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Relationship between Allan variances and Kalman Filter parameters

A relationship was constructed between the Allan variance parameters (H sub z, H sub 1, H sub 0, H sub -1 and H sub -2) and a Kalman Filter model that would be used to estimate and predict clock phase, frequency and frequency drift. To start with the meaning of those Allan Variance parameters and how they are arrived at for a given frequency source is reviewed. Although a subset of these parameters is arrived at by measuring phase as a function of time rather than as a spectral density, they all represent phase noise spectral density coefficients, though not necessarily that of a rational spectral density. The phase noise spectral density is then transformed into a time domain covariance model which can then be used to derive the Kalman Filter model parameters. Simulation results of that covariance model are presented and compared to clock uncertainties predicted by Allan variance parameters. A two state Kalman Filter model is then derived and the significance of each state is explained.

Vandierendonck, A. J.↗

GPS-Based Navigation And Orbit Determination for the AMSAT AO-40 Satellite

The AMSAT OSCAR-40 (AO-40) spacecraft occupies a highly elliptical orbit (HEO) to support amateur radio experiments. An interesting aspect of the mission is the attempted use of GPS for navigation and attitude determination in HEO. Previous experiences with GPS tracking in such orbits have demonstrated the ability to acquire GPS signals, but very little data were produced for navigation and orbit determination studies. The AO-40 spacecraft, flying two Trimble Advanced Navigation Sensor (TANS) Vector GPS receivers for signal reception at apogee and at perigee, is the first to demonstrate autonomous tracking of GPS signals from within a HEO with no interaction from ground controllers. Moreover, over 11 weeks of total operations as of June 2002, the receiver has returned a continuous stream of code phase, Doppler, and carrier phase measurements useful for studying GPS signal characteristics and performing post-processed orbit determination studies in HEO. This paper presents the initial efforts to generate AO-40 navigation solutions from pseudorange data reconstructed from the TANS Vector code phase, as well as to generate a precise orbit solution for the AO-40 spacecraft using a batch filter.

Davis, George↗

Observations of the Sea Ice Cover Using Satellite Radar Interferometry

The fringes observed in repeat pass interferograms are expressions of surface relief and relative displacements. The limiting condition in the application of spaceborne radar interferometry to the remote sensing of the sea ice cover is the large magnitude of motion between repeat passes. The translation and rotation of ice floes tend to decorrelate the observations rendering radar interferometry ineffective. In our study, we have located three images in the high Arctic during a period when there was negligible motion between repeat observations. The fringes obtained from these images show a wealth of information about the sea ice cover which is important in atmosphere-ice interactions and sea ice mechanics. These measurements provide the first detailed remote sensing view of the sea ice cover. Ridges can be observed and their heights estimated if the interferometric baseline allows. We have observed ridges with heights greater than 4m. The variability in the phase measurements over an area provides an indication of the large scale roughness. Relative centimetric displacements between rigid ice floes have been observed. We illustrate these observations with examples extracted from the interferograms formed from this set of ERS-1 SAR images.

sea ice cover, satellite, radar, interferometry↗

Tracking the Relative Motion of Four Space Payloads Launched from a Sub-Orbital NASA Rocket

One problem, which is comparatively new in the field of GPS applications, is the determination of the relative trajectories of space vehicles. Applications include the docking of spacecraft, collision avoidance in the area of space stations, and trajectory reconstruction of multiple payloads. The required precision in any of these applications will vary, according to the requirements of the task and abilities of GPS to cope with the environment and the dynamics. This paper describes the post-mission reconstruction of the relative trajectories of four GPS receivers attached to four payloads jettisoned from a Black Brant XII rocket. This vehicle was launched by the National Aeronautics and Space Administration (NASA) in January 1999 from the Poker Flats Research Range near Fairbanks, Alaska. The Black Brant XII is a sub-orbital rocket designed to carry payloads of 100 to 500 kg into the upper atmosphere. Flight time is generally in the order of 10-20 minutes. In this experiment, a GPS receiver and antenna was attached to each of the four payloads. One of the GPS receivers was assigned as the "base station", while the other 3 receivers were designated as remotes. GPS time, code and phase measurements were telemetered to a ground station for real-time processing and storage. The object of the mission was to re-compute the position and velocity of the remote units with respect to the base station during the launch phase and after the payloads separated. During the launch segment the 3 baseling distances between the 4 antennas are known from plans and are constant values until each payload is released. On the fly ambiguity determination was used to establish local coordinates from the base antenna to each of the other 3 GPS units during flight. Distance computations were made from the GPS-derived coordinates and compared to plan distances. Using this methodology an error analysis of the relative GPS accuracies has been presented and in addition a description given of the respective payload behaviour following separation from the vehicle.

Martell, Hugh↗

New Global Electron Density Observations from GPS-RO in the D- and E-Region Ionosphere

A novel retrieval technique is developed for electron density (N(sub e)) in the D- and E-region (80-120 km) using the high-quality 50-Hz GPS radio occultation (GPS-RO) phase measurements. The new algorithm assumes a slow, linear variation in the F-region background when the GPS-RO passes through the D- and E-region, and extracts the N(sub e) profiles at 80-130 km from the phase advance signal caused by N(sub e). Unlike the conventional Abel function, the new approach produces a sharp N(sub e) weighting function in the lower ionosphere, and the N(sub e) retrievals are in good agreement with the IRI (International Reference Ionosphere) model in terms of monthly maps, zonal means and diurnal variations. The daytime GPS-RO N(sub e) profiles can be well characterized by the alpha-Chapman function of three parameters (N(sub mE), h(sub mE) and H), showing that the bottom of E-region is deepening and sharpening towards the summer pole. At high latitudes the monthly GPS-RO N(sub e) maps at 80-120 km reveal clear enhancement in the auroral zones, more prominent at night, as a result of energetic electron precipitation (EEP) from the outer radiation belt. The D-/E-region auroral N(sub e) is strongly correlated with K(sub p) on a daily basis. The new N(sub e) data allow further comprehensive analyses of the sporadic E (E(sub s)) phenomena in connection with the background N(sub e) in the E-region. The layered (2-10 km) and fluctuated (less than 2 km) E(sub s) components, namely N(sub e_Layer) than N(sub e_Pert), are extracted with respect to the background N( sub e_Region) on a profile-by-profile basis. The N(sub e_Layer) component has a strong but highly-refined peak at approximately 105 km, with an amplitude smaller than N(sub e_Region) approximately by an order of magnitude. The N(sub e_Pert) component, which was studied extensively in the past, is approximately 2 orders of magnitude weaker than N(sub e_Layer). Both N(sub e_Layer) and N(sub e_Pert) are subject to significant diurnal and semidiurnal variations, showing downward progression with local time in amplitude. The 11-year solar cycle dominates the N(sub e) interannual variations, showing larger N(sub e_Region) and N(sub e_Layer) but smaller N(sub e_Pert) amplitudes in the solar maximum years. Enhanced Ne profiles are often observed in the polar winter, showing good correlation with solar proton events (SPEs) and geomagnetic activity. The new methodology offers great potential for retrieving low N(sub e) in the D-region, where radio propagation and communication blackouts can occur due to enhanced ionization. For space weather applications it is recommended for GPSRO operations to raise the top of high-rate data acquisition to approximately 140 km in the future.

GSP-R↗

Radiative lifetimes and band oscillator strengths for metal oxides. II - SiO E 1 Sigma /+/-X 1 Sigma /+/

Use of an electron-beam phase-shift apparatus to obtain the radiative lifetimes for vibrational levels of the SiO E 1 Sigma (+) state. It is found that the radiative lifetimes for the vibrational transitions of the E-X band are independent of the vibrational upper state. The measured phase shifts yield cascade free lifetimes of 10.5 plus or minus 1.1 nsec for v' from 1 to 7. Spectroscopic data from Elander and Lagerqvist (1971) were used to calculate potential curves by the Klein-Dunham procedure, and Franck-Condon factors and r-centroids for the transition were computed.

Elander, N.↗

NASA Tech Briefs, November 2005

Topics covered include: Laser System for Precise, Unambiguous Range Measurements; Flexible Cryogenic Temperature and Liquid-Level Probes; Precision Cryogenic Dilatometer; Stroboscopic Interferometer for Measuring Mirror Vibrations; Some Improvements in H-PDLCs; Multiple-Bit Differential Detection of OQPSK; Absolute Position Encoders With Vertical Image Binning; Flexible, Carbon-Based Ohmic Contacts for Organic Transistors; GaAs QWIP Array Containing More Than a Million Pixels; AutoChem; Virtual Machine Language; Two-Dimensional Ffowcs Williams/Hawkings Equation Solver; Full Multigrid Flow Solver; Doclet To Synthesize UML; Computing Thermal Effects of Cavitation in Cryogenic Liquids; GUI for Computational Simulation of a Propellant Mixer; Control Program for an Optical-Calibration Robot; SQL-RAMS; Distributing Data from Desktop to Hand-Held Computers; Best-Fit Conic Approximation of Spacecraft Trajectory; Improved Charge-Transfer Fluorescent Dyes; Stability-Augmentation Devices for Miniature Aircraft; Tool Measures Depths of Defects on a Case Tang Joint; Two Heat-Transfer Improvements for Gas Liquefiers; Controlling Force and Depth in Friction Stir Welding; Spill-Resistant Alkali-Metal-Vapor Dispenser; A Methodology for Quantifying Certain Design Requirements During the Design Phase; Measuring Two Key Parameters of H3 Color Centers in Diamond; Improved Compression of Wavelet-Transformed Images; NASA Interactive Forms Type Interface - NIFTI; Predicting Numbers of Problems in Development of Software; Hot-Electron Photon Counters for Detecting Terahertz Photons; Magnetic Variations Associated With Solar Flares; and Artificial Intelligence for Controlling Robotic Aircraft.

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Investigation of new techniques for aircraft navigation using the omega navigation

An OMEGA navigation receiver with a microprocessor as the computational component was investigated. A version of the INTEL 4004 microprocessor macroassembler suitable for use on the CDC-6600 system and development of a FORTRAN IV simulator program for the microprocessor was developed. Supporting studies included development and evaluation of navigation algorithms to generate relative position information from OMEGA VLF phase measurements. Simulation studies were used to evaluate assumptions made in developing a navigation equation in OMEGA Line of Position (LOP) coordinates. Included in the navigation algorithms was a procedure for calculating a position in latitude/longitude given an OMEGA LOP fix. Implementation of a digital phase locked loop (DPLL) was evaluated on the basic of phase response characteristics over a range of input phase variations. Included also is an analytical evaluation on the basis of error probability of an algorithm for automatic time synchronization of the receiver to the OMEGA broadcast format. The use of actual OMEGA phase data and published propagation prediction corrections to determine phase velocity estimates was discussed.

Baxa, E. G., Jr.↗

On obtaining the forward phase functions of Saturn ring features from radio occultation observations

It is noted that the near-forward scattering functions of particles in Saturn ring features are related to 3.6 cm radio occultation power spectra by a Fredholm integral equation of the first kind. The equation reduces to an algebraic system of equation whose solution by usual inversion techniques (that is, least mean squares) is ruled out by the near singularity of the forward transformation matrix. A combination of constrained linear inversion and a filtering algorithm based on eigenvector decomposition of the matrix reduces the instabilities; this yields derived phase functions valid over the range of zero to about 12 mrad. It is noted that these functions represent the collective forward diffraction lobe of particles greater than about 1 m in radius. Since multiple scattering of the signal is a significant effect, the measured phase functions must be adjusted to obtain the singly scattered component. This single-scattering correction is examined for two physical models, namely the monolayer and the classical discrete random slab; in addition, the fraction of opacity in submeter particles for each model for particular ring features is estimated.

Zebker, H. A.↗

Satellite interferometer as an advanced navigation/communication system

An orthogonal system of interferometry baselines aboard a geostationary satellite is proposed to be used for navigation, surveillance, and traffic control. Position determination is based on the relationship between the measured phase differences, the known and unknown transmitter locations, and other systematic error model parameters using a generalized least-squares estimation procedure. It is shown that position accuracy is critically dependent on the baseline length and on the magnitude of the random component of the measuring errors. Several trade-offs with respect to the system accuracies, the number of users, data rates, hardware costs, etc., are examined. Simultaneous use of the same channels for navigation and data transfer is found feasible and five candidate or 'strawman' interferometer system proposals are presented. It is concluded that the system's performance is excellent in comparison with present or planned systems, and that it is viable in meeting potential user's requirements.

Gopalapillai, G. S.↗

System for near real-time crustal deformation monitoring

A system is described for use in detecting earth crustal deformation using an RF interferometer technique for such purposes as earthquake predictive research and eventual operational predictions. A lunar based RF transmission or transmissions from earth orbiting satellites are received at two locations on Earth, and a precise time dependent phase measurement is made of the RF signal as received at the two locations to determine two or three spatial parameters of the antenna relative positions. The received data are precisely time tagged and land-line routed to a central station for real-time phase comparison and analysis. By monitoring the antenna relative positions over an extended period of months or years, crustal deformation of the Earth can be detected.

Macdoran, P. F.↗

Supersonic jet noise generated by large scale instabilities

The role of large scale wavelike structures as the major mechanism for supersonic jet noise emission is examined. With the use of aerodynamic and acoustic data for low Reynolds number, supersonic jets at and below 70 thousand comparisons are made with flow fluctuation and acoustic measurements in high Reynolds number, supersonic jets. These comparisons show that a similar physical mechanism governs the generation of sound emitted in he principal noise direction. These experimental data are further compared with a linear instability theory whose prediction for the axial location of peak wave amplitude agrees satisfactorily with measured phased averaged flow fluctuation data in the low Reynolds number jets. The agreement between theory and experiment in the high Reynolds number flow differs as to the axial location for peak flow fluctuations and predicts an apparent origin for sound emission far upstream of the measured acoustic data.

Seiner, J. M.↗

The Development of a Deflectometer for Accurate Surface Figure Metrology

Marshall Space Flight Center is developing the method of direct fabrication for high resolution full-shell x-ray optics. In this technique the x-ray optics axial profiles are figured and polished using a computer-controlled ZeekoIRP600X polishing machine. Based on the Chandra optics fabrication history about one third of the manufacturing time is spent on moving a mirror between fabrication and metrology sites, reinstallation and alignment with either the metrology or fabrication instruments. Also, the accuracy of the alignment significantly affects the ultimate accuracy of the resulting mirrors. In order to achieve higher convergence rate it is highly desirable to have a metrology technique capable of in situ surface figure measurements of the optics under fabrication, so the overall fabrication costs would be greatly reduced while removing the surface errors due to the re-alignment necessary after each metrology cycle during the fabrication. The goal of this feasibility study is to demonstrate if the Phase Measuring Deflectometry can be applied for in situ metrology of full shell x-ray optics. Examples of the full-shell mirror substrates suitable for the direct fabrication

X-ray optics metrology↗

An experimental evaluation of the application of the Kirchhoff formulation for sound radiation from an oscillating airfoil

The Kirchhoff integral formulation is evaluated for its effectiveness in quantitatively predicting the sound radiated from an oscillating airfoil whose chord length is comparable with the acoustic wavelength. A rigid airfoil section was oscillated at samll amplitude in a medium at rest to produce the sound field. Simultaneous amplitude and phase measurements were made of surface pressure and surface velocity distributions and the acoustic free field. Measured surface pressure and motion are used in applying the theory, and airfoil thickness and contour are taken into account. The result was that the theory overpredicted the sound pressure level by 2 to 5, depending on direction. Differences are also noted in the sound field phase behavior.

Brooks, T. F.↗

Optical phase-locked loop (OPLL) for free-space laser communications with heterodyne detection

Several advantages of coherent free-space optical communications are outlined. Theoretical analysis is formulated for an OPLL disturbed by shot noise, modulation noise, and frequency noise consisting of a white component, a 1/f component, and a 1/f-squared component. Each of the noise components is characterized by its associated power spectral density. It is shown that the effect of modulation depends only on the ratio of loop bandwidth and data rate, and is negligible for an OPLL with loop bandwidth smaller than one fourth the data rate. Total phase error variance as a function of loop bandwidth is displayed for several values of carrier signal to noise ratio. Optimal loop bandwidth is also calculated as a function of carrier signal to noise ratio. An OPLL experiment is performed, where it is shown that the measured phase error variance closely matches the theoretical predictions.

Win, Moe Z.↗

Testing Densities and Refractive Indices of Extraterrestrial Ice Components Using Molecular Structures - Organic Compounds and Molar Refractions

The use of infrared spectra to determine molecular abundances of icy astronomical objects and to study their chemistry requires laboratory measurements of reference spectra and related quantities, such as the index of refraction (n) and density (p) of candidate ices. Here we present new n and p measurements on ices involving over 30 C-, H-, and O-containing compounds, both acyclic and cyclic, representing seven chemical families. We examine the results in a way that is rare in the astrochemical literature, namely one in which data from an ice formed from molecules of a particular chemical family are compared to measurements on another member of the same family, such as of a homologous series or a pair of isomers. Apart from the intrinsic usefulness of the n and data, a structure-based comparison can help establish trends and identify possibly spurious results. As liquid-phase data sometimes are used in low-temperature astrochemical work in the absence of solid-phase measurements, we compare our new ice results to those for the corresponding room-temperature liquids. We emphasize the use of our n and p data to compute the molar refraction (RM) for each of our ices, and how the resulting RM values compare to those expected from molecular structures. The use of calculated RM values and measured n values to calculate ice densities, in the absence of direct measurements, is also addressed.

Hudson, Reggie L.↗

Stabilized Zeeman split laser

The development of a stablized Zeeman split laser for use in a polarization profilometer is discussed. A Hewlett-Packard laser was modified to stabilize the Zeeman split beat frequency thereby increasing the phase measurement accuracy from the Hewlett-Packard 3 degrees to an accuracy of .01 degrees. The addition of a two layered inductive winding converts the laser to a current controlled oscillator whose frequency is linearly related to coil current. This linear relationship between coil current and laser frequency permits phase locking the laser frequency to a stable crystal controlled reference frequency. The stability of the system is examined and the equipment operation procedures are outlined.

Source record↗

Precise time and frequency intercomparison between NPL, India and PTB, Federal Republic of Germany via satellite symphonie-1

A time and frequency intercomparison experiment conducted using Earth stations in New Delhi, India and Raisting, FRG is described. The NPL clock was placed at New Delhi Earth Station and the Raisting Clock was calibrated with PTB/Primary standard via LORAN-C and travelling clocks. The random uncertainity of time comparisons, represented by two sample Allan Variance sigma (30 seconds), was less than 10 nanoseconds. The relative frequency difference between the NPL and Raisting Clocks, SNPL, RAIS, as measured over the 44 days period was found to be -15.7 x 10 to the -13th power. The relative frequency difference between PTB Primary Standard and Raisting Clock, SPTB, RAIS, during this period, was measured to be -22.8 x 10 to the -13th power. The relative frequency difference between NPL clock and PTB Primary Standard, SNPL, PTB, thus, is +7.1 x 10 to the -13th power. The clock rate (UTC, India) of +7.1 + or - 0.5 x 10 to the -13th power, agrees well with that obtained via VLF phase measurements over one year period and with USNO travelling clock time comparisons made in September, 1980.

Mathur, B. S.↗