PACE OCI Pre-launch ETU Spatial Characterization using Time-delay Mode
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This document describes the partial derivatives for commonly estimated parameters including antenna positions, satellite position, and satellite velocity from a near-field VLBI delay model for Earth-orbiting satellites. This model was presented in the Journal of Geodesy by Jaron & Nothnagel (2019). In this context, we present a streamlined version of the near-field VLBI delay. From this simplified model, we deduce a delay rate expression and calculate partial derivatives, maintaining only the terms with significant impact on the computed derivatives’ magnitude. To verify the accuracy of the simplified model and the partial derivatives computed from it, we have created a simple simulation in Matlab of an Earth-orbiting satellite at the altitude of a typical Global Navigation Satellite Systems (GNSS) satellite. From this simulation, we compare the simplified and original delays, and we verify the magnitude and direction of the partial derivatives against the numerically computed derivatives from the original delay model. The partial derivatives and simplified VLBI delay model detailed here are implemented in Fortran in the open-source library VTD.
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Neutral density data were obtained near 400 km (1600 LT) from a microphone density gage on OGO-6 from 0 to 40 deg N geomagnetic latitude for 25 September through 3 October 1969. Several geomagnetic storms occurred during this period. Least squares fits were made to data points on density scatter diagrams. An equation representing the least squares fit was computed for each delay time. The equation of best fit (and the corresponding time delay between the density and the magnetic index which resulted in this best fit) was found by choosing the equation that gave the minimum standard error. The implications of the time differences associated with the best fits at various latitudes and longitudes are discussed with regard to the time delays involved in geomagnetic heating of the neutral upper atmosphere.
A method for measuring the acoustic velocity in a thin sheet of a graphite epoxy composite (GEC) material was investigated. This method uses two identical acoustic-emission (AE) sensors, one to transmit and one to receive. The delay time as a function of distance between sensors determines a bulk velocity. A lightweight fixture (balsa wood in the current implementation) provides a consistent method of positioning the sensors, thus providing multiple measurements of the time delay between sensors at different known distances. A linear fit to separation, x, versus delay time, t, will yield an estimate of the velocity from the slope of the line.
When high precision is required for range measurement on Earth space paths, it is necessary to correct as accurately as possible for excess range delays due to the dry air, water vapor, and liquid water content of the atmosphere. Calculations based on representative values of atmospheric parameters are useful for illustrating the order of magnitude of the expected delays. Range delay, time delay, and phase delay are simply and directly related. Doppler frequency variations or noise are proportional to the time rate of change of excess range delay. Tropospheric effects were examined as part of an overall consideration of the capability of precision two way ranging and Doppler systems.
Ground reflections generate undesirable effects on acoustic measurements such as those conducted outdoors for jet noise research, aircraft certification, and motor vehicle regulation. Cepstral techniques developed in speech processing are adapted to identify echo delay time and to correct for ground reflection effects. A sample result is presented using an actual narrowband sound pressure level spectrum. The technique can readily be adapted to existing fast Fourier transform type spectrum measurement instrumentation to provide field measurements/of echo time delays.
Ground reflections generate undesirable effects on acoustic measurements such as those conducted outdoors for jet noise research, aircraft certification, and motor vehicle regulation. This paper shows how cepstral techniques developed in speech processing can be adapted to identify the echo delay time and to correct for ground reflection effects. A sample result is presented using an actual narrowband sound pressure level spectrum. The technique can readily be adapted to existing fast Fourier transform type spectrum measurement instrumentation to provide field measurement of echo time delays.
The characteristics of the thematic mapper (TM) sensor onboard the LANDSAT 4 satellite are discussed. Topics include instantaneous field of view size, rise time, delay time, square wave response, bright target recovery, altitude effects, band to band registration, and scan profile linearity.
Time optimal control function and optimal trajectories solved for second order linear system with constant time delay
Test data and analytic evaluations are presented to show that relatively poor 100 KHz shielding of 12 Db can effectively provide an electromagnetic pulse transient reduction of 100 Db. More importantly, several techniques are shown for lightning surge attenuation as an alternative to crowbar, spark gap, or power zener type clipping which simply reflects the surge. A time delay test method is shown which allows CW testing, along with a convolution program to define transient shielding effectivity where the Fourier phase characteristics of the transient are known or can be broadly estimated.
Welding electron beam effects on Nextel AF-62 ceramic fabric enable a preliminary, tentative interpretation of electron beam fabric damage. Static surface charging does not protect fabric from beam penetration, but penetration occurs only after a delay time. The delay time is thought to be that required for the buildup of outgassing products at the fabric surface to a point where arcing occurs. Extra long delays are noted when the gun is close enough to the surface to be shut off by outgassing emissions. Penetration at long distances is limited by beam attenuation from electronic collisions with the chamber atmosphere.
Analytic and numerical techniques are presented which directly address the problem of propagation of wide bandwidth signals through random ionized media. This work is applicable to the problems of satellite communication and space based radar observation through a disturbed ionospheric propagation channel that would result from a high altitude chemical release or nuclear detonation. An analytic solution is presented for the two-position, two-frequency mutual coherence function for spherical wave propagation in the strong scattering limit. This solution is used to derive simple expressions for the power impulse response function and to determine its relationship to the important parameters of decorrelation distance and coherence bandwidth which describe the disturbed propagation channel. Results for mean time delay and time delay jitter are presented and compared to direct simulation results and to other theoretical calculations. A numerical/analytical solution to the parabolic wave equation is presented in the form of a multiple phase-screen (MPS) propagation simulation. In this very general solution technique, the random medium is divided into a finite number of layers. The field fluctuation through each layer is obtained by replacing the layer by a centrally located thin phase-screen, whose statistical properties are determined from the statistics of the electron-density irregularities. The waveform then propagates from phase-screen to phase-screen via an exact solution to the Fresnel-Kirchnoff equation. For wide bandwidth waveforms, numerical solutions are obtained at a number of discrete frequencies centered about the carrier and then time-domain solutions are obtained by Fourier transform techniques. Detailed results are presented for a number of interesting cases including propagation of a 20 MHz bandwidth signal through a finite barium cloud at a carrier frequency of 100 MHz. One of the major uses of the MPS propagation simulation has been to provide realizations of the received signal after propagation through a disturbed channel. The MPS simulation obtains a general solution of the parabolic wave equation under both weak and strong scattering conditions. A second technique to directly obtain realizations of wide bandwidth waveforms is presented here. This technique is limited to the case of strong scattering but requires only a fraction of the computer resources needed for MPS signal generation. Detailed comparisons of the two signal generation techniques are presented.
The mathematical models of space very long base interferometry (VLBI) observables suitable for least squares covariance analysis were derived and estimatability problems inherent in the space VLBI system were explored, including a detailed rank defect analysis and sensitivity analysis. An important aim is to carry out a comparative analysis of the mathematical models of the ground-based VLBI and space VLBI observables in order to describe the background in detail. Computer programs were developed in order to check the relations, assess errors, and analyze sensitivity. In order to investigate the estimatability of different geodetic and geodynamic parameters from the space VLBI observables, the mathematical models for time delay and time delay rate observables of space VLBI were analytically derived along with the partial derivatives with respect to the parameters. Rank defect analysis was carried out both by analytical and numerical testing of linear dependencies between the columns of the normal matrix thus formed. Definite conclusions were formed about the rank defects in the system.
The baseline stability margins for NASA's Space Launch System (SLS) launch vehicle were generated via the classical approach of linearizing the system equations of motion and determining the gain and phase margins from the resulting frequency domain model. To improve the fidelity of the classical methods, the linear frequency domain approach can be extended by replacing static, memoryless nonlinearities with describing functions. This technique, however, does not address the time varying nature of the dynamics of a launch vehicle in flight. An alternative technique for the evaluation of the stability of the nonlinear launch vehicle dynamics along its trajectory is to incrementally adjust the gain and/or time delay in the time domain simulation until the system exhibits unstable behavior. This technique has the added benefit of providing a direct comparison between the time domain and frequency domain tools in support of simulation validation. This technique was implemented by using the Stability Aerospace Vehicle Analysis Tool (SAVANT) computer simulation to evaluate the stability of the SLS system with the Adaptive Augmenting Control (AAC) active and inactive along its ascent trajectory. The gains for which the vehicle maintains apparent time-domain stability defines the gain margins, and the time delay similarly defines the phase margin. This method of extracting the control stability margins from the time-domain simulation is relatively straightforward and the resultant margins can be compared to the linearized system results. The sections herein describe the techniques employed to extract the time-domain margins, compare the results between these nonlinear and the linear methods, and provide explanations for observed discrepancies. The SLS ascent trajectory was simulated with SAVANT and the classical linear stability margins were evaluated at one second intervals. The linear analysis was performed with the AAC algorithm disabled to attain baseline stability margins. At each time point, the system was linearized about the current operating point using Simulink's built-in solver. Each linearized system in time was evaluated for its rigid-body gain margin (high frequency gain margin), rigid-body phase margin, and aero gain margin (low frequency gain margin) for each control axis. Using the stability margins derived from the baseline linearization approach, the time domain derived stability margins were determined by executing time domain simulations in which axis-specific incremental gain and phase adjustments were made to the nominal system about the expected neutral stability point at specific flight times. The baseline stability margin time histories were used to shift the system gain to various values around the zero margin point such that a precise amount of expected gain margin was maintained throughout flight. When assessing the gain margins, the gain was applied starting at the time point under consideration, thereafter following the variation in the margin found in the linear analysis. When assessing the rigid-body phase margin, a constant time delay was applied to the system starting at the time point under consideration. If the baseline stability margins were correctly determined via the linear analysis, the time domain simulation results should contain unstable behavior at certain gain and phase values. Examples will be shown from repeated simulations with variable added gain and phase lag. Faithfulness of margins calculated from the linear analysis to the nonlinear system will be demonstrated.
High time resolution hard X-ray rates with good counting statistics over 5 energy intervals were obtained using a large area balloon-borne scintillation detector during the 27 June 1980 solar flare. The impulsive phase of the flare was comprised of a series of major bursts of several to several tens of seconds long. Superimposed on these longer bursts are numerous smaller approximately 0.5 to 1.0 second spikes. The time profiles for different energies were cross-correlated for the major bursts. The rapid burst decay rates and the simultaneous peaks below 120 keV both indicate a rapid electron energy loss process. Thus, the flux profiles reflect the electron acceleration/injection process. The fast rate data was obtained by a burst memory in 8 and 32 msec resolution over the entire main impulsive phase. These rates will be cross-correlated to look for short time delays and to find rapid fluctuations. However, a cursory examination shows that almost all fluctuations, down to the 5% level, were resolved with 256 msec bins.