Satellite attitude determination refers to the use of vector measurement information obtained from satellite attitude sensors (such as star sensors) to obtain the attitude of the three axes of the satellite’s main coordinate system relative to a certain reference coordinate system in space. The input for attitude determination is the measurement information of the attitude sensor, and the output is the three-axis attitude of the satellite. Currently, satellite attitude determination algorithms are mainly divided into two categories: static deterministic algorithms and dynamic state estimation algorithms. Static deterministic algorithms use two or more vector measurement information to determine the satellite attitude; The dynamic state estimation algorithm establishes state equations and observation equations based on measurement information and satellite attitude motion models, and uses uncertain factors in the measurement process as estimated parameters for state estimation. It can effectively overcome the influence of uncertain factors and obtain the optimal estimation in statistical sense. The core issue of satellite attitude determination is to choose which type or several types of attitude sensors with what accuracy to obtain high-precision attitude measurement, and choose which parameters to describe the algorithm for attitude determination to obtain high-precision attitude. This chapter will conduct in-depth research on this issue.
(1) Principle of attitude determination method based on attitude sensor measurement vector
Taking a typical high-precision attitude sensor star sensor as an example, analyze the principle of attitude determination method based on attitude sensor measurement vector. The star sensor extracts star points from the observed star map, matches and identifies them, and compares the measured star vector with the real star vector to determine the satellite’s attitude.
(2) Typical Static Attitude Determination Method
Typical algorithms include Euler q method, MLS method, TRIAD method, QUEST method, SVD method, and FOAM method.
Among them, the SVD method has strong robustness, but due to the need for singular value decomposition, the computational complexity is large, resulting in low computational efficiency. To this end, Markley improved the SVD method and proposed the FORM method. The main difference between the FORM method and the SVD method is that the SVD method requires direct singular value decomposition, while the FORM method uses iterative methods for singular value decomposition, reducing computational complexity and improving operational efficiency.
At present, the use of star sensors and gyroscopes for combined attitude determination is a commonly used combination to achieve high accuracy. Combined attitude determination can effectively overcome the shortcomings of various sensors to improve attitude determination accuracy. The principle of combined attitude determination is shown in Figure 3.1. However, the typical star sensor/gyroscope attitude satellite determination algorithm uses a method of estimating the constant drift error and related drift error of the gyroscope to correct the angular velocity of the gyroscope. Although this method has high accuracy, the algorithm is complex and computationally intensive. This article proposes a star sensor/gyroscope satellite attitude determination algorithm based on simplified error correction. The algorithm uses high-precision star sensor measurements to provide a reference and only estimate the constant drift error of the gyroscope to simplify and correct the gyroscope angular velocity, reducing the state variables of the filter. While ensuring the accuracy of attitude determination, it reduces the complexity of the filter and reduces the computational complexity.
Figure 3.1 Combination pose determination principle diagram
(1) The measurement equation and measurement error model of the sensor: gyroscopic measurement equation and gyroscopic measurement error model.
(2) Measurement Error Model of Star Sensors
The main measurement errors of star sensors include system error, gradient error, and equivalent noise error. The system error is a constant value, mainly caused by the deviation between the star sensor coordinate system and the prism coordinate system, and can be compensated for; Gradient errors are mainly caused by factors such as catalog errors and optical system errors of star sensors, and can also be compensated for; The equivalent noise error is characterized by random irregularity and high-frequency variability, mainly caused by internal circuit noise. In the actual process, for the measurement output of the star sensor, we only need to consider the equivalent noise error that cannot be compensated and has a significant impact on the output of the star sensor, and then we can obtain an equivalent quaternion model of the measurement equation.
(3) Design of Attitude Determination Filter
Establishing a quaternion linear model for attitude error;
State variables and state equations: Based on relevant literature and preliminary simulation results, it has been found that the effect of gyro related drift is equivalent to the superposition of gyro constant drift and measurement noise. Therefore, it is possible to only estimate the gyro constant drift error to correct the gyro angular velocity. Therefore, this algorithm only takes the reduced error quaternion and constant drift estimation error as the state variables of the attitude determination filter;
Filtering process: Attitude prediction ->State update ->Attitude correction ->Flow chart
Figure 3.2 Attention filtering flowchart
According to the statistical results of simulation experiments, the computational complexity of the simplified filtering algorithm is only about one-third of that of typical filtering algorithms, which to some extent reduces the complexity of the filter and reduces the computational complexity.
Due to the fact that modifying the Rodrigues parameter is the minimum implementation of the attitude and also solves the singularity problem, it has great potential for practical engineering applications.
(1) Design of Attitude Determination Filter
Sensor measurement equation and measurement error model; Establishment of a linear model with Rodrigues parameters for attitude error; State variables and state equations; Filtering process: attitude prediction, state update, attitude correction, singularity detection.
Figure 3.10 Attention filtering flowchart
According to the simulation results, the attitude filtering algorithm based on Rodrigues parameters can achieve high accuracy in attitude determination.
The performance of the gyroscope may decrease or malfunction after long-term operation, and the use of attitude sensors for individual attitude determination has become a research hotspot. Using the measurement information of the attitude sensor and the attitude dynamics equation for attitude determination can effectively solve the problem of gyro failure, and it serves as a backup under normal circumstances.
(1) Design of Attitude Determination Filter
State variables and state equations: Nine variables, namely the reduced error quaternion, angular velocity estimation error, and constant disturbance torque estimation error, are selected as the state variables for the attitude determination filter;
Filtering process: attitude prediction, state update, attitude correction, flowchart
Figure 3.17 Attention filtering flowchart
This chapter briefly introduces the principle and typical methods of static determination algorithms using sensors to measure vectors. The research focus is on the EKF attitude determination method for composite satellites based on star sensors/gyroscopes. Through research, an improved EKF quaternion attitude determination filtering algorithm with simplified error models is proposed, and the EKF attitude determination filtering algorithm with modified Rodrigues parameters and the EKF attitude determination algorithm without gyroscopes are implemented. The specific work is as follows:
(1) The principle of static determination algorithm based on attitude sensor measurement vector and typical static attitude determination methods were introduced;
(2) By simplifying and merging gyro drift error compensation, a typical EKF algorithm was improved, and an EKF algorithm based on a simplified error model was designed. The simulation results showed that while ensuring the accuracy of attitude determination, the complexity of the filter was reduced and the computational load was reduced.
(3) The satellite attitude determination method was studied by using modified Rodrigues parameters, and compared with the quaternion method. The feasibility of this method was verified through simulation.
(4) By combining star sensor measurements with attitude dynamics equations, a satellite attitude determination algorithm without gyroscope was implemented, and the effectiveness of this method was verified through simulation.
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