Error probabilities for maximum likelihood detection of M-ary Poisson processes in Poisson noise
Error probabilities for maximum signal detection in presence of Poisson noise
Gagliardi, R. M.↗
SEARCH · Search NASA
Results for “Poisson process”
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.
AN OPTIMUM DEMODULATOR FOR POISSON PROCESSES- PHOTON SOURCE DETECTORS
Optimum demodulator for poisson processes is determined for signal processing of photon radiation
PHOTON-ELECTRON INTERACTION↗
Modeling laser velocimeter signals as triply stochastic Poisson processes
Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.
Mayo, W. T., Jr.↗
Convolutional Non-Homogeneous Poisson Process and its Application to Wildfire Ignition Risk Quantification for Power Delivery Networks
To quantify wildfire ignition risks on power delivery networks, the current practice predominantly relies on the empirically calculated fire danger indices, which may not well capture the effects of dynamically changing environmental factors. This article proposes a spatio-temporal point process model, known as the Convolutional Non-homogeneous Poisson Process (cNHPP), and applies the model to quantify wildfire ignition risks for power delivery networks. The proposed model captures both the current (i.e., instantaneous) and cumulative (i.e., historical) effects of key environmental processes (i.e., covariates) on wildfire risks, as well as the spatio-temporal dependency among different segments of the power delivery network. The computation and interpretation of the intensity function are thoroughly investigated. We apply the proposed approach to estimate wildfire ignition risks on major transmission lines in California, using historical fire data, meteorological and vegetation data obtained from the National Oceanic and Atmospheric Administration and National Aeronautics and Space Administration. Here, a comprehensive comparison study is performed to show the applicability and predictive capability of the proposed approach.
Non-homogeneous Poisson Process↗
A Poisson process approximation for generalized K-5 confidence regions
One-sided confidence regions for continuous cumulative distribution functions are constructed using empirical cumulative distribution functions and the generalized Kolmogorov-Smirnov distance. The band width of such regions becomes narrower in the right or left tail of the distribution. To avoid tedious computation of confidence levels and critical values, an approximation based on the Poisson process is introduced. This aproximation provides a conservative confidence region; moreover, the approximation error decreases monotonically to 0 as sample size increases. Critical values necessary for implementation are given. Applications are made to the areas of risk analysis, investment modeling, reliability assessment, and analysis of fault tolerant systems.
Arsham, H.↗
Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass
Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.
Saleh, B. E. A.↗
Optical Signal Processing: Poisson Image Restoration and Shearing Interferometry
Optical signal processing can be performed in either digital or analog systems. Digital computers and coherent optical systems are discussed as they are used in optical signal processing. Topics include: image restoration; phase-object visualization; image contrast reversal; optical computation; image multiplexing; and fabrication of spatial filters. Digital optical data processing deals with restoration of images degraded by signal-dependent noise. When the input data of an image restoration system are the numbers of photoelectrons received from various areas of a photosensitive surface, the data are Poisson distributed with mean values proportional to the illuminance of the incoherently radiating object and background light. Optical signal processing using coherent optical systems is also discussed. Following a brief review of the pertinent details of Ronchi's diffraction grating interferometer, moire effect, carrier-frequency photography, and achromatic holography, two new shearing interferometers based on them are presented. Both interferometers can produce variable shear.
Hong, Yie-Ming↗
Application of spatial Poisson process models to air mass thunderstorm rainfall
Eight years of summer storm rainfall observations from 93 stations in and around the 154 sq km Walnut Gulch catchment of the Agricultural Research Service, U.S. Department of Agriculture, in Arizona are processed to yield the total station depths of 428 storms. Statistical analysis of these random fields yields the first two moments, the spatial correlation and variance functions, and the spatial distribution of total rainfall for each storm. The absolute and relative worth of three Poisson models are evaluated by comparing their prediction of the spatial distribution of storm rainfall with observations from the second half of the sample. The effect of interstorm parameter variation is examined.
Eagleson, P. S.↗
The Poisson tensor completion non-parametric differential entropy estimator
We introduce the Poisson tensor completion (PTC) estimator, a non-parametric differential entropy estimator. The PTC estimator leverages inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial Poisson process. The Poisson tensor decomposition leads to a completion of the intensity measure over all bins—including those containing few to no samples—and leads to our proposed PTC differential entropy estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values and so can be safely used directly in entropy estimation. Our estimator is the first tensor-based estimator that exploits the underlying spatial Poisson process related to the histogram explicitly when estimating the probability density with low-rank tensor decompositions for the purpose of tensor completion. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.
42 ENGINEERING↗
Applying Flammability Limit Probabilities and the Normoxic Upward Limiting Pressure Concept to NASA STD-6001 Test 1
Repeated Test 1 extinction tests near the upward flammability limit are expected to follow a Poisson process trend. This Poisson process trend suggests that rather than define a ULOI and MOC (which requires two limits to be determined), it might be better to define a single upward limit as being where 1/e (where e (approx. equal to 2.7183) is the characteristic time of the normalized Poisson process) of the materials burn, or, rounding, where approximately 1/3 of the samples fail the test (and burn). Recognizing that spacecraft atmospheres will not bound the entire oxygen-pressure parameter space, but actually lie along the normoxic atmosphere control band, we can focus the materials flammability testing along this normoxic band. A Normoxic Upward Limiting Pressure (NULP) is defined that determines the minimum safe total pressure for a material within the constant partial pressure control band. Then, increasing this pressure limit by a factor of safety, we can define the material as being safe to use at the NULP + SF (where SF is on the order of 10 kilopascal, based on existing flammability data). It is recommended that the thickest material to be tested with the current Test 1 igniter should be 3 mm thick (1/8 inches) to avoid the problem of differentiating between an ignition limit and a true flammability limit.
flammability↗
The Use of Crow-AMSAA Plots to Assess Mishap Trends
Crow-AMSAA (CA) plots are used to model reliability growth. Use of CA plots has expanded into other areas, such as tracking events of interest to management, maintenance problems, and safety mishaps. Safety mishaps can often be successfully modeled using a Poisson probability distribution. CA plots show a Poisson process in log-log space. If the safety mishaps are a stable homogenous Poisson process, a linear fit to the points in a CA plot will have a slope of one. Slopes of greater than one indicate a nonhomogenous Poisson process, with increasing occurrence. Slopes of less than one indicate a nonhomogenous Poisson process, with decreasing occurrence. Changes in slope, known as "cusps," indicate a change in process, which could be an improvement or a degradation. After presenting the CA conceptual framework, examples are given of trending slips, trips and falls, and ergonomic incidents at NASA (from Agency-level data). Crow-AMSAA plotting is a robust tool for trending safety mishaps that can provide insight into safety performance over time.
Dawson, Jeffrey W.↗
The Poisson tensor completion parametric estimator
We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial non-homogeneous Poisson process. The Poisson tensor decomposition leads to a completion of the mean measure over all bins—including those containing few to no samples—and leads to our proposed estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values obviating the need for additional constraints to ensure non-negativity. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.
97 MATHEMATICS AND COMPUTING↗
Joint aircraft loading/structure response statistics of time to service crack initiation
A reliability analysis for predicting the statistical distribution of time to fatigue crack initiation for aircraft structures in service is presented. The present analysis utilizes the statistical data of the specimen fatigue tests, the full-scale structure tests, and the statistical dispersion of aircraft service loads. The statistical distribution of the time to fatigue crack initiation of the full-scale structure under laboratory loading spectrum is assumed to be Weibull. The service loads for gust turbulences are modeled as Poisson processes for transport-type aircraft, while the maneuver loads are modeled as compound Poisson processes for fighter and training aircraft. It is found that the statistical distribution of time to fatigue crack initiation for aircraft structures in service is not Weibull and that the prediction on the basis of the Weibull distribution is unconservative, in particular in the early service time.
Yang, J.-N.↗
Study of photon correlation techniques for processing of laser velocimeter signals
The objective was to provide the theory and a system design for a new type of photon counting processor for low level dual scatter laser velocimeter (LV) signals which would be capable of both the first order measurements of mean flow and turbulence intensity and also the second order time statistics: cross correlation auto correlation, and related spectra. A general Poisson process model for low level LV signals and noise which is valid from the photon-resolved regime all the way to the limiting case of nonstationary Gaussian noise was used. Computer simulation algorithms and higher order statistical moment analysis of Poisson processes were derived and applied to the analysis of photon correlation techniques. A system design using a unique dual correlate and subtract frequency discriminator technique is postulated and analyzed. Expectation analysis indicates that the objective measurements are feasible.
Mayo, W. T., Jr.↗
M-ary Poisson Detection and Optical Communications
Optical communications - maximum likelihood detection of M-ary Poisson processes in background of additive Poisson noise
Gagliardi, R. M.↗
Reliability growth modeling analysis of the space shuttle main engines based upon the Weibull process
The Weibull process, identified as the inhomogeneous Poisson process with the Weibull intensity function, is used to model the reliability growth assessment of the space shuttle main engine test and flight failure data. Additional tables of percentage-point probabilities for several different values of the confidence coefficient have been generated for setting (1-alpha)100-percent two sided confidence interval estimates on the mean time between failures. The tabled data pertain to two cases: (1) time-terminated testing, and (2) failure-terminated testing. The critical values of the three test statistics, namely Cramer-von Mises, Kolmogorov-Smirnov, and chi-square, were calculated and tabled for use in the goodness of fit tests for the engine reliability data. Numerical results are presented for five different groupings of the engine data that reflect the actual response to the failures.
Wheeler, J. T.↗
Spatial Correlations of the Poisson Model for Radiation Transport
Characterizing the relationship between bulk physical properties and mixing in randomly heterogeneous media is a central challenge across many areas of science and engineering. A benchmark model for such studies is the Poisson model, a random tessellation of space by a Poisson process of hyperplanes. In radiation transport studies, the lack of exact expressions for the Poisson model’s spatial multipoint functions has led to approximate methods being used, introducing unquantified sources of error. Here, we recently introduced an exact solution for the Poisson model’s multipoint functions and closely related conditional probability functions (CPFs), providing a new opportunity to understand and reduce these sources of error. In this paper, we enable a more rigorous investigation of radiation transport in stochastic media by applying the recently introduced exact solution for the Poisson model’s CPFs. This paper consists of three main contributions. First, we introduce a unified framework for CPFs of the Poisson model, encompassing the recently introduced exact CPFs as well as the previously introduced atomic mix, nearest-neighbor, and combination CPFs. This framework also includes existing pruning techniques for the approximate CPFs, such as angular exclusion, as well as a novel form of angular exclusion suitable for the exact CPFs. Second, we use the exact CPFs to characterize the spatial regions where each approximate three-point CPF is most accurate, thereby explaining the observed hierarchy of accuracy among the approximate models. Finally, we evaluate material transmittance, reflectance, and flux in a three-dimensional test problem using conditional point sampling, demonstrating the relationship between CPF accuracy and transport simulation accuracy.
Poisson model↗
Spatial modelling of total storm rainfall
The spatial structure of the depth of rainfall from a stationary storm event is investigated by using point process techniques. Cells are assumed to be stationary and to be distributed in space either independently according to a Poisson process, or with clustering according to a Neyman-Scott scheme. Total storm rainfall at the centre of each cell is a random variable and rainfall is distributed around the centre in a way specified by a spread function that may incorporate random parameters. The mean, variance and covariance structure of the precipitation depth at a point are obtained for different spread functions. For exponentially distributed centre depth and a spread function having quadratically exponential decay, the total storm depth at any point in the field is shown to have a gamma distribution. The probability of zero rainfall at a point is investigated, as is the stochastic variability of model parameters from storm to storm. Data from the Upper Rio Guaire basin in Venezuela are used in illustration.
Rodriguez-Iturbe, I.↗