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At least 253 records · Page 14
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NASA NTRS2002

Maximum Likelihood Estimation of Spectra Information from Multiple Independent Astrophysics Data Sets

The Maximum Likelihood (ML) statistical theory required to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments is developed in this paper. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral information based on the combination of data sets. The procedure is of significant value to both existing data sets and those to be produced by future astrophysics missions consisting of two or more detectors by allowing instrument developers to optimize each detector's design parameters through simulation studies in order to design and build complementary detectors that will maximize the precision with which the science objectives may be obtained. The benefits of this ML theory and its application is measured in terms of the reduction of the statistical errors (standard deviations) of the spectra information using the multiple data sets in concert as compared to the statistical errors of the spectra information when the data sets are considered separately, as well as any biases resulting from poor statistics in one or more of the individual data sets that might be reduced when the data sets are combined.

Howell, Leonard W., Jr.↗
NASA NTRS2002

Gyro-based Maximum-Likelihood Thruster Fault Detection and Identification

When building smaller, less expensive spacecraft, there is a need for intelligent fault tolerance vs. increased hardware redundancy. If fault tolerance can be achieved using existing navigation sensors, cost and vehicle complexity can be reduced. A maximum likelihood-based approach to thruster fault detection and identification (FDI) for spacecraft is developed here and applied in simulation to the X-38 space vehicle. The system uses only gyro signals to detect and identify hard, abrupt, single and multiple jet on- and off-failures. Faults are detected within one second and identified within one to five accords,

Wilson, Edward↗
NASA NTRS2002

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.

Howell, L. W.↗
NASA NTRS2003

Statistical Properties of Maximum Likelihood Estimators of Power Law Spectra Information

A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.

Howell, L. W., Jr.↗
NASA NTRS2002

Maximum Likelihood Estimation of the Broken Power Law Spectral Parameters with Detector Design Applications

The method of Maximum Likelihood (ML) is used to estimate the spectral parameters of an assumed broken power law energy spectrum from simulated detector responses. This methodology, which requires the complete specificity of all cosmic-ray detector design parameters, is shown to provide approximately unbiased, minimum variance, and normally distributed spectra information for events detected by an instrument having a wide range of commonly used detector response functions. The ML procedure, coupled with the simulated performance of a proposed space-based detector and its planned life cycle, has proved to be of significant value in the design phase of a new science instrument. The procedure helped make important trade studies in design parameters as a function of the science objectives, which is particularly important for space-based detectors where physical parameters, such as dimension and weight, impose rigorous practical limits to the design envelope. This ML methodology is then generalized to estimate broken power law spectral parameters from real cosmic-ray data sets.

Howell, Leonard W.↗
NASA NTRS1988

Method and apparatus for implementing a maximum-likelihood decoder in a hypercube network

A method and a structure to implement maximum-likelihood decoding of convolutional codes on a network of microprocessors interconnected as an n-dimensional cube (hypercube). By proper reordering of states in the decoder, only communication between adjacent processors is required. Faster and more efficient operation is enabled, and decoding of large constraint length codes is feasible using standard VLSI technology.

Pollara-Bozzola, Fabrizio↗
NASA NTRS1989

Method and apparatus for implementing a traceback maximum-likelihood decoder in a hypercube network

A method and a structure to implement maximum-likelihood decoding of convolutional codes on a network of microprocessors interconnected as an n-dimensional cube (hypercube). By proper reordering of states in the decoder, only communication between adjacent processors is required. Communication time is limited to that required for communication only of the accumulated metrics and not the survivor parameters of a Viterbi decoding algorithm. The survivor parameters are stored at a local processor's memory and a trace-back method is employed to ascertain the decoding result. Faster and more efficient operation is enabled, and decoding of large constraint length codes is feasible using standard VLSI technology.

Pollara-Bozzola, Fabrizio↗
NASA NTRS2010

Efficient Bit-to-Symbol Likelihood Mappings

This innovation is an efficient algorithm designed to perform bit-to-symbol and symbol-to-bit likelihood mappings that represent a significant portion of the complexity of an error-correction code decoder for high-order constellations. Recent implementation of the algorithm in hardware has yielded an 8- percent reduction in overall area relative to the prior design.

Moision, Bruce E.↗
NASA NTRS2010

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Erkmen, Baris I.↗
NASA NTRS2011

Assessing the Likelihood of Rare Medical Events in Astronauts

Despite over half a century of manned space flight, the space flight community is only now coming to fully assess the short and long term medical dangers of exposure to reduced gravity environments. Further, as new manned spacecraft are designed and with the advent of commercial flight capabilities to the general public, a full understanding of medical risk becomes even more critical for maintaining and understanding mission safety and crew health. To address these critical issues, the National Aeronautics and Space Administration (NASA) Human Research Program (HRP) has begun to address the medical hazards with a formalized risk management approach by effectively identifying and attempting to mitigate acute and chronic medical risks to manned space flight. This paper describes NASA Glenn Research Center?s (GRC) efforts to develop a systematic methodology to assess the likelihood of in-flight medical conditions. Using a probabilistic approach, medical risks are assessed using well established and accepted biomedical and human performance models in combination with fundamentally observed data that defines the astronauts? physical conditions, environment and activity levels. Two different examples of space flight risk are used to show the versatility of our approach and how it successfully integrates disparate information to provide HRP decision makers with a valuable source of information which is otherwise lacking.

Myers, Jerry G., Jr.↗
NASA NTRS2012

Modeling and Maximum Likelihood Fitting of Gamma-Ray and Radio Light Curves of Millisecond Pulsars Detected with Fermi

Pulsed gamma rays have been detected with the Fermi Large Area Telescope (LAT) from more than 20 millisecond pulsars (MSPs), some of which were discovered in radio observations of bright, unassociated LAT sources. We have fit the radio and gamma-ray light curves of 19 LAT-detected MSPs in the context of geometric, outermagnetospheric emission models assuming the retarded vacuum dipole magnetic field using a Markov chain Monte Carlo maximum likelihood technique. We find that, in many cases, the models are able to reproduce the observed light curves well and provide constraints on the viewing geometries that are in agreement with those from radio polarization measurements. Additionally, for some MSPs we constrain the altitudes of both the gamma-ray and radio emission regions. The best-fit magnetic inclination angles are found to cover a broader range than those of non-recycled gamma-ray pulsars.

Johnson, T. J.↗
NASA NTRS2012

Likelihood-Based Climate Model Evaluation

Climate models are deterministic, mathematical descriptions of the physics of climate. Confidence in predictions of future climate is increased if the physics are verifiably correct. A necessary, (but not sufficient) condition is that past and present climate be simulated well. Quantify the likelihood that a (summary statistic computed from a) set of observations arises from a physical system with the characteristics captured by a model generated time series. Given a prior on models, we can go further: posterior distribution of model given observations.

climate models↗
NASA NTRS2019

The Implementation of Maximum Likelihood Estimation in Space Launch System Vehicle Design

The Space Launch System uses a Maximum Likelihood Estimation process in conjunction with Design of Experiments to develop statistically representative vehicles for the Block 1 configuration. These vehicles are then used to estimate maximum load conditions for simulating stressing cases in other simulations. This paper discusses the modeling process and how SLS captures manufacturing uncertainty in the launch vehicle design. It also provides an overview of the differences between Block 1 statistical representations. This paper also discusses proper grid choice as well as which uncertainties drive the vehicle design.

Stein, W. B.↗
NASA NTRS2016

Maximum Likelihood Synchronization for Pulse Position Modulation with Inter-Symbol Guard Times

Deep space optical communications promises orders-of-magnitude growth in communication capacity, supporting high data rate applications such as video streaming and high-bandwidth science instruments. Pulse position modulation is the modulation format of choice for deep space applications, and by inserting inter-symbol guard times between the symbols, the signal carries the timing information needed by the demodulator. Accurately extracting this timing information is crucial to demodulating and decoding this signal. In this paper we propose a low complexity maximum likelihood timing estimator for pulse position modulation with inter-symbol guard times which significantly outperforms the prior art in this domain. We show that this estimator can achieve the same performance as prior estimators with an order-of-magnitude less signal flux, or multiple orders-of-magnitude less flux-accumulation time. Further we show that this estimator achieves the Cramer-Rao bound, making it asymptotically efficient. This method does not require an explicit synchronization sequence, freeing up channel resources for data transmission.

Rogalin, Ryan↗
NASA NTRS2022

Deriving Severe Hail Likelihood from Satellite Observations and Model Reanalysis Parameters using a Deep Neural Network

Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) series, have been observing severe convection at 15–60-minute intervals for over 40 years. When properly assessed, such a data record can be valuable in efforts of estimating severe storm risk throughout the diurnal cycle based on automated detection of patterns consistently found atop severe storms. Furthermore, environmental conditions favorable for severe weather are well-known and are thought to be represented well by modern reanalysis products. Promoting resilience against such hazards on local and global scales is a chief goal the NASA Disasters program, which seeks to encourage use of satellite observations to mitigate risk. For instance, hail is the costliest severe weather hazard across the globe in terms of insured loss, but reporting inconsistencies for hail events globally make it difficult to develop models that can quantify the risk. Satellite observation and model reanalysis taken together have the potential to, with reasonable skill and specificity, characterize environmental conditions that are favorable for hazardous weather, and thereby enable creation of hazard climatologie. Such climatologies are particularly useful over regions without extensive radar networks or storm reporting. By mapping the multivariate combination of observed cloud features and reanalysis environmental parameters/indices to United States Next Generation Weather Radar (NEXRAD) radar-estimated Maximum Expected Size of Hail (MESH) by way of a deep neural network (DNN), estimates of likelihood for potentially severe hail can be produced. Such estimates are of greater complexity and efficiency than could be performed with previous multivariate or logistic regression analyses for observed points within convective systems. Statistical distributions of convective parameters from satellite and reanalysis are shown to highlight non-severe/severe class separation for well-known hailstorm predictors, e.g., overshooting cloud top characteristics, deep-layer wind shear, mid-level stability, helicity, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN, which can efficiently produce a quantitative hail risk metric with better than 70% detection rate and under 30% false alarms. These hail classifications can then be aggregated across the satellite record to yield a hazard climatology for hail frequency and severity – knowledge of which is of particular interest to those who manage risk (e.g., insurers) and are seeking opportunities to identify hail-prone regions, particularly in developing nations. This NASA study uses satellite observations and model parameters in a DNN to perform climatological hailstorm analysis in support of catastrophe model development, with the hope of promoting risk resilience particularly in regions without adequate weather radar coverage.

Passive Remote Sensing↗