Semi-analytical investigations of high area-to-mass ratio geosynchronous space debris including Earth’s shadowing effects

This paper investigates the long-term perturbations of the orbits of geosynchronous space debris influenced by direct radiation pressure including the Earth’s shadowing effects. For this purpose, we propose an extension of our homemade semi-analytical theory [Valk, S., Lemaître, A., Deleflie, F. Semi-analytical theory of mean orbital motion for geosynchronous space debris under gravitational influence. Adv. Space Res., submitted for publication], based on the method developed by Aksnes [Aksnes, K. Short-period and long-period perturbations of a spherical satellite due to direct solar radiation. Celest. Mech. Dyn. Astron. 13, 89–104, 1976] and generalized into a more convenient non-singular formalism. The perturbations accounting for the direct radiation pressure with the Earth’s shadow are computed on a revolution-by-revolution basis, retaining the original osculating Hamiltonian disturbing function. In this framework, we compute the non-singular mean longitude at shadow entry and shadow exit at every orbital revolution in opposition to classical approaches where the singular eccentric anomalies at shadow entry and shadow exit are computed. This new algorithm is developed using non-singular variables. Consequently, it is particularly suitable for both near-circular and near-equatorial orbits as well as orbits which transit periodically around null eccentricities and null inclinations.The algorithm is tested by means of numerical integrations of the equations, averaged over the short periods, including radiation pressure, J₂, the combined Moon and Sun third body attraction as well as the long-term effects of the 1:1 resonance occurring for geosynchronous objects. As an extension of [Valk, S., Lemaître, A., Anselmo, L. Analytical and semi-analytical investigations of geosynchronous space debris with high area-to-mass ratios influenced by solar radiation pressure. Adv. Space Res., doi:10.1016/j.asr.2007.10.025, 2007b], we especially apply our analysis to space debris with area-to-mass as high as 20 m²/kg. This paper provides numerical and semi-analytical investigations leading to a deep understanding of the long-term evolution of the semi-major axis. Finally, these semi-analytical investigations are compared with accurate numerical integrations of the osculating equations of motion over time scales as high as 25 years.     

High resolution science with high redshift galaxies

We summarize the high-resolution science that has been done on high redshift galaxies with Adaptive Optics (AO) on the world’s largest ground-based facilities and with the Hubble Space Telescope (HST). These facilities complement each other. Ground-based AO provides better light gathering power and in principle better resolution than HST, giving it the edge in high spatial resolution imaging and high resolution spectroscopy. HST produces higher quality, more stable PSF’s over larger field-of-views in a much darker sky-background than ground-based AO, and yields deeper wide-field images and low-resolution spectra than the ground. Faint galaxies have steadily decreasing sizes at fainter fluxes and higher redshifts, reflecting the hierarchical formation of galaxies over cosmic time. HST has imaged this process in great structural detail to z  6, and ground-based AO and spectroscopy has provided measurements of their masses and other physical properties with cosmic time. Last, we review how the 6.5 m James Webb Space Telescope (JWST) will measure First Light, reionization, and galaxy assembly in the near–mid-IR after 2013.     

Tracking the Frequency Translation of a Sum of Orthogonal Sinusoids

The maximum likelihood approach is used to derive a method for estimating and tracking the frequency translation of a signal consisting of a sum of orthogonal sinusoids corrupted by additive white noise. The likelihood function is reduced to an equivalent statistic expressed in terms of the squared magnitude of the finite Fourier transform of the received signal. A function that generates an error signal for a frequency translation tracking loop is derived, and a method of generating the error signal using the discrete Fourier transform (DFT) of the received signal weighted by a linear ramp is suggested. Two noise-free examples are presented.     

Carrier Tracking by Smoothing Filter Improves Symbol SNR

The potential benefit of using a smoothing filter to estimate a carrier phase over use of phase-locked loops (PLL) is determined. Numerical results are presented for the performance of three possible configurations of an all-digital coherent demodulation receiver. These are residual carrier PLL, sideband-aided residual carrier PLL, and finally sideband aided with Kalman smoother. The average symbol SNR after losses due to carrier phase estimation is computed for different total power SNRs, symbol rates, and symbol SNRs. It is found that smoothing is most beneficial for low symbol SNRs and low symbol rates. Smoothing gains up to 0.7 dB over sideband-aided residual carrier PLL, and the combined benefit of smoothing and sideband aiding relative to residual carrier loop is often in excess of 1 dB.     

Composite Bound on Arrival Time Estimation Errors

Time of arrival (TOA) estimation of narrowband signals is a problem of considerable practical interest in radar and sonar applications. A new technique is presented to analyze the mean square error (MSE) performance of TOA estimation schemes, based on recently developed lower bound. We obtain a complete characterization of the MSE as a function of the signal and noise parameters. The results are given in a simple closed-form analytical expression.     

Test Results with an Experimental Direction-Finding System

A direction-finding system was built that can simultaneously estimate the arrival angles of two incident signals. It is conceptually straightforward to extend the system to cases with greater numbers of signals. The system is designed to work with uncorrelated signals whose form is unknown, e.g., two communications signals residing in the same bandwidth. Pulsed as well as continuous signals can be handled. The technique involves the determination of the received signal's correlation matrix as an intermediate step. Pattern range tests were performed to determine angle estimate bias and accuracy.     

Investigations of Stability & Dynamic Performances of a Current-Injected Regulator

The stability and dynamic performances of a buck/boost regulator employing a current-injected control are examined. Small-signal models for the power state, the multiloop error processor, and the duty-cycle pulse modulator are developed. The error-processor model which incorporates the current-injected loop, the dc loop, and the compensation network permits evaluation of the effects of each individual control loop and their combined efforts toward shaping the performance characteristics of the closed-loop system. Comparisons are made between this modeling approach and earlier approaches. Some important yet subtle dissimilarities are discussed. This model predicts the constant-frequency 50-percent duty-cycle instability which is inherent to the current-injected control.