Method for determining satellite attitude using star sensors under jitter conditions

Due to the complex and variable actual situation of satellite in orbit motion, the mechanical motion of attitude control system and load pointing system, as well as the influence of external interference torque, inevitably generates satellite jitter, which seriously affects the accuracy of attitude sensor(such as star sensors) measurement data. This will lead to a sharp decline in the stability and accuracy of satellite attitude determination system, and also seriously affect the pointing accuracy of payload. At present, the mainstream jitter processing solution at home and abroad is to set up multiple distributed attitude sensors to provide feedback signals for suppressing or compensating jitter. However, this still fails to fundamentally eliminate the impact of jitter. It only uses multiple attitude sensors to measure and to some extent eliminate the attitude error caused by jitter, improving the accuracy of attitude determination. However, this increases the system cost and requires simulation analysis to optimize the distribution of attitude sensors. In terms of engineering implementation, due to limited onboard resources, the cost of the satellite should be considered while considering its mass and volume, which is likely to result in a small number of attitude sensors that can be installed on the satellite and limited measurement bandwidth. Starting from studying the mechanism of jitter generation, this chapter models attitude jitter and uses the original EKF filtering algorithm to simulate and analyze the impact of jitter amplitude, frequency, and attitude sensor measurement frequency on attitude determination accuracy; A satellite attitude determination method based on equivalent installation error was proposed for satellite attitude determination under shaking conditions, and its effectiveness was verified through simulation.

1. The impact of jitter on the accuracy of satellite attitude determination

(1) Attitude Jitter Model

On the one hand, the internal structure of the satellite is complex, resulting in disturbances from within the satellite, such as attitude control systems, load pointing control systems, and other movable components causing jitters with a high frequency component and generally higher frequency; On the other hand, during orbital operation, the frequency range of vibrations caused by many external torques is relatively wide. The shaking phenomenon generally has periodicity, and in simple cases, it can be seen as shaking causing the satellite’s attitude to shake in the plane, and the shaking form follows a sine law.

Considering that the joint action of different frequencies of shaking on the satellite results in different three-axis shaking attitude angles caused by satellite shaking, there are several situations where the attitude shaking caused by a single shaking source on the satellite is as follows:

1) When the attitude jitter frequency f Δ When the measurement frequency fs of the attitude sensor is less than half, the Nyquist sampling theorem shows that the measurement information of the attitude sensor contains information about the satellite attitude jitter. From theoretical analysis, the existence of such jitter in the satellite attitude has little impact on the accuracy of attitude determination;

2) The situation where the attitude jitter frequency is slightly greater than half of the measurement frequency of the attitude sensor;

3) The situation where the attitude frequency is much greater than half of the measurement frequency of the attitude sensor.

(2) Experimental simulation

Combining the amplitude frequency characteristics of jitter with the measurement frequency and accuracy of attitude sensors, using existing satellite attitude determination algorithms to simulate and analyze the impact of attitude jitter caused by a single jitter source on attitude determination accuracy. Through simulation results, quantitatively analyze the frequency and amplitude of jitter error, as well as the relationship between the measurement frequency of attitude sensors and attitude determination accuracy.

Table 4.1 Typical Simulation Parameter Table

This simulation experiment mainly quantitatively analyzes the impact of jitter amplitude and frequency on the accuracy of attitude determination and direction determination; The attitude determination effect of different measurement frequencies of attitude sensors on jitters of different amplitudes and frequencies. Simulate and analyze different jitters using existing combined pose determination algorithms.

2. Satellite attitude determination method based on equivalent installation error

The impact of jitter on attitude determination is very complex, and there is currently very little research. The main focus is to treat it as Gaussian noise, which is not in line with the actual situation of satellite operation as analyzed by simulation in the previous section. Therefore, this article explores and studies the attitude determination methods under jitter conditions, and proposes a satellite attitude determination method based on equivalent installation error. The jitter is treated as the installation error matrix of the attitude sensor, and a filter is used to estimate the installation error matrix.

(1) Design of Attitude Determination Filter

Equivalent installation error model: For the measurement of one axis of the attitude sensor, it is equivalent to the specific form of the installation matrix with installation errors; When the shaking causes the three axis measurements of the attitude sensor coordinate system to undergo the aforementioned deflection, the equivalent installation error matrix caused by the shaking can be obtained.

Filter design: The estimation of equivalent installation error matrix parameters can be combined with filtering algorithms. Therefore, the state variables to be estimated by the filter not only include satellite attitude error parameters, gyro constant drift errors, but also time-varying parameters of the equivalent installation error matrix.

(2) Experimental simulation

The equivalent installation error algorithm mainly estimates the equivalent installation matrix error caused by jitter, and is used to correct the attitude sensor measurement data. Therefore, the selected jitter frequency in this section is 0.5 or 1 times the measurement frequency of the attitude sensor, and the selected jitter amplitude is 2 or 4 times the measurement noise amplitude of the attitude sensor for simulation. The existing combined attitude determination algorithm and equivalent installation error algorithm are compared for simulation.

This chapter establishes an attitude jitter model and uses algorithm simulation to analyze the impact of different jitter amplitudes, jitter frequencies, attitude sensor frequencies, and other factors on attitude determination accuracy. Based on the analysis of simulation results, the following preliminary conclusions can be drawn:

1) When the jitter amplitude is less than or equal to the measurement noise amplitude of the attitude sensor, the change in jitter frequency has little impact on the accuracy of attitude determination; When the jitter amplitude is greater than the measurement noise amplitude of the attitude sensor, the higher the jitter frequency, the worse the attitude determination accuracy. When the jitter frequency multiple is between 0.5 and 2, there is a sharp decline in attitude determination accuracy. However, when the jitter frequency is very high, the rate of decline in attitude determination accuracy slows down;

2) When the jitter frequency is less than or equal to half of the measurement frequency of the attitude sensor, the change in jitter amplitude has little effect on the accuracy of attitude determination; When the shaking frequency is greater than half of the measurement frequency of the attitude sensor, the larger the shaking amplitude, the worse the accuracy of attitude determination;

3) Under shaking conditions, the lower the measurement frequency of the attitude sensor, the poorer the accuracy of attitude determination; Increasing the measurement frequency of the attitude sensor can improve the accuracy of attitude determination, but when the jitter frequency is less than half of the measurement frequency of the attitude sensor, increasing the measurement frequency of the attitude sensor has no significant effect on improving the accuracy of attitude determination;

4) The simulation has verified the effectiveness of the satellite attitude determination method based on equivalent installation error proposed in this article, which is an exploration of studying satellite attitude determination methods under jitter conditions.

With the development of aerospace technology and the increasing complexity of space missions, higher requirements have been put forward for the accuracy and stability of satellite attitudes. How to utilize limited onboard resources to improve the accuracy of satellite attitude determination has become a major research topic.

Modeling the attitude jitter, using the original EKF filtering algorithm to simulate and analyze the impact of jitter amplitude, frequency, and attitude sensor measurement frequency on attitude determination accuracy; A satellite attitude determination method based on equivalent installation error was proposed to determine the attitude of star sensors under shaking conditions. Its effectiveness was verified through simulation. This method is an exploration of satellite attitude determination methods under shaking conditions.

The use of star sensors and gyroscopes for combined attitude determination is a commonly used combination to achieve high accuracy. Due to the different measurement characteristics of the two sensors, combining them to determine the attitude of a satellite platform can effectively overcome the shortcomings of each sensor and improve the accuracy of attitude determination to meet the task requirements of modern satellites with high attitude accuracy.