I normally create vector art of anime related stuff (screenshots, official artwork, etc), but after seeing the artwork of my favorite champ in the new comic, I had to make these!! Originally made them to create a desktop wallpaper with, and decided to share them here as well in case someone else wants to use them!!
Based on the usual Fedosov construction of star products for a symplectic manifold M, we give a simple geometric construction of a bimodule deformation for the sections of a vector bundle over M starting with a symplectic connection on M and a connection for E. In the case of a line bundle, this gives a Morita equivalence bimodule, and the relation between the characteristic classes of the Morita equivalent star products can be found very easily within this framework. Moreover, we also discuss the case of a Hermitian vector bundle and give a Fedosov construction of the deformation of the Hermitian fiber metric.
A star sensor is a camera device which measures the direction of a star in the spacecraft coordinate system. Star sensors are widely used in spacecraft attitude determination because they produce higher accuracy attitude estimates than any other existing sensor [3, 4]. But the star sensor can only output attitude angle of aircraft relative to the inertial coordinate system for aircraft control system. However, the position and velocity information must be provided for the satellite from other sensors.
Infrared earth sensor is an optical measurement instrument, which measures the earth and the sky difference of infrared radiation and accesses satellite attitude information. Infrared earth sensors are usually used for measuring the pitch angle of aircraft attitude angle and the rolling attitude angle [5, 6]. The current satellite autonomous navigation system uses star sensor and infrared earth sensor. The starlight angular distance observed information is obtained through infrared earth sensor installation matrix vector under vehicle body coordinate system to geocentric direction of projection, and it is depending on the radius of the earth. Then, the observed variable is starlight angular distance, and the radius of earth, as the combination of satellite orbit dynamics model and filtering technology, can determine the position of the vehicle information. However, due to the fact that earth's infrared radiation characteristic is not stable, the measurement accuracy of earth radius calculated with infrared earth sensor is reduced. So, the satellite navigation information accuracy is reduced because the radius of the earth precision is reduced [7, 8].
where, X=[xyzvxvyvz]T is the state vector, x is the position scalar quantity of X axis at J2000.0 coordinate system, y is the position scalar quantity of Y axis at J2000.0 coordinate system, z is the position scalar quantity of Z axis at J2000.0 coordinate system, vx is the velocity scalar quantity of X axis at J2000.0 coordinate system, vy is the velocity scalar quantity of Y axis at J2000.0 coordinate system, vz is the velocity scalar quantity of Z axis at J2000.0 coordinate system, μ is the earth' gravitational constant, r is the position vector at J2000.0 coordinate system, J2 is the coefficient of earth's gravity, ΔFxΔFyΔFz are the disturbance factor from the moon, the pressure of the sun, and atmosphere of the earth, and Re is the radius of the earth.
where the r obtained from at FOV2 is the satellite position vector at J2000.0 coordinate system, the vector S obtained from at FOV1 is the optical axis direction of FOV1 at J2000.0 coordinate system, and νa is the observed noise.
A sensor that integrated ultraviolet earth sensor and star sensor is laid on the test bench. The star simulator is laid in front of the lens of star sensor. The star simulator is adjusted, which results in the angle between the optical axis vector of star simulator, and the optical axis vector of star sensor is 180. The ultraviolet simulator is laid in front of the lens of ultraviolet earth sensor. The ultraviolet simulator is adjusted, which results in the angle between the optical axis vector of ultraviolet simulator, and the optical axis vector of ultraviolet earth sensor is 180. Let the sensor that integrated ultraviolet earth sensor and star sensor put on. The RS422 is connected between the integrated ultraviolet earth sensor and star sensor and the PC. Let the star simulator and ultraviolet simulator put on. The real-time satellite orbit parameters are sent to star simulator and ultraviolet simulator with Ethernet network from orbit dynamics simulator. The star image is sampled by the star sensor of integrated sensor, and the ultraviolet image is sampled by ultraviolet earth sensor of integrated sensor. The autonomous navigation data of satellite are calculated by integrated sensor with the star image and ultraviolet image. Then, the autonomous navigation data of satellite are sent to the PC with RS422 from the integrated sensor. At the same time, the ideal navigation data of satellite to the PC are from orbit dynamics simulator. Then the errors of navigation data of satellite are calculated and saved between autonomous navigation data and ideal navigation data of satellite in the PC. The errors curves of position and velocity of satellite are showed with offline errors of navigation data in Figure 8.
In order to further compare the errors accuracy of navigation using a sensor that integrated ultraviolet earth sensor and star sensor with the errors accuracy of navigation using a sensor that integrated infrared earth sensor and star sensor. The errors of navigation data of satellite are tested with a sensor that integrated infrared earth sensor and star sensor. The errors curves of position and velocity of satellite are showed with offline errors of navigation data in Figure 9.
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