General relativistic radiation hydrodynamics: Mixed-frame approach

I show how general relativistic 3D radiation hydrodynamic equations can be derived from the tensor formulation. Radiation quantities are differentiated with respect to the fixed coordinates while the interaction between matter and radiation is described by the comoving frame quantities. The formulation is covariant, and can be applied to any coordinates or spacetime; I show the derivation for the Schwarzschild spacetime as an example.     

Multiposition alignment of strapdown inertial navigation system

The authors demonstrate that the stationary alignment of strapdown inertial navigation system (SDINS) can be improved by employing the multiposition/technique. Using an observability analysis, it is shown that an optimal two-position alignment not only satisfies complete observability conditions but also minimizes alignment errors. This is done by analytic rank testing of the stripped observability matrix and numerical calculation of the error covariance. It is also shown that an optimal three-position alignment accelerates the convergence of the alignment error compared with two-position alignment     

Space experiments aboard the Lomonosov MSU satellite

At present, the Institute of Nuclear Physics of Moscow State University, in cooperation with other organizations, is preparing space experiments onboard the Lomonosov satellite. The main goal of this mission is to study extreme astrophysical phenomena such as cosmic gamma-ray bursts and ultra-high-energy cosmic rays. These phenomena are associated with the processes occurring in the early universe in very distant astrophysical objects, therefore, they can provide information on the first stages of the evolution of the universe. This paper considers the main characteristics of the scientific equipment aboard the Lomonosov satellite.     

Singularity avoidance of control moment gyros by one-step ahead singularity index

A steering law of control moment gyros for spacecraft attitude control by using one-step ahead singularity index is addressed in this paper. In some recent studies, the null motion approaches or singularity robustness steering laws have been extensively investigated to avoid singular configurations for a control momentum gyro (CMG) cluster. As a novel approach different from them, the proposed approach is based on optimization technique by minimizing the one-step ahead singularity index. Modified approaches are also presented in this paper. The proposed one-step prediction method ultimately gives an optimized solution of gimbal rates with advanced ability to avoid a singularity. A singularity index for reliable computation of a gradient vector is also introduced. Finally, performance of the proposed algorithm is demonstrated by numerical simulations.     

Hybrid optimization for multiple-impulse reconfiguration trajectories of satellite formation flying

A hybrid optimization method is developed for fuel-optimal reconfigurations of a group of satellites flying in formation. The genetic algorithm performs a global search to find two-impulse trajectories, and primer vector analysis finds multiple-impulsive local optimal trajectories with the two-impulse trajectories as initial guesses. Hybrid optimization finds globally optimal trajectories for formation reconfigurations, including formation resizing, reassignment and reorientation maneuvers. Multiple-impulse trajectories reduce the fuel consumption from the two-impulse trajectories by up to 4.4% for those maneuvers. In real missions, satellites can follow two-impulse trajectories to gain the advantage of a smaller number of impulses, with the cost of slightly more propellant. The qualitative characteristics of the optimal trajectories are analyzed from the number of optimal trajectories found by hybrid optimization.     

Strapdown INS error model for multiposition alignment

The relationship between quaternion errors and tilt angles from true navigation frame to analytic platform frame is newly derived for strapdown inertial navigation system (SDINS). Using the relationship it is shown that the quaternion error model for attitude and velocity is equivalent to the conventional perturbation error model. Based upon the equivalency, the quaternion errors during a multiposition alignment are determined and analyzed. Furthermore, it is shown that the heading rotation of 180 deg achieves the minimal quaternion error for 2-position ground alignment     

Comprehensive data reduction package for the Immersion GRating INfrared Spectrograph: IGRINS

We present a Python-based data reduction pipeline package (PLP) for the Immersion GRating INfrared Spectrograph (IGRINS), an instrument that covers the complete H- and K-bands in one exposure with a spectral resolving power of 40,000. The reduction steps carried out by the PLP include flat-fielding, background removal, order extraction, distortion correction, wavelength calibration, and telluric correction using spectra of A type standard stars. As the spectrograph has no moving parts, the PLP automatically reduces the data using predefined functions for the processes of order extraction, distortion correction, and wavelength calibration. Before the telluric correction of the target spectra, the intrinsic hydrogen absorption features of the standard A star are removed with a Gaussian fitting algorithm. The final result is the flux of the target as a function of wavelength. Users can customize the predefined functions for the extraction of the spectrum from the echellogram and adjust the parameters for the fitting functions for the spectra of celestial objects, using “fine-tuning” options, as necessary. Presently, the PLP produces the best results for point-source targets.     

Onboard orbit determination using GPS observations based on the unscented Kalman filter

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1σ) and 0.5 m/s (1σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites.     

Optimal air-launching rocket design using system trades and a multi-disciplinary optimization approach

Compared with the conventional ground rocket launching, air-launching has many advantages. However, a comprehensive and integrated system design approach is required because the physical geometry of air launch vehicle is quite dependent on the installation limitation of the mother plane. For the selection of the best system alternative, a trade study for the first stage engine type and launching speeds is performed using a sequential optimization technique, confirming the feasibility of the baseline air-launching rocket. Then, a system design has been performed using the multi-disciplinary feasible (MDF) design optimization method. Analysis modules include mission analysis, staging, propulsion analysis, configuration, weight analysis, aerodynamics analysis and trajectory analysis. As a result of multi-disciplinary system optimization, a supersonic air launching rocket with total mass of 1244.9 kg, total length of 6.36 m, outer diameter of 0.60 m has been successfully designed to launch a satellite of 7.5 kg to the 700 km circular orbit.     

Noise covariances estimation for systems with bias states

This paper presents a new approach to noise covariances estimation for a linear, time-invariant, stochastic system with constant but unknown bias states. The system is supposed to satisfy controllable/observable conditions without bias states. Based on a restructured data representation, the covariance of a new variable that consists of measurement vectors is expressed as a linear combination of unknown parameters. Noise covariances are then estimated by employing a recursive least-squares algorithm. The proposed method requires no a priori estimates of noise covariances, provides consistent estimates, and can also be applied when the relationship between bias states and other states is unknown. The method has been applied to strapdown inertial navigation system initial alignment. Simulation results indicate a satisfactory performance of the proposed method