompression sickness (DCS) as a surrogate for actual venous N2 tension. Published results of 12 tests involving 179 hypobaric exposures in altitude chambers after PB, with and without air breaks, provide the complex protocols from which to model N2 kinetics. DCS survival time for combined control and air breaks were described with an accelerated log logistic model where N2 uptake and elimination before, during, and after the air break was computed with a simple exponential function or a function that changed half-time depending on ambient N2 partial pressure. P1N2-P2 = delta P defined DCS dose for each altitude exposure, where P2 was the test altitude and P1N2 was computed N2 pressure at the beginning of the altitude exposure. The log likelihood (LL) without DCS dose (null model) was -155.6, and improved (best-fit) to -97.2 when dose was defined with a 240 min half-time for both N2 elimination and uptake during the PB. The description of DCS survival time was less precise with asymmetrical N2 kinetics, for example, LL was -98.9 with 240 min half-time elimination and 120 min half-time uptake. The statistical regression described survival time mechanistically linked to symmetrical N2 kinetics during PBs that also included air breaks. The results are data-specific, and additional data may change the conclusion. The regression is useful to compute additional PB time to compensate for an air break in PB within the narrow range of tested conditions.

Conkin, Johnny↗