According to the design requirements of the star sensors, it is necessary to determine the various technical indicators of the star sensor, and guide the actual design work through these technical indicators.
Measurement accuracy is the most important indicator and parameter that characterizes the performance of star sensors. According to the standard measurement model of star sensors, 𝑤𝑖 = 𝐴𝑣𝑖, vi is the direction vector of the navigation star in the celestial coordinate system, which is high-precision astronomical observation data with an accuracy of milliseconds and almost constant, Therefore, the main accuracy of the attitude matrix 𝐴 depends on the star point processing accuracy (𝑥, y) in the star map and the focal length of the star sensor. There are two main ways to represent the accuracy of star sensors, one is single star measurement accuracy, and the other is three-axis attitude accuracy.
1) Single satellite measurement accuracy
The measurement accuracy of a single star is the foundation of the overall accuracy of a star sensor, which directly affects the measurement accuracy of the final attitude angle. The factors that affect the measurement accuracy of a single star include the size of the detection field of view, the resolution of the detector, and the precision that can be achieved by the single star centroid interpolation subdivision algorithm. Among them, the precision of centroid interpolation subdivision, also known as sub pixel resolution, is the key to determining the accuracy of single star measurement. In theory, if the resolution is high, the final single star measurement accuracy will reach the ideal accuracy. However, in reality, due to the presence of various noises, the star signal can be affected by noise fluctuations, resulting in measurement errors. Therefore, the accuracy of subdivision positioning is closely related to the signal-to-noise ratio of the star signal.
2) Three axis attitude accuracy
The three-axis accuracy describes the measurement accuracy of the attitude angle in the pitch axis, yaw axis, and rolling axis of the star sensor. The three-axis attitude accuracy of the star sensor is related to the measurement accuracy of a single star, as well as the number of navigation stars used for calculation. The attitude measurement accuracy of the pitch axis and yaw axis direction increases with the increase of single star measurement accuracy and the number of navigation stars available for calculation, while the measurement accuracy of the roll axis increases with the increase of the number of navigation stars involved in calculation and the angular distance between navigation stars. Among them, the size of the field of view and the number of navigation stars that can be used for calculation are mutually constrained. The larger the detection field of the star sensor, the lower the three-axis attitude accuracy; The more navigation stars in the field of view that can be used for calculation, the higher the resolution of the detector and the higher the three-axis attitude accuracy. However, it should be noted that for detectors with a certain resolution, if more navigation stars need to be included in the field of view, the size of the detection field needs to be increased. Therefore, for the three-axis attitude accuracy, there is a mutual constraint relationship between the size of the detection field of view and the number of navigation stars involved in the calculation.
The magnitude limit of a star sensor refers to its ability to detect the darkest navigation star in its field of view, which is an important indicator of the detection ability of a star sensor. The magnitude limit of a star sensor is related to the performance of the detector, the effective aperture of the lens, and the integration time of the image sensor during photography. The better the detector performance, the larger the effective aperture of the lens, and the longer the integration time, the higher the magnitude limit that the star sensor can detect.
The detection sensitivity of star sensors refers to the ability of the photoelectric system to accurately obtain the target to be detected, and the detection sensitivity determines the magnitude limit detected by the star sensor. In order to effectively detect stars, the star map captured by the detector needs to meet a certain signal-to-noise ratio.
The smaller the focal length of the star sensor lens, the higher the resolution, and the larger the pixel size, the larger the detection field of the star sensor and the more navigation stars it detects.
According to astronomical statistics, the empirical formula for the total number of stars distributed throughout the celestial sphere varies with magnitude. In fact, the more navigation stars detected, the better. As the number of navigation stars detected by the star sensor increases, the number of navigation stars in the pre prepared catalog also increases. This will increase the hardware storage requirements of the star sensor and increase the search and matching time during star map recognition, thereby reducing the update rate of the star sensor. After extensive research, it has been found that the navigation stars in any field of view follow a Poisson distribution. Therefore, when designing the detection field of view for star sensors, it is necessary to simultaneously consider the magnitude limit of the detection, while meeting the number of navigation stars required for star map recognition without being too many.
With the continuous development of microsatellite technology, higher requirements have been put forward for star sensors targeting microsatellites in terms of volume, quality, and power consumption. The volume and mass of star sensors are mainly determined by their optical and electrical systems, while the power consumption is mainly determined by the electrical system. Therefore, in order to reasonably reduce the power consumption, quality, and volume of the star sensor, we should consider both the optical and electrical systems of the star sensor.
In terms of optical systems, appropriate lens sizes can be selected based on actual indicator requirements, thereby reducing the overall volume and quality of star sensors. In terms of electrical systems, CMOS image sensors can be prioritized when selecting image sensors. Compared to CCD type image sensors, this type of image sensor has the advantages of simple peripheral circuits, single power system, and high integration. This is very effective in reducing the volume, quality, and power consumption of star sensors. At present, there is no unified solution for the system architecture of star sensors, such as some schemes using CPLD/FPGA+DSP architecture, and some using ARM architecture. The selection of different architectures determines the selection of devices. Therefore, a reasonable selection of electrical devices for star sensors and appropriate retention of design margins have a significant impact on the overall volume, quality, and power consumption of star sensors.
The update rate of star sensors is generally determined by the combination of exposure time and star map processing time. Generally, in order to improve the signal-to-noise ratio of star maps, it is necessary to extend the exposure time for collecting star maps. If the exposure time is increased, the image sensor will obtain more photons, and the output star map signal will be enhanced, resulting in an increase in the signal-to-noise ratio of the star map signal. However, for bright stars, an excessively high signal-to-noise ratio can lead to saturation, resulting in a decrease in the accuracy of star center positioning and an increase in positioning error. Excessive exposure time can also lead to trailing phenomena when collecting star maps, which affects the quality of the map and reduces the update rate of the star sensor. When reducing exposure time, it will reduce the measurement accuracy of star points and the detection sensitivity of dark stars, resulting in inaccurate star map recognition. Therefore, when determining the exposure time, it is necessary to ensure the measurement accuracy of the star sensor and determine the final exposure time according to the actual task needs.
The star map processing time is determined by the algorithm actually used by the star sensor, without a specific measurement standard. However, when designing the algorithm, it is necessary to appropriately design the complexity of the algorithm according to the actual task needs to ensure the task requirements of the update rate.
Focus on analyzing the main factors that affect the various indicators of the star sensor, and lay the foundation for the subsequent design of the star sensor by analyzing the relationship between various mutually constraining factors On the foundation.
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TY-Space Technology (Beijing) Ltd. is professional focusing on advanced attitude optical sensors, especially Star Trackers for space industry.
