An Algorithm for Tracking a Maneuvering Target in Clutter

We consider the problem of tracking a maneuvering target in clutter. In such an environment, missed detections and false alarms make it impossible to decide, with certainty, the origin of received echoes. Processing radar returns in cluttered environments consists of three functions: 1) target detection and plot formation, 2) plot-to-track association, and 3) track updating. Two inadequacies of the present approaches are 1) Optimization of detection characteristics have not been considered and 2) features that can be used in the plot-to-track correlation process are restricted to a specific class. This paper presents a new approach to overcome these limitations. This approach facilitates tracking of a maneuvering target in clutter and improves tracking performance for weak targets.     

Fourth-order theories for orbit predictions for low- and high-eccentricity orbits in an oblate atmosphere with scale height dependent on altitude

Two new fourth-order non-singular analytical theories for the motion of near-Earth satellite orbits with air drag are developed for low- and high-eccentricity orbits in an oblate atmosphere with variation of density scale height with altitude. Uniformly regular Kustaanheimo–Stiefel (KS) canonical elements are utilized for low-eccentricity orbits and KS element equations are employed for high-eccentricity orbits. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. The analytical solutions are compared with the numerically integrated values up to 100 revolutions, and found to be quite accurate over a wide range of eccentricity, perigee height and inclination.     

On prediction of re-entry time of an upper stage from GTO

The evolution of objects in geostationary transfer orbit (GTO) is determined by a complex interplay of atmospheric drag and luni-solar gravity. These orbits are highly eccentric (eccentricity >0.7) and have large variations in velocity and perturbations during a revolution. The periodic changes in the perigee altitudes of these orbits are mainly due to the gravitational perturbations of the Sun and the Moon. The re-entry time of the objects in such orbits is sensitive to the initial conditions. The aim of this paper is to study the re-entry time of the cryogenic stage of the Indian geo-synchronous launch vehicle, GSLV-F04/CS, which has been decaying since 2 September 2007 from initial orbit with eccentricity equal to 0.706. Two parameters, initial eccentricity and ballistic coefficient, are chosen for optimal estimation. It is known that the errors are more in eccentricity for the observations based on two line elements (TLEs). These two parameters are computed with response surface method using a genetic algorithm for the selected eight different zones, based on rough linear variation of the mean apogee altitude during 200 days orbit evolution. The study shows that the GSLV-F04/CS will re-enter between 5 December 2010 and 7 January 2011. The methodology is also applied to study the re-entry of six decayed objects (cryogenic stages of GSLV and Molniya satellites). Good agreement is noticed between the actual and the predicted re-entry times. The absolute percentage error in re-entry prediction time for all the six objects is found to be less than 7%. The present methodology is being adopted at Vikram Sarabhai Space Centre (VSSC) to predict the re-entry time of GSLV-F04/CS.     

Decay of high eccentricity satellite orbits with air drag using uniformly regular KS canonical elements

A non-singular analytical theory for the motion of high eccentricity satellite orbits under the influence of air drag is developed in terms of the Uniformly Regular Kustaanheimo and Stiefel (URKS) canonical elements, by assuming the atmosphere to be oblate with variation of density scale height with altitude. The series expansions include up to fourth-order terms of an independent variable Δ=λ² (function of eccentric anomaly) and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically due to symmetry in the equations of motion. Comparison of the important orbital parameters semi-major axis and eccentricity up to 1000 revolutions, obtained with the present analytical solution and the KS theory, shows the superiority of the present solution over the KS elements analytical solution. The theory can be used effectively for the orbital decay of aero-assisted orbital transfer orbits during mission planning.     

Degradation of thermal control materials under a simulated radiative space environment

A spacecraft with a passive thermal control system utilizes various thermal control materials to maintain temperatures within safe operating limits. Materials used for spacecraft applications are exposed to harsh space environments such as ultraviolet (UV) and particle (electron, proton) irradiation and atomic oxygen (AO), undergo physical damage and thermal degradation, which must be considered for spacecraft thermal design optimization and cost effectiveness. This paper describes the effect of synergistic radiation on some of the important thermal control materials to verify the assumptions of beginning-of-life (BOL) and end-of-life (EOL) properties. Studies on the degradation in the optical properties (solar absorptance and infrared emittance) of some important thermal control materials exposed to simulated radiative geostationary space environment are discussed. The current studies are purely related to the influence of radiation on the degradation of the materials; other environmental aspects (e.g., thermal cycling) are not discussed. The thermal control materials investigated herein include different kind of second-surface mirrors, white anodizing, white paints, black paints, multilayer insulation materials, varnish coated aluminized polyimide, germanium coated polyimide, polyether ether ketone (PEEK) and poly tetra fluoro ethylene (PTFE). For this purpose, a test in the constant vacuum was performed reproducing a three year radiative space environment exposure, including ultraviolet and charged particle effects on North/South panels of a geostationary three-axis stabilized spacecraft. Reflectance spectra were measured in situ in the solar range (250–2500 nm) and the corresponding solar absorptance values were calculated. The test methodology and the degradations of the materials are discussed. The most important degradations among the low solar absorptance materials were found in the white paints whereas the rigid optical solar reflectors remained quite stable. Among the high solar absorptance elements, as such the change in the solar absorptance was very low, in particular the germanium coated polyimide was found highly stable.     

On the limiting mass of a dense stellar matter

In the present work, we have derived an expression $\text{M}{}_{\mathrm{L}}\text{? 4.738 M}{}_{\mathrm{\odot }}$ (M_⊙ = 1.985 × 10³³ g = mass of the Sun) giving the “limiting” value of the mass of a dense stellar matter, by introducing the concept of nuclear size correction in the theory of relativistic Thomas Fermi model for a compressed atom. We find that $\text{M}{}_{\mathrm{L}}\text{? 5.1571 M}{}_{\mathrm{<mtext>Ch</mtext>}}\text{and}\text{=3.2750(M}{}_{\mathrm{<mtext>O</mtext>}}\text{)}{}_{\mathrm{<mtext>Prev</mtext>}}$ [M_Ch and (M_O)_Prev denote respectively the Chandrasekhar and author's “limiting” masses]. By making a comparative study with those of previous results it has been shown that our present treatment would provide satisfactory results for the density ranges from ? ? 10⁸ up to $\text{? ? 10}{}^{11}\text{g}\text{/}\text{cm}{}^3$. Other results of cognate interest in the non-relativistic regime 10³ < ? ? 10⁵ (without the nuclear size effect) are presented. The astrophysical implications of the results are mentioned.     

Growth and decay of weak discontinuities in radiative gasdynamics

Growth and decay properties of weak discontinuities headed by wave fronts of arbitrary shape in three dimensions are investigated in a thermally radiating inviscid gas flow. The effects of radiative transfer are treated by the use of a general differential approximation for a grey gas of arbitrary opacity including effects of radiative flux, pressure and energy density. The transport equations representing the rate of change of discontinuities in the normal derivatives of the flow variables are obtained, and it is found that the nonlinearity in the governing equations does not contribute anything to the radiation induced waves. In contrast to the radiation induced waves, the nonlinearity in the governing equations plays an important role in the interplay of damping and steepening tendencies of a modified gasdynamic wave. An explicit criterion for the growth and decay of a modified gasdynamic wave along bicharacteristics curve in the characteristic manifold of the governing differential equations is given and the special reference is made of diverging and converging waves. It is shown that there is a special case of a compressive converging wave for which the stabilizing influences of thermal radiation and the wave front curvature are not strong enough to overcome the tendency of the wave to grow into a shock.     

Simulation software for the spiral trajectory of our Moon

At 4.56 Ga, the accretion of the slowly rotating Solar Nebula led to the formation of Sun and its Planets in the plane of disc of accretion. Moon was formed by accretion from a circumterrestrial disk of debris generated by the glancing angle impact of the young Earth by a Mars size planetary embryo at about 4.5 Ga at a distance of 15,000 km. The Moon since then has migrated to the present position of 384,400 km from the center of the Earth. In course of this outward migration it has slowed down the spin rate of Earth and caused the lengthening of diurnal day length from 5 h initially to 24 h presently. The basic mechanics of Earth–Moon System has been worked out and theoretical determination of lengthening of day curve is carried out. This theoretical lengthening of day curve is compared with the observed lengthening of day curve based on paleobotanical evidences, ancient tidalites and Australian Banded Iron Formation. There is a remarkable correspondence between the two curves except for intermittent deviations due to geographical and geophysical factors. Based on the theoretical curve of lengthening of day, an empirical formula for the lunar orbital radius expansion is determined. Based on this empirical formula, simulation software is developed that gives the correct evolution of the semi-major axis (a) of our Moon for any time span from the inception to the time chosen under study. For mathematical simplicity the system is considered to be a two body rotating system throughout its evolutionary history of 4.5 Gyrs. This simulation draws the Moon’s spiral trajectory from its inception to any subsequent epoch. The terminal epoch is an input to the simulation software to arrive at the spiral trajectory of the Moon from the inception to the given epoch. The basic mechanics of Earth–Moon System and this simulation can be generalized to lay the foundation of simulation software for any Planet–Satellite pair or any Sun-Planet pair in our Solar System or Star-Planet pair in any Extra-Solar System. The basic dynamics has been found to be valid for Star–Planet pair also. So this Simulation Methodology can as well be applied to study the migratory evolution of Gas Giants also.