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Probability density function and distribution function of distance from random point in polygon to the nearest corner in lattice
Apparatus for doubling the data density rate of an analog to digital converter or doubling the data density storage capacity of a memory deviced is discussed. An interstitial data point midway between adjacent data points in a data stream having an even number of equal interval data points is generated by applying a set of predetermined one-dimensional convolute integer coefficients which can include a set of multiplier coefficients and a normalizer coefficient. Interpolator means apply the coefficients to the data points by weighting equally on each side of the center of the even number of equal interval data points to obtain an interstital point value at the center of the data points. A one-dimensional output data set, which is twice as dense as a one-dimensional equal interval input data set, can be generated where the output data set includes interstitial points interdigitated between adjacent data points in the input data set. The method for generating the set of interstital points is a weighted, nearest-neighbor, non-recursive, moving, smoothing averaging technique, equivalent to applying a polynomial regression calculation to the data set.
Using near-simultaneous full disk Solar X-ray images and He I 10830 lambda, spectroheliograms from three recent rocket flights, dark points identified on the He I maps were compared with X-ray bright points identified on the X-ray images. It was found that for the largest and most obvious features there is a strong correlation: most He I dark points correspond to X-ray bright points. However, about 2/3 of the X-ray bright points were not identified on the basis of the helium data alone. Once an X-ray feature is identified it is almost always possible to find an underlying dark patch of enhanced He I absorption which, however, would not a priori have been selected as a dark point. Therefore, the He I dark points, using current selection criteria, cannot be used as a one-to-one proxy for the X-ray data. He I dark points do, however, identify the locations of the stronger X-ray bright points.
Using near-simultaneous full disk Solar X-ray images and He I 10830 lambda, spectroheliograms from three recent rocket flights, dark points identified on the He I maps were compared with x-ray bright points identified on the X-ray images. It was found that for the largest and most obvious features there is a strong correlation: most He I dark points correspond to X-ray bright points. However, about 2/3 of the X-ray bright points were not identified on the basis of the helium data alone. Once an X-ray feature is identified it is almost always possible to find an underlying dark patch of enhanced He I absorption which, however, would not a priori have been selected as a dark point. Therefore, the He I dark points, using current selection criteria, cannot be used as a one-to-one proxy for the X-ray data. He I dark points do, however, identify the locations of the stronger X-ray bright points.
The CLARREO (Climate Absolute Radiance and Refractivity Observatory) Pathfinder (CPF) mission will measure Earth-reflected sunlight with unparalleled accuracy over existing reflected solar (RS) sensors and will also serve as an on-orbit inter-calibration reference to other orbiting sensors. In order to achieve these goals, the HySICS (HyperSpectral Imager for Climate Science) instrument will need to be pointed at a diverse set of targets including: nadir earth, co-aligned earth scans with other orbiting sensors, the Sun, and the Moon. The HySICS Pointing System (HPS) was developed to provide independent pointing at these targets from its mounting location on the ISS. This paper is focused on the HPS and describes: an overview of the CPF mission, an overview of the HPS requirements, the HPS hardware architecture, the various pointing modes that allow the HPS to point at its targets, challenges associated with performing this mission on the ISS, test results from subsystem-level HPS testing, and finally lessons learned that pertain to algorithm/software development and to the benefits of reusing pointing control hardware/architecture from the TSIS-1 mission that also has a 2-axis pointing system on the ISS from the development process.
An annular suspension and pointing system consisting of pointing assemblies for coarse and vernier pointing is described. The first assembly is attached to a carrier spacecraft (e.g., the space shuttle) and consists of an azimuth gimbal and an elevation gimbal which provide 'coarse' pointing. The second or vernier pointing assembly is made up of magnetic actuators of suspension and fine pointing, roll motor segments, and an instrument or experiment mounting plate around which is attached a continuous annular rim similar to that used in the annular momentum control device. The rim provides appropriate magnetic circuits for the actuators and the roll motor segments for any instrument roll position. The results of a study to determine the pointing accuracy of the system in the presence of crew motion disturbances are presented. Typical 3 sigma worst-case errors are found to be of the order of 0.001 arc-second.
The problem of determining whether or not a point lies inside a given polygon occurs in many applications. In air traffic management concepts, a correct solution to the point-in-polygon problem is critical to geofencing systems for Unmanned Aerial Vehicles and in weather avoidance applications. Many mathematical methods can be used to solve the point-in-polygon problem. Unfortunately, a straightforward floating- point implementation of these methods can lead to incorrect results due to round-off errors. In particular, these errors may cause the control flow of the program to diverge with respect to the ideal real-number algorithm. This divergence potentially results in an incorrect point-in- polygon determination even when the point is far from the edges of the polygon. This paper presents a provably correct implementation of a point-in-polygon method that is based on the computation of the winding number. This implementation is mechanically generated from a source- to-source transformation of the ideal real-number specification of the algorithm. The correctness of this implementation is formally verified within the Frama-C analyzer, where the proof obligations are discharged using the Prototype Verification System (PVS).
This paper presents results obtained during testing in optically-accessible, JP8-fueled, flame tube combustors using swirl-venturi lean direct injection (LDI) research hardware. The baseline LDI geometry has 9 fuel/air mixers arranged in a 3 x 3 array within a square chamber. 2-D results from this 9-element array are compared to results obtained in a cylindrical combustor using a 7-element array and a single element. In each case, the baseline element size remains the same. The effect of air swirler angle, and element arrangement on the presence of a central recirculation zone are presented. Only the highest swirl number air swirler produced a central recirculation zone for the single element swirl-venturi LDI and the 9-element LDI, but that same swirler did not produce a central recirculation zone for the 7-element LDI, possibly because of strong interactions due to element spacing within the array.
Experiments were performed with two different focused laser differential interferometer (FLDI) instruments to assess the relative amplitude response of each instrument to a traveling shockwave generated by a laser spark in air. The first FLDI instrument generated two slightly-separated measurement points, with each measurement point providing sensitivity to density fluctuations induced by the shockwave. By performing a cross-correlation between the signals obtained from each measurement point, the phase velocity of density fluctuations can be obtained. The second FLDI instrument generated a measurement line that was oriented parallel to the shockwave direction of travel with the resulting interference pattern sampled at multiple equally-spaced points along the line. As a result, this instrument provides density fluctuation measurement capability at multiple points simultaneously. When the measurement line is oriented parallel to the shockwave direction of travel, the phase velocity, rate of change of the phase velocity, and acceleration of density fluctuations traveling along each line can be obtained by performing a cross-correlation between points along the line. Numerical computations of the shockwave generated by the laser spark are used to simulate the response of each instrument and are compared to the experimental results. High-speed schlieren imaging has also been performed and is compared with the FLDI measurements and computational results.
Experiments were performed with two different focused laser differential interferometer (FLDI) instruments to assess the relative amplitude response of each instrument to a traveling shockwave generated by a laser spark in air. The first FLDI instrument generated two slightly-separated measurement points, with each measurement point providing sensitivity to density fluctuations induced by the shockwave. By performing a cross-correlation between the signals obtained from each measurement point, the phase velocity of density fluctuations can be obtained. The second FLDI instrument generated a measurement line that was oriented parallel to the shockwave direction of travel with the resulting interference pattern sampled at multiple equally-spaced points along the line. As a result, this instrument provides density fluctuation measurement capability at multiple points simultaneously. When the measurement line is oriented parallel to the shockwave direction of travel, the phase velocity, rate of change of the phase velocity, and acceleration of density fluctuations traveling along each line can be obtained by performing a cross-correlation between points along the line. Numerical computations of the shockwave generated by the laser spark are used to simulate the response of each instrument and are compared to the experimental results. High-speed schlieren imaging has also been performed and is compared with the FLDI measurements and computational results.
Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.
The National Aeronautics and Space Administration (NASA), Jet Propulsion Laboratory (JPL)-Deep Space Network (DSN) subnet of 34-m Beam Waveguide (BWG) Antennas was recently upgraded with Ka-Band (32-GHz) frequency feeds for space research and communication. For normal telemetry tracking a Ka-Band monopulse system is used, which typically yields 1.6-mdeg mean radial error (MRE) pointing accuracy on the 34-m diameter antennas. However, for the monopulse to be able to acquire and lock, for special radio science applications where monopulse cannot be used, or as a back-up for the monopulse, high-precision open-loop blind pointing is required. This paper describes a new 4th order pointing model and calibration technique, which was developed and applied to the DSN 34-m BWG antennas yielding 1.8 to 3.0-mdeg MRE pointing accuracy and amplitude stability of 0.2 dB, at Ka-Band, and successfully used for the CASSINI spacecraft occultation experiment at Saturn and Titan. In addition, the new 4th order pointing model was used during a telemetry experiment at Ka-Band (32 GHz) utilizing the Mars Reconnaissance Orbiter (MRO) spacecraft while at a distance of 0.225 astronomical units (AU) from Earth and communicating with a DSN 34-m BWG antenna at a record high rate of 6-megabits per second (Mb/s).
Validation of in-orbit instrument performance is a function of stability in both instrument and calibration source. This paper describes a method using lunar observations scanning near full moon by the Clouds and Earth Radiant Energy System (CERES) instruments. The Moon offers an external source whose signal variance is predictable and non-degrading. From 2006 to present, these in-orbit observations have become standardized and compiled for the Flight Models -1 and -2 aboard the Terra satellite, for Flight Models-3 and -4 aboard the Aqua satellite, and beginning 2012, for Flight Model-5 aboard Suomi-NPP. Instrument performance measurements studied are detector sensitivity stability, pointing accuracy and static detector point response function. This validation method also shows trends per CERES data channel of 0.8% per decade or less for Flight Models 1-4. Using instrument gimbal data and computed lunar position, the pointing error of each detector telescope, the accuracy and consistency of the alignment between the detectors can be determined. The maximum pointing error was 0.2 Deg. in azimuth and 0.17 Deg. in elevation which corresponds to an error in geolocation near nadir of 2.09 km. With the exception of one detector, all instruments were found to have consistent detector alignment from 2006 to present. All alignment error was within 0.1o with most detector telescopes showing a consistent alignment offset of less than 0.02 Deg.
Lunar photography from Zond 6 showed half the side of the moon which is not visible from the earth, and this made it possible to construct a photogrammetric grid encompassing the entire Western Hemisphere and referenced to points of the visible side, whose coordinates were taken from the Goloseyev catalog. The problem was solved using two pictures taken from approximately 9000 km above the lunar surface. The photogrammetric grid was constructed by joint statistical analysis of the measurements of both pictures and the selenographic coordinates of the catalog points. A special algorithm was developed and a program compiled realizing the maximum likelihood method which permitted working with up to 120 catalog points simultaneously.
A study of the environmental constraints and engineering aspects of the acoustic portion of a system for making geodetic ties between undersea reference points and others on land is described. Important areas in which to make such observations initially would be from the California mainland out to oceanic points seaward of the San Andreas fault, and across the Aleutian Trench. The overall approach would be to operate a GPS receiver in a relative positioning (interferometric) mode to provide the long range element of the baseline determination (10 to 1,000 km) and an array of precision sea floor acoustic transponders to link the locally moving sea surface GPS antenna location to a fixed sea floor point. Analyses of various environmental constrants (tides, waves, currents, sound velocity variations) lead to the conclusion that, if one uses a properly designed transponder having a remotely controllable precise retransmission time delay, and is careful with regard to methods for installing these on the sea floor, one should, in many ocean locations, be able to achieve sub-decimeter overall system accuracy. Achievements of cm accuracy or better will require additional understanding of time and space scales of variation of sound velocity structure in the ocean at relevant locations.
Simultaneous observations of the quiet sun at 20 cm radio and He I wavelengths are used to establish the relationship between coronal bright points, as inferred from the 20-cm radio emission, and He I dark points. It is shown that the 20-cm radio emission, which originates from the low corona-transition region, is always associated with regions of enhanced He I absorption; however, it does not always coincide with strong He I 10830 A absorption regions known as He I 'dark points'. Significant fluctuations in the intensity of 20-cm radio emission and He I absorption take place on time scales of minutes.
The pointing control system on the Hubble Space Telescope was designed to keep an image stable in the focal plane to 0.007 arc seconds (rms) for observations lasting from seconds to hours. Following the on-orbit deployment, this level of pointing performance was achieved only for short intervals during each orbit because of unexpected disturbances originating in the Solar Arrays. Since this problem was first recognized, several control system redesigns have been carried out and uplinked to the spacecraft with increasing degrees of success. This paper presents a chronology of those activities. In addition, sufficient background material is included regarding the pointing control system and the Solar Array disturbance so that the contents can be understood without reverting to the details in the reference material.
The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.