Weak convergence of probability measures on product spaces with applications to sums of random vectors
Weak convergence of probability measures on product spaces with applications to sums of random vectors
Iglehart, D. L.↗
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On the probability density function of the squared envelope of a sum of random phase vectors
Weber et al. (1980) have found that a generic problem arises in the study of multiuser FHMA/MFSK systems. According to this problem, the presence of the other channel users acts as interference to reception of the desired user's transmission. The present investigation is concerned with a recursive solution in which the recursion parameter is the number of vectors in the sum. A mathematical characterization of such a solution is presented, taking into account the simple two-vector case in which a well-known closed form result is possible. Some numerical results are also discussed. It is pointed out that the considered recursive solution provides a break in the bottleneck associated with the exact computation of the error probability performance of multiuser FHMA/MFSK systems and single access MFSK systems corrupted by multitone jamming.
Simon, M. K.↗
Properties of sums of pseudo-random variables in feedback shift registers Final report
Synthesis of pseudorandom distribution for sum values in feedback shift registers
Healy, T. J.↗
Microwave scatter and sea state estimation - Two-scale ocean wave models
The efficient estimation of ocean wave-structure parameters with a remote, narrow-beam, pulsed, microwave radar at intermediate incidence angles is discussed. The sea surface is described as the sum of random small- and large-scale structures (waves), the latter the sum of a sinusoid and a random field. It is shown that the small-scale structure is responsible for scattering and that the scatter depends parametrically on the large-scale structure. For the estimation problem it is assumed, reasonably, that the received signal is normally distributed: a relatively simple processor which will efficiently estimate parameters of the sinusoidal structure is illustrated and its performance discussed. A brief comparison is made with a normal incidence system with which the variance of the large-scale random roughness can be estimated.
Harger, R. O.↗
Experiments with digital computer simulations of pseudo-random noise generators.
Digital computer simulations of pseudorandom noise generators, determining empirical sum distribution approximation of binomial variable
SUM↗
Theory of radio occultation by Saturn's rings
The radio occultation technique, as applied to Saturn's rings, is developed as a new method for the study of the physical properties of planetary ring systems. The rings are treated as a Doppler-spread radar target composed of an ensemble of discrete scatterers. The mathematical formulation of the received signal as a random-phasor-sum process is carried out following a conventional radar theory approach, providing a convenient starting point for deriving coherent signal parameters. A classical result is rederived for the equivalent refractive index of the medium. The analysis is generalized to include ringlets of arbitrary width and it is shown that when the width is such that two adjacent rays are differentially perturbed in phase, ray bending that causes focusing of the coherent signal may result. The diffuse component is also treated in detail.
Marouf, E. A.↗
Quantification of Cross-coupling and Motion Feedthrough for Multiaxis Controllers Used in an Air Combat Flying Task
A real-time piloted simulation of an air-to-air combat flying task using a wings-level-turn aircraft and various novel controllers was conducted. One objective is to quantify how the pilot interacts with the controllers and control modes, including: (1) controller versus aircraft response; (2) proprioceptive cross-coupling among axes of the controllers; and (3) biodynamic cross-coupling between the aircraft motions and the controllers. In order to aid in identifying the items listed above, both the target aircraft and the large amplitude multimode aerospace research simulator (LAMARS) motion system were distributed with quasi-random sums-of-sinusoids. Since the disturbances were separated in frequency, spectral analysis techniques were used to identify the three items listed. The results of the spectral analysis of controller motions from the two-axis side stick, a twist grip mounted on the side stick, a thumb button mounted on the side stick, and conventional rudder pedals are presented. Conclusions and recommendations for further research are also presented.
Jewell, W. E.↗
Measurement of human pilot dynamic characteristics in flight simulation
Fast Fourier Transform (FFT) and Least Square Error (LSE) estimation techniques were applied to the problem of identifying pilot-vehicle dynamic characteristics in flight simulation. A brief investigation of the effects of noise, input bandwidth and system delay upon the FFT and LSE techniques was undertaken using synthetic data. Data from a piloted simulation conducted at NASA Ames Research Center was then analyzed. The simulation was performed in the NASA Ames Research Center Variable Stability CH-47B helicopter operating in fixed-basis simulator mode. The piloting task consisted of maintaining the simulated vehicle over a moving hover pad whose motion was described by a random-appearing sum of sinusoids. The two test subjects used a head-down, color cathode ray tube (CRT) display for guidance and control information. Test configurations differed in the number of axes being controlled by the pilot (longitudinal only versus longitudinal and lateral), and in the presence or absence of an important display indicator called an 'acceleration ball'. A number of different pilot-vehicle transfer functions were measured, and where appropriate, qualitatively compared with theoretical pilot- vehicle models. Some indirect evidence suggesting pursuit behavior on the part of the test subjects is discussed.
Reedy, James T.↗
A Search Model for Imperfectly Detected Targets
Under the assumptions that 1) the search region can be divided up into N non-overlapping sub-regions that are searched sequentially, 2) the probability of detection is unity if a sub-region is selected, and 3) no information is available to guide the search, there are two extreme case models. The search can be done perfectly, leading to a uniform distribution over the number of searches required, or the search can be done with no memory, leading to a geometric distribution for the number of searches required with a success probability of 1/N. If the probability of detection P is less than unity, but the search is done otherwise perfectly, the searcher will have to search the N regions repeatedly until detection occurs. The number of searches is thus the sum two random variables. One is N times the number of full searches (a geometric distribution with success probability P) and the other is the uniform distribution over the integers 1 to N. The first three moments of this distribution were computed, giving the mean, standard deviation, and the kurtosis of the distribution as a function of the two parameters. The model was fit to the data presented last year (Ahumada, Billington, & Kaiwi, 2 required to find a single pixel target on a simulated horizon. The model gave a good fit to the three moments for all three observers.
Ahumada, Albert↗
Development of a Sensorimotor Ground Analog from Astronaut Postflight Experience
Exploration class missions including Artemis, Gateway, and beyond will require a new level of autonomy around periods of gravitational transition, where sensorimotor disturbances are great. Because of this, there is a need to define sensorimotor assessment thresholds that indicate when performance in operational tasks might be impacted or unsafe. To define these thresholds, a Sensorimotor Adaptation Analog (SAA) was proposed that could induce varying levels of sensorimotor disorientation through combined vestibular, visual, and proprioceptive disruptions. The purpose of this study was to gather subjective feedback on the SAA from previously flown astronauts that would mimic their post-flight experience and functional performance immediately after landing (R+0-4hrs; high level) and post-landing (R+24-48hrs; low level). The SAA consisted of galvanic vestibular stimulation (GVS), visual disorientation goggles, and a weighted suit to alter proprioceptive feedback and replicate subjective heaviness. A random sum-of-sines profile between 0-1Hz was used for the GVS with peak amplitudes ranging from 1-4mA. The GVS was applied first at the low (2mA) and high (3mA) levels, followed by the weighted suit alone, then combined with the GVS at the low (20% body weight) and high levels (40% body weight). Last, the disorientation goggles were applied alongside both the GVS and weighted suit at the low (0.07-0.10+ blood alcohol content (BAC)) and high (0.12-0.15+ BAC) levels. Each element of the SAA could be increased or decreased depending on crew feedback to find the disorientation levels that best matched their experience. Five USOS astronauts (1 male, 4 female) who had previously flown (average time since flight: 377 days) participated. Crewmembers reported that GVS alone replicated ~80-90% of their post-flight performance with the weighted suit fine-tuning the experience to replicate an additional 5-10% of their experience. Crewmembers did not believe the disorientation goggles represented either the visual disruptions or illusory sensations that they experienced, nor did they impact performance in post-flight tasks similarly. The final SAA, resulting from crewmember feedback, includes the GVS at the levels described above and the weighted suit at 15% and 30% body weight. The disorientation goggles were removed from SAA. These results provided a more realistic SAA that can be used to define the sensorimotor assessment thresholds through ground subjects and potentially expanded for use in countermeasure testing and as a pre-flight training tool.
S. C. Moudy↗
Where Lies the Quantumness Behind Detecting Electromagnetic Waves for Frequencies from Infrared and Up?
The synthesis of Newtonian concept of corpuscles during emission with Huygens’ concept of secondary-wavelets during propagation implies that all EM radiations from quantized atoms and molecules are released as discrete amount of energies. However, they propagate out as time-finite Maxwellian light pulses. Huygens also underscored that his secondary wavelets keep propagating as independent pulses in the absence of any interacting medium, or until intercepted by an interface with a medium or a detector. Then we use the Superposition Principle and the coherence theory to derive Einstein’s photoelectric equation by summing innumerable random time-finite pulses. This process driven approach should yield the characteristic statistical variations of photoelectron current pulses, as generated by photodetectors for different kinds of light sources. Lamb & Scully originally proposed this semiclassical approach without assuming that light actually consists of time finite pulses. The quantumness remains confined within the excitation and de-excitations processes in the material particles.
Electromagnetic Waves↗
Design of state-feedback controllers including sensitivity reduction, with applications to precision pointing
The design procedure of feedback controllers was described and the considerations for the selection of the design parameters were given. The frequency domain properties of single-input single-output systems using state feedback controllers are analyzed, and desirable phase and gain margin properties are demonstrated. Special consideration is given to the design of controllers for tracking systems, especially those designed to track polynomial commands. As an example, a controller was designed for a tracking telescope with a polynomial tracking requirement and some special features such as actuator saturation and multiple measurements, one of which is sampled. The resulting system has a tracking performance comparing favorably with a much more complicated digital aided tracker. The parameter sensitivity reduction was treated by considering the variable parameters as random variables. A performance index is defined as a weighted sum of the state and control convariances that sum from both the random system disturbances and the parameter uncertainties, and is minimized numerically by adjusting a set of free parameters.
Hadass, Z.↗
Using EEG To Detect and Monitor Mental Fatigue
This project aims to develop EEG-based methods for detecting and monitoring mental fatigue. Mental fatigue poses a serious risk, even when performance is not apparently degraded. When such fatigue is associated with sustained performance of a single type of cognitive task it may be related to the metabolic energy required for sustained activation of cortical areas specialized for that task. The objective of this study was to adapt EEG to monitor cortical energy over a long period of performance of a cognitive task. Multielectrode event related potentials (ERPs) were collected every 15 minutes in nine subjects who performed a mental arithmetic task (algebraic sum of four randomly generated negative or positive digits). A new problem was presented on a computer screen 0.5 seconds after each response; some subjects endured for as long as three hours. ERPs were transformed to a quantitative measure of scalp electrical field energy. The average energy level at electrode P3 (near the left angular gyrus), 100-300 msec latency, was compared over the series of ERPs. For most subjects, scalp energy density at P3 gradually fell over the period of task performance and dramatically increased just before the subject was unable to continue the task. This neural response can be simulated for individual subjects using, a differential equation model in which it is assumed that the mental arithmetic task requires a commitment of metabolic energy that would otherwise be used for brain activities that are temporarily neglected. Their cumulative neglect eventually requires a reallocation of energy away from the mental arithmetic task.
Montgomery, Leslie↗
Feasibility of quasi-random band model in evaluating atmospheric radiance
The use of the quasi-random band model in evaluating upwelling atmospheric radiation is investigated. The spectral transmittance and total band adsorptance are evaluated for selected molecular bands by using the line by line model, quasi-random band model, exponential sum fit method, and empirical correlations, and these are compared with the available experimental results. The atmospheric transmittance and upwelling radiance were calculated by using the line by line and quasi random band models and were compared with the results of an existing program called LOWTRAN. The results obtained by the exponential sum fit and empirical relations were not in good agreement with experimental results and their use cannot be justified for atmospheric studies. The line by line model was found to be the best model for atmospheric applications, but it is not practical because of high computational costs. The results of the quasi random band model compare well with the line by line and experimental results. The use of the quasi random band model is recommended for evaluation of the atmospheric radiation.
Tiwari, S. N.↗
The distribution and properties of a weighted sum of chi squares
Distribution and properties of weighted sum of chi squares random variables
Delaney, F. C.↗
Digital decorrelator saves time and expense in acoustic testing of structures
Instantaneous signals from coherent random sound field are summed and time delayed to avoid introducing vectorial addition errors. Resultant statistically independent signals are applied to spectrometer. Displayed sound pressure level is proportional to square root of sum of squares of sound pressure levels taken over frequency range of interest.
Nakich, R. B.↗
Ambiguous Tilt and Translation Motion Cues in Astronauts after Space Flight
Adaptive changes during space flight in how the brain integrates vestibular cues with visual, proprioceptive, and somatosensory information can lead to impaired movement coordination, vertigo, spatial disorientation, and perceptual illusions following transitions between gravity levels. This joint ESA-NASA pre- and post-flight experiment is designed to examine both the physiological basis and operational implications for disorientation and tilt-translation disturbances in astronauts following short-duration space flights. The first specific aim is to examine the effects of stimulus frequency on adaptive changes in eye movements and motion perception during independent tilt and translation motion profiles. Roll motion is provided by a variable radius centrifuge. Pitch motion is provided by NASA's Tilt-Translation Sled in which the resultant gravitoinertial vector remains aligned with the body longitudinal axis during tilt motion (referred to as the Z-axis gravitoinertial or ZAG paradigm). We hypothesize that the adaptation of otolith-mediated responses to these stimuli will have specific frequency characteristics, being greatest in the mid-frequency range where there is a crossover of tilt and translation. The second specific aim is to employ a closed-loop nulling task in which subjects are tasked to use a joystick to null-out tilt motion disturbances on these two devices. The stimuli consist of random steps or sum-of-sinusoids stimuli, including the ZAG profiles on the Tilt-Translation Sled. We hypothesize that the ability to control tilt orientation will be compromised following space flight, with increased control errors corresponding to changes in self-motion perception. The third specific aim is to evaluate how sensory substitution aids can be used to improve manual control performance. During the closed-loop nulling task on both devices, small tactors placed around the torso vibrate according to the actual body tilt angle relative to gravity. We hypothesize that performance on the closed-loop tilt control task will be improved with this tactile display feedback of tilt orientation. The current plans include testing on eight crewmembers following Space Shuttle missions or short stay onboard the International Space Station. Measurements are obtained pre-flight at L-120 (plus or minus 30), L-90 (plus or minus 30), and L-30, (plus or minus 10) days and post-flight at R+0, R+1, R+2 or 3, R+4 or 5, and R+8 days. Pre-and post-flight testing (from R+1 on) is performed in the Neuroscience Laboratory at the NASA Johnson Space Center on both the Tilt-Translation Device and a variable radius centrifuge. A second variable radius centrifuge, provided by DLR for another joint ESA-NASA project, has been installed at the Baseline Data Collection Facility at Kennedy Space Center to collect data immediately after landing. ZAG was initiated with STS-122/1E and the first post-flight testing will take place after STS-123/1JA landing.
Clement, G.↗
Chemical Analysis of Primitive Objects Using a Slitless Ultraviolet Meteor Spectrometer (CAPO-SUMS)
Measure the elemental composition in both random meteors and in the bolides forming specific meteor streams (these are traceable to specific small bodies in the solar system). These will yield the average chemical composition and degree of chemical variability in a statistically significant number of planetesimals. CAPO-SUMS is functionally equivalent to a series of multiple, small-body sample analysis missions, but provides much more analytical capability than is possible on any orbital or flyby mission due to the vaporization, ionization and ultraviolet emission from the ablating bolide as it enters the atmosphere. CAPO-SUMS will provide a chemical context from which the detailed analytical studies provided by a cometary or asteroidal lander mission can be interpreted.
Nuth, J. A.↗