This article mainly studies the attitude determination algorithm for micro satellites based on star sensor vector observation. It is mainly divided into two parts: 1) attitude determination algorithm that only relies on star sensor measurement; 2) Satellite attitude estimation algorithm based on star sensor/gyroscope combination.
The former is suitable for satellite attitude determination systems without gyroscopes or in the case of abnormal gyroscopes, while the latter is suitable for general situations where both star sensors and gyroscopes measure normally.
Microsatellites refer to artificial satellites weighing less than 1000kg. After more than thirty years of development, modern microsatellites have entered an explosive period in recent years, with the number of 100kg satellites launched increasing from 36 in 2012 to over 300 in 2017. The number of launches in 2018 remained around 270. Since 2014, China has introduced a series of policies to encourage the development of commercial aerospace, and the scale of China’s commercial aerospace market has been increasing year by year since 2015. This has also led to the rapid development of micro satellites in China. Microsatellite technology has been applied to Earth observation constellations such as Flock and Lemur-2, demonstrating the universality, standardization, and modularity of microsatellite platforms. The advantages of microsatellites include: low launch cost; Capable of completing tasks that large satellites cannot complete, such as in situ measurement, in orbit inspection of large satellites, and communication constellations; Used for research, testing and qualification before applying new devices or methods to more expensive spacecraft.
In the process of widespread application of microsatellites, their most typical feature is the use of low-cost sensors and actuators, which also poses obstacles to platform development. In the past two decades, a large number of research achievements in attitude determination and control practicality have promoted the development and maturity of micro satellite platforms. Previously, high-precision attitude determination and control were limited by volume, mass, and cost, which hindered the further development of micro satellites. However, in recent years, with the development of MEMS technology, high-precision sensors and drivers, such as star sensors and reaction wheels, have achieved miniaturization and can be applied to small satellites.
The attitude determination system is a necessary component of the satellite attitude control system, and attitude measurement and determination are also prerequisites for attitude control. The main task of attitude measurement and determination is to accurately estimate the three-axis attitude of the satellite by measuring information through attitude sensors. On the one hand, it provides feedback information for the attitude control system to control the satellite; On the other hand, it provides payload usage. Some space tasks do not require attitude control of satellites, but the accuracy of satellite attitude measurement and determination directly affects the magnitude of attitude pointing error, as shown in Figure 1.1. A represents attitude pointing error, s represents attitude stability, k represents attitude measurement error, and c represents control error.
Figure 1.1 Relationship of attribute determination in attribute control
Under the premise of certain attitude control errors, according to the relationship shown in Figure 1.1, achieving accurate attitude pointing requires sufficiently high attitude determination parameters. That is, while seeking high-precision measurement sensors, appropriate and effective attitude measurement and determination methods are also needed. From this perspective, it is very important to study algorithms for high-precision attitude determination based on attitude sensors that can be carried on small satellites.
To ensure that satellites successfully complete specific scientific, civilian, and military tasks, it is first necessary to clarify their own attitude in space, that is, to obtain the satellite’s attitude through attitude measurement instruments or measurement information processing.
Satellite attitude sensors can measure the direction of a reference celestial body in a defined attitude reference coordinate system. The commonly used reference celestial bodies include the Earth, the sun, stars, and landmarks on the Earth’s surface, corresponding attitude sensors are Earth sensors, sun sensors, star sensors, etc. The unit vector pointing from the satellite to the reference celestial body becomes the reference vector. The commonly used attitude sensors for microsatellites include gyroscopes, astronomical observation sensors, and magnetometers.
(1) Gyroscope
Gyroscopes measure the angular velocity of the three axes of a satellite relative to the inertial space, and are mainly divided into two types: mechanical gyroscopes and fiber optic gyroscopes. Compared to mechanical gyroscopes, fiber optic gyroscopes have the characteristics of no wear and high reliability, making them widely used in military and civilian fields. The gyroscope has a high output frequency and high accuracy in a short period of time, but due to the drift of the gyroscope, the feasibility of using the gyroscope alone to determine the attitude is poor. So gyroscopes are often combined with other attitude sensors for attitude determination, and in practical applications, gyroscopes are essential attitude sensitive devices.
Gyroscopes are relatively expensive, so there has been some research on gyroscopic attitude determination systems in recent years. The availability of some other inexpensive sensors, such as magnetometers, accelerometers, etc., also makes gyro free attitude determination possible. In many practical applications, the use of gyroscope free systems alone is limited due to some reasons. Firstly, these gyroscopic systems typically cannot provide high bandwidth attitude information. Secondly, effective attitude solutions cannot be generated during certain spacecraft maneuvers. Finally, although the attitude solutions generated by these systems are usually drift free, they may generate relative noise due to their low bandwidth. Therefore, in most practical satellites, especially in the case of initial attitude instability after spacecraft separation, gyroscopes are essential.
(2) Sun sensor
A sun sensor is a navigation instrument used to detect the position of the sun. There are three types of solar sensors: existing, analog, and digital.
The existing sun sensor provides binary output to indicate whether the sun is within the sensor’s field of view;
The continuous function of the incident angle of sunlight output by the analog solar sensor; The digital sun sensor generates a coded discrete output of the incident angle of sunlight.
The digital sun sensor is the most accurate of the three types of sun sensors.
By making two sensors perpendicular to each other, the direction of the sun can be completely determined. However, traditional solar sensors can only provide two independent equations and are not suitable for determining the three-axis attitude. Carl C. Liebe et al. proposed a pose determination sensor technology based on sun rotation axis measurement, which can convert traditional two axis sun sensors into three axis pose determination sensors. In addition to being able to determine the two axis attitude of the sun, this sensor can also obtain a third attitude information by imaging the Doppler frequency shift of the atmosphere, making it possible to measure the sun’s rotation axis. This three-axis sun sensor can be applied to rapidly rotating spacecraft, especially for deep space exploration. In addition to the disadvantage of only obtaining two parameters, the sun sensor must also be visible, which limits its application in non illuminated areas. Therefore, for satellites with solar eclipses, in addition to sun sensors, other sensors must also be equipped.
(3) Infrared horizon sensor
Due to the fact that the appearance of the Earth in the infrared band is more uniform than in the visible light band, infrared horizon sensors can use the Earth’s own infrared radiation to measure the attitude of satellites relative to the local horizon. Horizon sensors can basically be divided into two categories: static horizon sensors and small scanning horizon sensors. The static horizon sensor contains multiple sensors and senses infrared radiation from the Earth’s surface, with a field of view slightly larger than that of the Earth. The accuracy of determining the center of the Earth is 0.1 ° in low Earth orbit and 0.01 ° in geostationary orbit. Their use is generally limited to satellites in circular orbits. Scanning horizon, commonly known as radiation thermal horizon, measures a narrow beam of light focused on a sensing element using a rotating mirror or prism.
One reason that affects the accuracy of infrared horizon sensors is that the Earth is not a standard sphere. Another reason is that the horizon is highly susceptible to interference from the sun, moon, and other factors.
(4) Star sensor
A star tracker or star tracker is an optical device that uses photocells or cameras to measure the position of stars. Due to the fact that the positions of many stars have been accurately measured by astronomers and recorded in ephemeris. So it is possible to use onboard star sensors to obtain images of stars and obtain their relative directions to satellites, in order to compare them with the absolute positions in the ephemeris.
In history, star sensors were not used as primary attitude determination instruments due to their low sensitivity and output frequency. Later, this situation changed when high-light sensitive technologies such as star sensors based on charge coupled devices (CCD) and complementary metal oxide semiconductors (CMOS) were introduced. Since the first CCD image sensor was developed in the 1970s, it has been used as the mainstream image sensor for star trackers. The CMOS sensor, which originated in the 1990s, has a wider field of view (FOV) compared to CCD, and can image brighter stars in FOV, thus requiring lower requirements for star storage. Moreover, CMOS sensors are more easily highly integrated, have lower manufacturing costs, and are more suitable for the use of small satellites. The following is an introduction to the performance of several new star sensors on the foreign market, as shown in Table 1.1. Among them, the AURIGA star sensor is specifically designed for small satellites and has been mass-produced because of its low price and stable performance, which is favored.
Table 1.1 Performance Comparison of Attention Sensors
Star sensors can obtain accurate attitude information of the platform in static or low dynamic states. However, when the satellite is in high dynamics, attitude accuracy will rapidly decrease, motion blur, and trajectories will appear on the star map. Therefore, star sensors are not used solely for attitude determination in most cases, and are often supplemented by other sensors such as gyroscopes. Roelof uses Time Delay Integration (TDI) technology to achieve image motion compensation for its X-axis, allowing the satellite to operate normally even when rotating at a speed of 2.1 deg/s. Ma proposed an attitude related framework (ACF) for handling motion blur problems, which uses a combination of frame sequences and gyroscopes to determine the attitude information of the platform under high dynamic conditions. In the TDI and ACF technologies mentioned above, accurate angular rate information is required to compensate for satellite rotation.
Installation errors also have a significant impact on the accuracy of star sensors. Yang proposed an integration algorithm based on star vector observation, which uses Kalman filtering to estimate the installation error of star sensors. Based on observable matrix rank analysis, the installation error of star sensors is fully visible. However, the error is related to the temperature that changes over time and has complex nonlinear characteristics. Therefore, traditional methods may not be able to solve this problem.
(5) Magnetometer
A magnetometer is an instrument that measures the direction, intensity, or relative variation of a magnetic field at a specific location. Due to the fact that the magnetic field around the Earth can be determined by referencing the International Geomagnetic Field (IGRF), the information measured by a magnetometer can be compared to obtain the satellite’s attitude relative to the geomagnetic field.
A single three-axis magnetometer measurement can only obtain the attitude values of the two axes, without information on speed or disturbance torque. However, by recursively processing the magnetometer measurement sequence through Kalman filtering, it is possible to simultaneously estimate the three-axis attitude, speed, and disturbance torque. Psiaki attempted to use the Extended Kalman Filter (EKF) to estimate this information for gravity gradient stabilized spacecraft. Roberts studied the attitude determination method for deploying spin stabilized spacecraft, using a low-cost commercial magnetometer and initial orientation knowledge. The method was applied to the sounding flight data of a certain rocket, and the effectiveness of the determined attitude solution was verified using the measurement results of a certain rocket sounding test. However, the IGRF model did not consider time-varying characteristics, which limits the use of magnetometers in high-precision attitude determination.
Various attitude sensors have their application ranges, as shown in Table 1.2. It can be seen that attitude sensors have their own advantages and disadvantages, and sometimes they can complement each other, and spatial systems often have redundancy. Therefore, in most cases, micro satellites use multiple sensors to determine their attitude. Before the maturity of star sensors, solar sensors were often used as the main measurement sensors. With the maturity of star sensors and the increase in commercial products, star sensors became the preferred choice for high-precision measurements. When star sensors are not suitable in certain special situations, other sensors are used as redundancy or supplementation.
Table 1.2 Performance Comparison of Attention Sensors
Satellite attitude determination is a complex system task that involves many fields such as optics, mechanics, structure, algorithms, software, etc. This article only provides a partial introduction to satellite attitude determination algorithms based on star sensor observation vectors.
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